Document [original]

Essays on Financial Market Failures

and the Green Transition

vorgelegt von

M. Sc.

Emilie Skovbjerg Rosenlund Soysal

ORCID: 0000-0001-7597-2718

an der Fakultät VI – Planen Bauen Umwelt –

der Technischen Universität Berlin

zur Erlangung des akademischen Grades

Doktorin der Wirtschaftswissenschaften

- Dr. rer. oec. -

genehmigte Dissertation

Promotionsausschuss:

Vorsitzender: Prof. Dr. Stefan Heiland

Gutachter: Prof. Dr. Ottmar Edenhofer

Gutachter: Prof. Dr. Sebastian Rausch

Tag der wissenschaftlichen Aussprache: 20. Dezember 2023

Berlin 2024

Abstract

Keeping global warming below 2 degrees Celsius requires an unprecedented mobil-

isation of financial resources for investment in mitigation. While the realised invest-

ments in renewable energy and energy efficiency appear to fall short of the needed,

financial resources are still put into carbon-intensive energy sources. In this thesis, I

discuss the role of financial market failures in the allocation of capital during in the

green transition.

By analysing the interaction between financial market failures and specific other

pricing mechanisms that appear in the economy, this thesis show that financial mar-

ket failures has the power to distort the allocation of funds. For the purpose, three

equilibrium models of different complexity and scope were developed. They all in-

clude an informational asymmetry between the financier and the financed firms,

however, each model captures a distinct aspect of the failure though the model econ-

omy in which it is placed. The first model focuses on the interaction between finan-

cial market failures and flow of foreign funds in small open economies, the second,

on the merit-order effect of wholesale electricity markets, and the third, on the pos-

sibility of firms to impact share prices through share buybacks.

Three core findings emerge: First, financial market failures lead to a suboptimal

allocation of financial resources. Specifically, there is under-investment in mitiga-

tion efforts and over-investment in fossil fuel-related capital. Second, financial mar-

ket failures increase the costs associated with transitioning to green alternatives. The

failures drive up the cost of capital for clean energy projects, making the substitution

of fossil fuels with clean alternatives more expensive. At the same time, they may

lower the cost for polluting investments. As a result, the costs of the green transition

become higher. Third, uncertainty plays a significant role in the impact of financial

market failures. There is significant risk associated with technological change, but

financial market failures distort the pricing of this risk. Uncertainty is identified as

a key factor causing over-investment in fossil fuel assets and under-investment in

clean energy.

Overall, the thesis suggests that climate policies aiming to facilitate the green

transition should address the issues arising from financial market failures. Appropri-

ate policy interventions reduce uncertainty and provide a credible and predictable

environment for investors.

Zusammenfassung

Um die globale Erwärmung unter 2 Grad Celsius zu halten, ist eine noch nie dagewe-

sene Mobilisierung von Finanzmitteln für Investitionen in Klimaschutzmaßnahmen

erforderlich. Während die realisierten Investitionen in erneuerbare Energien und

Energieeffizienz hinter dem notwendigen Bedarf zurückzubleiben scheinen, wer-

den weiterhin finanzielle Mittel in kohlenstoffintensive Energiequellen investiert. In

dieser Arbeit erörtere ich die Rolle des Finanzmarktversagens bei der Energiewende.

Durch die Analyse der Interaktion zwischen Finanzmarktversagen und bestimmten

anderen Preisbildungsmechanismen, die in der Wirtschaft auftreten, zeigt diese Ar-

beit, dass das Finanzmarktversagen die Mittelzuweisung verzerren kann. Zu diesem

Zweck wurden drei Gleichgewichtsmodelle unterschiedlicher Komplexität entwick-

elt. Sie alle beinhalten eine Informationsasymmetrie zwischen dem Finanzier und

den finanzierten Unternehmen. Jedes Modell erfasst einen bestimmten Aspekt des

Versagens, in der Modellwirtschaft, inder es angesiedelt ist. Das erste Modell konzen-

triert sich auf die Interaktion zwischen Finanzmarktversagen und dem Fluss aus-

ländischer Gelder in kleinen offenen Volkswirtschaften, das zweite auf den Merit-

Order-Effekt von Stromgroßhandelsmärkten und das dritte auf die Auswirkungen

von Aktienrückkäufen. Drei Hauptergebnisse zeichnen sich ab: Erstens führt das Fi-

nanzmarktversagen zu einer suboptimalen Allokation der finanziellen Ressourcen.

Insbesondere wird zu wenig in Klimaschutzmaßnahmen und zu viel in Kapital für

fossile Brennstoffe investiert. Zweitens erhöht das Finanzmarktversagen die Kosten,

die mit der Umstellung auf grüne Alternativen verbunden sind. Dieses Versagen

treibt die Kapitalkosten für saubere Energieprojekte in die Höhe und macht die Sub-

stitution fossiler Brennstoffe durch saubere Alternativen teurer. Drittens spielt die

Ungewissheit eine wichtige Rolle bei den Auswirkungen eines Versagens der Finanzmärkte.

Mit dem technologischen Wandel ist ein erhebliches Risiko verbunden, aber das Fi-

nanzmarktversagen verzerrt die Preisbildung für dieses Risiko. Unsicherheit wird als

ein Schlüsselfaktor identifiziert, der zu Überinvestitionen in fossile Brennstoffe und

zu Unterinvestitionen in saubere Energie führt.

In dieser Arbeit wird vorgeschlagen, dass politische Maßnahmen zur Erleichterung

der Energiewende die Probleme angehen sollten, die sich aus dem Versagen der Fi-

nanzmärkte ergeben. Geeignete politische Interventionen verringern die Unsicher-

heit und schaffen ein berechenbares Umfeld für Investoren.

Acknowledgement

I would like to express my gratitude to the Doctoral Committee consisting of Prof.

Stefan Heiland, Prof. Sebastian Rausch and Prof. Ottmar Edenhofer, for their insight-

ful and constructive comments and for making the scientific defense an enjoyable

experience. A special thanks to Prof. Edenhofer, who in addition served as my su-

pervisor. The substantial knowledge and experience that he brought to my doctoral

research helped to heighten its standards, and his valuable feedback helped me re-

flect on my research and purpose.

The completion of this thesis would not have been possible without the support

of Dr. Kai Lessmann, who acted as my daily supervisor and unofficial mentor. I want

to thank him for providing guidance through the tangled paths of economic research

- always open to discussion of new perspectives, always finding time for questions,

and always being fun to work with.

I would also like to thank Hendrik Schuldt. I truly appreciated our collaboration

and discussions on nitty-gritty modelling details.

A huge thanks is extended to all of my colleagues at the Potsdam Institute for Cli-

mate Impact Research especially those of the FutureLab for Public Economics and

Climate Finance. Not only have they added scientific depth to my work through con-

tinuous feedback, they have also been a source of joy during the often long work-

days. In particular, after the breakout of the COVID-19 pandemic, my daily online

exchanges with them helped me stay sane in a world that went crazy.

Finally, I gratefully acknowledge the financial contribution of the German Fed-

eral Ministry of Education and Research, who funded the research presented in this

dissertation (grant number 01LN1703A).

Contents

1 Introduction 2

2 Financial Frictions and Climate Policy in an Open Economy: Promoting a

low-cost Green Transition through Clean Energy Investments 20

3 There’s no bad weather, only bad prices: Market-based wind power invest-

ments under financial frictions 62

4 Share Buybacks and Investor Beliefs about Carbon Risk 105

5 Synthesis and Outlook 139

A Statement of Contributions 149

Chapter 1

Introduction

The urgency of the climate crisis cannot be overstated. The Earth is experiencing

unprecedented levels of environmental degradation, with rapidly heating oceans

and atmosphere, rising sea-levels and increased frequency and severity of extreme

weather events. Already now, climate change has significantly reduced food and wa-

ter security, increased human mortality through extreme heat, paved the way for

infectious diseases, and caused human suffering through displacement and loss of

livelihoods (IPCC 2023).

Global awareness of the damaging impact of climate change let to the Paris Agree-

ment, a landmark international treaty adopted in 2015 by nearly every country in the

world. Signatories committed to combat climate change by limiting global warming

to below 2 degrees Celsius above pre-industrial levels, with efforts to limit the in-

crease to 1.5 degrees Celsius. Despite the intentions outlined in the treaty, global

greenhouse gas emissions persist at levels that are excessively elevated and off track

with respect to the target (UNEP 2021).

The complex nature of the climate crisis and the need for comprehensive sys-

temic changes complicate achieving the goals of the Paris Agreement. In particular,

insufficient substitution of fossil fuel with clean energy alternatives contributes to

over-shooting emission targets. Despite the recent surge in clean energy finance,

Kreibiehl et al. (2022) estimate that global investment in mitigation needs to scale

up by 3 to 6 times current levels in order to limit global warming beyond 2 degrees

Celsius. For investments in renewable energy, efficiency and other transition re-

lated technologies, the International Renewable Energy Agency (2023) estimates a

required growth from USD 1.3 trillion to USD 5 trillion annually during the 2023-

2030 period to align with the 1.5 degrees Celsius target. Bridging this ‘financing gap’

appears as a formidable task.

Consequently, transitioning into a low-emission economy necessitates an urgent

and unparalleled redirection of funds from fossil fuels to clean energy sources, and

in this process, the capital markets play a crucial role. A well-functioning financial

system directs the flow of funds to where they are the most productive, and hence,

Chapter 1 3

Figure 1.1: Global investment in energy supply. Source: International Energy Agency

(2023).

financial markets become the invisible hand that guides the efficient allocation of

capital.

Recognizing the enormous power of financial market actors, finance has become

a prominent topic within environmental economic research, providing new insights

on a wide range of aspects. However, while much attention has been dedicated to

the question of how financial markets distribute capital, little focus has been placed

on why financial markets seemingly fail to deliver the capital needed for the clean

transition. Understanding the barriers to financing the green transition is crucial

because the root of the problem has implications for the best choice of remedies.

Theories of financial market failures offer an explanation, and for this reason,

I explore in this thesis the impact of financial market failures on the allocation of

capital under the green transition. I show that imperfections in the capital mar-

kets hinder sufficient investment in the low-carbon economic activities and prolong

investments in polluting assets. Accordingly, financial market failures slow down

the transition and make it more costly. The findings entail that to discern climate

policies that are simultaneously effective and efficient, striking the delicate balance

of being adequate for achieving the outlined climate targets while avoiding undue

short-term costs, consideration of financial market failures is needed.

In the rest of this chapter, I will first provide the background and context of this

thesis (Section 1.1), and then introduce the three chapters that make up its body

Chapter 1 4

(Section 1.2). Then, a brief comparison of the content of the three chapters is offered

(Section 1.3). I finish this chapter by emphasizing the specific contribution of this

thesis (Section 1.4) and clarify a few terms that are used throughout the following

chapters (Section 1.5)

1.1 Market failures and the green transition

There are four types of market failures that can disrupt the efficient allocation of oth-

erwise perfect markets: externalities, public goods, market power, and asymmetric

information. Externalities occur when the social costs or benefits associated with

a good or service are not adequately factored into market prices. Public goods, for

which there exists no market and no market price, are suboptimally supplied by mar-

kets. Market power arises when self-interested economic agents utilise their power

to manipulate market prices and quantities, leading to a deviation from the opti-

mal outcome. Asymmetric information causes buyers and sellers to have differing

valuations of goods, leading to incomplete markets and inefficient allocation.

Environmental economics directs its attention towards the disappearing supply

of natural resources, suggesting wastefulness with the common resources as they

can be exploited free of charge. The negative externality caused by environmen-

tal degradation suggests that markets fail to find the socially optimal usage of the

common resource. The problem of climate change can be understood with a sim-

ilar framework: polluters use the atmosphere as storage space for green-house gas

emissions without paying for the damage they are causing the present and future

inhabitants of the planet through climate change.

If the emission externality was the only market failure, proposing a ‘first-best’

economic policy to solve the climate change problem would be a fairly straight for-

ward task. Polluters should pay for carbon emissions, and the price level should be

set such that the marginal cost of emission equals the marginal benefit of a cleaner

environment (Metcalf & Weisbach 2009). This Pigouvian fee on emission, imple-

mented either directly through taxation or indirectly through a cap-and-trade sys-

tem, forces polluters to internalise the cost of the externality, resulting in an efficient

level of emissions (Jenkins 2014).

However, a growing body of literature recognises that there are other market fail-

ures that may affect the optimal choice of climate policies. In particular, under the

existence of a positive externality from technological development, the optimal set

of instruments to mitigate climate change, include policies that are designed to stim-

ulate innovation and technological diffusion (Jaffe et al. 2005). This view was re-

cently expressed by Krugman (2022):

The likelihood of positive externalities from alternative energy makes a

subsidy-based approach to climate better than your usual second-best

Chapter 1 5

policy. [...] Given those externalities, a carbon tax wouldn’t be first-best

either. If there were no political constraints, we’ld probably want a mix

of emission taxes and industrial policy.

The evidence for under-investment in innovation is compelling, (Martin 1998)

and implying that “invention creates spillovers whose value is not incorporated into

market prices”(Bryan & Williams 2021). Some market failures causing under-investment

affect the demand for funds. When firms are unable to capitalise on the positive

externalities of their investment, they may not wish to undertake the investments.

Positive supply chain externalities that lead to cost reductions also in benefit of com-

petitors are a prominent example.

However, financial market failures cause disruption to the supply of funds, and

hence, provide another explanation of the insufficient investment level: Imperfec-

tions related to the financial intermediation cause a constrained and suboptimal

amount of supply of financial resources. Examples of such failures are asymmetric

information between firms and financiers, causing adverse selection of investment

projects and collateral constraints (see e.g. Mishkin 2010, Ch. 8). Under the pres-

ence of financial market failures, there is no guarantee that financial markets lead to

the efficient outcome.

1.1.1 Financial market failures

In the perfect world with perfect markets, suboptimal allocation would not occur.

According to Fisher’s Separation Theorem (Fisher 1930) perfect credit markets allow

for a separation between the firm’s investment decision and the preferences of the

financier (the shareholders). This means that the firm can make investment deci-

sions that maximise return on investment without considering shareholders’ needs.

The Separation Theorem is a cornerstone in financial theory, because it suggests that

credit markets allow for capital to flow towards the most productive investment op-

portunities and, hence, provide an efficient allocation of the financial resources.

If credit markets are not perfect, they may fail to allocate capital optimally. Un-

der asymmetric information about the future pay-off of the borrower, a profit maxi-

mizing financial intermediator may choose to ration credit (Bhattacharya & Thakor

1993). Credit rationing occurs when demand for credit exceeds the supply at the

equilibrium interest rate. Steijvers & Voordeckers (2009) find that collateral require-

ments are a remedy to increase the credit supply under informational asymmetries.

However, they still constitute a constraint on the borrowing. Collateral constraints

shift the funding decision away from the future productivity of the borrower to the

existing wealth of the borrower, and hence, distort the allocation of capital and lead

to productivity losses (Moll 2014).

Another cornerstone in financial theory is the Efficient Market Hypothesis pro-

posed by Fama (1970). Markets are considered (informationally) efficient if all avail-

Chapter 1 6

able information is reflected in the prices. The hypothesis implies that there are no

arbitrage opportunities, and that price fluctuations are truly random. If financial

markets are perfect, the prices of financial assets are also efficient. Inefficient prices,

on the other hand, are a sign of a market failure and suboptimal allocation.

Against this background, Thomä & Chenet (2017) argue that financial markets

fail to price climate change related risk correctly, suggesting market imperfections

are at play. Within climate finance, the study of financial market failures has split

into two distinct, but connected, branches:

Macro-financial instability

The first branch focuses on macro-financial instability. These studies are inspired

by the financial crisis literature that gained renewed attention following the global

financial crisis of 2007-2009 (Quadrini 2011). The central concept in this strand of

literature is that financial market imperfections contribute to macroeconomic insta-

bility by amplifying business cycle fluctuations.1

Campiglio & Van Der Ploeg (2022) find that the green transition can lead to in-

stability through the following three channels: abrupt decline in the profitability of

fossil fuel assets, rapid improvements in clean technologies, and sudden change of

consumer preferences. These changes could cause an abrupt write-down of fossil

fuel assets. Write-down of assets may have systemic effects through investors’ linked

balance sheets (see e.g. Battiston et al. 2017). Under the presence of financial mar-

ket frictions, the sudden write-down of the asset value causes fast contraction of the

balance sheet of the lenders, who then react by restricting new loans. The limited

supply of financial resources could then potentially trigger a new crisis (Diluiso et al.

2020).

Allocation

The second branch focuses on the problem of allocation. This literature discusses

the role of financial markets in the promotion of the green transition through alloca-

tion of funds. Compared to the number of studies on macro-financial instability, the

number of studies within this branch appears much scarcer. Lessmann & Kalkuhl

(2023) study the role of costly financial intermediation on emission levels. To this

end, they introduce a spread between deposit rate and lending rate in a macroeco-

nomic model with energy sectors and find that low to moderate bank spreads lead

to higher emissions through lower capital investments. However, for high spreads,

the economy contracts, leading to lower emission levels.

1The importance of the theories behind this strand of literature was highlighted by the recognition

of two prominent scholars, B. S. Bernanke, P. H. Dybvig and D. Diamond, who were awarded the

Nobel Memorial Prize in Economic Sciences in 2022 for their work on banking and financial crises.

Other prominent contributions to the financial frictions and crises literature are e.g. Kiyotaki & Moore

(1997), Brunnermeier & Sannikov (2014).

Chapter 1 7

To investigate the role of credit rationing to the allocation of credit between clean

and polluting energy technologies, Haas & Kempa (2023) develop a model of energy

sector investments under the presence of market failures. They introduce informa-

tional asymmetries between lender and borrower and conclude that the market fail-

ure leads to credit rationing and a socially undesirably low level of investments.

Schuldt & Lessmann (2022) argue that due to different characteristics, clean and

polluting capital investments are affected asymmetrically by financial market fail-

ures. They find that financial frictions can distort the transmission of climate policy,

and by limiting the availability of debt, financial frictions have the power to slow

down the green transition substantially.

In this thesis I focus on the role of allocation of capital between fossil fuel and

clean energy assets, and hence, the chapters of this thesis contribute to the limited

allocation literature. Except in the case of credit rationing, where there is no mar-

ket for credit regardless of the price, financial market failures impact allocation by

distorting the cost of capital.

1.1.2 The cost of capital

The cost of capital has important implication for investments in the green transition

because low-carbon technologies are more capital intensive than conventional fuel-

based technology. The cost of mitigation technologies are more sensitive to varia-

tions in the cost of capital, and consequently, the level of the cost of capital has ma-

jor implications for the competitiveness of these technologies (Steffen & Waidelich

2022). High costs of capital would dramatically reduce the optimal investment in

renewable energy despite high carbon prices (Hirth & Steckel 2016).

Hence, increasing interest rates could put the green transition at risk. Schmidt

et al. (2019) estimate that a return to the interest rate levels prior to the financial cri-

sis 2007-2009 in Germany, results in an increase in the levelised cost of electricity

of renewable energy of 11-25 percent depending on the technology. In other words,

when accounting for increasing financing costs, the cost of electricity increases de-

spite declining capital and operational expenditures. Empirical research on the cost

of capital for renewable energy firms suggests that risk premiums have declined

(Kempa et al. 2021), which has been attributed to increasing technology reliability,

lower cost, better assessment tools, and stable policies (Egli 2020).

Risk exposure is a crucial determinant for the cost of capital, and the risk is af-

fected by the energy policies in place (Neuhoff et al. 2022, Ðukan & Kitzing 2021).

Hence, it has been argued that policies aimed to effectively promote the green tran-

sition should reduce the investment risk (Polzin et al. 2019). However, risk is in itself

not a reason for market intervention. Under the assumption of perfect capital mar-

kets, these markets should be able to price the risk correctly and allocate the risk to

the economic agents that are best suited for carrying the risk.

Chapter 1 8

The impact of climate policies on the cost of capital for firms operating in the

fossil fuel sector has, too, been under scientific scrutiny, though with mixed results.

Under a carbon pricing policy, high emission firms may experience lower access to

permanent forms of bank financing and higher interest rate on loans (Ivanov et al.

2022). However, when carbon emission permits can be used as collateral, they can

lead to lower costs of capital for polluting firms (Antoniou et al. 2020).

The starting point of this thesis is that capital markets are unable to price the

risk correctly due to the existence of financial market failures. Uncertainty among

investors about future profitability of firms drives a premium on capital that is not

justified by perfect-market risk considerations. The financial market failures — not

the risk itself — open for a discussion of policy instruments for promoting the green

transition in addition to a carbon price.

1.2 Objective and outline

The research presented here focuses on exploring key factors that influence the al-

location between clean and dirty capital. By delving into the driving forces behind

this allocation, we can gain valuable insights into the supply-side constraints of fi-

nancing the green transition. This understanding becomes crucial in formulating

appropriate policies that address the financial market failures effectively.

1.2.1 Research questions

Accordingly, this thesis pursues the following two overarching research questions:

1. Do capital market imperfections prevent efficient financing of the transition to

a low-emission economy, and if so, how do the market imperfections constrain

the redirection of funds?

2. What implications do such imperfections have for the design of climate poli-

cies under consideration of the effectiveness and efficiency of the interven-

tions?

The first question pertains to understanding the underlying mechanism that drives

financial decisions, resulting in under-investment in clean energy sources and over-

investment in fossil fuel intensive capital. A thorough mapping of the investment

incentives affected by financial market failures allows for deeper insights into policy

interventions aimed to address the capital allocation issue. This leads to the second

question, which aims to tackle the design of such policy interventions.

The thesis comprises three distinct chapters, Chapter 2-4, each addressing the

two stated research questions. The chapters complement each other by shedding

Chapter 1 9

light on the same two questions under different assumptions and point of perspec-

tive. That is, they depart from each other in terms of market focus. As the chapters

do not directly build upon one another, they are not required to be read in a sequen-

tial order, nevertheless the structure of the thesis is chosen to gradually develop the

research questions.

Chapter 2 starts from the macro-perspective and discusses the role of financial

market failures in the allocation of capital among energy producers in an open econ-

omy. The assumption that there is just one price of energy regardless of its origin is

relaxed in Chapter 3. In this chapter, I explore the interaction between market pric-

ing of wind power and the cost of capital under financial frictions. Chapter 4 then

turns to the cost of equity of fossil fuel firms. Before exposing the similarity and dif-

ferences between the research presented in the three chapters, a short introduction

to their content is appropriate.

1.2.2 International markets (Chapter 2)

In Chapter 2, the problem of financial market failures from the perspective of a de-

veloping economy is investigated. The majority of the global clean energy invest-

ments are to be undertaken in this group of countries, however, they are generally

more capital constrained and hence, face the largest clean energy financing gap. The

connection between financial market frictions and two aspects that are specifically

important for this group of countries is studied: financial openness in terms of sen-

sitivity to fluctuations in the borrowing rate in international capital markets, and

the fact that fossil fuels are an internationally traded goods and largely priced in in-

ternational markets. These features are embedded into a New-Keynesian dynamic

stochastic general equilibrium model calibrated to Brazil. The model is then used

for simulating the macroeconomic response to the introduction of a carbon tax as a

policy to reach an exogenous emission target.

The financial market frictions follow the costly state verification problem of Townsend

(1979) and Bernanke et al. (1999). In this framework, defaults have adverse effects

on lenders, who have to pay a cost to verify the underlying value of the defaulted

firm. The existence of this cost leads lenders to demand a risk premium on borrowed

funds, leading to higher cost of debt and a limit to leverage.

The simulation results reveal that financial frictions and financial openness in-

teract during the green transition: frictions exacerbate the costs of the low-carbon

transition and reduce the competitiveness in international capital markets, with ad-

verse effects on the inflow of foreign funds. Failure to attract foreign funds leads to

welfare losses. The simulations of the open economy suggest that carbon taxation is

an effective tool for scaling down emissions even in the presence of financial market

frictions, however, the frictions increase the welfare costs because the costs of clean

energy capital increase, making the replacement of dirty energy more costly.

Chapter 1 10

The modelling framework builds on Schuldt & Lessmann (2022), who introduce

a similar type of friction in a closed economy model without explicit energy sectors.

The model economy is opened to international markets, by distinguishing between

tradable and non-tradable goods, as in Schmitt-Grohe & Uribe (2014). Fossil fuel is

added as an input to production as in Fischer & Springborn (2011). In addition, New-

Keynesian elements, such as a price rigidity, are also added to the model. The main

contribution of this chapter to the existing knowledge is the finding that financial

openness leads to a response of the economy to the carbon tax that is significantly

different from the response of a closed economy. In the open economy, carbon tax-

ation leads to a steep decline in the inflow of foreign funds. The results highlight

that considering financial market responses and international capital market inte-

gration in designing efficient climate policies for developing countries is of utmost

importance.

1.2.3 Electricity markets (Chapter 3)

With this chapter, I move from the macro- to the micro-perspective. I analyse the

role of financial market failures for the financing conditions of wind power, given

participation on the power markets and the presence of financial market frictions.

The financing conditions of renewable energy are important because these tech-

nologies are more capital intensive and their profitability hence more sensitive to

variations in the cost of capital (Hirth & Steckel 2016). Like in the previous chapter,

the financial market failure is introduced through a cost that lenders have to pay in

case of default, and this cost causes a premium on debt and influences the choice

between debt and equity in the financing mix. The restriction in debt capacity is

particularly important for the cost of capital.

The presented analysis consists of two parts: First, I develop a novel framework

for power price forecasting based on recent advances in machine learning method-

ology. The model is a variation of an adaptive network-based fuzzy inference system

(Jang 1993). The model reflects the shape of the power supply curve, and hence,

is able to capture ’merit-order effects’, referring to the observation that hours with

large generation of variable renewable energy experience lower electricity price. The

pricing model is fitted to data from West-Denmark, and it is used to generate sim-

ulations of wind generations, prices, and revenue under different levels of installed

wind power capacity.

In the second step, the simulated revenues are turned into return distributions

for the wind power plant. From this distribution, an optimal debt contract is deter-

mined. The debt contract sets the lending rate on debt and the required amount of

equity. The results show that because the return to wind power diminishes as the in-

stalled capacity increases, more wind leads to higher cost of capital. The higher cost

reduces the value of wind power projects with up to 20 percent. It further shows, that

Chapter 1 11

the pass-through of the carbon price diminishes with the level of installed capacity,

and hence, for high levels of installed capacity the carbon price looses its power to

promote investment. Acknowledging that the financing cost depends on the condi-

tions under which the renewable power plants operate is important for evaluating

the cost of the green transition and developing well-designed policies for incentivis-

ing the green transition.

1.2.4 Asset markets (Chapter 4)

In Chapter 4, I focus on the ability of financial markets to price of fossil fuel assets ef-

ficiently, i.e. whether prices reflect the underlying value of the assets. Over-valuation

of fossil fuel assets is a sign of inefficient allocation of funds. With growing aware-

ness about the risk that market interventions could lead fossil fuel assets to become

stranded, shareholders revaluate their positions in firms related to the fossil fuel sec-

tors. Divestment results in lower market value. However, it appears that fossil fuel

firms do not remain passive towards the growing share price pressure. Indeed, I pro-

vide empirical evidence in support of the hypothesis that fossil fuel firms scale up

their share repurchasing activities to combat negative price movements.

In the chapter, I first establish an empirical link between awareness of sustain-

able finance and buybacks within the fossil fuel sector. Subsequently, I introduce a

portfolio choice model that offers predictions consistent with the observed relation-

ship. The model builds on the seminal work of De Long et al. (1990). In the baseline

model, investors can choose between investing in a risk-free asset and a firm that

may repurchase its own shares. There are two types of investors — those who hold

true beliefs about future distributions of prices, and those who systematically over-

estimate future prices. The model demonstrates how companies can strategically

utilise share repurchases to counteract price movements caused by investors updat-

ing the false beliefs. In this way, by controlling the number of shares outstanding,

the firms optimise market capitalisation and offset potential devaluation resulting

from increased investor awareness.

The analysis reveals that share buybacks may lead to a persistent presence of

investors holding misguided beliefs about firm value. Consequently, buybacks can

contribute to investors’ inability to accurately assess the value of potentially stranded

assets.

1.3 Similarities and differences between chapters

Table 1.1 provides an overview of the content of the three chapters, highlighting sim-

ilarities and differences.

Chapter 1 12

Table 1.1: Overview of chapters

Chapter 2 Chapter 3 Chapter 4

Market focus International markets for

capital and fossil fuel

Electricity markets under

high shares of wind power

Financial asset

markets with buybacks

Source of failure default costs default costs false beliefs

Effect dirty over-investment,

clean under-investment clean under-investment dirty over-investment

Effect timing Transition Post-transition Transition

Equilibrium General Partial Partial

Main method modelling;

calibrated

modelling;

estimated

modelling;

analytical

1.3.1 Market focus

All chapters discuss financial market failures in the context of a market with a spe-

cific price setting mechanism. The markets in focus separate the three chapters from

each other, and provide the basis for the distinct contribution of each chapter to the

established knowledge on the interaction between financial market failures and the

green transition.

In Chapter 2, fossil fuel is a good that is traded at international markets, and

hence, the exchange rate affects its price. In addition, the economy is exposed to

international financial markets. Through the introduction of foreign markets and

foreign currency, the open economy is unable to set its own prices, and this creates

a response to a carbon tax that is different from those of a closed economy.

In Chapter 3, the price-setting mechanism under investigation is that of elec-

tricity. The merit-order effect has great impact on the return on wind power invest-

ments, and hence, the cost of capital under the presence of financial frictions.

In Chapter 4, the active role of the firm itself in the market for its shares consti-

tutes the market mechanism under investigation. It turns out that active participa-

tion can increase the distortion of the signals of the share price under the presence

of investors with systematically false beliefs about the future.

1.3.2 Source of failure

There are several ways to model financial market failures. In Chapter 2 and Chapter

3, I adopt the costly state verification framework that imposes a default cost on the

lender. In this framework, the productivity of the firm is uncertain, but the distribu-

tion is known to the borrower. The lender, on the other hand, does not need to know

the distribution as long as the borrowing firm repays its debt. In case the produc-

tivity turns out too low to repay the debt to the lender, the firm defaults. The lender

then takes over the firm’s assets and sell them at the capital markets. However, in

this process, a fraction of the remaining capital value is lost. To compensate for the

expected loss, the lender requires a premium on debt. Then, to reduce the risk of

Chapter 1 13

default, the borrower uses equity as collateral to back its capital investments.

There are two ways of interpreting the default costs: first, as a cost paid by the

lender to assess the value of the capital, and second, as an economic loss occurring

from the informational asymmetry between the firm and the lender. With the first

interpretation, the default cost is a transaction cost that only occurs in certain sit-

uations. However, the second interpretation implies that the source of the loss is

the lender’s failure to assess the true value of the defaulted assets before offering the

loan. The premium is hence a result of a diverging valuation between the lender and

the borrower.

Under the first interpretation, the default costs should be passed on to other

agents in the economy (e.g. through wages to asset recovery professionals). In Chap-

ter 2, I adopt the second interpretation, because the default costs are indeed ’lost’

from the economy, and not recouped by another agent. The modelling framework

in Chapter 3 is silent about the root of the default cost. However, differences in the

ability to valuate investments correctly appear as a plausible assumption, because

the project holder is likely to know the business and the markets better. The risk pre-

mium implied by the default cost is hence imposed on the borrower as a precaution

for the lender’s potentially faulty valuation.

In Chapter 4, the source of failure is the systemically wrong belief of one group

of investors buying shares in fossil fuel assets. The misperception of the underlying

value of the asset is a sign of informational asymmetry between the firm and one

group of investors. Under the efficient market hypothesis, investors with wrong be-

liefs ought not to exist, because they would be crowded out by the investors who

are better informed. The analysis shows, however, that misperceptions can persist,

and that the firm can take advantage of the informational asymmetry by engaging in

buybacks.

1.3.3 Effect and its timing

During the green transition, financial markets should redirect funds from fossil fuel

(dirty) investments to low-carbon (clean) investments. Financial market imperfec-

tions may distort this allocation in two ways: First, failure leads to over-investment

in dirty assets, and second, failure leads to under-investment in clean assets.

Chapter 2 points to both effects. Financial market failures impact both the clean

and the dirty energy sectors through the adjustment of the financing premium dur-

ing the transition. The financing premium of clean capital increases with the intro-

duction of policies aimed at reducing carbon emissions, while it drops for the dirty

capital. This creates inertia in the transition of both energy capital stocks to the new

low-carbon state. The post-transition economy is unaffected by the frictions, but

the trajectory towards the new state indicates that financial frictions slow down the

Chapter 1 14

transition.2

Chapter 3 focuses purely on the problem of under-investment in clean energy.

The results show that financial market failures increase the cost of capital and lower

the wind power project value. Hence, the financial frictions shift the feasible level of

wind power capacity remunerated through market pricing. In other words, it moves

the equilibrium level of wind power capacity downwards. The simulation results

suggest that while for low levels of wind power the cost of capital is also low, it in-

creases with increased investments. Therefore, the relevance of financial frictions in

relation to wind power investments appear as we approach capacity targets.

Despite using a similar framework, Chapter 3’s suggestion that financial market

failures affect quantities of the possible post-transition state, is different from the

effect timing suggested in Chapter 2. The reason is differences in the assumptions on

the cause of uncertainty: In Chapter 2, the distributions of the return on capital are

exogenous and constant, which technically implies that the distortionary capability

of the frictions is the same throughout the simulated trajectory. In Chapter 3 on the

other hand, the return distributions change, and with the increasing level of clean

energy capacity new investments gradually become more risky.

Chapter 4 investigates one aspect of over-investment in fossil fuel assets. While

the real effect of the resulting mispricing is not explored, the consequences of over-

valued financial assets can certainly be real. For instance, higher equity value would

allow fossil fuel firms to obtain loans at more favourable rates, leading to lower cost

of capital and higher net present values of investment projects. As a result, over-

priced fossil fuel assets could lead firms to undertake investment projects that would

otherwise not be considered. It is fair to assume that the informational asymmetry

between investors and firms regarding the future of the fossil fuel business models

ceases to exist at the end of the transition. At this point all investors would have re-

alised a potential mispricing of fossil fuel assets, and hence, the interaction between

buybacks and wrong beliefs among investors is a transitional issue.

1.4 Significance of the contributions

The notion that financial market failures have the power to distort the allocation of

capital is already a well-established fact. With this thesis, I discuss the problem in

relation to the green transition. The main contribution to the existing knowledge

on the topic lies in the in-depth analysis of the interaction between financial market

failures and conditions governing specific markets, i.e. financial integration of open

economies, the merit-order effect of electricity markets, and firms’ engagement in

share repurchases. The research highlights mechanisms through which the supply-

2The model economies with and without frictions have different starting points, so the observation

that frictions do not matter for the post-transition economy is valid only if measured as percentage

deviation from the starting point.

Chapter 1 15

side failure of the financial market work.

Shifting focus away from describing barriers and towards the market imperfec-

tions that caused the barriers, would help identity appropriate policy interventions

(Pauw et al. 2022). Hence, the main contribution of this research is an improved un-

derstanding of the underlying mechanisms that cause suboptimal allocation of cap-

ital in the green transition. The three chapters introduce financial market failures as

a core part of the models and provide the micro-foundations of collateral require-

ments and premiums on debt in Chapter 2 and 3, and mispricing of fossil fuel assets

in Chapter 4.

Though the markets under consideration are different in the three chapters, the

findings point in the same direction: When financial market failures are driven by

asymmetrical information between the firm and the financier, limiting uncertainty is

crucial. Uncertainty provides the room for diverging valuation of risk, exacerbating

the impact of the failure. Hence, the overall findings of the chapters suggest that

financial market failures cause a mispricing of risk and hence, policy interventions

that seek to reduce the effects of financial market failures ought to reduce the risk.

The examination of policy implications is presented in detail in Chapters 2-4, and a

comprehensive conclusion is provided in Chapter 5.

In addition, the research has important implication for energy investment mod-

els that take the cost of capital as input. With financial market failures, the cost of

capital becomes endogenous, depending on the market conditions, the policies, and

even the conditions of the borrower. Failing to take into account the endogenous na-

ture of the cost of capital may lead to incorrect estimates of the cost of the transition

and the effectiveness of climate policies.

1.5 Clarification of concepts

Before ending this introduction, I would like to clarify some concepts that are re-

peatedly referred to throughout this thesis, though may be a source of confusion.

Below I explain the difference between failures and frictions, and different types of

investors.

1.5.1 Failures and frictions

A financial market friction is a wedge between the savings rate and the lending rate

(Hall 2018). This wedge may have several sources, for instant monopolistic compe-

tition in the banking sector or the existence of a transaction cost. Financial market

failures can result in a wedge, and this is the case in Chapter 2 and Chapter 3, where

the default cost leads to a premium on funds. In these two chapters, the two words

— frictions and failures — are used interchangeably, though in other contexts it may

not mean the same.

Chapter 1 16

1.5.2 Real and financial investors

An investor is an agent that makes an investment, that much is clear. However, there

are two types of investments considered in this thesis — real and financial. An in-

vestor who decides on the real capital investments is a real investor. On the other

hand, an investor that finances the capital purchases by buying financial assets is a

financial investor.

In Chapter 2, ’the entrepreneurs’ are real investors, because they decide on the

capital investments. Entrepreneurs are owned by households, and as it is ultimately

the households who benefit from the return, the households are the financial in-

vestor.

In Chapter 3, the real investor is referred to as ’the project holder’. The project

holder decides on the real investment and the optimal allocation between debt and

equity. The project holder may not need to be the equity owner, but she does act as

to maximise return on equity.

In Chapter 4, the optimal portfolio choice model consider the decision of the

’shareholders’. They distribute their funds among financial assets and have nothing

to do with the real investment decisions. Hence, this paper only considers the role

of financial investors.

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Chapter 2

Financial Frictions and Climate Policy

in an Open Economy: Promoting a

low-cost Green Transition through

Clean Energy Investments

Submitted for publication in Macroeconomic Dynamics. July 16, 2023

SUBMITTED TO MACROECONOMIC DYNAMICS

Financial Frictions and Climate Policy in an Open

Economy: Promoting a low-cost Green Transition

through Clean Energy Investments

Emilie Rosenlund Soysal,*†‡ Hendrik Schuldt,†¶ and Kai Lessmann§|0

†Potsdam Institute for Climate Impact Research, P.O. Box 60 12 03, 14412 Potsdam, Germany

‡Technische Universität Berlin, Straße des 17. Juni 135, 10623 Berlin, Germany

¶Technische Universität Berlin, Berlin, Germany

§Potsdam Institute for Climate Impact Research, Potsdam, Germany

|0Mercator Research Institute on Global Commons and Climate Change (MCC), Berlin, Germany

*Corresponding author. Email: soysal@pik-potsdam.de

Abstract

To achieve the goals of the Paris Agreement, substantial investments in clean energy are needed in

developing countries. We study the challenges faced by developing countries in accessing financial

resources for clean energy investments during the low-carbon transition in a dynamic stochastic

general equilibrium model calibrated to Brazil. Our findings reveal that financial frictions exacerbate

the costs of the low-carbon transition and reduce the competitiveness in international capital markets

with adverse effects on the inflow of foreign funds. We explore revenue recycling schemes and

highlight the advantages of combining carbon taxation with clean energy subsidies to attract foreign

funds and accelerate clean capital accumulation. These results underscore the importance of consid-

ering financial market responses and international capital market integration in designing efficient

climate policies for developing countries. Policymakers can leverage carbon pricing instruments and

targeted measures to incentivize clean energy investments, promoting sustainable economic growth.

Keywords

currency risk; costly state verification; DSGE modeling; carbon taxation

Chapter 2 21

1. Introduction

To meet the targets of the Paris Agreement, decarbonizing economic activity requires an effort from

all nations worldwide. Kreibiehl et al. (2022) estimate that the mitigation investments of developing

economies need to increase by factor 4-7 compared to the 2015 levels and as a result, this group

of countries faces a financing gap that surpasses that of developed economies. While developing

economies often have lower costs to reduce emissions (Liu and Feng 2018), mobilizing the necessary

financial resources is challenging for mainly two reasons:

First, in lower-income countries the financial sector generally constitutes a relatively small

part of the overall economy (Čihák et al. 2013) and consequently, there may be limited access

to financial resources across all sectors. Lack of financial development has severe implications for

economic activity. A well-developed financial system is a prerequisite for direct investment to

positively contribute to the growth of the country (Hermes and Lensink 2000). Compared to firms in

industrialized economies, firms in developing economies are more frequently capital constrained with

adverse consequences for their capital accumulation (Moll 2014) and economic activity in general (De

Soto 2000). With less developed financial systems and less access to international financial markets,

developing countries are also more severely affected by financial market imperfections (Levine 2005).

Financial market failures result in sub-optimal allocation of funds and, hence, lead to welfare losses.

The transition to a green economy where fossil fuel-intensive capital is replaced by clean capital is

therefore slowed, delayed, and more costly (Schuldt and Lessmann 2022). In the presence of financial

frictions, a sudden write-down of fossil fuel assets decreases the debt capacity of the non-financial

sectors, challenging macroeconomic stability and investment capacities (Comerford and Spiganti

2022). Frictions in the banking sector may not only reduce the efficiency of climate policies, but also

increase the welfare costs of the transition (Diluiso et al. 2020; Benmir and Roman 2020; Carattini,

Heutel, and Melkadze 2021; Lessmann and Kalkuhl 2023).

Second, developing economies are more vulnerable to variations in foreign direct investments

compared to advanced economies (IMF 2023). To remain attractive to foreign investors, their

rate of return on investment in these economies needs to be competitive in international markets.

Addressing climate change through policies that increase the cost of energy makes it difficult to

maintain competitiveness. For instance, carbon taxation not only decreases short-term returns on

fossil fuel related capital but also lowers the return on any productive capital that requires energy

as an input. Furthermore, due to the international flow of funds, open economies can experience

impacts of climate policies that are different from those of a closed economy. Environmental policies

generate cross-border spillovers leading to international coordination problems (Ganelli and Tervala

2011), although the spillover effects of economic shocks depend on the carbon policy instrument

in place (Annicchiarico and Diluiso 2019). According to Grüning (2022) the most costly way to

decarbonize an open economy is an international increase in the price of fossil fuel, while Xiao

et al. (2022) finds that internationally linked emission trading systems lead to economic benefits for

all parties involved.

Previous studies on the macroeconomic impact of financial market frictions and climate policies

all refer to models of closed economies that neither account for the role of international flow of funds,

variations in the real exchange rates, nor for the fact that the price of fossil fuels is (largely) set by

international markets. It has not been studied to what extent their policy recommendations generalize

to open economies. A climate policy that ignores financial market imperfections or openness may

fail to incentivize investments where they are most urgently needed or implement the transition

in an unnecessarily costly way. With this paper, we provide insight into the interactions between

financial market frictions, financial openness and climate policy. To this end, we analyze financial

frictions in a small, open economy, where some goods and all foreign debt are denominated in

foreign currency. Through this additional layer of analysis, we generate insights that are particularly

relevant to developing countries.

Chapter 2 22

The paper investigates the impact of financial market frictions on a low-carbon transition in a

small open economy. We identify the potential short-term to medium-term impacts of introducing

carbon pricing instruments that aim to reduce emissions in line with an exogenous climate target, and

analyze the response of the flow of funds to the policy. We discuss the implications of the financial

market imperfections and financial openness for the design of the climate policy, both in terms of

carbon taxation level and tax revenue recycling.

As the basis of our analysis, we use a dynamic stochastic general equilibrium model of a small

open economy with financial frictions. We calibrate the model to Brazil in 2019. Among developing

countries, Brazil stands out with a large share of private investment in its cross-border financial flows,

making Brazil’s producing sectors highly connected to international capital markets. Furthermore,

the spreads of commercial banks in Brazil are among the highest in the world (Torres and Zeidan

2016), suggesting substantial financial market premiums. With a GDP per capita of 8,717 USD (in

2019), Brazil is classified as an upper middle income country and as a developing country according to

UN (2019). Brazil has implemented a number of policies to reduce emissions, including incentivizing

renewable energy investments through support auctions and channeling funds through the Brazilian

Development Bank (Isah et al. 2023). Direct carbon taxation is not yet among Brazilian policies

(ICAP 2022).

In the model, investments are financed by a mix of domestic and foreign funds. Domestic funds

are household savings, channeled through bank deposits, while foreign funds are borrowed on

international credit markets at an internationally determined borrowing rate. Variations in the flow

of foreign debt impact not only investment levels, but also the real exchange rate of the economy

and the debt denoted in foreign currency. In the model, entrepreneurs are subject to default risk

and, when taking out bank loans, they must pay a risk premium to cover expected losses. In this way,

their equity positions (net worth) become collateralized. The resulting constraint to entrepreneurial

debt leads to decelerated capital accumulation.

The model framework allows us to simulate the response of the economy to a sudden introduction

of a carbon tax applied to the usage of fossil fuels. A carbon tax increases the cost of using fossil

fuels for production of energy goods, and hence promotes substitution of emission-intensive (dirty)

energy with capital-intensive (clean) energy. However, the tax increases the cost of energy used as

input to other production sectors, which drives up the costs of final goods, causing cost-push inflation

and lowering aggregate investment, production, and consumption. Financial frictions amplify these

effects by creating inertia in the clean energy investment response. Frictions drive up the cost of the

clean energy substitute and reduce the availability of energy for productive purposes.

Our model simulations of the response to an introduction of a carbon tax in an open economy

indicate that the higher cost of energy reduces the return on capital and thus the competitiveness of

the economy on international capital markets. As a consequence, the inflow of foreign funds declines

and the domestic currency depreciates. Currency depreciation further increases the relative cost of

fossil fuels, as well as the real debt burden of foreign debt denominated in foreign currency. We find

that financial frictions and financial openness hardly influence the effectiveness of the carbon tax in

terms of emission reductions. However, financial frictions strongly increase the cost of the transition

in an economy integrated with international financial markets.

We explore two different carbon tax revenue recycling schemes to cushion the slowdown of

capital accumulation. We find that recycling the tax revenue to households in a lump-sum fashion

leads to a significant drop in foreign lending, inflation and depreciation of domestic currency. This

results in overall lower consumption despite the direct tax transfers to households. In contrast,

combining the carbon tax with a subsidy to clean energy can ensure a faster build-up of clean capital.

Subsidies reduce the cost of energy, keep inflation stable, increase the return on capital, and ultimately

sustain the inflow of foreign funds.

We conclude that policy makers ought to account for the response of financial markets when

Chapter 2 23

designing climate policy. Our findings suggest that economies that are well integrated with inter-

national capital markets could benefit from combining carbon taxation with instruments designed

specifically to attract clean energy investments.

The paper is organized in the following way. Section 2 outlines the modeling framework. Section

3 describes the model calibration. Section 4 presents the simulation results in two parts. First, we show

the response of the main economic variables to the introduction of a carbon tax using a benchmark

model with financial frictions. We compare the response to that of a model without frictions, and

further discuss the role of financial openness (Section 4.1). Then we explore scenarios that combine

carbon taxation with a clean energy subsidy, and discuss the implications for the usage of foreign

financial aid (Section 4.2). Section 5 concludes the paper.

2. Model

This section presents the model framework. We develop a dynamic stochastic general equilibrium

model suitable for analyzing the interaction between climate policy, financial frictions, and financial

openness. To this end, our model integrates three features:

To capture the exposure of developing countries to international borrowing conditions, we adopt

a small open economy setting, where capital purchases can be funded domestically and from

abroad via a capital mutual fund (CMF). Foreign loans are denominated in foreign currency.

Goods are either tradable or non-tradable as in Schmitt-Grohe and Uribe (2014, Chapter 8).

Financial intermediation of capital via the CMF is subject to financial friction that add rigidity to

the financing of new capital. We follow the seminal model of Bernanke, Gertler, and Gilchrist

(1999, from here on BGG), who adapted the costly state verification problem (Townsend 1979)

for a closed economy, such that the financing conditions become dependent on the net worth of

the borrower.

To investigate the low-carbon transition, we differentiate between clean and dirty energy

production by introducing fossil fuels as a type of good (similar to Fischer and Springborn 2011).

We assume that fossil fuel is a tradable good and therefore priced by the international market.

The model economy consists of a representative household, entrepreneurs producing energy

goods, tradable and non-tradable goods, aggregators of energy and wholesale goods, retailers, capital

producers, a capital mutual fund, and a central bank. This section introduces the model assumptions

and equations. Figure 1 provides a schematic presentation of the model agents together with the

main economic flows. All prices are in real terms, and the final good is the numeraire.

2.1 Households

The representative household maximizes its expected welfare (i.e. the discounted utility) by choosing

consumption C

, labor L

and deposits D

t+1

subject to budget constraint in Eq.

(3)

. Welfare is a

function of consumption and time worked.

Ut=

∞

t=0

βtu(Ct,Lt)(1)

with instantaneous utility in each period given by

u= log(Ct)+ log(1 – Lt)(2)

At time t, the representative household places deposits D

t+1

in the capital mutual fund to earn

an interest at the gross risk-free domestic interest rate R

t+1

. They furthermore receive a lump-sum

Chapter 2 24

Figure 1. Model overview. The model consists of a representative household, who provides labor to entrepreneurs and

savings to the capital mutual fund (CMF). The CMF combines savings with foreign debt and lends it out to entrepreneurs.

The entrepreneurs buy capital from capital producers. Clean and dirty energy is aggregated and used as input to production

by tradable and non-tradable goods producer. Retailers differentiate final goods and secures rigid prices. The central bank

sets the nominal rate on savings.

transfer tax revenues T

from the government, a net transfer of wealth T

when entrepreneurs decide

to go out of business, and any profits ΠR

tmade in the retail sector. The budget constraint reads:

Ct+Dt+1 =wtLt+RH

tDt+Tt+Te

t+ΠR

t(3)

Maximization of E[U

] subject to the budget constraint yields the following first order conditions:

wt=Ct

1 – Lt(4)

Ct=βEt1

Ct+1 RH

t+1(5)

2.2 Capital producers

In the model economy, there are four representative capital goods producers, one for each sector.

The capital producer of sector isell capital at the real price Q

to the entrepreneurs in the sector,

who will use it to produce goods. At the end of the period, capital producers buy depreciated capital

back from entrepreneurs at price

and decide the level of new investments I

. Capital depreciates

at rate

and has a real adjustment cost

2Ii

t–δ2

. Adjustment costs are a standard feature of

DSGE models, as they reduce the variance in the capital stock and prevent capital re-purposing (i.e.

negative investments).

The maximization problem of the capital goods producers is given by:

max

t,Ki

tKi

t+1 –Ii

t–¯

t(1 – δ)Ki

t(6)

Chapter 2 25

s.t.:

t+1 =Ii

t+(1 – δ)Ki

t–χ

2Ii

–δ2

t(7)

which results in the following first order conditions:

t=1

1 – χIi

t–δ(8)

t=Qi

t1 + 1

1 – δ

2Ii

–δIi

+δ (9)

The capital market is assumed to be perfectly competitive, and capital producers make no profit.

2.3 Capital mutual fund

The representative capital mutual fund (CMF) provides loans to entrepreneurs on the basis of two

types of liabilities: deposits from households in domestic currency and loans from the international

financial markets in foreign currency. The perfectly competitive CMF balances return on loans to

entrepreneurs with the interest paid on liabilities, and makes no profit. At the end of period tthe

CMF issues new domestic deposits D

t+1

and creates new loans. The profit maximization problem of

the CMF takes the following form:

max

Dt+1,BF

t+1

Rt+1Bt+1 –RH

t+1Dt+1 +RF

t+1St+1BF

t+1(10)

subject to

Bt+1 =Dt+1 +StBF

t+1 (11)

where B

t+1

is the total amount of loan given to entrepreneurs, due in period t+ 1. B

t+1

is the

foreign debt denominated in foreign currency. S

is the real exchange rate that determines the real

value of one unit of foreign currency at time t. The constraint in Eq.

(11)

implies that the CMF can

only lend out what has been deposited or borrowed from abroad. It is therefore not possible for the

CMF to engage in a Ponzi scheme where interest payments are covered by new liabilities. Both types

of CMF creditors, i.e. foreign lenders and domestic depositors, demand risk-free rates; therefore,

the CMF is indifferent when it comes to the source of the funding. The first order condition with

respect to foreign debt gives the covered interest parity condition:

t+1 =RF

t+1 Et[St+1]

St(12)

In addition, we get the following requirement for the real, risk free domestic rate:

t+1 =Rt+1 (13)

We further assume that the foreign risk-free rate at which the CMF obtains foreign loans depends

on the availability of foreign funds, expressed through the foreign risk free rate and the level of

foreign debt denominated in foreign currency:

t+1 =zt¯

RF+κeBF

t+1–η– 1(14)

is the steady state foreign borrowing rate, z

is a stochastic shock variable, taking the value of 1

in steady state, and the second term on the right hand side is the foreign borrowing premium. The

Chapter 2 26

parameter

can be interpreted as the country’s debt capacity. Eq.

(14)

closes the open economy

model and the functional form of the foreign borrowing rate secures a stationary level of indebtedness,

following Gertler, Gilchrist, and Natalucci (2007) and Schmitt-Grohe and Uribe (2003).

The price level of the tradable good in foreign currency is exogenous and set to the numeraire.

This implies that the real price of tradable goods pT

tequals the real exchange rate:

t=St(15)

2.4 Entrepreneurs

t– 1 •...

•Borrows Bj

tfrom CMF

•Buys new capital Kj

tat price Qi

t•Observes productivity of capital ωj

•Chooses Lj

tand Ej

•Produces and sells Yj

•Resells depreciated capital at price ¯

•Repays debt and interest RtBj

tto CMF

•Borrows Bj

t+1 from CMF

•Buys new capital Kj

t+1

t+ 1 •Observe productivity of capital ωj

t+1

•...

Figure 2. Timeline of financial and operational decisions of entrepreneur joperating in sector i.

An entrepreneur jis an individual who owns and manages a productive firm. Heterogeneity

between the firms is introduced through differentiated net worth positions. The economy has four

entrepreneurial sectors: clean energy (c), dirty energy (d), tradable (T) and non-tradable (N) goods.

Each sector consists of a continuum of entrepreneurs who take different types of inputs to their

production. Clean and dirty energy goods become energy goods used for production by the other

sectors. Tradable and non-tradable goods are aggregated into whole-sale goods.

2.4.1 Technologies in entrepreneurial sectors

Inthefollowing superscriptjdenotestheindividualentrepreneur, whilethesuperscripti

∈

{T,N,c,d}

refers to the sector in which the entrepreneur joperates. Parameters and prices are common for all

entrepreneurs in the same sector and therefore take index i, while variables are individual for each

entrepreneur and are indexed with juntil aggregation.

Entrepreneur jin the goods sectors, i

∈

{N,T}, produces output Y

from the inputs of capital

t, labor Lj

t, and energy Ej

t. The production function takes the form of a nested CES-function:

t=¯

Aiϕi(Kj

t)αi(Lj

t)1–αi1–ϵi+ (1 – ϕi)Ej

t1–ϵi1

1–ϵi(16)

with share parameter

ϕi

, substitution parameters

ϵi

and output elasticity of capital in the nested

function αi.

The economy has two types of energy producers, clean cand dirty d. Like the goods production

sectors, the output of entrepreneurs in the energy sectors, denoted M

, is given by a nested constant

elasticity of subsitution (CES) function taking labor and capital as input, but instead of energy the

Chapter 2 27

third input is fossil fuel Xj

t=¯

Aiϕi(Kj

t)αi(Lj

t)1–αi1–ϵi+ (1 – ϕi)Xj

t1–ϵi1

1–ϵi(17)

We set the share parameter of the clean energy sector

ϕc

equal to one, which means that the clean

energy production function collapses to a Cobb-Douglas function with only capital and labor, and

hence, the clean energy sector takes no fossil fuel as input. In this model, fossil fuel is a type of

tradable good. Its price is therefore the same as the price of the tradable goods.

While the types of output and inputs differ between entrepreneurs in the four sectors, the way

they choose input levels and debt is the same. The next section describes the entrepreneurs’ decision

problem.

2.4.2 Entrepreneurs’ labor, energy and fossil fuel choices

Entrepreneur jbelonging to sector imaximizes her profit through a two-step process: First she

obtains a loan B

from the CMF to buy capital K

from the capital producers at the sector specific price

. Second, only a fraction

ωj

of the capital turns out effective,

ωj

. Once the entrepreneur

knows how much effective capital she has, she decides on the amount of other inputs to use in the

production. The inputs depend on the sector (labor and energy or fossil fuels). The produced goods

are then sold at the clearing price for sector i,p

, and the depreciated capital is sold back to the capital

producers at price ¯

First, consider the second step of the maximization problem of entrepreneur j. The return on

invested capital (ROI) is given by

ROIj

t=OPj

t+¯

t(1 – δ)¯

t(18)

where

is the depreciation rate of capital,

is the resell price obtained from the capital goods

producers, Y

is the output of entrepreneur jand OP

are the operational profits, i.e. the total revenue

minus the accumulated cost of inputs other than capital. The expression of operational profits depends

on the production function. For tradable and non-tradable goods sectors the operational profits are

OPj

t=pi

tYj

t–wtLj

t–pE

tEj

t(19)

Hence, maximization of ROI with respect to labor and energy gives the following first order

conditions:

wt=pi

t¯

A(1–ϵi)

i(1 – αi)ϕiˆ

Ai(Kj

t)αi(Lj

t)(1–αi)(1–ϵi)(Yj

t)ϵi

(20)

t=pi

t(¯

Ai)(1–ϵi)(1 – ϕi) Yj

t!ϵi

(21)

Entrepreneurs in the dirty energy sector take labor and fossil fuel as input in addition to capital.

Hence, the operational profits are given by

OPj

t=pd

tMj

t–wtLj

t– (pX

t+τX

t)Xj

t(22)

Chapter 2 28

The cost of using fossil fuel is the price of p

and a carbon tax

τX

. Maximization of the dirty energy

entrepreneurs’ ROI with respect to labor and fossil fuel input gives the first order conditions:

wt=pd

t¯

A(1–ϵd)

d(1 – αd)ϕdˆ

Ad(Kj

t)αd(Lj

t)(1–αd)(1–ϵd)(Mj

t)ϵd

(23)

t+τX

t=pd

t(¯

Ad)(1–ϵd)(1 – ϕd) Mj

t!ϵd

(24)

Finally, the clean energy entrepreneurs takes only labor as input in addition to capital. On top of

the price on clean energy they receive a price subsidy

τc

on the output and hence, their operational

profits and first order condition with respect to labor is given by:

OPj

t=(pc

t+τc

t)Mj

t–wtLj

t(25)

wt=(pc

t+τc

t)(1 – αc)Mj

(26)

Although the production function and operational profits depend on the sector in which the

entrepreneur is operating, all functions exhibit constant-return-to-scale. Therefore, the ROI for

optimal choices of labor and energy or fossil fuel for entrepreneur j(regardless of sector) can be

expressed in terms of the gross return on capital Rk,j

tof entrepreneur j:

ROIj

t=ωj

tRk,j

tQi

t–1Kj

t(27)

It can be shown that due to the constant-return-to-scale properties the return to capital is independent

from any j-specific values and hence equivalent for all entrepreneurs within the same sector, i.e.

k,j

k,i

for j

∈

i. Eq.

(27)

provides a useful notation in the first step of the entrepreneur’s problem,

i.e. choosing the optimal amount of capital and debt.

2.4.3 Financial contract

The first step of the entrepreneurs’ problem is choosing the amount to be borrowed from the CMF

and the capital to be used in the next period. Here, we adopt the approach of the seminal paper of

BGG.

In the end of period tthe entrepreneur uses its net worth N

t+1

and a loan B

t+1

to buy new capital

to be used in next period, i.e.

tKj

t+1 =Bj

t+1 +Nj

t+1 (28)

Entrepreneurs agree to pay the CMF a Z

interest rate for the loan. However, if the effective

capital remains below a threshold, the entrepreneur will not generate sufficient ROI to repay their

debt obligations and will default. In this case, only a fraction 1 –

of the entrepreneur’s value is

recovered, the rest becomes frictional losses. Therefore, the equilibrium interest rate Zmust take into

account this default risk. For the CMF a loan to entrepreneur jhas the following return, conditional

on the realisation of effective capital:

ΠCFM,j

t=(Zj

tBj

tin case of non-default, ωj

t>¯

ωj

(1 – µ)(ωj

tRk,i

tQi

t–1Kj

t) otherwise (29)

Chapter 2 29

where

ωj

is the threshold value for the effective capital to lead to default. Here, the CMF anticipates

the optimal ROI realized by the entrepreneur according to Eq.

(27)

. The lending rate Z

is given by

the following condition:

Rk,i

t+1Qi

t¯

ωj

t+1Kj

t+1 =Zj

t+1Bj

t+1 (30)

The expected return for the loan to entrepreneur jis given by

EhΠCFM,j

ti=1 – F(¯

ωj

t+1)Zj

t+1Bj

t+1

+Z¯

ωj

0(1 – µ)ωj

t+1Rk,i

t+1Qi

tKj

t+1dF(ωj

t+1) (31)

=Rk,i

t+1lj

t+1Nj

t+1(Γ(¯

ωj

t+1) – µG(¯

ωj

t+1)) (32)

where F

ωj

t+1

is the cumulative distribution function of

ωj

t+1

. The gross share of profits that go

to the lender is given by Γ(¯

ωj

t+1), and µG(¯

ωj

t+1) is the frictional loss.

Γ(¯

ωj

t+1) = ¯

ωj

t(1 – F(¯

ωj

t+1)) + Z¯

ωj

t+1

0ωj

t+1dF(ωj

t+1) (33)

G(¯

ωj

t+1) = Zωj

t+1

0ωj

t+1dF(ωj

t+1) (34)

The zero profit condition of the CMF implies that the expected return on the loan is equal to its

opportunity costs of funds (determined by the risk free rate):

Rt+1Bj

t+1 =Rk

t+1lj

t+1Nj

t+1(Γ(ωj

t+1) – µG(ωj

t+1)) (35)

Using Eq. (28) we write the right hand side in terms of leverage:

Rt+1Bj

t+1 =Rt+1(lj

t+1 – 1)Nj

t+1 (36)

where the entrepreneur’s leverage ratio l

is defined as the ratio between the real value of its capital

and its net worth.

t=Qi

t–1Kj

(37)

Substitution these equations into Eq. (35), we get the following zero profit condition of the CMF:

Rt+1(lj

t+1 – 1)Nj

t+1 =Rk,i

t+1lj

t+1Nj

t+1(Γ(¯

ωj

t+1) – µG(¯

ωj

t+1)) (38)

In case there exists aggregate risk, the threshold productivity of capital

ωj

t+1

will depend on the

ex-post realisation of R

k,i

t+1

(i.e. a realisation of the aggregate state of the sector, see Section 3.2 in BGG

for more details). Entrepreneurs are risk-neutral and hence offer the lender "a (state-contingent)

non-default payment that guarantees the lender a return equal in expected value to the riskless rate"

(ibid.). Thus, the borrower chooses the leverage ratio l

t+1

and the threshold productivity of capital

ωj

t+1

that are optimal for the expected return on capital, however, the borrowing rate and the actual

threshold value are contingent on the aggregate realization of Rk,i

t+1.

Chapter 2 30

2.4.4 Entrepreneurs’ choice of capital

The entrepreneur’s problem of choosing optimal capital stock and borrowing can then be expressed

in the following way:

max

t+1,¯

ωj

t+1

EhRk

t+1lj

t+1Nj

t+1(1 – Γ(¯

ωj

t+1))i(39)

subject to Eq.

(38)

, i.e. the zero profit constraint of the CMF. It should be noted that since the

borrowed amount is determined at the end of the previous period, the leverage ratio l

t+1

is fixed at

time t.

Schuldt and Lessmann (2022) show for the costly state verification problem that the choices of

ωj

t+1

and l

t+1

are the same for all entrepreneurs in each sector iregardless of the individual capital

stock, so we can drop the index j. Let

Πi

be the aggregate entrepreneurial profit in sector iafter

repayment of debt:

Πi

t=Rk,i

tQi

t–1Ki

t– Rt+µG(¯

ωi

t)Rk,i

tQi

t–1Ki

t–Ni

t!Qi

t–1Ki

t–Ni

t(40)

The profit equals to the return on capital minus the cost of debt. An expression for the external

finance premium (defined as the margin on top of the risk-free rate paid on debt) is evident from the

second term in Eq. (40).

In each period of time, a fraction 1 –

of entrepreneurs close their business and transfer their

net worth to households. At the same time, new entrepreneurs enter, endowed by households with

initial seed finance SF

. These assumptions ensure that the entrepreneurial net worth is stationary.

The aggregation of net worth, borrowing and capital stock leads to the following set of aggregate

first order conditions of the entrepreneurs in sector i:

t+1 =νΠi

t+SFi(41)

Ce,i

t= (1 – ν)Πi

t(42)

0 = Γ(¯

ωi

t+1) – µG(¯

ωi

t+1)Rk,i

t+1li

t+1 –Rt+1 li

t+1 – 1(43)

0 = Rk,i

t+1

Rt+1 1 – Γ¯

ωi

t+1

+Γ′¯

ωi

t+1

Γ′¯

ωi

t+1–µG′¯

ωi

t+1 Γ¯

ωi

t+1–µG¯

ωi

t+1Rk,i

t+1

Rt+1 – 1!(44)

Eq.

(41)

gives the evolution of the sectorial net worth, Eq.

(42)

gives the period sectorial transfer

of wealth to households, Eq.

(43)

is the zero profit constraint of the CMF and Eq.

(44)

defines

the optimal debt contract by relating return on capital R

k,i

t+1

to the risk free rate R

t+1

and default

productivity threshold

ωi

t+1

. The total net transfer from entrepreneurs to households is then the

entrepreneurial consumption less the seed finance:

t=X

Ce,i

t–SPi(45)

2.5 Aggregators

Tradable and non-tradable goods are aggregated into a whole-sale good through a representative

goods aggregator. The aggregator operates under perfect competition, makes no profits, and uses a

Chapter 2 31

standard CES function for aggregation:

t=(ϕW)1

ϵW(YT

t)1– 1

ϵW+ (1 – ϕW)1

ϵW(YN

t)1– 1

ϵWϵW

ϵW–1 (46)

where

ϕW

is a share parameter and

ϵW

is a substitution parameter. Y

is the whole-sale output,

is the output of non-tradable goods entrepreneurs, and Y

is the tradable goods available for the

whole-sale goods market, i.e. the tradable goods entrepreneurial output plus net imports minus the

fossil fuel used for production of energy.

The wholesale good aggregator maximizes its profit according to

max

t,YT

tYW

t–pT

tYT

t–pN

tYN

t(47)

subject to Eq. (46). The first order conditions gives the following expressions of sectorial prices:

t=pW

t(1 – ϕW)YW

t1

ϵW(48)

t=pW

t(1 – ϕW)YW

t1

ϵW(49)

where p

are the prices of the tradable good, non-tradable good and aggregated wholesale

good, respectively.

Like the tradable and non-tradable goods, clean and dirty energies are aggregated into an energy

product through a representative CES aggregator. The aggregation leads to the following model

equations:

Mt=(ϕE)1

ϵE(Md

t)1– 1

ϵE+ (1 – ϕE)1

ϵE(Mc

t)1– 1

ϵEϵE

ϵE–1 (50)

t=pE

t (1 – ϕE)Mt

t!1

ϵE(51)

t=pE

t(1 – ϕE)Mt

t1

ϵE(52)

where M

is the aggregated energy output, M

and M

is the output of the clean and dirty energy

sectors. The price of energy is given by p

, while p

and p

are the prices of clean and dirty energy.

2.6 Retailers

The wholesale goods aggregator sells its products in the fully competitive whole-sale market to a

continuum of retailers, who then differentiate their products and sell them on the final goods market.

By assuming that retailers jface monopolistic competition and have quadratic price adjustment costs

à la Rotemberg (Rotemberg 1982), we introduce nominal rigidity in the model. The final output is a

composite of individual retailers’ output:

Yt=Z1

0(Yj

t)θ–1

θdjθ

θ–1 (53)

Chapter 2 32

and we define the aggregate price level:

1 = Z1

0(pj

t)1–θdj1

1–θ(54)

The left hand side of the equation above is the real price of the final good, which per definition is 1.

For any level of output demand for the individual retailer’s product is then given by:

t=pj

t–θYt(55)

Retailer jpays a marginal cost P

for its input together with a quadratic price adjustment cost (i.e.

menu cost), which depends on the cost parameter

and the size of the price adjustment. The profit

of retailer jis:

ΠR,j

t+1 = (pj

t+1 –pW

t+1)Yj

t+1 –ψ

2 pj

t+1

– 1!2

t+1 (56)

This leads to the following maximization problem of the retailers:

max

k=0

βkEhΠR,j

t+ki(57)

where

is the discount factor used to discount profits from period t+kto period t. Taking the

first order condition and recognizing that all retailers are symmetric (i.e. they face the same costs)

and therefore sets the same price, we obtain the New Keynesian Phillips Curve from the first order

condition:

0 = 1 – θ1 – pW

t–ψ(1 + πt)πtYt+βψπt+1 (πt+1 + 1)Yt+1 (58)

where πtis the price inflation of the final good from period t– 1 to t.

2.7 Central bank

The central bank sets the nominal interest rate through a Taylor rule, which, in a slightly altered

formulation, has been applied to the Brazilian economy by Carvalho and Castro (2017).

RH∗

t+1

R=RH∗

RγRπt

πγπGDPt

GDP γy1–γR(59)

where

is the equilibrium nominal interest rate given an inflation target

GDPt

is the gross

national production at time t,

γπ

and

γy

are the weighing parameters of the rule.

GDP

is an measure

of domestic production smoothed over time through its moving average:

GDPt=ρ¯

GDPt–1 +(1 – ρ)GDPt(60)

We calculate GDP through the expenditure method adjusting for the net cross border flow of funds,

i.e.

GDPt=It+Ct+RF

tBF

t–BF

t+1St(61)

The nominal rate defines the relation between the real risk free rate of the economy and inflation

and hence, by setting the nominal interest rate through the Taylor rule, the central bank indirectly

controls inflation. However, because of price adjustment costs, real returns are also influenced by

inflation. As the difference between foreign and domestic rates determines the real exchange rates,

setting the nominal rate also affects the real exchange rate.

Chapter 2 33

2.8 Market clearing conditions

2.8.1 Labor market

The labor market clears when labor supply by households equals the demand by the four en-

trepreneurial sectors:

Lt=X

t(62)

2.8.2 Energy market

The aggregated energy supply equals the energy demanded by the non-tradable and tradable goods

sectors, i.e.:

Mt=EN

t+ET

t(63)

where Mtis the aggregated energy output.

2.8.3 Final goods

Final goods (net of retailers’ menu cost and frictional losses in the financial intermediation) are either

consumed or invested. The market clearing condition for the final goods is given by the following

equation:

1 – ψ

2(πt– 1)2YW

t–X

µG(¯

ωi

t)Rk,i

tQi

t–1Ki

t=Ct+It(64)

where the sum in the second term on the left-hand side is the total losses due to financial frictions in

the four entrepreneurial sectors, and Itis the total investments.

2.8.4 Tradable and non-tradable goods

Non-tradable goods can only be produced and consumed domestically, hence the output of the

non-tradable goods entrepreneur equals the goods available for aggregation. This is not the case for

the tradable goods. The tradable goods available for aggregation (Y

) are the output of the tradable

goods entrepreneurial sector Y

T,output

less the fossil fuel consumed by the dirty energy sector, and

then adjusted for the net cross border flow of funds. This results in the following market clearing

condition:

t=YT,output

t–Xt+BF

t+1 –RF

tBF

t(65)

The market clearing conditions complete the set of model equations.

2.9 Climate policy, shocks and stochastic simulation

We model the low-carbon transition through a sudden introduction of a carbon tax

τX

applied to the

use of fossil fuels and paid by the dirty energy producers. The carbon tax is fixed, inflation adjusted

(given in real terms), and once introduced, it remains in place. The carbon tax is a fundamental part

of all climate policies analyzed in this paper. In the benchmark scenario, the carbon tax is recycled

directly to households in terms of lump-sum transfers T

. In the alternative tax recycling scenario,

the proceeds of the carbon tax are awarded to the clean energy producers as a subsidy (

τc

). The

level of subsidy depends on tax revenues and clean energy production for each period. In addition

to the sudden introduction of the climate policy, we simulate the transition under variations to the

international borrowing rate. We do this by analyzing the model response to the introduction of

Chapter 2 34

carbon tax coinciding with a shock to the foreign rate. The foreign borrowing rate is adjusted by z

which is determined by the following equation:

zt=ρzzt–1 +εz

t(66)

where ρzis a persistence parameter and εz

tis the shock variable. We set ztto 1 in steady state.

3. Calibration

3.1 Benchmark calibration

For the calibration of the model to the Brazilian economy, we utilize literature estimates, data from

the GTAP database (Narayanan 2008), the World Bank (World Bank 2022a) and the Banco Central

do Brasil (Banco Central do Brasil 2022). An overview of parameter values is provided in Table 1

and we evaluate the fit of the model’s steady state to empirical counterparts in Table 2.

We choose a standard quarterly discount factor

equal to 0.9855 such that the model generates

a steady state real risk-free rate of 6 percent.

We follow Carvalho and Castro (2017) by setting the quarterly depreciation rate of capital

producers

to 0.02 and, following Christensen and Dib (2008), we set the investment adjustment

cost parameter χto 0.59.

We approximate the parameter of foreign debt capacity

to 0.47 such that the ratio of foreign

debt to GDP is close to its empirical value in Table 2, row 5. The sensitivity parameter

determines

the response of foreign debt to variations in the foreign borrowing rate. We estimate a

equal to

0.044 by fitting Eq.

(14)

to historical Brazilian foreign debt data during the period 1999-2019 (World

Bank 2022b). We use the US real interest rate as a proxy for the international borrowing rate (World

Bank 2022c).

Estimates for the output elasticity of capital in the dirty and clean sector

αd

and

αc

, the share

parameter for the capital labor composite in the production of dirty energy

ϕd

, and the elasticity

of substitution between the capital labor composite and fossil fuel 1/

ϵd

are borrowed from Diluiso

et al. (2020). The efficiency of dirty energy production

is set such that the steady state features

the fossil energy ratio reported in Table 2, row 3.

We utilize the GTAP database to determine parameter estimates in the tradable and non-tradable

goods producing sectors.

The equations used for calibration are described in Appendix 3 and the

parameter values are reported in Table 1. Estimates of the inverse elasticity of substitution

ϵT/N

are

borrowed from Diluiso et al. (2020).

All types of entrepreneurs in this model obtain debt through financial intermediaries that are

subject to financial friction. The strength of frictions is determined primarily through the parameters

bankruptcy costs

, the uncertainty of the success of entrepreneurs

, and the survival probability

of entrepreneurs

. The World Bank (2022a) reports recovery rates for Brazil ranging from 12.7

to 18.3 percent for the period 2015 to 2019. Therefore, we set the share of realized profits lost in

bankruptcy to

= 0.873. The standard deviation of log(

), expressing the uncertainty of the success

of entrepreneurs, is fixed at

= 0.32 and the survival probability of entrepreneurs at

= 0.92 to

match the debt equity ratios and bankruptcy rates reported in Table 2, rows 9 and 10. Values for

bankruptcy cost

, entrepreneurial success uncertainty

, and entrepreneurial default rates 1 –

are

above the conventional ranges used in the literature (e.g. Bernanke, Gertler, and Gilchrist (1999),

Gertler, Gilchrist, and Natalucci (2007) and L. J. Christiano, Motto, and Rostagno (2014)) and are

Within the GTAP database, we aggregate data as follows: regions are Brazil and the rest of the word; sectors are energy

(oil, gas, coal, petroleum, coal products and electricity), non-tradable (construction, trade, transport, communication, financial

services, insurance, business services, recreation, administration, health, defense, education and dwellings) and tradable (all

other); factors of production are capital (capital, land, natural resources) and labor (skilled and unskilled). For the calibration

we consider agents’ prices instead of market prices to also include tax liabilities (and subsidies) associated with the factors of

production and intermediate goods.

Chapter 2 35

expressions of the relative challenging economic conditions in Brazil when compared to the rather

developed economies in the model regions for mentioned publications. For the transfer of funds

from households to entrepreneurs SF, we choose an infinitesimal small value below the estimate

of L. Christiano, Motto, and Rostagno (2010) to not generate an additional significant source of

entrepreneurial net worth.

For energy aggregators, the values for the share parameter for dirty energy

ϕE

, and the elasticity

of substitution between dirty and clean energy

ϵE

are taken from Diluiso et al. (2020) and reported

in Table 1.

The share parameter of tradable goods

ϕW

with the goods aggregator is calculated using GTAP

data, following the procedure described in Appendix 3. The elasticity of substitution between

tradable and non-tradable goods is borrowed from Cavalcanti and Vereda (2016).

Retailers are subject to price rigidities à la Rotemberg (1982) and we adopt the price adjustment

cost parameter

and the elasticity of substitution between goods varieties

from Diluiso et al. (2020).

The Taylor rule parameters

γR

γπ

, and

γy

are borrowed from (Carvalho and Castro 2017)

who apply a similar rule to describe the Brazilian central bank. Inflation targets for the period from

2015 to 2019 are obtained from (Banco Central do Brasil 2022) and averaged to calculate

. The

equilibrium interest rate ¯

Ris set such that observed inflation is achieved (cf. Table 2).

3.2 Climate policy and foreign aid scenarios

Though lately in decline, Brazilian emissions from land-use related activities have historically been

substantial, while energy-related per capita greenhouse gas emissions are low (La Rovere 2017). In

this paper, we focus on energy-related emissions only. To calibrate the climate policy, we use Brazil’s

’fair share’ contribution that is compatible with the global warming target of 1.5 degree. Brazil’s

fair share contribution amounts to 856 Mt CO

e (excl. LULUCF) in 2030 according to Climate

Tracker (2022). The absolute emission level was 1,110 MtCO

e in 2019 (Climate Transparency

2022), which gives approx. 23 percent ’fair share’ reduction until 2030. Assuming that climate policy

was introduced in the first quarter 2020, the time horizon to be modeled is 10 years, i.e. 40 quarters.

We hence simulate the economy’s response to introduction of an unannounced and flat carbon tax

schedule that yields emission reductions of 23 percent over 40 periods in the benchmark economy.

The model considers only one generic ’fossil fuel’. Translating model prices into real world prices

requires calculating a weighted price and weighted emission index of one unit of fuel equivalent,

i.e. the average fuel in the primary energy mix. We use primary energy supply data (IEA 2022),

fuel price data (World Bank 2023) and carbon intensity for each fuel type (EPA 2021) to do so.

The calculation is based on oil (assumed crude oil) and natural gas only, since the Brazilian coal

consumption is insignificant. The resulting carbon tax level is 43 USD per tCO2.

International aid could potentially incentivize the introduction of strict climate policy in develop-

ing countries by compensating for some of the associated cost. To date, Brazil has received 394.4

million USD in support from the Green Climate Fund, which is approximately 3.3 percent of the

total funds (12 billion USD as of 2023) (Green Climate Fund 2023). If the fund were to fulfill its

target of 100 billion USD per year, and Brazil continued to receive the same share, then it would

receive 3.3 billion USD per year. We calibrate the aid introduced in the model to this level. Brazil

received on average 797 million USD in Official Development Assistance (Gross ODA) in 2019-2020

and 28 percent of the bilateral ODA went to infrastructure investments (OECD 2022), hence 3.3

billion USD is a fairly large figure.

For policy comparisons of the net present value of GDP changes, we follow Moore, Boardman,

and Vining (2020) and set the social discount rate to 4.36 percent, fairly close to the risk-free rate (cf.

Table 2, row 13).

Chapter 2 36

Table 1. Calibrated parameters (time unit of model: quarter)

Households

βdiscount factor 0.9811

Capital good producers

χCapital depreciation rate 0.02

βInvestment adjustment cost parameter 0.59

Financial intermediation

µBankruptcy cost 0.226 (0)

σSuccess uncertainty 0.3

νSurvival rate 0.971

SF Seed finance 0.001

Foreign behaviour

ηDebt capacity 0.47 (0.895)

κScaling parameter 0.044

Energy producers

αc/dOutput elasticity of capital 0.3 / 0.3

Ac/dProductivity 1.58 / 1.0

ϕdShare parameter 0.7

ϵdINVERSE elasticity of substitution 3.333

Goods producers

αT/NOutput elasticity of capital 0.497 / 0.372

AT/NProductivity 1.539 / 1.325

ϕT/NShare parameter 0.774 / 0.721

ϵT/NINVERSE elasticity of substitution 2 / 2

Energy aggregators

ϕEShare parameter 0.75 (0.70)

ϵEElasticity of substitution 5

Goods aggregators

ϕWShare parameter 0.54

ϵWElasticity of substitution 2

Retailers

ψPrice adjustment cost 93.2

θRElasticity of substitution 9

Central bank

πAnnual Inflation target 0.045

REquilibrium interest rate 0.027

γRTaylor rule parameter 0.825

γπTaylor rule parameter 1.966

γyTaylor rule parameter 0.185

ρMoving average parameter 0.9

shock parameters

ρzpersistence parameter 0.999999

Chapter 2 37

3.3 Counterfactual frictionless calibration

The response of the economy with financial frictions is compared with that of a frictionless economy.

To model the frictionless economy, we set the bankruptcy cost parameter

to zero, which implies

there are no costs related to defaults. To ensure that the steady state emission intensity is comparable

to the model with friction, we adjust the share parameter

ϕe

of the energy aggregator. In addition,

the debt capacity parameter

of the foreign borrowing constraint is updated to 0.895 for the model

to produce a similar foreign debt to GDP ratio for the frictionless model. The parameters are reported

in parentheses in Table 1.

3.4 Counterfactual more open and less open calibrations

The sensitivity of the foreign debt level to fluctuations in the foreign borrowing rate is expressed

through the parameter

in Eq.

(12)

, calibrated in the benchmark model as described above. To

study the sensitivity of the model response to the degree of openness, we vary the value of

. A high

value implies little or no variation in the foreign debt level in response to changes in the lending rates,

which is expected for an economy that is poorly integrated with the global financial system. We shall

refer to such an economy as ’less open’. In contrast, a low value implies large variations, implying a

more pronounced reaction to changes in the global financial system. We call this economy ’more

open’. For the counterfactual modeling we set

to 2 orders of magnitude smaller or larger than the

benchmark value, respectively.

3.5 Model fit

Table 2 reports steady state values of the model and corresponding empirical counterparts. Most values

are within the range of empirical counterparts, or close to it. Data for GDP shares of investment and

consumption, for the fossil energy ratio, and net trade in goods (rows 1-4) are taken from the World

Development Indicators (World Bank 2022c). From the same source, we use the ’Price level ratio of

PPP conversion factor (GDP) to market exchange rate’ as a measure for the real exchange rate (row

5). Values on foreign debt (international debt issues), bank deposits, bank credit and debt to equity

(rows 6-9) are reported in the Global Financial Development database (World Bank 2022b). The

debt-to-equity ratio is calculated as the ratio of gross portfolio debt liabilities to gross portfolio equity

liabilities. The annual bankruptcy rate (row 10) is borrowed from Bortoluzzo et al. (2022) who report

rates for small, medium and large companies. Total bankruptcy costs (row 11) are calculated as one

minus the recovery rate reported in the Doing Business data set (World Bank 2022a) weighted by the

ratio of non-performing bank loans to GDP from the Global Financial Development database (World

Bank 2022b). The World Development Indicators (World Bank 2022c) also provide data on real

interest rates, risk premiums on lending, and inflation rates. Risk premiums on lending are recorded

as the difference between the lending rate and the ’risk-free’ treasury bill interest rate. Such mark-ups

on the lending rate finance operating costs, tax expenditures, profits, and loan-loss provisions on the

banks’ income statements. In the model, external finance premiums finance loan-loss provisions only

and we therefore apply the share of loan-loss provisions of net interest income for Brazil from Calice

and Zhou (2018, Table 3) as a factor to the risk premium obtained from World Bank (2022c). The

resulting nominal external finance premiums are divided by inflation to yield real annual external

finance premiums (row 12) for Brazil. The real risk-free rate (row 13) is calculated by subtracting

the real risk premium on lending from the real interest rate.

4. Results

We report results in two parts. In the first part, we examine the role of financial frictions and financial

openness in a small open economy when the low-carbon transition is driven by a carbon tax. The

tax is paid by the dirty energy producers for the use of fossil fuels and the tax revenues are recycled

to households as lump sum transfers. In the benchmark version of the model, the economy is open

Chapter 2 38

Table 2. Steady state values and empirical counterparts. Ranges represent minimum and maximum values in years from

2015 to 2019 or ranges found in the literature. Data sources by rows: 1-5, 12-13: World Bank (2022c); 6-9: World Bank (2022b);

10: Bortoluzzo et al. (2022); 11: World Bank (2022a, 2022b, 2022c); 14: Banco Central do Brasil (2022).

# Model Data

1 Gross capital formation to GDP I/GDP 0.097 0.155-0.174

2 Final consumption expenditure to GDP C/GDP 0.895 0.837-0.851

3 Fossil energy ratio Ed/(Ed+Ec)0.588 0.565-0.591

4 Net trade in goods to GDP (RFBF–BF)/GDP 0.010 0.001-0.028

5 Real exchange rate S0.807 0.576-0.684

6 Foreign debt to GDP SBF/GDP 0.138 0.136-0.159

7 Bank deposits to GDP D/GDP 0.4178 0.570-0.687

8 Bank credit to bank deposits PiBi/D1.329 0.904-1.173

9 Debt to equity PiBi/PiNi0.844 0.502-1.541

10 Annual bankruptcy rate F(¯

ωT/N/d/c)0.033-0.036 0.001-0.040

11 Total bankruptcy costs to GDP 0.015 0.016-0.019

12 Annual external finance premium ZT/N/d/c–R0.027-0.029 0.053-0.096

13 Annual risk-free rate R0.060 0.053-0.148

14 Annual inflation rate π0.057 0.035-0.090

and financial frictions are calibrated as described in Section 3.1. We compare the model response

to a ’no frictions’ scenario, in which there are no costs associated with defaults (cf. Section 3.3) and

show that the frictions only have a relatively small effect on the emission path, but greatly increase

the costs of the transition by reducing the inflow of foreign funds. We then explore the role of

openness by varying the degree to which foreign debt responds to the introduction of a carbon tax

and combine the carbon tax with variations in the foreign borrowing rate. We find that, just like

financial frictions, the degree of openness does not affect the emission path, but alters the impact of

the policy on consumption and output.

In the second part, we discuss the impact of policy design on the low-carbon transition trajectories

in the open economy with financial frictions. We introduce a targeted industrial support to the

clean energy sector (clean energy subsidies) as an alternative use of the carbon tax revenues and

analyze the response of the economy to such a policy scheme. We show that subsidies allow for a

much faster scale-up of clean energy, and by keeping the cost of energy low, a subsidy policy can

significantly reduce the short-term welfare losses implied by the carbon tax. Finally, we model the

effects of foreign aid on the low-carbon transition and show that foreign aid can counteract some of

the negative welfare implications from the climate policy.

4.1 Financial frictions in the open economy

Financial frictions act like an adjustment cost that creates inertia in the adjustment of the capital

structures. As such, they affect the steering effect of the policy during the transition, but have little

impact on the post-transition steady states.

The basic transmission mechanism of an unannounced and flat carbon tax schedule remains

intact throughout all model variations studied in this paper. We thus summarize its mechanics before

we discuss specific scenarios. We use the benchmark model simulation in Figure 3 to illustrate the

explanation. The same forces are at play in the other scenarios below.

Figure 3 shows the response of the benchmark model of selected economic variables following

the introduction of a climate policy, modeled as a permanent carbon tax shock (

τX

in Eq.

(22)

). The

carbon tax increases the cost of using fossil fuels in energy production, making fossil fuel-based

Chapter 2 39

(dirty) energy more expensive, and hence, promoting substitution towards fossil fuel free (clean)

energy (Figure 3A). The declining proftability of dirty energy entrepreneurs is reflected in the

corresponding reductions in investment and capital stock in this sector (Figure 3B). By the end of year

2030 the dirty energy capital stock is reduced 19 percent, while the clean energy stock has increased

14 percent. The increasing cost of fossil fuel increases the price of energy with approximately 3

percent, leading to a decrease in overall energy consumption.

As energy is an input to the goods producing sectors, the higher price of energy drives up the

input costs, leading to less energy consumption. Less energy as input to production lowers the

marginal return on capital and labor. In this way, carbon taxes lead to lower production (Figure 3G).

The lower return on capital implies a reduction in the overall level of investment and domestic savings

(Figure 3H). It also impedes the inflow of foreign funds, leading to a drop in the level of foreign

debt (Figure 3J). With the decelerating inflow of foreign funds, less tradable goods are available in

the economy, driving up the price of the tradable good and, hence, the real exchange rate. At the

same time, higher production costs and lower domestic production increase inflation (Figure 3F),

leading to losses (menu costs) that add to the contractionary pressure on the economy. The estimated

impact on inflation is an increase from 5.6 percent per year in steady state to 6.2 percent upon the

introduction of the carbon tax.

Since this model does not consider economic damages from climate change, the carbon tax

appears distortionary.

The following sections show how financial frictions and financial openness

may aggravate these distortions.

4.1.1 The role of frictions in the open economy

The debt of the dirty energy sector decreases, while the growth of the clean energy sector is

accompanied by an expansion in its debt level. However, the net worth of the clean energy sector

increases only slowly with the accumulating capital stocks. As a result, the leverage ratio peaks

(Figure 3C) followed by a higher risk of default. In the presence of financial frictions, the external

finance premium of the clean sector increases, resulting in higher costs for clean energy.

At the same time, the finance premium in the dirty sector is falling. Despite the adverse effect

of climate policy on the net worth of the dirty energy sector, its low demand for new investments

drives down the leverage ratio (Figure 3F) and therefore the finance premium.

Figure 3 also indicates the role of financial frictions during the transition by highlighting the

differences from the model without frictions. In an economy without frictions, there is no cost

related to defaults, and hence external finance premiums are zero throughout. Entrepreneurs are not

restricted when borrowing from banks and are nearly completely financed through debt. For this

reason, the leverage ratio plays no role and is not shown in the figure.

A comparison between the economy with frictions and the counterfactual frictionless indicates

that frictions and the growing external finance premiums on clean energy loans have a clear impact

on the speed with which clean energy capital is scaled up (Figure 3B). For instance, we estimate

that clean energy capital would increase by 11 percent by 2025 in the presence of financial frictions,

compared to a 17 percent increase if there were no financial frictions. Due to the decelerated clean

energy investments, frictions slow the substitution of dirty energy and thus, a larger share of the

energy is subject to the carbon tax. This implies slightly higher energy prices, which further reduces

the return on capital in the goods sectors, leading to an overall lower level of investment. The

additional pressure on the energy costs under frictions results in a stronger decline in foreign debt,

indicating that financial frictions make it harder to stay competitive in international capital markets.

The drop in the inflow of foreign funds (Figure 3J) in turn has adverse effects on consumption

(Figure 3I), which clearly suffer more under frictions.

The benefits of emission reductions are long-term and depend on global emissions. For our short-term analysis of

national policies, we therefore abstract from climate change impacts.

Chapter 2 40

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Figure 3. The benchmark model response to the introduction of a carbon tax. Response values are reported as percentage

of steady state values, except inflation that is reported in percentage points. The shaded area indicates the difference to the

same model without frictions. The leverage ratio is not shown for the frictionless model, as the lack of frictions implies fully

debt-financed investments.

Chapter 2 41

The simulation results indicate that the relative change in fossil fuel consumption is almost

identical in the two models (Figure 3D). Financial frictions slow down the decarbonization slightly

in the short term but by 2030 the difference has but vanished. However, frictions result in a 6 percent

increase in emissions that accumulate during the transition period.

In the short term, the policy’s ability to foster replacement of dirty energy capital with clean

energy capital greatly depends on the level of frictions. Without a cheap, clean substitute for fossil

fuel-based energy, the transition becomes costly. In conclusion, the main impact of frictions on the

low-carbon transition is not on the effectiveness of the carbon tax but rather in the economic cost of

the policy: frictions lead to a much stronger decline in the inflow of foreign funds, higher incentive

for savings, and therefore less consumption.

4.1.2 The role of openness in the frictions economy

The section above discussed the role of financial frictions in a small open economy and showed that

financial frictions interact with the inflow of foreign funds. Frictions reduce the return on capital

making the economy less competitive on international markets. In this section, we explore this

property further - we turn the question around, and discuss the role of financial openness in an

economy with frictions. We show that the emission path remains largely unaffected by the degree of

financial openness, however, output and consumption are affected.

Note that fossil fuel is assumed to be a good available for international trade. Therefore, it is

valued and priced as a tradable good with a price equivalent to the real exchange rate. Consequently,

variations in the level of foreign debt, which affects the exchange rate, also have implications for the

cost of fossil fuels.

Figure 4 shows the response of the benchmark model to the sudden introduction of a carbon tax

together with the response of the model where the sensitivity parameter

is 2 orders of magnitude

smaller or greater than the benchmark value, respectively.3

The tax increases the cost of fossil fuels and induces a reduction in its use. As fossil fuel is a

tradable good, the fuel savings increases the amount of tradable goods available for consumption and

investments. However, the carbon tax lowers the return on capital by increasing the cost of energy,

and hence, in the open economy, the level of foreign debt declines (Figure 4J). The simultaneous

reduction in the foreign debt reduces the number of goods available in the economy. This effect

increases with the level of openness: the figure indicates that a decline in foreign debt in the more

open economy is far greater than that of the benchmark model. The steep reduction in the supply of

tradable goods increases the real exchange rate (Figure 4K) and thus makes fossil fuel more expensive.

That is, in the open economy the tax not only increases the cost of fossil fuel usage with the taxed

amount, it also increases the relative price of the fuel. The increased price of fossil fuel implies

the opposite effect of that usually observed in closed economy models, where a carbon tax reduces

demand for fossil fuels, leading to lower fuel prices.

In the less open version of the economy, the foreign debt level does not adjust, and therefore the

lack of demand for fossil fuel leads to a short-term excess supply of tradable goods, which in turn

causes a currency appreciation and lower energy prices in the first periods.

Despite the differences in the impact on the model economies, Figure 4A-4D indicate that the

level of financial openness only has a minor impact on the transition path. Emissions (Figure 4D) are

almost identical in the three cases shown. Additionally, capital stocks in the energy sectors (Figure

4B) evolve almost identically following the introduction of a carbon tax. The reason behind this

result is the difference in output: The drop in foreign debt in the more open economy, reduces

the number of goods available in the economy, and creates an incentive for domestic production.

The steady state level of foreign debt is the same as in the benchmark model. The focus of the section lies on the role of

the degree of sensitivity towards variation in international markets, not the steady state debt size, although in real life, these

two properties may be connected.

Chapter 2 42

  











  













  













  













  













  













  











  











  













  











(

real

)



  



















  











wtLt

Figure 4. The benchmark model response to the introduction of a carbon tax.. Response values are reported as percentage

of steady state values, except inflation that is reported in percentage points. The shaded areas show the response for

variations in the

parameter that determines the sensitivity of foreign debt level to variations in the foreign borrowing rate.

Chapter 2 43

Hence, the more open economy may experience higher output compared to the benchmark. More

output leads to higher demand for inputs, including energy, which implies an increased demand for

fossil fuels despite higher prices. Domestic production cannot offset the drop in inflow of foreign

funds, and therefore high sensitivity to international borrowing conditions has adverse effects on

consumption (Figure 4I), inflation (Figure 4F), and price adjustment costs during the transition.

The analysis of the impact of financial frictions on foreign debt presented in Section 4.1.1 indicates

that frictions exaggerate the decline in foreign debt following the introduction of a carbon tax. Here,

we find that the degree of openness interacts with the frictions. A more open economy experiences

higher prices that increase the net worth of entrepreneurs. Higher net worth implies lower leverage

ratios (Figure 4 C) and therefore lower frictional losses. It should be noted that the leverage ratio of

both the clean and dirty energy sectors, is lower in the more open economy, whereas it is higher

for both sectors in the less open economy. Because the degree of openness pushes the leverage ratio

of the two sectors in the same direction, openness does not offer any relative advantage for either

sector. Consequently, there is no effect on the substitution dynamics of the two capital stocks during

the transition.

4.1.3 Variations in the foreign borrowing rate

Financial openness implies that the economy is sensitive to variations in the foreign borrowing rate,

hence, any changes in the borrowing conditions in the international capital markets will carry over to

the domestic economy. We find that such variations only have only minor effects on the effectiveness

of climate policy and its ability to facilitate clean energy investment, but they dominate short-term

effects on consumption, output, inflation and foreign debt. In this section, we discuss the response of

the economy to a carbon tax under variations of the foreign borrowing rate, i.e. at the same time

the tax is introduced, a shock to the borrowing rate on the international market materializes (z

Eq.

(12)

). Figure 5 shows the response to foreign rate shocks corresponding to

1 and

2 standard

deviations, where one standard deviation implies a change in the foreign rate of approximately 1.5

percentage points per year.

Variations in the level of the foreign borrowing rate have a substantial impact on the foreign debt

level. When the cost of foreign debt declines (for a negative shock to the foreign borrowing rate),

the level of debt increases substantially (Figure 5J). The intensified inflow of foreign funds depresses

the real exchange rate in the short term (currency appreciation, cf. Figure 5K), making fossil fuels

and, subsequently, energy cheaper. The deflationary pressure (Figure 5F) following a negative shock

to the foreign borrowing rate exacerbates the drop in output (Figure 5G). The increased levels of

foreign debt lead to higher consumption levels (Figure 5I), despite lower labor income.

The opposite is true if the borrowing rate in international markets increases while the carbon tax

is introduced. The increased costs of foreign funds lead to higher prices and higher output.

The simulations of the economic response to a positive shock to the foreign borrowing rate point

to the importance of foreign debt for the value of firms. Higher borrowing rates imply higher prices

for all goods, which cause a short-term increase in net worth for both the clean and the dirty energy

sectors. With higher net worth, leverage ratios are lower and investments can be made at lower cost

(Figure 5C).

In conclusion, financial openness towards international markets does not matter much for the

effectiveness of the carbon tax to reduce emissions but the effects of foreign rate shocks alter the

economic effects of the carbon tax in the short term. Increased foreign rates create inflation, which

is good for those with debt: our model suggests that a higher foreign rate lowers foreign debt level

and boosts domestic production, leading to higher energy consumption and more use of fossil fuels.

But while GDP (Figure 5G) increases with the foreign borrowing rate, a larger share of GDP goes

to foreign lenders to service debt, leaving less for domestic consumption.

In the benchmark model, foreign debt is in foreign currency, while deposits and debt to en-

Chapter 2 44

  











  













  













  













  











  











  











  











  











  













(

real

)



  



















  













wtLt

Figure 5. The model response to the introduction to a carbon tax under variations of the foreign borrowing rate, i.e. at the

same time the tax is introduced, shocks happen to the borrowing rate at the international market. Response values are

reported as percentage of steady state values, except inflation that is reported in percentage points.

Chapter 2 45

  















  























Figure 6. The leverage ratio in response to the introduction to a carbon tax under variations of the foreign borrowing rate,

i.e. at the same time the tax is introduced, shocks happen to the borrowing rate at the international market. The three

models differ in terms of currency of the activities of the financial intermediator.

trepreneurs are in domestic currency. The choice of currency affects the sensitivity towards foreign

rate shocks. Figure 6 shows the effect of two model variations on sectoral leverage ratios (as in

Figure 5C). The two variations are: (1) entrepreneurial debt contracts are in foreign currency, and

(2) both entrepreneurial debt and household deposits are in foreign currency. The variations move

the exposure to currency risk to entrepreneurs and households, respectively. The figure shows that

leverage is more affected by the foreign rate shock in (1), when entrepreneurial debt is denominated

in foreign currency, but deposits are not. This effect is a sign of ’currency mismatch’ of the en-

trepreneur, i.e. due to the use of different currencies, there is a discrepancy between changes in the

value of the liabilities (debt) and in the value of the produced output. The currency risk is borne by

the entrepreneur. With a decline in the foreign borrowing rate, the leverage ratio of entrepreneurs

increases because their net worth, which depends mainly on domestic prices, does not increase as

much. In case (2) where household deposits are also in foreign currency, the households are also

exposed to currency risk. However, this means that their purchasing power and hence the net worth

of the entrepreneur depend on the foreign borrowing conditions. As a result, the currency mismatch

of the entrepreneurs is reduced. It should be noted, however, that the choice of currency in the

financial contract has no effect on the emission path induced by the carbon tax. This is because the

effect on leverage takes the same direction for both clean and dirty energy producers, offering no

relative advantage.

4.2 Policy design in the open economy with frictions

In the previous sections, the carbon tax revenue is recycled directly to households as lump sum

transfers. Our simulations of the response of an open economy with financial frictions indicate that

introducing a carbon tax increases the cost of energy, lowers the return on capital, and makes the

economy internationally less competitive. Frictions makes this problem worse by preventing a fast,

cheap scale-up of clean capital. In this section we will discuss alternative policy designs that can

address this issue. We first explore an alternative method for recycling the tax revenue, i.e. a subsidy

to clean energy, then we discuss how foreign aid is best suited to promote the low-carbon transition.

4.2.1 Clean energy subsidy

Figure 7 illustrates the impact of a carbon tax on the key economic variables when the tax revenue is

either recycled to households or utilized as a subsidy for clean energy. The simulations indicate that

for the same tax level, recycling the tax revenue as a subsidy to clean energy leads to emissions falling

faster (and remaining lower) (Figure 7G) while most of the negative impacts of carbon taxation can

be avoided, including the increase in inflation (Figure 7I) and the drop in consumption (Figure 7L)

and output (Figure 7J). It appears that a targeted technology subsidy can improve welfare without

Chapter 2 46

  











  











  













  







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

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

(

real

)



  

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  

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

wtLt

Figure 7. The model response to the introduction of a carbon tax when the tax revenue is recycled to households or as a

subsidy to clean energy. Response values are reported as percentage of steady state values, except inflation that is reported

in percentage points.

Chapter 2 47

undoing the emission reductions. The combined tax and subsidy addresses distortions in the economy,

i.e. features where our model departs from the standard idealized assumptions of welfare economics,

that a tax alone cannot address. Before providing an analysis of the impact of the specific model

features, we discuss the result of the policy response simulations.

The reason for the difference in the response between the lump-sum transfer and the subsidy

policy is the price of energy: by subsidizing clean energy, the price of energy increases only slightly

upon the introduction of a carbon tax, and the price goes back to steady state level relatively fast. On

the contrary, if tax revenues are returned to the household, the price of energy remains high above

steady state levels.

The lower cost of energy also implies that the return on capital remains high and hence, the

rate on debt stays competitive in international markets. For this reason, a carbon tax combined with

a targeted subsidy does not lead to a reduction in foreign debt as much as if the tax was used for

household transfers (Figure 7M).

Figure 7 also highlights the role of financial market frictions under the two policy schemes

(the shaded areas indicate the difference between the economy with and without frictions). The

difference between the fossil fuel consumption in the economy with and without frictions is larger

under the subsidy scheme (Figure 7G). This is a consequence of the stronger steering effect of the

subsidy policy. The clean energy capital undergoes a larger adjustment in a short period of time and

therefore the leverage ratio during the transition is higher. Due to the constraints imposed by the

leverage ratio on borrowing possibilities, the effectiveness of the carbon tax combined with a clean

energy subsidy scheme is more sensitive to financial frictions than the benchmark case where the tax

revenue is recycled to households.

While the subsidy scheme appears as the most effective policy independent of the level of frictions,

the simulations indicate that policy makers considering the introduction of a subsidy scheme ought

to recognize the impact on financial market frictions on the policy response.

Lump-sum transfers of the tax revenue to households is a non-distortive policy, while the subsidy

policy is not. Hence, in a standard model the lump-sum transfer is expected to be the policy with

the lowest welfare cost, but our model simulations indicates otherwise. This result originates from a

combination of model assumptions that are different from standard neo-classical climate-economy

models without market distortions. To investigate the importance of the different assumptions we

remove model features one by one, and estimate the emission reductions and welfare costs in terms

of consumption equivalents under the two policy schemes.

Model variation M0 corresponds to the benchmark model as presented in Section 2 and calibrated

according to Section 3.1. We have identified in total five distinct features of the benchmark model

that effects the ranking of the policy instruments in terms of welfare. Each model variation removes

one feature.

In M1, there are no financial market frictions: the default cost

is set to 0. In M2, we remove the

price rigidity in the retail sector by setting the price adjustment cost parameter ψto 0. In addition,

to eliminate the profits from the final goods sector from the household budget, we introduce near-

perfect competition by increasing the substitution elasticity

θR

to a large number (10000). In M3,

there is no foreign debt, i.e. B

is 0 for all periods t. In M4, transfers from entrepreneurs are excluded

from the household budget constraint.

In M5, fossil fuel is no longer a tradable good, but instead it

is an endowed resource that every period enters into the budget constraint of the household.

The

Compared to the benchmark model, where households consume a share of the entrepreneurial wealth each period,

excluding the transfers imply that the equity positions of the entrepreneurs only affects the household income indirectly

through the labor demand from the firms and return on deposits. To maintain market balance, the entrepreneurial transfers

instead become a part of the final good market clearing constraint.

The resource can either be used for production of energy or be wasted. That is, unlike in the benchmark model fossil

fuel cannot be exchanged with other tradable goods and used for consumption and investment. While the fixed resource

endowment is not the most realistic way to model fossil fuel production, this alternative is the simplest way to remove the

Chapter 2 48

endowment is equal to the steady state fossil fuel usage in the benchmark model. The fixed resource

assumption has implications for the modeling of the climate policy: since it will always be optimal

to use the entire resource endowment, a carbon tax cannot reduce the consumption of fossil fuel.

Hence, to reduce the fossil fuel consumption the carbon tax is combined with a reduction in the

endowment, representing an emission cap. In the case where tax revenue is recycled directly to

households, the tax level makes no difference as the tax will be offset by the fossil fuel price. However,

the tax level is important in case the tax revenue is recycled as a subsidy, because its size determines

the level of subsidies.

Finally, we also provide estimates for the welfare implications when all the features are removed

at the same time. M6aincludes all the corrections as in M1 to M4 in combination, and M6balso

includes M5 on top of M1 to M4.

Table 3 provides an overview of the model variations. Figure 8 summarizes the differences in the

economic impact of the policy in place – represented in the figure in terms of the impact on emission

reductions (Figure 8A), discounted GDP change (Figure 8B) and the welfare effect in consumption

equivalents (Figure 8C). The consumption equivalents measure the policy schemes’ implications for

household welfare in units of 2019-consumption. A detailed derivation can be found in Appendix 1.

While recycling tax revenues as lump-sum transfers to households has a relatively large negative

impact on GDP in the benchmark model (1.62 percent), the subsidy policy has only little effect

on the output (0.18 percent). The consumption equivalents tell a similar story: Household welfare

reductions are equivalent to 1.07 percent of 2019-consumption in the benchmark model with

household transfers, while only 0.32 percent when the carbon tax is combined with a subsidy

scheme despite the significantly higher emission reductions. However, in model versions where

financial frictions are excluded (M1), the impact on household welfare can be much lower. This is a

consequence of the short term increase in consumption combined with a large drop in supplied labor.

The comparison between the model economies with and without frictions indicates that models

without financial frictions greatly underestimate the welfare effects of carbon taxes.

Figure 8 shows that the ranking of the two policy schemes in terms of welfare impact remains

robust to removal of financial frictions (M1) and price rigidity in the retail sector (M2). The openness

alone also cannot explain the difference in welfare outcomes between the two policies (M3). At

the same time, the estimate reveals that household welfare is affected by the climate policies mainly

through transfers from the entrepreneurial sectors. While removing entrepreneurial transfers from

the household budget contraint (M4) reduces welfare impacts, it does not change the ranking of the

policies. More details on the impact of transfers on the household budget constraint can be found in

Appendix 2.

The assumption that fossil fuel is a tradable good also appears important for the welfare implication

of climate policies: if instead fossil fuel is a fixed resource endowment awarded to households every

period, the costs of climate policy becomes high (M5). Under the endowment assumption, the fossil

fuel resource is lost if unused, whereas under the tradable goods assumption, any saved fossil fuels

can be exchanged with other tradable goods. Despite the importance of the endowment assumption

for welfare costs, it does not change the ranking of the two investigated policy schemes - the subsidy

policy remains the one with the lowest welfare costs. However, when all the variations from the

benchmark model are combined, the ranking changes (M6a and M6b). This result implies that it is

the totality of the modeling choices including the combination of various market frictions that leads

to lower welfare cost of subsidy scheme compared to the lump-sum tax transfer.

The benefit of green subsidies implied by our model simulations aligns with the findings of

Grüning (2022), who argue that in a small open economy GDP is almost unaffected when carbon

tax revenues are distributed to the green sector. Likewise, Diluiso et al. (2020), who study the role

on capital taxes in a closed economy with financial friction, find that tax on fossil fuel debt combined

tradable goods assumption, and hence, it offers the most straight forward comparison to the benchmark model.

Chapter 2 49

   

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

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   





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

  

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

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   







Figure 8. Comparison of the model response to the introduction of a carbon tax under different tax revenue recycling

schemes and variations of the modeling assumptions. Panel A and B provides the ’average annual’ which is the yearly

average until the end of 2030. GDP change in panel B is discounted before the average was calculated. The figure highlights

the within-model ranking of policy schemes but cannot be used for ranking policies between model variations. This is

because the model variations have different steady states, and their responses are therefore not directly comparable.

with a subsidy on clean energy debt significantly reduces inflationary pressure and output losses.

However, Diluiso et al. (2020) point out that this policy scheme leads to a greater risk of financial

instability due to a stronger devaluation of fossil fuel assets on the banks’ balance sheets. In contrast,

by focusing on the role of default risks of the entrepreneurs, we do not observe any reason for the

clean energy output subsidies to challenge macro-stability: Although the net worth of dirty energy

producers surely decreases faster under the subsidy scheme, dirty energy firms simultaneously reduce

their debt. In sum, their leverage is reduced, falling faster and making them less likely to default in

the subsidy scenario.

4.2.2 Foreign aid

The effects of foreign aid worth 3.3 billion USD introduced as the same time as the carbon policy,

would hardly be visible in the response functions in Figure 7, and are therefore not plotted. The

limited impact can be attributed to the relatively modest scale of aid in relation to the overall size

of the economy. However, the simulation results indicate that aid introduced simultaneously with

a carbon tax and given directly to households may offset some of the short-term negative impacts

on consumption caused by the carbon tax, however, in the long run, this effect will be outweighed

by the decline in output. Aid given directly to household mainly creates inflation and lowers the

incentive for domestic savings and production. As a result, it has only little effect on the fossil fuel

consumption and the scale up of clean energy capital.

If instead the aid and tax revenues are used as a clean energy subsidy, the response of the model

economy is very different. In this case, the aid increases the level of investments in clean energy,

causing a stronger decline in the use of fossil fuel, which in combination leads to a lower price of

energy. This boosts production and investments.

Our results indicate that aid may help alleviate negative effects on consumption caused by taxes

but if not targeted directly towards clean investment, it creates additional inflationary pressure on

the economy without any direct impact on emissions. Targeted industry policies can help keep the

Chapter 2 50

Table 3. Model variations are made to the benchmark model, which is described in Section 2 and calibrated according to

Section 3.1. Variation 4 implies that the transfers to an from the entrepreneurial sector is separated from the households’

budget constraint. Hence, the households cannot derive utility from consumption of entrepreneurial net worth. In variation

5 fossil fuel is no longer a tradable good, but instead a resources endowed to households in each period. In this case, the

emission target is reach by limiting the endowment each period.

Variation M1 M2 M3 M4 M5 M6a M6b

1 No financial frictions (µ= 0) X X X

No menu costs, perfect competition in the

retail sector

X X X

3 No foreign debt (BF

t= 0) X X X

No entrepreneurial transfers (T

) to house-

holds

X X X

5 Fossil fuel as an endowment X X

cost of energy low by alleviating adverse effects on exchange rates and inflation.

Figure 9 summarizes the economic impact of foreign aid under the two tax revenue policies, and

with and without financial frictions. Panel A shows the yearly average emission reductions until

2030. Since using tax revenues as a clean energy subsidy is a more effective strategy than lump-sum

transfers to households, the emission reductions are significantly higher. This result holds regardless

of the presence of financial frictions and foreign aid. Figure 9 also shows that that foreign aid may

not have a large impact on the emission reductions, especially not when used as direct household

transfers, but if used differently, it may have strong implication for the welfare costs of transition.

According to the model simulations, if the foreign aid is used as a subsidy for clean energy, it can

remove approximately two thirds of the consumption equivalent impact of the climate policy (from

-0.32 to -0.12 percent).

  





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  



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    





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









Figure 9. Comparison of the model response to the introduction of a carbon tax under different tax revenue recycling

schemes, presence of financial frictions and availability of foreign aid. Panel A shows the annual average emission reductions

until 2030 in MtCO2. Panel B shows the discounted average annual impact on GDP until 2030 in percent of 2019-level. Panel

C shows the estimated consumption equivalents in percent of 2019-level of consumption.

5. Conclusion

Constrained availability of financial resources decelerates the green transition and increases its cost.

Financial markets ability to foster sufficient clean energy investments is in particular causing concern

to developing economies, where the clean energy financing gap is large and financial resources

are scarce. In this paper, we investigate the role of financial market failures in the green transition

and their implications for climate policy in an open economy. To this end, we introduce financial

Chapter 2 51

frictions in a dynamic, stochastic model of a small open economy calibrated to Brazil. Through

simulations of the economic response to policies designed to mitigate climate change, we explore the

role of frictions and financial openness for the effectiveness and efficiency of the interventions.

The analyses presented in this paper highlights that frictions interact with the financial openness

of the economy. Both frictions and openness have implications for the economic costs of carbon

policies. In our benchmark model, the carbon tax leads to higher cost of fossil fuel usage, which

drives up the energy prices. Energy is an input to the tradable and non-tradable goods producing

sectors, and the higher cost of usage lowers the return on capital. In an open economy, the lower

return on capital reduces the competitiveness of the economy on international capital markets, which

in return reduces the inflow of foreign funds, driving prices even further up. Frictions slow down

the investment in clean capital and increase the cost of the clean energy substitute for dirty energy.

In this way, replacing fossil fuels with clean energy becomes difficult.

Mitigating the damages caused by climate change through a reduction of fossil fuel consumption

will undoubtedly have positive welfare effects in the long run, however, we find that introducing

a carbon tax has strong short-term negative effects on the economy and household welfare under

the presence of financial frictions. With the lack of a low-cost green substitute, the only way to

scale down fossil fuel usage is through scaling down economic activity. We find that a carbon tax is

an effective policy instruments for reducing emissions, however, it causes cost-push inflation and a

reduction in inflow of foreign funds, which implies a large welfare cost.

Using carbon tax revenues to lower the costs of clean energy can help alleviate some of the

negative effects caused by the carbon tax. Clean energy subsidies increase the net worth of clean

energy companies and allow for a faster scale-up of clean energy capital, keeping the price of energy

low and the inflow of foreign funds high. If combined with foreign aid, our model simulations

indicate that all short term negative impacts of introducing climate policy can be removed.

The low-carbon transition requires significant new investments in clean energy infrastructure,

especially in developing countries. However, financial frictions may restrict the flow of funds toward

clean energy investments. When the borrowing conditions of clean energy investors depend on

their net worth, the economic environment matters for the cost of the transition. Financial openness

is a requirement for attracting foreign funds, but it also puts the economy at the mercy of foreign

investors. Interventions aiming to address the issue of climate change need to be carefully designed

so that they attract, rather than appall, investors.

Competing interests

The authors declare none.

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Appendix 1. Consumption equivalents

Consumption equivalents capture the welfare implications for households of a policy intervention

pcompared to the alternative, no policy np. Consumption equivalents measure how much of

consumption in the no policy scenario the households would have to give up in order to obtain the

same change in discounted utility as the change implied by the policy.

The total expected utility is given by the discounted sum of each period’s utility:

E[Ut]=E"∞

t=0

βtu(Ct,Lt)#(67)

with u(Ct,Lt) = log(Ct) + log(1 – Lt)

Then define the

as the consumption equivalent of pas a fraction of consumption of np such

that policy pand np gives the same expected discounted utility:

EhUp

ti=EhUnp

t(ε)i=EhXβtu(Cnp

t(1 + ε),Lnp

t)i(68)

is greater than 0, the policy results in greater welfare than the no policy case, and if it takes

a negative value the policy implies a welfare loss compared to the no policy case. Inserting the

expression for the period utility and rearranging Eq. (68) gives:

EhUp

ti=log(1 + ε)

1 – β+EhUnp

ti(69)

and hence, the consumption equivalents takes the following form:

ε=e(E[Up

t]–E[Unp

t])(1–β)– 1 (70)

Appendix 2. Details on the household budget under the transition

In this section we describe in detail what happens to the household budget constraint under the

introduction of the two climate policies scheme. In the first (benchmark) policy, a carbon tax is

combined with a lump-sum transfer of tax revenues to the households. In the second, the tax revenue

is recycled as a subsidy to clean energy.

Figure 10 shows the evolution of the budget constraint in the two cases. With the benchmark

policy, the labor income declines sharply. At the same time the transfers from the entrepreneurial

sectors drop. The transfers from entrepreneurial sectors decline because the carbon tax slowly

diminishes the net worth of the sectors. In addition, with increasing inflation, the profits from

the retail sector drops. The drop in income is partly compensated by the large tax transfer, but

the transfer is not large enough to cover all income losses. As a result, the household much reduce

consumption to keep a balanced budget.

In case the carbon tax revenue is used to subsidies clean energy investments, there is hardly any

effect on the household budget. Because the cost of energy remains low, the marginal productivity

of labor and capital remains at steady state levels. This means there is no decline in labor income,

neither in the net worth of the entrepreneurial sector.

Chapter 2 55



















































wtLt







+ 1

RtDt



Figure 10. The budget constraint of the households under policy intervention. The figure show income (left panels) and

expenditures (right panels) for the two policies.

Appendix 3. Calibration with GTAP data

This appendix described the methods and equations used for calibrating parameters through the

GTAP data.

Appendix 3.1 Final goods aggregation

Aggregators have the following production function

t=At ϕ

εW

WYT

εW–1

εW+(1 – ϕW)1

εWYN

εW–1

εW!εW

εW–1

The parameter that governs the substitution elasticity will be extracted from the literature. To get

the share parameter ϕWsolve

minpT

tYT

t+pN

tYN

s.t.

t≤At ϕ

εW

WYT

εW–1

εW+(1 – ϕW)1

εWYN

εW–1

εW!εW

εW–1

L=pT

tYT

t+pN

tYN

t+λ

YW

t–At ϕ

εW

WYT

εW–1

εW+(1 – ϕW)1

εWYN

εW–1

εW!εW

εW–1 



Chapter 2 56

The first order condition with respect to YT

tis

t=λ

At ϕ

εW

WYT

εW–1

εW+(1 – ϕW)1

εWYN

εW–1

εW!εW

εW–1 –1

εW

WYT

εW–1

εW–1



t=λ

A

εW–1

εW

tYW

YW

tεW–1

εW

WYT

εW–1

εW–1



t=λAεW–1

tϕWYW

t1

εW

and

t=λAεW–1

t(1 – ϕW)YW

t1

εW

=(1 – ϕW)

ϕW

t1

εW

By an appropriate choice of units for final, tradable and non-tradable goods, prices can be set equal

to one, i.e. pN

t=pT

t=pt= 1 and the equation becomes

1 = (1 – ϕW)

ϕW

t1

εW

ϕWYN

t=YT

t–ϕWYT

and

ϕW=YT

t+YT

(71)

1 – ϕW=YN

t+YT

(72)

We also need to calibrate productivity A.

A=YW

εW

WYT

εW–1

εW+(1 – ϕW)1

εWYN

εW–1

εW!εW

εW–1

According to Euler’s theorem with perfect competition and prices equal to one (assumption from

above still holds) we have

t+YN

t=Yt

Chapter 2 57

such that

A=YT

t+YN

YT

t+YT

t1

εWYT

εW–1

εW+YN

t+YT

t1

εWYN

εW–1

εW!εW

εW–1

A=YT

t+YN

(YN

t+YT

t)1

εW!εW

εW–1

A= 1 (73)

Appendix 3.1.1 Data Table

We can now calculate

ϕW

(Eq.

(71)

and

(72)

) and A(Eq.

(73)

) through Y

and Y

. With our

assumptions on prices we can use GTAP in the following way

Table 4

Variable Data Calibration

Tradable goods d

tYT

t(by setting pT

t= 1)

Non-tradable goods d

tYN

t(by setting pN

t= 1)

Tradable and non-tradable goods are both calculated as the sum of the GTAP variables ’interme-

diates, firms’ purchases at agents’ prices’ and ’intermediates, firms’ imports at agents’ prices’.

Appendix 3.2 Tradable and non-tradable goods entrepreneurs

For this calibration we extract the firms from the entrepreneurs to ease calculations and make the

rental rate of capital explicit. Firms’ production functions are

t=¯

Aj

ϕjKj

αjLj

1–αjεj–1

εj+1 – ϕjEj

εj–1

εj



εj

εj–1

were j

∈{T,N}

indicatessectoraffiliationbut willbeomittedforthe remaindertoincreasereadability.

All equations equally apply for both sectors.

Appendix 3.2.1 Capital-labor composite

First, we extract the capital-labor composite and calibrate αthen move to the CES and calibrate ϕ.

We define

Zt=Kα

tL1–α

Chapter 2 58

With perfect competition, profit maximization implies

wt=pZ

δZt

δLt=pZ

t(1 – α)Zt

→1 – α=wtLt

tZt

rt=pZ

δZt

δKt=pZ

tαZt

→α=rtKt

tZt

Combining first order conditions with Euler’s Equality

tZt=pZ

δZt

δKtKt+pZ

δZt

δLtLt

tZt=rtKt+wtLt

such that

α=rtKt

rtKt+wtLt(74)

1 – α=wtLt

rtKt+wtLt(75)

We get r

from GTAP (remuneration of endowments are included in input-output tables)

and calculate factor shares. See data table below 5.

Appendix 3.2.2 Upper layer

We now move to the upper layer of the CES and calibrate ϕ.

t=¯

Aj ϕjZj

εj–1

εj+1 – ϕjEj

εj–1

εj!εj

εj–1

Cost minimization yields

minpZ

tZj

t+pEtEj

s.t.

t≤¯

Aj ϕjZj

εj–1

εj+1 – ϕjEj

εj–1

εj!εj

εj–1

L=pZ

tZj

t+pEtEj

t+λj

t



Yj

t–¯

Aj ϕjZj

εj–1

εj+1 – ϕjEj

εj–1

εj!εj

εj–1 





Chapter 2 59

The first order conditions with respect to Zj

tand Ej

tare:

t=λj

t



¯

Aj ϕjZj

εj–1

εj+1 – ϕjEj

εj–1

εj!εj

εj–1 –1

ϕjZj

εj–1

εj–1





t=λj

t



¯

Aj ϕjZj

εj–1

εj+1 – ϕjEj

εj–1

εj!εj

εj–1 –1 1 – ϕjEj

εj–1

εj–1





Dividing first order conditions yield

=ϕj

1 – ϕj Ej

t!1

εj

By setting prices equal to one, pEt = 1 (above assumption holds), the equation becomes

t=ϕj

1 – ϕj Ej

t!1

εj

t1 – ϕjZj

εj=ϕjEj

t1

εj

tZj

εj=ϕjEj

t1

εj+ϕjpZ

tZj

εj

ϕj=pZ

tZj

εj

Ej

t1

εj+pZ

tZj

εj

(76)

We get estimates for E

from GTAP and, through GTAP, Eq. (78) and Eq. (79), calculate Z

and p

(see table below).

We also need to calibrate productivity ¯

Aj.

Aj=Yj

ϕjZj

εj–1

εj+1 – ϕjEj

εj–1

εj!εj

εj–1

According to Euler’s theorem with perfect competition and p

= 1 (assumption from above still

holds) we have

tZj

t+Ej

t=Yj

Chapter 2 60

such that

Aj=pZ

tZj

t+Ej





pZ

tZj

εj

Ej

t1

εj+pZ

tZj

εj

Zj

εj–1

εj+

Ej

t1

εj

Ej

t1

εj+pZ

tZj

εj

Ej

εj–1

εj



εj

εj–1

Aj=pZ

tZj

t+Ej



pZ

tZj

t+Ej

Ej

t1

εj+pZ

tZj

εj



εj

εj–1

Aj=



Ej

t1

εj+pZ

tZj

εjεj

tZj

t+Ej







εj–1

(77)

Appendix 3.2.3 Data Table

By an appropriate choice of units for labor and energy, wages w

and prices p

can be set equal to

one. The rental price of capital

= 0.08. Here, we assume a value that is ultimately identical to the

endogenously generated model variable R.

Table 5

GTAP variable Data Calibration

Labor d

wtLtLt(by setting wt= 1)

Capital d

rtKtrtKt⇒Kt=

rtKt

Energy pE

tEtEt(by setting pEt = 1)

Labor andcapital arereportedin GTAPasvariables’endowments, firms’ purchasesatagents’ prices’

(we consider the tradable and non-tradable goods sectors). For energy, the corresponding GTAP

variable is the sum of ’intermediates, firms’ purchases at agents’ prices’ and ’intermediates, firms’ im-

ports at agents’ prices’ (we consider the energy sector).

For YT

tand YN

trefer to the first data table. The capital-labor nest

Zt=Kα

tL1–α

Zt= d

rtKt

rt!αd

wtLt1–α(78)

and prices from the Euler condition

t=d

rtKt+d

wtLt

Zt(79)

Chapter 2 61

Chapter 3

There’s no bad weather, only bad

prices: Market-based wind power

investments under financial frictions

Submitted for publication in Energy Economics. July 18, 2023

There’s no bad weather, only bad prices: Market-based

wind power investments under financial frictions

Emilie Rosenlund Soysala,b

aPotsdam Institute for Climate Impact Research, P.O. Box 60 12 03, 14412

Potsdam, Germany

bTechnische Universitaet Berlin, Straße des 17. Juni 135, 10623 Berlin, Germany

Abstract

While technological advancements have reduced the cost of renewable energy,

the viability of subsidy-free investments depends on market conditions and

revenue streams. This paper explores the crucial connection between market

exposure, carbon pricing policies, and the financing costs of renewable en-

ergy projects. From the impact of return distributions on the cost of capital

it examines the market conditions necessary for financing market-based re-

newable energy projects. The findings highlight that increasing wind power

capacity not only lowers the return on investment but also increases financ-

ing costs by limiting the feasible level of debt in the financing mix. Higher

carbon prices can improve return distributions and lower financing costs,

but its effectiveness diminishes at high levels of installed wind capacity. To

estimate the cost of capital of wind power in West-Denmark, this study em-

ploys simulated return distributions based on historical power market data.

A novel probabilistic forecasting method using the Adaptive Network-based

Fuzzy Inference System is proposed. The costly state verification framework

is used to determine the optimal debt contracts, considering default risks and

their associated costs. The results emphasise the importance of recognizing

the endogenous changes in financing costs for accurate assessments of the

green transition’s cost and the design of effective incentivizing policies for

renewable energy investments.

Keywords: Cost of capital, Default risk, Carbon pricing, Forecasting,

Machine learning

Preprint submitted to Energy Economics July 18, 2023

Chapter 3 63

1. Introduction

Technological development has greatly lowered the cost of renewable en-

ergy, suggesting that the end of subsidised generation is right around the

corner. From this point on, countries may rely on carbon prices for driving

the green transition in the electricity sector. However, despite the declining

capital expenditure, high cost of capital would lead to no significant deploy-

ment of renewable electricity capacity even if moderate carbon taxes are in

place (Hirth and Steckel, 2016). Therefore, understanding the relationship

between market exposure, carbon pricing policies and the financing costs of

renewable energy projects becomes crucial. By studying the effect of return

distributions on the cost of capital, this paper examines the market con-

ditions necessary for financing market-based renewable energy projects and

finds that increased wind power capacity increases the cost of capital.

Rising interest rates increases the levelised cost of electricity (LCOE) of

variable renewable energy generation and could potentially jeopardise the

green transition (Schmidt et al., 2019). While interest rates affect the cost of

renewable energy (RE), the viability of subsidy-free RE investments depends

not only on the costs but also the revenue stream obtained from the power

markets. RE may be the option with the lowest costs, but if it is not prof-

itable, no investor would undertake the investments (Gillich and Hufendiek,

2022). Profits of capital intensive RE plants are more sensitive to power price

risk compared to traditional generation methods (Tietjen et al., 2016). For

this reason, effective energy policies address risk and return simultaneously

(Polzin et al., 2019) and remuneration schemes that reduce the exposure to

market risks tend to have a decreasing effect on the financing costs (Neuhoff

et al., 2022). Until now, many countries have implemented subsidy schemes

aimed at incentivising renewable energy investments by significantly improv-

ing the risk-return profile of the supported project. The International Energy

Agency lists 70 countries who have or had feed-in-tariffs or feed-in-premiums

as a support mechanism for renewable energy (International Energy Agency,

2022), and clearly, the risk-return-improving support mechanisms have con-

tributed to the low cost of capital observed in the clean energy sector (Roth

et al., 2021; May and Neuhoff, 2021).

Though direct subsidies to renewable energy have been frequently imple-

mented, they have also received vast criticism for lack of cost-efficiency and

distortionary effects on the energy markets (Kalkuhl et al., 2013). Instead,

economic scholars generally favour carbon pricing policies to drive the green

Chapter 3 64

transition (Jenkins, 2014). Such policies puts a price directly on the emission

externality, aiming to align private and social cost of emissions. As the de-

bate on the phase-out of RE subsidies intensifies (Held et al., 2019; Melliger

and Chappin, 2022), it remains an open question to what extent carbon pric-

ing alone can drive the green energy transition. Carbon pricing appears to

be an effective instrument for reducing short term carbon emissions through

shifting the operation of existing installed capacities (Abrell et al., 2022),

however, its ability to foster technological change lack conclusive evidence,

cf. the dispute between Lilliestam et al. (2021) and Van Den Bergh and

Savin (2021).

For carbon pricing to stimulate investment, it needs to be transformed

into profit for the renewable energy producers. It may do so when power

plants are remunerated through market pricing, and the power market price

is set by fossil fuel-based technology. In theory, (pay-as-clear) day-ahead

electricity markets promote efficient use of available resources and incen-

tivise producers to offer power at their short-run marginal costs (Djørup

et al., 2018). For intermittent RE producers, such as wind and solar plants,

marginal costs are close to zero as there are no fuel costs. Therefore, wind

power generation reduces the electricity price (Keles et al., 2013), and the

average price obtained per MWh generated wind energy is lower than the

average market price. This ‘merit order effect’ comes with another caveat:

Increasing shares of renewable energy reduce the number of hours in which

fossil fuel based generation sets the market price, and hence, restricts the

transmission of the carbon price signal to the remuneration of the renewable

power plants.

While existing literature on the topic of optimal investment in RE recog-

nises that carbon pricing alone is unlikely to be sufficient to achieve high

shares of renewable energy sources in the power sector if capital costs are

high (Steckel and Jakob, 2018) or if financial markets are distorted by fric-

tions (Haas and Kempa, 2021), no studies have been devoted to estimating

the effects of market conditions on the cost of capital. This paper addresses

the research gap by using predicted return distributions (i.e. the return

profile) under various market conditions to determine the cost of capital en-

dogenously.

The novel contribution of this paper is to establish a connection between

power market conditions, climate policies and the cost of capital. As the

cost of capital is a crucial component of all energy system models, a better

understanding of it will allow for better forecasts of the cost of the green

Chapter 3 65

transition, estimation of the optimal deployment of renewable energy and

identification of policies appropriate for incentivising target-aligned green in-

vestments. On the contrary, failing to recognise the endogenous changes in

the financing cost could lead to a premature conclusion on the competitive-

ness of renewable technology.

I find that increasing deployment of wind power lowers the return on the

invested wind power capital, and increases the financing cost by reducing the

feasible level of debt in the financing mix. The increased cost of capital leads

to an effective limit of the market based deployment of wind power. While

carbon pricing can improve the return distribution and lower the financing

costs, it only works up to a certain level of wind power deployment after

which increases in the carbon price does not significantly affect the return on

installed wind capacity. At high levels of installed wind power capacity, the

transmission of carbon pricing into the remuneration of wind power plants

becomes so weak, that the carbon price level no longer matters.

The findings emerge from the analysis of simulated return distributions

of wind power plants under different levels of installed wind capacity and

carbon prices. Using historical power market data from West-Denmark, this

paper forecasts the distribution of returns of wind power plants, and subse-

quently uses the return distributions to estimate the cost of capital of wind

power. The approach is data-driven hence the specific results are linked to

the selected region and its historical data, however, the general finding of a

clear link between implemented policy and the cost of capital can readily be

generalised to any system with high levels of renewable energy.

To simulate the return distributions, I develop a new method for prob-

abilistic forecasting of long term electricity prices: I propose a variation of

the Adaptive-Network-based Fuzzy Inference System (ANFIS) (Jang, 1993).

Combining electricity market insights with state-of-the-art machine learning

techniques, the model predicts hourly electricity prices from the gas price,

carbon price and residual load, i.e. the hourly electricity consumption after

subtracting the generated variable renewable energy. The pricing model con-

tains no recursive elements, so despite generating hourly prices, the model

can be used for long term forecasting without the problem of accumulating

errors. The ANFIS model reflects the characteristics of the electricity supply

curve, and hence, accounts for effects that are observable on the hourly time

scale and important for the wind power remuneration, but is still suitable for

long-term predictions.

The return distributions are translated into a cost of capital through the

Chapter 3 66

costly state verification (CSV) framework (Townsend, 1979) applied to bank

lending (Bernanke et al., 1999). The CSV framework introduces a financial

friction by imposing a default cost and provides the micro-foundations for

collateral constraints. In the CSV setup, projects can be financed either

through debt or equity. Debt financing introduces a risk of default, i.e. the

situation where the revenues are insufficient for repaying debt. If the project

defaults, the lender has to face a cost proportional to the remaining value

of the project. This leads the bank to require a premium on debt and set

a limit to leverage. Higher default risk implies a lower leverage ratio and a

higher premium, which in return makes debt repayment more difficult and

increases the default risk. Hence, frictions drive up the financing costs and

lower the value of wind power projects.

The paper is organised as follows: Section 2 presents the modelling frame-

work. Section 3 describes the data used and the model validation. Section

4 shows the results and discusses implications of market pricing for cost of

capital. Section 5 concludes.

2. Modelling framework

The aim of the paper is to identify the transmission channel from market

conditions to the financing costs. The channel works through the market

pricing that results in a return distribution. The risk implied by the return

distribution results in a limit on debt financing and a premium on the bor-

rowing rate. Section 2.1 explains the modelling framework for calculating

the optimal leverage ratio and identifying viable investment projects. The

investment model takes return distributions as the input. These return dis-

tributions are the result of simulations from a electricity price model. Section

2.2 describes the pricing model. Finally, section 2.3 described the simulation

method.

2.1. Investment model

This section presents the investment model that determines whether an

investment is undertaken or not. The fundamental assumption is that a

project developer builds a new (marginal) power plant at time 0, if the value

of the project value Q0exceeds its initial costs C0. The value is determined

by the investor, who uses initial equity E0and bank debt B0to finance the

purchase of the project.

Chapter 3 67

Action of the investor at period t Debit Credit

(1) raises equity Et

(2) takes a loan Bt

(3) buys the project capital Qt−1

(4) obtains operational profits πt

(5) sells remaining capital Qt

(6) repays the loan at the contract rate ZtBt

Table 1: The cash balance the investor

Q0=E0+B0> C0(1)

The present value of the project depends not only on the stream of profits,

but also on the cost of capital for the investor. Debt can be refinanced every

period throughout the lifetime. For this reason, it is helpful to break down

the decision to within each period t. Table 1 provides an overview of period

ttransactions of the investor.

The wind power plant has a lifetime Tduring which it generates an

operational profit πtequal to the revenue less of the operational costs. The

yearly gross return on capital is the operational profits plus the year-end

value of the capital.

t=πt+Qt

Qt−1

(2)

The operational profit is the difference between the obtained revenue

stream and the variable costs. The yearly revenue is the sum of the hourly

revenue stream generated from the hourly output. If the hourly price and

wind power output were independent, the expected revenue could be reduced

to the product of the average yearly price with average yearly generation.

However, as will be discussed below, the price of electricity depends on the

wind power generation, making such simplification faulty.

Since the return on capital is stochastic, it can be defined in terms of its

expectation ˆ

t+1 and a stochastic variable ωt+1 that reflects the normalised

distribution of the return.

t+1 =ωt+1 ˆ

t+1 (3)

Chapter 3 68

The raised capital (debt and equity) is used to buy the project.

Qt−1=Bt+Et(4)

Out of the profits from the project, the investor pays a gross rate Zt

on debt to the lender, e.g. a bank, and the remaining profits accrues the

investor. The sum of the actions is next period’s equity position (in case of

non-default):

Et+1 =Et+Bt−Qt−1+πt+Qt−ZtBt=RE

tEt(5)

while in case of default RE

tis zero and all equity value is lost.

If the return on capital turns out so low that debt cannot be repaid, the

project defaults, i.e. the wind power plant is liquidated. In this case, the

equity holder gets nothing while the lender gets the remaining asset value

less of a default cost proportional to the asset value. This assumption follows

the ’costly state verification’ formulation of Townsend (1979), adapted by

Bernanke et al. (1999) to the optimal financial contract. The formulation

implies that verification of the default state is costly. Because of the default

cost, the lender needs to take the risk of default into account when setting

the contract rate Zt. The return on debt is given by:

tBt=(ZtBtin case of non-default, ωt≥¯ωt

(1 −µ)(ωtˆ

tQt−1) otherwise (6)

where µis the default cost parameter, ¯ωtis the threshold value for the return

on capital that leads to default. Eq. (6) implies the following relation between

the contract rate Zt+1 and the default threshold ¯ωt:

ZtBt= ¯ωtˆrK

tQt−1(7)

The expected return on debt hence depend on the contract rate, the

distribution of return on capital and the default threshold:

Bt+1ERB

t+1= (1 −F(¯ωt+1)) Zt+1Bt+1 +Z¯ωt

(1 −µ)ωt+1 ˆ

t+1qtKt+1dF(ωt+1)

(8)

=ˆ

t+1 (lt+1 + 1) Et+1(Γ(¯ωt+1)−µG(¯ωt+1)) (9)

Chapter 3 69

where F(ωt) is the cumulative distribution function of ωt,lt+1 is the leverage

ratio defined as debt-to-equity Bt+1/Et+1, Γ(¯ωt+1) is the gross share of profits

going to the lender, and µG(¯ωt+1)) is the expected default costs:

Γ(¯ωt+1) = ¯ωt(1 −F(¯ωt+1)) + Z¯ωt+1

ωt+1dF(ωt+1) (10)

G(¯ωt+1) = Zωt+1

ωt+1dF(ωt+1) (11)

The bank only lends if the expected return on the loan is at least its

opportunity costs of funds determined by the risk free rate, i.e. ERB

t+1≥

t+1. In case no combination of leverage ratio lt+1 and contract rate Zt+1

fulfills this requirement, debt financing will not be offered to the project.

The condition for the bank can be expressed by the following inequality:

t+1lt+1 ≥¯ωt+1 ˆ

t+1(lt+1 + 1)(Γ(ˆωt+1)−µG(ˆωt+1)) (12)

If the banking market is fully competitive and banks make no profits, the

expected return on the loan equals the risk free rate. In that case, the

condition above holds with equality and the equation is referred to as ’the

zero profit condition’ of the bank.

The return to the project holder is the part of the operational profits that

remains after repayment of debt in case of non-default and zero in case of

default. The expected return is therefore expressed as:

ERE

t+1Et+1 =Z∞

¯ωt+1 ωt+1 ˆ

t+1Qt−Zt+1Bt+1dF (ωt+1) (13)

ERE

t+1=ˆ

t+1 (lt+1 + 1) (1 −Γ(¯ωt+1)) (14)

The project holder chooses among the feasible debt contracts the one

that maximises expected return on equity. The debt contract can be fully

characterised by the leverage ratio and the default threshold:

max

(lt+1,¯ωt+1)

t+1 (lt+1 + 1) (1 −Γ(¯ωt+1)) (15)

subject to the profit constraint of the bank in Eq. (12). The optimisation

problem leads to the following optimality condition:

t+1

= 1 −µG(¯ωt+1) + (1 −Γ(¯ωt+1))G′(¯ωt+1)

Γ′(¯ωt+1)(16)

Chapter 3 70

From the optimality condition for the financial contract in Eq. (16), the

zero profit constrain of the bank in Eq. (12) and the expected return on

equity in Eq. (14) that is set equal to the required return, it is possible to

determine the project value of the wind power project recursively: Starting

from the last period in the lifetime of the project (period T), the value of

the capital is calculated for T−1, then put into previous period’s return, to

calculate the value of capital at T−2 and so on. This process continues until

a value is obtained for the first period. Returns are assumed log-normal and

for simplicity, to have the same distribution all years throughout the lifetime.

The distribution of ωtis assumed log-normal. To avoid negative values for

ωt(negative values are not allowed for log-normal distributions) the terminal

value QTof the project is set just above the minimum simulated return. If

the initial project value Q0is higher than the investment cost, the investment

is considered feasible.

2.1.1. Frictionless model variation

It is useful to compare the results to the case where there are no frictions

in the financial system. Under the assumption that µequals zero, it is easy to

see from Eq. (16) that the maximisation problem of the equity holder leads to

the equivalence of expected return on capital and the risk free rate. Without

financial frictions, the optimal contract also implies that the expected return

on equity is the risk free rate. However, since the risk free rate is lower than

the required return on equity, there can be no equity in the financing mix,

i.e. entire project is debt financed.

2.2. The market pricing model

This section presents the framework for generating the yearly return dis-

tributions characterised by ωtand the expectation ˆrk

t. A core assumption of

this study is that ’market-based’ wind power remuneration means that wind

power is priced on the day-ahead market.1In the following ’the electricity

1In principle, there are other markets where the plant can participate, for instance the

intraday market. However, the prices on this market is usually centered around the spot-

price. In addition, wind power producers may enter power purchase agreements (PPAs)

with commercial off-takers, who may seek to limit uncertainty about electricity costs. Such

agreements can eliminate the price risk for the wind power plant, however, instead they

introduce counterpart risk, i.e. the risk that the counterpart of the PPA fails to meet its

payment obligations. While PPAs are an increasingly popular way to secure remuneration

for the power producer, their ability to support a large-scale installations is questionable.

Chapter 3 71

price’ refers to the spot price.

The hourly electricity prices and the wind power generation are nega-

tively correlated because of the merit-order effect. The merit-order char-

acterises the hourly supply curve. Hence, the challenge is to make yearly

return forecast while taking into consideration the hourly price and gen-

eration processes. I overcome the challenge by using a power price model

without auto-regressive properties. Instead, the model is designed to reflect

the merit-order effect in the hourly price setting.

The core of the power price model is a variation of the Adaptive-Network-

based Fuzzy Inference System (ANFIS) developed by Jang (1993). As the

name implies ANFIS is a fuzzy rule-based system, implemented with the

methods of an adaptive network. The ANFIS model is a type of regression

model where the output is a non-linear combination of linear regression mod-

els. The weights used to determine the combination depends on the state

of the input variables. I will use the ANFIS framework to model the re-

lationship between the electricity price and a set of explanatory variables,

including the gas prices, the CO2price and the residual load. The ANFIS

model had previously been applied for power system modelling in Dragomir

et al. (2010), who generate balancing forecast, but the ANFIS framework has

not been used for electricity price modelling.

There are many ways to forecast electricity prices. Weron (2014) provides

an overview of the methods and divides existing methods into five broad cat-

egories: multi-agent equilibrium, fundamental, reduced form, statistical, and

computational intelligence models. The two former categories contains mod-

els that consider the physical characteristics of the agents in the power mar-

ket, while the three latter types of models rely on the statistical properties of

observed data without regards to how this data was produced. Following this

classification the ANFIS model with the chosen input variables is a hybrid

model: it is a fundamental model in the sense that it reflects the structure

of the power market, yet it relies on a fuzzy neural network, i.e. a type of

computational intelligence model, and it takes inputs determined through

statistical methods. While time series econometric models usually provide

more accurate short-term forecasts, fundamental models are considered more

suitable for medium- or long-term predictions.

Similar to Kanamura and ¯

Ohashi (2007) the ANFIS model predicts power

prices depending on the level of the demand. Kanamura and ¯

Ohashi (2007)

divides the supply curve into three regions and fit a linear regression to

each region. Likewise, the ANFIS model results in a combination of linear

Chapter 3 72

regression models based on the state of input variables. The benefit of the

ANFIS model is that it provides a continuum of regression models for the

continuous input variables. In additions, it allows for more than one input

variable determining the state of the system.

2.2.1. ANFIS

This section explains how the fuzzy inference system works, how the

adaptive network is used for estimation, and how I modified the standard

model for the specific purpose of forecasting power prices.

A fuzzy inference system maps an input Xto an output Yusing fuzzy

logic. The mapping is conditional on the state of X, i.e. the mapping rule

takes the form: if X is s then Y is fs(X). Unlike in Boolean logic, where

the evaluation of a statement can be either 0 for a false statement or 1 for a

true statement, the fuzzy logic allows any value in the interval [0,1] reflecting

a degree of uncertainty about the truth of the statement.

The states are defined in terms of the labels (or linguistic terms) that

can be attached to the each feature of the input X, e.g. low/medium/high,

hot/cold or fast/slow. For an input Xwith more than one feature, there

is a state for each possible combination of labels, e.g. number of states is

mnif there is nfeatures with mlabels each. Figure 1 show the network

architecture when there are two input features with two labels each.

The final, unconditional output is a weighted sum of the conditional out-

puts. Fuzzy inference comprises several ways of determining the weights and

calculating the final output (Bhattacharyya and Dutta, 2012). This papers

uses Takagi-Sugeno-Kang inference (TSK) due to its simplicity (Takagi and

Sugeno, 1985).

The ANFIS model with TSK inference performs better than a standard

regression model in case the optimal regression parameters depends on the

state of the input. It is easy to recognise the applicability to power prices

that are tied to the merit-order of the power market: When the renewable

energy generation is large enough to clear the market, fossil fuel prices will

not effect the power price, and the level of the fossil fuel prices do not matter.

However, when the renewable energy production is low and the demand is

high, fossil fuel based capacity could be the price setter, and the power price

depends on fossil fuel costs.

Let the input variable X1be the residual load, i.e. the consumption less

of the variable renewable energy generation (VRE) in a given hour. VRE

comprises solar power and onshore and offshore wind power, i.e. the near-

Chapter 3 73

Figure 1: The network architecture of ANFIS, where the input has two features X1and

X2. The features have two labels each, leading to in total four states. Square nodes

contain parameters to be estimated, while circles do not.

zero marginal cost generation technologies that shifts the electricity supply

curve to left. The residual load has three possible labels, l:low,medium and

high. Each label has a corresponding membership function whose output µ

quantifies the degree to which the label fits to the value of the input variable.

In the first layer of the ANFIS model, the membership function outputs are

calculated for each of the input variable and label. The membership functions

for the labels low and high are sigmoid functions:

MFl(X1) = 1

1 + e−al(X1−bl)) (17)

For the label medium the membership function is generalised bell-shaped:

MFl(X1) = 1

1 + X1−cl

al2bl(18)

In the second layer of the model, each state is represented by a weight,

that reflects the importance of the state for the final output. The weight

of the state is calculated as the product of the membership functions for

the labels that are included in the respective state. Since X1only has one

feature, there are three states s, each corresponding to one label. The weight

Chapter 3 74

of the state equals the output of the membership functions:

ws=µl(19)

In the third layer the weights of the three states are normalised, such that

they sum up to one. The output of layer three with respect to sis given by:

¯ws=ws

Pi∈Swi

(20)

With the third layer, the normalised weights of the states are determined.

The next step is to find the output of each state: in the fourth layer the

output of each state is calculated and multiplied by the weight of the state.

Until this point, the ANFIS model applied in this paper follows the layout of

the standard ANFIS model, however, in the fourth layer, the model deviates:

Instead of using the same input variables as in layer one (the residual load)

the model takes a new input variable into layer four. The new input variable,

X2, has two features: the natural gas price and the carbon price. This

variation allows the model to reflect the shape of the power supply curve, i.e.

the residual load determines the state of the supply system, but the carbon

and gas price determines the price level given the state of the system. The

output functions for each state fs(X2) are linear functions of the features of

the input variable. Hence, the output of the fourth layer for state sis:

ps= ¯wsasXgas

2+bsXcarbon

2+cs(21)

Finally, layer five produces the output of the model, which is the sum of all

layer four outputs:

p=X

i∈S

pi(22)

The model has two sets of parameters: membership function parameters

used in Layer 1 (premise parameters) and regression parameters of the out-

put functions used in Layer 4 (consequent parameters). The parameters are

estimated using a hybrid learning scheme (Jang, 1993). The scheme finds

the premise parameters using forward and backward propagation. The con-

sequent parameters, on the other hand, are estimated using ordinary least

square minimization.

Chapter 3 75

2.3. Simulation method

The return distributions of onshore and offshore wind are generated through

Monte Carlo simulations. The simulations use sampled inputs to generate

hourly market price and return forecast, which are aggregated into yearly

averages.

The list below gives the pseudo code for the nsimulations. Let Zbe the

set of simulated input variables that are needed to calculate price and return.

•For k= 1...n

–Generate a random path Zk

tfor t= 0...8760 :

∗Sample solar capacity, consumption growth, gas and carbon

prices from calibrated distributions.

∗Sample hourly consumption and capacity factors of solar and

wind power from existing observations.

–Calculate hourly VRE production as the product of installed ca-

pacity and hourly capacity factors.

–Calculate the residual load.

–Generate random path Yk

tof hourly prices and revenues from the

sample Zk

∗Predict hourly electricity prices with ANFIS model.

∗Calculate hourly wind power revenues given predicted prices

and simulated wind generation.

–Aggregate hourly revenue into yearly forecasts: Yk=PtYk

In order to create a distribution, 3000 simulations were conducted. Each

of the nsimulations represents a potential return obtained during the year

2030, conditional on the input levels of installed wind capacity and carbon

price levels. Based on this return distribution, I calculate the expected re-

turn, default probability, and external finance premium using the costly state

verification framework.

For each simulation a number of input variables is needed: Consump-

tion, VRE production, carbon prices and gas prices. The sampling of input

variables are described in Section 3.2.

Chapter 3 76

3. Data, estimation and cross-validation

3.1. Data for estimation

The ANFIS model needs consumption and VRE generation, gas prices,

and carbon prices for estimation. The residual load is calculated as the

difference between consumption and VRE generation. Consumption, wind

power and solar power are provided by the Danish TSO (Energinet, 2023b).

As a reference for the power price in West-Denmark, I use Nord Pool’s

hourly day-ahead market prices ’Elspot’ in DK1. This price is also provided

by Energinet (2023a).

The carbon price proxy is determined by the Ecarbix index, which is

calculated by the European Energy Exchange AG (EEX). Ecarbix serves

as a spot price index for carbon permits within the EU Emission Trading

Scheme. The index is computed for every business day. During weekends

and holidays, when no prices are available, I utilises the price of the most

recent available day.

The gas price is set to the monthly TTF price index reported by the

International Monetary Fund (2022). The TTF is often used as reference for

the European gas prices. This price is given in USD, but is for the purpose

converted to EUR through the historical exchange rates.

The final data-set consist of data from 2016-2021 in total 52,608 data

points, corresponding to the number hours in the six year period.

3.2. Data for simulation

In addition to the inputs required for estimating the ANFIS model, sim-

ulations require inputs. These inputs encompass VRE production, consump-

tion, carbon prices, and gas prices. Production and consumption are derived

from the targets established by the Danish government for the year 2030.

Prices are provided at the 2021 level.

Weather related VRE generation and consumption follow highly complex

time series structure, with seasonal effects, mean-reversion, and co-variation,

making it difficult to simulate. I adopt here the simplest possible approach,

using data sampled from observations rather than simulated from distribu-

tions: First, observed VRE generation is scaled by the installed capacity and

observed consumption is de-trended. The data is then grouped according to

week of the year. For each yearly simulation, I sample 52 weeks by drawing

one week from each group. Since week 1 may be shorter than 7 days for some

of the years, I draw extra days from week 1 and week 52 until a sample of

Chapter 3 77

365 days (8760 hours) is achieved. By sampling weekly data throughout the

year, hourly, weekly and seasonal effects are captured. Installed capacities

in West-Denmark are estimated from the records of installed capacity per

municipality provided by (Energinet, 2023b). Each municipality is assigned

to either DK1 or DK2, for the purpose of using only capacities in DK1.

In the data, onshore wind power is showing a particularly low average

capacity factor (0.24). According to International Renewable Energy Agency

(2022) the capacity factor for onshore plants installed in Denmark in 2021 is

nearly 0.4. Since the aim of the study is to analyse the profitability of the

marginal investment, setting the capacity factor to the historically observed

would lead to an underestimation of the plant output and hence, profitability.

To correct for the higher capacity factor of modern turbines, the hourly

observed capacity factor is scaled by moving the duration curve upwards.

More details on the scaling of the capacity factor of onshore wind is available

in Appendix A.

As a benchmark for 2030 installed capacities and consumption we use

politically set targets as communicated by the Danish Energy Agency. The

growth rate of consumption is set to reflect the Danish 2030 forecasts. The

Danish Energy Agency published several forecasts, ranging from 50 TWh per

year to 71 TWh per year (Klima-, Energi- og Forsyningsministeriet, 2021). I

assume that the 2030-consumption is normally distributed, and accordingly

set the mean to the average between the two forecasts and the variance

such that the two forecasts marks the 10 percent upper and lower quantiles.

The consumption growth is assumed equivalent in the two Danish regions

and hence, to simulate the consumption for 2030 for DK1 it is sufficient to

multiply the sampled growth rate with the 2021 level.

For solar PV capacity the target is 20 GW in 2030 for all of Denmark

(Klimaaftalen, 2022). As of 2021 there were 1.6 GW installed, of which 1.1

GW was in DK1. This makes approximately 70 percent, and assuming a sim-

ilar distribution between East- and West-Denmark in the future, the targeted

installed capacity is 14.1 GW in DK1. The 14.1 GW target corresponds to

a growth of 11.5 times 2021 level, however, the installed capacity in 2030

is subject to uncertainty. Therefore, I assume the growth of installed solar

capacity is normally distributed with a variance of 2.5, which gives a capacity

growth between 6.6 and 16.40 times 2021-level with 95 percent confidence.

The targets for installed wind power capacity is set exogenously in the

simulations and hence, the identified targets are useful only as a point of

reference for the analysis of the results. The targeted offshore wind capacity

Chapter 3 78

in Denmark in 2030 is 9.0 GW (Klimaaftalen, 2022). In the end of 2021 there

were 2.3 GW installed capacity of which 1.256 GW were in West-Denmark

(DK1). Assuming half of the new capacity is to be installed in DK1, I set

target for DK1 to approx. 6 GW in DK1.

The national 2030-target for onshore wind capacity is 8.2 GW (Klimaaf-

talen, 2022). As of 2021, there were 4.7 GW installed in all of Denmark, of

which 4.0 GW were in DK1, implying that approximately 85 percent of the

total capacity was placed in DK1. If a similar distribution between East- and

West-Denmark holds in the future, approximately 7 GW of the of 8.2 GW

will be placed in DK1. For this reason, 7 GW is the approximate target.

According to a review study by Pahle et al. (2022) five out of six models

predicted a EUA price around 130 to 160 EUR per tCO2in their default

scenarios by 2030. This range is used to set the mean of the assumed normally

distributed of carbon prices to 145 EUR per tCO2. The prices reported are

in 2022 price level, and hence brought 2021-level by dividing by the gross

inflation of 2022. The variance depicted in the reviewed models only includes

differences in applied modelling framework and hence, not policy or market

uncertainty. Such uncertainties may well result in even larger variation, and

to reflect these as well, the variance is set to 21, selected to give a 50 percent

change of the carbon price being within reported range. The selected mean

and variance assumptions give a 95 percent confidence interval of the carbon

price between 92.43 and 174.75 EUR per tCO2in 2021-prices.

Finally, the gas price is assumed to be log-normally distributed. Following

the price forecast for European natural gas published by World Bank Group

(2021), I set the mean to 6.3 USD per MBTu in 2010 prices. The price is

converted into 2021 prices2and then converted to EUR through the 2021

exchange rate. Using the observed variance in the historical prices, I set the

standard variation of the underlying normal distribution to 0.69186, resulting

in a 95 percent confidence interval 1.77 to 26.74 EUR per MBTu.

3.3. Financial data

Table 3 presents the assumptions utilised in the calculation of the opti-

mal financial contract, taking into account both onshore and offshore wind

power projects. The assumptions of capital expenditure (CAPEX) and oper-

ational expenditure (OPEX) are derived from International Renewable En-

2Price index based on yearly inflation given by World Bank Group (2023)

Chapter 3 79

Table 2: Overview of the calibrated distributions of the input variables

Parameter 2030 target Distribution Parameters

Solar power 20 GW Normal 11.5, 2.5

Consumption 50-71 TWh Normal 0.896,0.257

Gas price 5.91 EUR/mBTU Log-normal 1.78, 0.458

Carbon price 130-160 EUR/tCO2Normal 145, 35

Table 3: Financial parameters

Unit Value

CAPEX Onshore million EUR per MW 1.76

CAPEX Offshore million EUR per MW 2.03

OPEX Onshore thousand EUR per MW per year 28

OPEX Onshore thousand EUR per MW per year 34

Risk free rate (Rf−1) percent per year 3.0

Required return on equity percent per year 10.0

Recovery rate (1 −µ) percent 70

Project lifetime (T) years 25

ergy Agency (2022). Additionally, the risk-free rate is set at 3 percent per

year.

The recovery rate, denoting the rate at which capital is recuperated in the

event of default, is equal to 1 −µ. In the baseline estimations, 70 percent of

the project value can be recovered, indicating that 30 percent of the project

value become frictional losses in case of default (µ= 0.3). To examine the

impact of frictions on project valuation, the situation there are no default

costs (µ= 0) will also be explored.

3.4. Tools

The ANFIS model is implemented using an ANFIS package for Python

developed by Lenhard (2022). However, the code underwent a few mod-

ifications: First, to improve the convergence properties, the optimization

algorithm was changed to follow the hybrid approach (Jang, 1993). Second,

to accommodate for the non-standard input structure proposed in this paper,

inputs were split in two such that those entering the Layer 1, X1, are different

from those used for regression in Layer 4, X2. Third, to allow for combina-

tion of different types of membership function I modified the initialisation of

Layer 1.

Chapter 3 80

4000 2000 0 2000 4000 6000

Residual load in MWh

0.0

0.2

0.4

0.6

0.8

1.0

Membership

function

Low

Medium

High

Figure 2: Estimated membership functions

3.5. Cross-validation

The model input variables and hyper parameters were selected through

cross-validation. Appendix B provides an overview of the model choice under

consideration and the cross-validation results.

4. Results

This section presents the findings derived from the model estimation and

return simulations. The first part showcases how the parameter estimates of

the ANFIS pricing model effectively capture the merit-order effect in hourly

electricity price forecasts. The second part offers yearly distributions of av-

erage prices and wind power revenues resulting from the model simulations.

The simulation results indicate that the level of installed wind power ca-

pacity significantly reduces the value of wind power. In the third part, the

price simulations are transformed into return distributions, allowing for the

derivation of optimal leverage and the cost of capital in the presence of fi-

nancial market frictions. It becomes evident that financial market frictions

contribute to increased financing costs and reduced project value. Based

on this observation, the feasibility of wind power deployment is examined,

and the role of carbon price as a guiding policy for transitioning to greener

alternatives is discussed.

4.1. The ANFIS estimates

Figure 2 show the membership functions corresponding to the premise

parameters in Table 4. The membership functions divides the residual load

Chapter 3 81

Table 4: Estimated ANFIS parameters.

Membership function Low Medium High

Premise parameters a -10.264 0.24325 8.953

b 0.01433 1.8455 0.2433

c 0.5777

Consequent parameters Gas price 88.347 44.735 329.364

Carbon price -4.879 15.141 90.627

Constant -1.347 17.791 19.236

into three areas of which each of the membership functions are dominating.

As expected, the estimated consequent parameters (also presented in table

4) reveal that the importance of the gas and the carbon price for the power

price depends on the residual load, i.e. the regression coefficients are high

for membership function corresponding to a high residual loads, and low for

the membership function corresponding to a low residual load.

Figure 3 displays the electricity price predictions as it relates to residual

load for various carbon price levels (left) and gas price levels (right). The

figure demonstrates that elevated carbon and gas prices result in higher elec-

tricity prices. However, the influence of price changes depends on the residual

load: specifically, while prices at low residual load levels are minimally af-

fected by increases in carbon or gas prices, higher residual loads indicate a

substantial increase in electricity prices in response to higher carbon and gas

prices. This observation reflects the merit-order effect.

From the presented model estimates, I find that an increase in the carbon

price from 100 to 200 EUR per tCO2is associated with an increase in the

price of electricity from 52 to 94 EUR per MWh (42 EUR per MWh) when

the residual load is zero, but from 80 to 154 EUR per MWh (74 EUR per

MWh) when the residual load is 2000 MWh.

Even when the residual load levels reach zero or below, the ANFIS model

estimates indicate that carbon and gas prices continue to influence electricity

prices. This observation is likely attributed to the interconnection of the

analysed price zone with other zones. Interconnection means that at times

where all the consumption within the price zone can be covered by VRE

generation, there may still be electricity export, resulting in prices above

zero.

Chapter 3 82

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Figure 3: Price prediction of the ANFIS model as functions of residual load for different

levels of CO2 price and gas price.

4.2. The market value of wind

The estimated ANFIS model is used to generate 3000 simulations of elec-

tricity prices based on sampled input data and different levels of installed

wind power capacities. The simulations reveals that the average price of

wind decreases as the level of wind power capacity increases. At the same

time, the uncertainty about the average price appears to decline.

Both effects are evident in Figure 4, which illustrates the distribution of

prices under various levels of installed wind capacity. Panel (A)-(C) shows

the price under different levels of onshore wind capacity, with the assumption

that there are 4 GW offshore wind power installed. Panel (D)-(F) presents

prices related to various levels of offshore wind capacity, under the assump-

tion that there is 5 GW onshore wind installed. The price of wind power

appears lower compared to consumption prices, reflecting the negative cor-

relation between prices and wind power generation as anticipated by the

merit-order effect. The distributions of obtained revenue per GW installed

capacity (Panel (C) and (F)) is particularly sensitive to the decreasing value

of wind, pointing at a declining marginal revenue.

4.3. The cost of debt

While the previous section presented the pricing implications of the AN-

FIS model estimate and simulations, this section will focus on the implied

Chapter 3 83

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Figure 4: The value of onshore and offshore wind power

Chapter 3 84

financing options of the wind power projects. Specifically, the possible rev-

enue stream to wind power is transformed into return distributions, which

are then modelled according to the costly state verification framework pro-

vided in Section 2.1. The calculations show that the return distributions

have impact on the optimal mix between debt and equity and hence, have

consequences for the cost of capital.

To illustrate the optimal financial contract, Figure 5 shows the return on

debt and the return on equity as a function of leverage level ltand contract

rate Zfor installed wind power capacity of 6 GW onshore and 5 GW offshore.

In the left panel, the dark blue area show the feasible contracts, i.e. the

contracts for which the expected return to the lender is greater or equal to

the risk free rate. The project holder chooses among the feasible contracts,

the one that maximises the return on equity. The return on equity increases

with leverage ratio, but decreases with the contract rate as shown in the left

panel of the figure. The optimal contract is marked on the border of the

feasible contracts area.

As presented in the end of Section 2.1, the project value Q0is determined

recursively over the entire project lifetime at each specific capacity level. Fig-

ure 6, panel (A) and (C), show the estimated project value of onshore and

offshore wind installations for different levels of installed capacities. Invest-

ments in additional capacity is considered feasible as long as the marginal

project value is higher than the CAPEX, and hence, the interception between

the project value lines and the CAPEX line marks the market clearing ca-

pacities. The market clearing caused by declining profitability of wind power

establishes an upper limit to the feasible investment on market conditions.

Onshore wind capacity reduces the value of the marginal offshore project

and likewise, offshore wind capacity reduces the value of onshore wind. Ac-

cording to the model estimates, the maximum feasible level of offshore wind

power capacity is in the range from 3 to 6 GW depending on the level of

onshore wind. For onshore wind, the limit occurs between 4.5 GW and 9

GW, however, for offshore capacities above 7 GW, there is no feasible invest-

ments above the already existing 4 GW. The estimated target of the Danish

government of 6 GW offshore and 7 GW onshore appear outside the feasible

set of investments.

Figure 6, Panel (B) and (D), show the effect of capacity composition on

the WACC. The lower the project value, the higher the WACC. The main

driver of the WACC is the optimal leverage ratio - when operational profits

are low, the investment cannot be sufficiently levered and this increases the

Chapter 3 85

      

























      



























































Figure 5: The figure illustrates the location of the optimal contract for 6 GW onshore and

5 GW offshore installed capacity. The left panel shows the return to the bank as a function

of leverage ratio and contracts rate. The dark blue area contains all feasible contracts,

i.e. contracts for which the expected return to the bank is greater or equal to the risk free

rate. The project holder chooses the contract that maximises return on equity.

Chapter 3 86

       



































       































     













































     

































Figure 6: The figure show the estimated marginal project value of offshore wind energy for

different levels of installed capacities of onshore and offshore wind energy (A). The ’feasible

limit’ indicates the capacities for which the marginal project value equals CAPEX (marked

with a dashed line). Panel (B) show the project WACC for various levels of installed

capacities. The WACC increases with decreasing project value.

cost of capital and decreases the project value. The figure illustrates a central

result of this paper: market conditions drive the cost of capital by altering

the risk-return profile of the installation. Hence, market pricing affects the

profitability of the wind power plants through two channels: the income

stream and the costs of capital.

4.3.1. Financial fictions

The financial frictions results in a premium on debt contracts and lower

leverage, which both contributes to higher cost of capital and lower project

value. For comparison, I estimate the project value in case there are no

default costs. As shown in section 2.1.1, the the return on capital equals the

Chapter 3 87

       





































     







































Figure 7: The effect of financial frictions on the value of the marginal investment project.

The figure compare offshore and onshore project value under frictions to the case where

there were no frictions (the project could be financed at the risk free rate). The figures

indicate that investment with overall lower project value are more effected by the existence

of frictions

risk free rate.

Figure 7 show the difference in estimated project value under the no fric-

tions assumption. The frictions lower the project value with between 6 and

20 percent depending on installed capacities and installation type (onshore

and offshore) and hence, reduces the level of feasible capacity. Addition-

ally, the negative impact of financial frictions on project value is in relative

terms highest when the project value is low. This implies that the frictions

exacerbate the implications of poor risk-return profiles for project feasibility.

In this section has discussed the value of the marginal project under

market-based pricing and shown that estimates for both onshore and offshore

wind indicates that more wind capacity reduces the viability of additional

wind capacity - not only by reducing the power price, but also by increasing

the cost. In the next section, the carbon price is no longer uncertain. By

setting the carbon price to a specific value, it is possible to study both the

role of the carbon price level and the role of carbon price uncertainty on the

cost of capital.

4.4. Carbon price, return on wind and the cost of debt

The price simulations for fixed carbon prices reveals a clear pattern in the

effect of the carbon price on the wind power price: For low levels of installed

Chapter 3 88

wind power capacity, an increase in the carbon price greatly increases the

average price of wind power, but for high levels of installed capacity the

carbon price hardly have any effect on the price of wind. Hence, carbon

price hikes do not lead to any substantial change in the price obtained by

wind power generators. Figure 8 show a selection of the simulation results

to highlight this point.

The price of consumption exhibits a similar pattern: For low levels of

installed wind power capacity, the carbon price increases lead to significantly

higher consumption prices, but the higher the installed capacity, the lower the

impact on average prices. While the effect of installed wind power capacity on

the prices are similar for the wind power price and the consumption price, the

consumption price appears to be more sensitive to the carbon price regardless

of the level of installed wind power capacity. This implies that for high levels

of installed wind power capacity, increasing costs of carbon emissions are

passed on to consumers, while it does not result in increasing profits for

wind power plants.

When wind power plants are compensated at market prices, the targeted

levels of installed onshore and offshore wind capacity (approximately 7 GW

and 6 GW, respectively) fall outside the estimated feasible investment range.

At these capacity levels, carbon prices have a minimal impact on the expected

return on capital. Increasing the carbon price from 100 EUR per tCO2to

200 EUR per tCO2can result in an increase in the average electricity price

for onshore from 30 to 35 EUR per MWh, and for offshore from 29 to 33

EUR per MWh. Consequently, this increase does not significantly enhance

the profitability of wind power. Therefore, the carbon price has limited

effectiveness in incentivizing additional investments.

The implications of carbon pricing on the return distribution are reflected

in the financial contract. Figure 9 and Figure 10 illustrate the values of on-

shore and offshore wind power projects for different wind power capacity

levels, considering varying carbon price levels. A higher carbon price corre-

sponds to a higher expected return for wind power plants. However, while

this effect is prominent for lower installed capacities, it becomes negligible

for higher levels. Accordingly, the impact of a higher carbon price only

brings minor improvements to the financial conditions when there is already

a substantial presence of wind energy. The declining ability to improve prof-

itability of the projects is reflected in the two figures by the convex contour

lines. Besides the marginal project value incl. the feasible limit defined by

the CAPEX line, the figures show WACCs and leverage ratios.

Chapter 3 89

   



































   



































   



































   



































Figure 8: Simulated average wind power and consumption prices as a function of installed

wind capacity and carbon price. For (A) and (B) the installed onshore wind is set to 6

GW. For (C) and (D) the level of offshore wind capacity is fixed to 5 GW). The figure

shows how the carbon price signal diminishes as the level of installed wind power capacity

increases. The carbon price is measured in EUR per tCO2.

Chapter 3 90

The ability to obtain debt financial has crucial implications for the WACC.

If debt cannot be obtained, capital must be financed through equity, which

leads to higher WACC. The leverage ratio, i.e. the ratio between debt and

equity, is therefore a strong indicator for the cost of capital.

4.5. Sources of uncertainty

The price uncertainty combined with uncertainty about the wind power

output leads to large uncertainty in the revenue stream. As an example

of the magnitude of the uncertainty, Figure 11 presents the histogram of

the simulated hourly return to offshore wind power, under the assumption

of 6 GW onshore and 5 GW offshore wind. Panel (A) shows the revenue

distribution under the assumption of market prices. Panel (B), presents

the simulated revenue distribution under the assumption that the offshore

plant receives a fixed feed-in-tariff (FIT) for the generated power, hence, all

uncertainty in the revenue distribution is caused by uncertainty in the plant

output. The level of the FIT is set equal to the average market price of

offshore wind. When comparing the two distributions, it is clear that market

pricing is a the main source of uncertainty - not the variation in output of

the power plant. The FIT effectively reduces the revenue risk.

Can a strong and certain carbon price signal achieve the same outcome?

To answer this question, Figure 11, Panel (C) presents the histogram of a

sub-sample of the simulations, for which the carbon price is in the corridor

between 130 and 140 EUR per tCO2. It is clear, that despite the limited

variation in the carbon price, there is still strong variation in the revenue.

However, it seems that the carbon price corridor reduces the occurrences

of very low revenue streams. Down-side risk is important for the financing

costs. Hence, while certainty about future carbon prices does not have a

significant diminishing effect on overall level of uncertainty, it may contribute

to reducing the cost of financing the wind power investments.

4.6. The limit to market-based wind power

The level of installed wind power has great impact on energy prices, and in

particular the prices obtained by wind power plants if remunerated through

market pricing. More wind power capacity worsens the risk-return profile of

wind, lowers the project value and leads to an economic upper limit to wind

power capacity. The findings leads to two propositions:

First, the level of installed wind power capacity affects the cost of capital.

Under the presence of financial frictions, the lender needs to be compensated

Chapter 3 91

    























    



















    



















    























    



















    



















    



















    



















    

































































































































































Figure 9: Onshore feasibility. Panel (A1) - (A3) show the project value of onshore wind

projects for different levels of installed onshore capacity and carbon price. The CAPEX

line marks the limit to feasible investments. Panel (B1) - (B3) show the estimated cost of

capital. While higher carbon prices decreases the WACC, installed capacity increases it.

Panel (C1) - (C3) show the optimal leverage ratio. The leverage ratio is the main driver

of the WACC.

Chapter 3 92

  























  



















  



















  























  



















  



















  























  



















  

































































































































































Figure 10: Offshore feasibility. Panel (A1) - (A3) show the project value of onshore wind

projects for different levels of installed onshore capacity and carbon price. The CAPEX

line marks the limit to feasible investments. Panel (B1) - (B3) show the estimated cost of

capital. While higher carbon prices decreases the WACC, installed capacity increases it.

Panel (C1) - (C3) show the optimal leverage ratio. The leverage ratio is the main driver

of the WACC.

Chapter 3 93

     













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Figure 11: Distribution on yearly operational revenue for offshore wind under different

pricing assumptions. Installed capacity is 6 GW onshore and 5 GW offshore. Panel (A)

corresponds to full market pricing. Panel (B) show the distribution under the assumption

the wind power plant recieves a feed-in-tariff. In Panel (C) the carbon price is constrained

to a corridor between 130 and 140 EUR per tCO2.

Chapter 3 94

for additional risk even if the lender is risk neutral. Frictions increases the

cost of capital by limiting the leverage ratio and causing a premium on debt.

Hence, the limit to wind power capacity arises not only because of the de-

pressed revenue stream, but also because of the increasing costs of financing

the project. This proposition has implications for any analysis aiming to

identify the economic optimal or feasible level of wind power installation.

It questions the validity of the assumption of fixed and exogenous costs of

capital usually made in energy systems models with investments.

Second, there are limits to the ability of carbon pricing as the guiding

policy instruments to generate new capacity investments in wind power. For

high levels of installed wind capacity, the carbon price has little impact on

the remuneration. The pass-through of the carbon price signal to the value of

wind power becomes weaker with installed wind power capacity, and hence,

increasing the carbon price may result in higher average costs of electricity

for the consumers without generating additional wind installations. If carbon

pricing is to become the main policy tool for promoting the green transition

in the electricity sector, other market developments may be needed to achieve

high levels of installed VRE.3

5. Conclusion

Renewable energy technologies are more capital intensive than traditional

power generation technologies and their profitability is therefore more sensi-

tive to the cost of capital. Understanding the relationship between market

exposure, carbon pricing policies, and the financing costs of renewable en-

ergy projects is important as support schemes are phased out and renewable

energy plants are expected to compete on market conditions. The cost of

capital is a crucial factor in most energy system models and a better under-

standing of it will lead to more accurate estimates of the cost of the transition

and the optimal generation mix. This paper contributes to the discussion on

3One such market development could be the development of electricity-based hydrogen

infrastructure. Advances in hydrogen technology may impact the demand for electricity

and change the the pass-through of carbon prices into the electricity price. Through the

process of electrolysis, electricity can be used to produce hydrogen and the market price of

hydrogen determines the electricity price at which it is feasible to use power for hydrogen

production. Since the price of hydrogen is tied to the costs of using natural gas, it also

depends on the carbon price (Ruhnau, 2022).

Chapter 3 95

the transition to a low carbon power system, by showing that the costs of

capital depends on the electricity market conditions and the policy in place.

By studying the return distributions, I show that under the presence of

financial market frictions modelled a default cost, revenue uncertainty con-

tributes to higher financing costs through a risk premium on debt and lower

leverage ratios. The estimations presented in this paper, indicate that finan-

cial frictions lower the value of wind power projects with 5 to 15 percents.

Profitability depends not only on the revenues but also on the costs, which

increases with the higher costs of capital.

Under a fully market based electricity system, carbon pricing - rather

than subsidy schemes - may be the guiding principle for the green transition.

However, the data indicate that the ability of carbon prices to affect revenue

streams of wind power depend on the level of wind power capacity in the

system. The pass-through rate of carbon prices lowers as the level of wind

power capacity increases. This empirical finding is a reflection of the merit-

order effect and questions the ability of carbon prices to lead to targeted

capacity investments. As the carbon price has only little influence on the

revenue stream for high levels of installed wind capacity, it cannot counteract

the negative effects of financial frictions on the cost of capital, and hence,

the financing costs remain high.

The findings of this paper was derived from simulations from an ANFIS

model fitted to the power market data of West-Denmark. The model predicts

hourly electricity prices based on the variable renewable energy production,

the demand for electricity, and the gas and carbon prices.

The simulations indicate that the 2030-capacity target set by the Danish

government lie outside of the feasible investment space when wind power

plants face market pricing. However, the result is sensitive to the various

modelling choices, in particular the assumptions on the risk free rate and the

required return on equity and the distribution of future gas and carbon prices,

and consumption level. It should be noted, that the aim of the paper is to

establish the link between the market conditions and the cost of capital and

not to determine exactly where the upper limit to market based investment

lies as clearly, market participants would know this better.

Likewise, immediate market intervention may not be necessary, but rather

the findings highlight that awareness about the possible implications of the

increasing risk is important. Lower revenue stream makes investment more

risky and risk drives up the financing costs. Hence, policy makers should be

careful not to conclude the discussion on the phase-out of renewable energy

Chapter 3 96

subsidies too early: it is still unclear to what extend there will be a need

for additional policies addressing the risk and return of new generation. The

analysis presented in this paper show that indeed there is a link between

electricity market conditions and the cost of capital, and continued research

may be needed to more carefully estimate the magnitude of the effects and

to identify viable approaches to translating the endogenous relationship into

large scale energy system models.

Disclosure statement

There are no competing interests to declare.

Funding

The research for this study was funded by the German Federal Ministry

of Education and Research (BMBF), research grant 01LN1703A, which I

gratefully acknowledge.

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Appendix A. Capacity factors

This section provides details on the observed capacity factors and the

simulation of the capacity factor of new onshore wind power plants. First,

Figure A.12 presents the capacity factors of the various technologies, averages

by year (A), by month (B), and by hour of the day (C). The figure reveals

that average capacity factors have remained stable over the entire period

of observation, however, they show a clear seasonal variation. The figure

also show that offshore wind has a significantly higher capacity factor than

onshore wind power. This difference is likely due to offshore wind plants have

newer turbines and the fact that the wind resources are generally better over

sea than over land.

According to International Renewable Energy Agency (2022), new on-

shore wind power plants in Denmark can expect an capacity factor of almost

0.4, which is significantly higher than the observed 0.24. For this reason

historical capacity factors cannot be used for estimating the profitability of

onshore wind. To estimate a capacity factor CPest for new installations, I

modify the observed duration curve. I create a linear combination between

Chapter 3 101

2016 2017 2018 2019 2020 2021

Year

0.0

0.1

0.2

0.3

0.4

0.5

0.6

Capacity factor

(A) Average by year

Onshore

Offshore

Solar

M01 M02 M03 M04 M05 M06 M07 M08 M09 M10 M11 M12

Month

0.0

0.1

0.2

0.3

0.4

0.5

0.6

Capacity factor

(B) Average by month

000102030405060708091011121314151617181920212223

Hour

0.0

0.1

0.2

0.3

0.4

0.5

0.6

Capacity factor

Figure A.12: Average observed capacity factors of VRE

Chapter 3 102

0 2000 4000 6000 8000

Hours

0.0

0.2

0.4

0.6

0.8

1.0

Capacity factor

(A) Onshore - durations curve

Observed

Estimated

0 2000 4000 6000 8000

Hours

0.0

0.2

0.4

0.6

0.8

1.0

Capacity factor

(B) Offshore - durations curve

Observed

Figure A.13: Duration curves for onshore and ofshore wind power.

the observed curve CPobs and a straight line, l, that runs between the two

points (0,1) and (8760,0):

CPest =aCPobs + (1 −a)l(A.1)

The parameter ais set to 0.43 such that the obtained average estimated ca-

pacity factor for new technology equals 0.4. Figure A.13 show the observed

and estimated duration curves. I should be noted, that the estimated du-

ration curve is only used for simulating the output of new onshore capacity,

while the output of all existing onshore capacity is simulated on the basis of

the observed capacity factor.

Appendix B. Cross-validation

In the process of finding the best forecasting model a number of modelling

options are tested. The options include selection of hyper parameters, such

as number of membership functions, but also the two sets of input variables.

The options investigated are presented below:

•Input variables to Layer 1

–Option 1: consumption and VRE generation

–Option 2: residual load, i.e. the difference between consumption

and VRE generation

Chapter 3 103

Table B.5: Model variations tested during cross-validation

Model M1 M2 M3 M4

Consumption, VRE X X

Residual load X X

Membership functions 2 2 3 3

•Number of membership functions

–Option 1: 2 (sigmoid)

–Option 2: 3 (two sigmoid, one generalised bell-shaped)

•Number of epochs

The combination of input variables and number of membership functions

gives in total four model variations. In the case of two membership functions,

these belong to the family of sigmoid functions, representing input values that

are ’low’ and ’high’, respectively. In case of three membership functions,

a generalised bell-shaped function is added to the two sigmoid functions,

representing input values that are ’medium’.

The models are compared using K-fold cross-validation, through which

the data set is divided into years. Four consecutive years are used for training

and then tested on the following year. With six years of data, this gives two

train-test data sets. The four model variations are estimated for each of

the train-test data sets and Figure B.14 provides an overview of the mean

average testing error (test-MAE) for up to 30 epochs.

The figure shows that the four models are not very different in terms of

test error, however, it appears that the models with the residual load as input

parameter to Layer 1 (M2 and M4), performs better than the models where

consumption and VRE generation are considered separately (M1 and M3).

In addition, M4 appear to lead to slightly lower test error compared to M3.

Hence, for this reason, I choose M4.

Figure B.14 also indicates that the model has fairly poor convergence

properties and adding more epochs does not decrease the test error. Based

on the visual inspection of the test error, I set the number of epochs to 5.

Chapter 3 104

Chapter 4

Share Buybacks and Investor Beliefs

about Carbon Risk

Submitted for publication in the Journal of Sustainable Finance and Investment.

June 22, 2023

This is the original manuscript of an article submitted to Taylor & Francis in the Jour-

nal of Sustainable Finance and Investment.

105

Share Buybacks and Investor Beliefs about Carbon Risk

Emilie Rosenlund Soysala,b and Kai Lessmanna,c

aPotsdam Institute for Climate Impact Research, Potsdam, Germany; bTechnische

Universit¨at Berlin, Berlin, Germany; cMercator Research Institute on Global Commons and

Climate Change (MCC), Berlin, Germany

ARTICLE HISTORY

Compiled June 22, 2023

ABSTRACT

With the growing awareness of the economic consequences of climate change and

its mitigation, investors are revaluating their fossil assets due to carbon risk. As

fossil fuel firms experience share price pressure, they also appear to scale up their

share repurchasing activities. This paper investigates the role of buybacks for fossil

fuel firms, when investors update their beliefs about firm value. After establishing an

empirical relationship between awareness about sustainable finance and buybacks in

the fossil fuel sector, we present a portfolio choice model that predicts the observed

relationship. We show that firms can strategically deploy buybacks to maximize

valuations and counteract reductions in market capitalization that would otherwise

result from investor awareness. Our analysis suggests that buybacks can lead to a

persistent share of investors holding false beliefs about the firm value. Buybacks

may contribute to investors’ failure to accurately value potentially stranded assets,

and inflate the carbon bubble.

KEYWORDS

share repurchases; carbon bubble; stranded assets; portfolio optimization; false

expectations

1. Introduction

The announcement of the Paris Agreement on climate change in December 2015 sent

a clear political signal to the world’s financial markets. Not only did its signatories

commit to keeping global warming well below 2°C, the agreement also spelled out

the implications for investors worldwide: financial flows need to become “consistent

with a pathway towards low greenhouse gas emissions and climate-resilient develop-

ment” (UNFCCC 2015, article 2) implying substantial new investment in low-carbon

technology and divestment from the fossil fuel industry (cf. IPCC 2014).

Investors are becoming increasingly aware that limiting global warming requires

policies that discourage the use of fossil fuels, eventually invalidating the traditional

business model of fossil fuel and related industries. Target aligned climate policies

reduce the value of fossil fuel assets, and even when conceding the large uncertainties

regarding when and how such policies will take effect, fossil fuel assets expose their

owners to transition risk, i.e. to a potential devaluation by stringent climate policy.

Consequently, an increasing number of investors are seeking to manage carbon risk

or committing to phase out investment in fossil fuel firms from their portfolios all

CONTACT Emilie Rosenlund Soysal. Email: soysal@pik-potsdam.de

Chapter 4 106

together.1

However, the fossil fuel firms do not remain passive towards the devaluation pres-

sure. A recent study by Choi et al. (2023) finds that increasing price pressure leads

high-emission firms to the downscale operations and create more innovation in green

technology. They also find that high-emission firms tend to increase their payout

through share repurchases. Our paper picks up on the observation that fossil firms

under price pressure tend to buy back shares and investigate their potential moti-

vation. Like Liu and Swanson (2016), we argue that firms buy back shares when

overvalued. We use a simple portfolio choice model to identify the optimal strategy

to respond to changes in investors’ believes about the firm’s future valuation. Engag-

ing in buybacks turns out to maximize shareholder wealth. In addition, we show that

this optimal buyback strategy supports an equilibrium with investors who persistently

overestimate the value of the firm.

This paper contributes to the understanding of firms’ financial behaviour when

investors become aware of sustainability issues and subsequently update valuation of

fossil fuel assets. We show that if investors are risk-averse and have diverging believes

about the future value, firms can deploy an optimal buyback strategy to maximise their

overall valuation and hence counteract a loss in market capitalisation. Our analysis

indicates that in comparison to firms who do not engage in buyback activities, firms

who actively manage their number of shares outstanding can increase the number of

investors who persistently overestimate future share prices. The implication for firms

that hold (potentially stranded) fossil fuel assets is clear: buybacks can lead investors

to maintain a false perception about future value. Hence, repurchase programs may

not only lead to increased share prices but also to an excessive market capitalization

of firms.

The paper is organised as follows: Section 2 summarizes the concepts of stranded

assets and share buybacks, including an overview of the most relevant literature on the

two topics. Also, we use past data to establish a co-integration relationship between the

mean buyback rate in the fossil fuel sector and the pressure for greening the financial

system. Section 3 develops a theoretical model that explains the relation between

share prices and optimal buyback under systematic overestimation of future prices. In

section 4 we discuss the model’s static and dynamic properties. Section 5 concludes.

2. Carbon risk and share buyback

2.1. The carbon bubble

Assets that have “suffered from unanticipated or premature write downs, devaluations

or conversion to liabilities” are commonly defined as stranded assets (Ansar, Caldecott,

and Tibury 2013). Assets of firms whose business model is based on fossil fuel are in

risk of stranding during the transition to a green and sustainable economy. This is

particularly the case for companies holding fossil fuel reserves. McGlade and Ekins

(2015) found that in order to meet the 2 degree target, 80 percent of the coal, half of

the gas and one third of the global oil reserves are to remain unburned.

Lack of accounting for stranding risk in asset valuation implies an over-valuation

of assets which is also known as ’the carbon bubble’. Ritchie and Dowlatabadi (2015)

identify two types of bubbles: the downside bubble, where climate policy reduces de-

1See, for example, the increasing membership in organisations such as the UN-convened Net-Zero Asset Owner

Alliance or the Powering Past Coal Alliance.

Chapter 4 107

mand for fossil fuels, and the upside bubble, where higher cost of fossil fuels will lead

to its replacement by renewable energy.

Whether the risk of stranding is reflected in current market prices remains contro-

versial. On one hand, Silver (2017) claims that mainstream investors resist integrat-

ing the climate risk into investment decisions, and due to simple risk measures such

as volatility and divergence from bench-marking, decision makers become blind to

the risk of stranding. Likewise, Riedl (2022) finds that myopic investment behaviour,

agency costs, and bounded rationality distorts the corporate and financial climate risk

management. Thom¨a and Chenet (2017) argues from a theoretical point view that

mispricing of climate risks can exist due to market failures. On the other hand, Byrd

and Cooperman (2018) finds that news about breakthroughs in the carbon capture

technology are connected with a positive reaction in coal asset prices. The findings

indicate that investors have already incorporated stranding risk into their valuation

of coal assets. In addition, a survey by Krueger, Sautner, and Starks (2020) among

institutional investors indicate that investors are beginning to manage (transitional)

climate risk, and though the surveyed investors do believe that the risk is not priced

correctly for all fossil fuel assets, the perceived overvaluations are small.

The carbon bubble and the risk it imposes on investors is one of the arguments

driving the divestment movement, urging investors to sell off financial assets in fossil

fuel companies. According to the Global Fossil Fuel Divestment Database (2023), 1560

institutional investors with a total value of approx. USD 40 trillion, have pledged to

fully or partly divest from fossil fuel assets (as of April 2023). Fossil fuel divestment

is a type of shareholder activism that aims to target the industry infrastructure and

activists see divestment as part of a bigger strategic plan that ultimately seeks the end

of the fossil fuel industry (Hestres and Hopke 2020). Edmans, Levit, and Schneemeier

(2022) argue that divestment may be a less effective strategy for reducing emissions

compared to shareholder engagement (’tilting’). Likewise, Berk and van Binsbergen

(2021) finds that the impact on cost of capital from socially motivated divestment is

too small to meaningfully affect real investment decisions. Nevertheless, according to

Ayling and Gunningham (2017), the fossil fuel divestment movement has been effective

in causing controversy and directing public attention to the issue of financing fossil fuel.

Hence, while the direct effects on capital markets of the divestment movement itself

is unclear, the divestment movement surely helped increase the focus on sustainable

finance.

Figure 1 shows the number of google searches (as indexes) for various terms related

to stranded assets and sustainable finance in the period 2010-2019. While searches on

’fossil fuel divestment’ peaked around the signing of the Paris Agreement (December

2015), the number of searches for ’sustainable investment’, ’sustainable finance’ and

’ESG investment’ 2continues increasing, indicating a growing interest in this topic.

Even without the ultimate commitment to divest from fossil fuel assets, investors

who recognise the potential risk of stranded assets can contribute to downwards pres-

sure on fossil fuel asset prices through an updated valuation. Choi et al. (2023) find

evidence for a growing tendency that high-emission firms tend to have lower price-to-

book ratios than low-emission firms in the same country. In addition, they find that

under price pressure, polluting firms tend to reduce carbon emission intensities, in-

crease green innovation activities, and downsize their operations. Finally, they show

that price pressure leads to an increase in the payout to shareholders through buy-

ESG is short for for Environmental, Social and Governance, referring to the three main components sustain-

able business practices.

Chapter 4 108

backs. In this paper, we investigate the potential motivation for such relationship and

develop a argument why repurchasing shares may be the optimal response of the firm

when investors updates their beliefs about future asset value.

[Figure 1 about here.]

2.2. Buying back shares

Together with other strategic financial decisions, firms need to define a payout policy

that determines the disbursement of corporate earnings to shareholders. Fundamen-

tally, there exist two ways for a firm to remunerate shareholders: one way is paying

out dividends (either as regular cash dividends or specially designated dividends),

the other is buying back shares (either through open-market repurchases, intra-firm

tender offers, or targeted repurchases) (Barclay and Smith 1988). Regular dividends

and open-market repurchases are by far the most popular means of shareholder re-

muneration (ibid.). While dividends are a direct transfer of cash from the firm to the

shareholders, share repurchases (or buybacks) occur when companies purchase their

own shares and thus reduce the number of shares available on the public markets

(shares outstanding). Generally, buybacks lead to higher share prices: the reduced

number of shares results in greater earnings per share, and for a fixed payout ratio the

payout per share will increase and hence raise the value of each share remaining on

the market. Since the deregulation of the US financial market in 1982, share buybacks

have become an increasingly popular method for remuneration (Smith 2011) and as of

2015 share repurchases comprised approx. 50 percent of the total shareholder payouts

(Tonev and Jose 2015). Deregulation of share buybacks was implemented in Japan and

Germany in 1994 and 1998, respectively (Economist 2014), and today share buybacks

appear in almost all major markets (ECB 2007). Figure 2 (A) illustrates the shift of

dividends to buybacks as preferred payout method by showing the historical buybacks

of publicly traded firms. Figure 2 (B) shows the total buybacks the mean buyback rate

in the fossil fuel industry. Variations in total payout through buybacks appear to be

driven by Exxon Mobile Corp. who by far repurchases the largest quantities. However,

the changes in mean buyback rate, appear to be driven by an increasing number of

firms involved in buyback schemes.

[Figure 2 about here.]

According to the famous Mogdigliani-Miller theorem, the value of a firm depends

neither on its capital structure nor its payout policy, and it is therefore irrelevant

to the firm value whether capital is re-invested or distributed to investors through

dividends or buybacks. However, there are several reasons for the irrelevance theorem

not to hold, leading firms to engage in buyback programs rather than remunerating

shareholders through dividend payments:

Taxation Asymmetry in taxation provides a strong incentive for choosing one payout

method over another. When dividends are taxed more heavily than capital gains, firms

can induce tax savings for shareholders by shifting from dividends to buybacks (Tonev

and Jose 2015).

Undervaluation Besides taxation asymmetry, informational asymmetry between

firm management and investors may also provide an incentive for buybacks (Ver-

Chapter 4 109

maelen 1981). Managers, representing the firm, can announce buyback programs to

signal undervaluation. Numerous papers provide evidence that announcement of re-

purchase programs leads to abnormal positive returns (e.g. Comment and Jarrell 1991;

Ikenberry, Lakonishok, and Vermaelen 1995).

Management Incentives In an attempt to align corporate managers’ personal in-

centives with those of shareholders, it has become common practice to award managers

with instruments linked to the performance of the company, e.g. stock options (Dittmar

2000). Such instruments may have the undesired result that managers try to inflate

the stock option value by driving up the underlying share price trough buybacks.

Flexibility Buyback schemes are considered more flexible as compared to dividends

payouts (Iyer and Rao 2017), thus allowing greater payout variation from year to year

without having negative impact on shareholders’ long term expectations.

Share Dillution Firms can use buyback schemes to counteract the dilutive effect of

employee stock options (Bens et al. 2003). Weisbenner (2000) found that remuneration

with stock options is associated with increased share repurchases and increased total

payouts.

Furthermore, the equity reducing effect of share buybacks provides a way to adjust

the firms capital structure and leverage position, and an ongoing buyback program

raises the minimum price of purchasing the firms shares which makes takeover more

costly and could therefore work as deterrence (Dittmar 2000).

Both investment professionals (e.g. Smith 2011) and academics have strongly criti-

cised buyback programs. For instance, Lazonick (2015) argues that firms’ spending on

share repurchases impedes capital investment, undermines innovative capability, and

may eventually lead to suboptimal economic growth and lower real wages. Almeida,

Fos, and Kronlund (2016) investigate the real effects of buybacks and show that buy-

backs targeting earnings-per-share leads to lay-offs and lower investments. Edmans,

Fang, and Huang (2022) finds that buybacks are being used to boost the short-term

stock prices and equity sale proceeds, and that repurchasing is followed by negative

long-term returns over two to three years. Similarly, and unlike the theory that implies

that buybacks indicate undervaluation, Liu and Swanson (2016) provides evidence that

a significant motive for increasing corporate share repurchases is to support the price

of already overvalued equity.

This paper picks up on the idea of Liu and Swanson (2016) that there exists a strate-

gic incentive to undertake repurchases when firms are overvalued. After establishing

a connection between interest in sustainable finance and fossil fuel repurchasing, we

argue that buying back shares is indeed the best response to a growing price pressure

on polluting firms. Similar to e.g. Hsu and Krause (2016), we assume firms conduct

repurchasing in a way that maximises shareholder value and study share buybacks

as a strategic reaction of the firm to a revaluation of its share price by a fraction

of its investors. To study this optimal response in isolation, we assume that firms’

strategic behaviour exclusively targets maximisation of shareholder value, i.e. there

are no potential perverse incentives of managers, cash gains from trading or employee

shares. We also abstract from potential market distortions occurring from asymmetric

pay-out taxes. We capture the firms’ reaction by assuming that firms maximise share-

holder value (i.e. total market capitalisation) through buyback schemes when share

prices are determined from the market equilibrium. We find that in a market with risk

Chapter 4 110

averse investors, optimal buybacks reduce the negative effect of price volatility, which

increases share prices and hence the market capitalisation.

2.3. Buybacks and the green transition

The following analysis provides empirical evidence of a relationship between observed

buybacks in the fossil fuel sector and investor attitudes towards fossil fuel assets. The

aim is to show that increased interest in sustainable finance has happened simultane-

ously with growing repurchasing activity in the fossil fuel sector. If growing awareness

about sustainable finance issues makes investors update their beliefs about climate

risk, then the observed relationship implies that fossil fuel firms react to the resulting

price pressure by buying back shares. We test for a co-integration relationship between

a sustainable finance awareness index and the mean buyback rate of fossil fuel firms as

we are interested in the the long-term statistical relationship between the time series

variables.

We define a proxy for awareness as the sum of the global Google Trends search

index of the search terms presented in Figure 1 (for similar use of Google Trend data

see Archibald and Butt 2018 and Choi et al. 2023). The Google Trend search index

counts the number of google searches for the specific phrase within a specific period,

normalised to the time and location by the total number of searches and then scaled

to the range between 0 and 100 (Google Trends 2023). As a measure of fossil fuel

firm buyback activity, we take the mean buyback rate of Lehofer (2023). Appendix ??

provides more details.

In the model below ytis the mean buyback rate, and xtis the scaled awareness

index. Both time series appear non-stationary and this is confirmed by the Augmented

Dickey-Fuller (ADF) test results presented in Table 1. If xtand ytare co-integrated

there exists a series {zt}that is stationary:

yt=θxt+zt(1)

To test for the existence of a co-integration relationship, we apply the augmented

Engle-Granger method (Engle and Granger 1987), i.e. we first estimate θusing an OLS

regression and second, apply an ADF test to the sequence of residuals ztto confirm

that it is stationary. The estimated regression coefficient ˆ

θis 0.4176 (with standard

variation 0.028). The ADF test rejects the null-hypothesis that ztis non-stationary

at 1 percent confidence level, and we therefore conclude there exists a co-integration

relationship between xt(awareness) and yt(mean buyback rate). In other words, there

is evidence that buyback rate increases with the awareness on sustainability issues in

finance. Table 1 provides an overview of the test parameters and statistics, and Figure

3 illustrates the results.

[Table 1 about here.]

[Figure 3 about here.]

Two previous studies have investigated the link between buybacks and investor

valuation of carbon risk with mixed conclusions. Choi et al. (2023) use country specific

differences in the price-to-book ratio for polluting firms and other firms as a measure

of price pressure. Choi et al. apply a linear regression model to firm level panel data;

they find that firms in countries with higher price pressure significantly buy back more.

The second study is Lehofer (2023) who analyses the role of fossil fuel divestment

Chapter 4 111

pledges in the repurchase decision of fossil fuel firms and finds a negative correlation

in quarterly observations, implying that a positive increase in the new pledges leads to

less buybacks. However, changes in divestment pledges may not fully reflect investor

attitudes as some investors may manage carbon risk, without openly committing to

divestment.

Our analysis provides evidence for a positive long-term relationship between aware-

ness and buyback activity in the fossil fuel sector, however, on aggregate level. Further

research could be conducted to explore the relationship between share repurchases and

climate risk awareness, considering the specific behaviors and strategies adopted by

individual firms. The co-integration relationship that we have identified suggests a

link between divestment and share buyback but does not identify the mechanism that

creates this link. In the following sections we use a theoretical model to show that

share repurchase is a rational response of firms to divestment from their stock.

3. Static market model with repurchasing

This section introduces the model that we use to investigate the effects of share repur-

chases on prices and market capitalization of the company. The model presented in

this paper is applicable beyond firms with potentially stranded assets. However, our

assumptions regarding investors’ price expectations corresponds to an overvaluation

of assets, which we consider the main outcome of investors neglecting to account for

carbon risk in their valuation of fossil fuel shares.

A core element of behavioural finance is the causes and impacts of irrational beliefs

among investors. Hirshleifer (2001) reviews the psychology of imperfect rationality.

Investors with false expectations are often referred to as ’noise traders’, because they

add noise to the price signal and cause the asset price to depart from the fundamental

value. There exists various theoretical models identifying price impacts of heteroge-

neous, irrational beliefs among investors, e.g. Lux (1995), who study the role of herd

behaviour in shaping the beliefs, Daniel, Hirshleifer, and Subrahmanyam (1998), who

suggest overconfidence in private information as a source of irrationality among in-

vestors, and Brock and Hommes (1998), who classify investors based on their price

prediction strategy and show that rapid switching between strategy leads to unsta-

ble prices. Though noise trader models aim to describe asset price formation when

investors have diverging beliefs about the future prices, none of the models consider

the role of share repurchases on the formation investor beliefs.

In this paper, we build on the seminal paper by De Long et al. (1990), who propose

an optimal portfolio choice model with one group of traders that systematically over-

estimate future prices. This paper extends the original model by introducing the firm

as an active player in the market, optimising the total shareholder value by adjusting

the number of shares outstanding. In this way, we can study the effect of repurchasing

on the price formation. In the model, the control of the quantity of shares available

to the market participants represents the firms’ ability to buy back shares or emit

new ones. Furthermore, due to the different scope of this paper, as compared to the

original, we adjust the assumption on the price expectations of the investors.

The model considers the optimal trading strategy of three types of agents, i.e. two

groups of investors (Aand B) and the firm itself, in a two-period setting. In the

first period the investors allocate their wealth between a risk free asset and a risky

asset (the firm’s shares) with the intention to maximise their expected risk-adjusted

return in second period. In the maximisation problem, the investors consider future

Chapter 4 112

prices, however, their ability to accurately predict the future prices and their expected

value differs among the investor types. Investor group Apredicts future expected

prices accurately on average, while investor group Bmakes a systematic error in their

prediction. In this study, the systematic error is an overvaluation of the share value,

which corresponds to the assumption that investors who undervalue carbon risk hold

the wrong believe.3All investors act as if they were price takers, and hence, do not

consider their own impact on prices.

The firm maximises its total shareholder value, i.e. the market capitalization, by

choosing the number of shares outstanding, qt. When repurchasing shares the firm

can reduce the number of shares outstanding, leading to increased share prices. In

this way, they counteract value reduction occurring due to changing investor expec-

tations. Maximising market capitalization is fundamentally a trade-off between price

and quantity: when the quantity of shares available at the market decreases the share

price increases and vice versa.

We define the equilibrium of the model as the solution to the agents’ maximisation

problems under the restrictions of the market clearing condition.

3.1. Investor behaviour

At time tthe investor iholds wealth wi

t. The investor selects a part of her wealth λi

tto

invest in the risky asset, i.e. the firm share, and places the rest wi

t−λi

tin the risk free

assets. While the latter pays r+ 1 in the second period, the share is bought for price

Ptand is sold for Pt+1 in the next period. Furthermore, we assume that the risky asset

pays a dividend Dt+1 in the second period. For simplicity, we assume the risk-free rate

ris given exogenously and short positions are allowed. We start with a simple model

with two assets, but in Appendix C the model is expanded to include investment in

the market portfolio. After one period, the wealth of the investor has grown to:

t+1 =wi

t(r+ 1) + Pt+1 +Dt+1

−(1 + r)λi

t(2)

The second term defines the excess return on the investments in the risky asset. We

assume that investors are price takers, i.e. they do not consider the impact of their

investment decision on share prices. Furthermore, we assume that investors are risk

averse with constant absolute risk aversion (CARA) expressed through an exponential

utility function with risk aversion parameter γ. Given normally distributed returns

on wealth, investors selects λi

tto maximize risk adjusted expected wealth in the next

period, which is equivalent to solving the following optimisation problem:

max

λi

E[wi

t+1]−1

2γσ2

t+1 (3)

To choose λi

tadequately investors need to know the expected value of their wealth,

which depends on the expected value of the future prices. Investor groups Aand Bare

distinguished in the way they form their expectations regarding prices in the second

3In principle, it could be the investors who believe in a strong impact of climate change and regulation, who

have the wrong believes, and hence, the systematic error leads to undervaluation. However, such investors will

not survive in the market - see De Long et al. (1990) for a discussion.

Chapter 4 113

period:

t+1 =E[Pt+1] + ϵt,∀i∈A(4)

t+1 =E[Pt+1] + ρ+ϵt,∀j∈B(5)

where ϵt∼N(0, σ2

ϵ) is an error term common to all investors participating in the

market, and ρ > 0 is the systematic overestimation of future prices exhibited by

investors in group B, the rationale being that investors in group Bdo not expect

the implementation of climate policy and base their decisions on systematically wrong

expectations. Unlike the model presented by De Long et al. (1990) we do not assume

that non-fundamental price volatility exclusively originates from the investor group

that systematically overestimates future prices, i.e. in our model, also investor type

Afail to accurately predict the mean of the price in the next period. This approach

is similar to Cabrales and Hoshi (1996). Though herd behaviour among investors is

not modelled explicitly, we let the random error term ϵtbe the result of optimism or

pessimism about future share prices shared among all investors. Unlike investors in

group B, the estimation error of the Atype investors has zero mean, hence the time

average of their price expectation is consistent with the true price expectation. The

optimisation problem for investors can now be described as:

max

λi

ˆwi

t+1 −1

2γσ2

t+1 (6)

where

ˆwi

t+1 =wi

t(r+ 1) + ˆ

t+1 +E[Dt+1]

−(1 + r)!λi

t(7)

σ2

t+1 =λi

tσ2

Pt+1 +σ2

Dt+1 (8)

∀i∈A∪B.

3.2. Firm

To adjust the model to account for share repurchasing schemes, we introduce next the

firm as a third type of actor in the market. The firm selects the optimal number of

shares outstanding that maximises its total market capitalisation, i.e. the product of

the outstanding shares and the share price:

max

qtPt(9)

Unlike investors, the firm does consider its impact on share prices. The maximisation

problem of the firm is then equivalent to that of a monopolist: the firm alone chooses

the supply of shares to the market, while taking into account the price effect of its

Chapter 4 114

actions. The firm selects the optimal number of shares outstanding in each period

independently, i.e. it takes future share prices as given. In this model, the optimal

buyback can always be financed without affecting the intrinsic value of the firm. Other

ways of allocating the money used for buybacks are not considered, and therefore

we abstract from the budget constraint of the firm. Though these assumption entail

a significant simplification of the firm optimisation problem it is reasonable in this

case. First, the optimal buyback strategy emerging from this model is a ’buy low, sell

high’ strategy and therefore self-financing around the steady state. Consequently, the

question of financing is only relevant in the case of changes in the steady state, e.g.

in relation to a permanent change in investors’ beliefs. Second, alternative ways of

allocating the funds such as dividends can be neglected because the current period’s

share price is affected only by the expected value of next period’s dividend payout.

Hence, in order to raise firm value through dividends in steady state the firm would

need to generate a permanent increase in the dividend level. If the firm does not have

access to such investment opportunities, the firm cannot use the dividend level to

increase firm value, and hence dividends are no alternative to repurchase schemes.

3.3. Market clearing

The total demand for shares in the firm must be equal to the amount of shares supplied

by the firm. The demand for shares equals the wealth invested in the firm divided by

the share price, while the supply is simply the number of shares outstanding. We get

the following market clearing condition for the risky asset:

i∈A

λi

t+X

j∈B

λj

t=qt(10)

This condition is equivalent to setting the amount of wealth invested in the firm’s

shares equal to the market capitalisation of the firm, i.e. the share price times the

number of shares outstanding.

3.4. Model solution

The first order conditions of the investors’ optimisation problem give an expression

for the share of wealth invested in the risky asset by each investor.

ˆ

Pt+1+E[Dt+1]

Pt−(1 + r)−γλi

tσ2

Pt+1 +σ2

Dt+1 = 0 (11)

Assuming there are ainvestors in group Aand bin group Bwith the expectations to

future prices of the risky assets as in equation (4) and (5), respectively, the market

clearing condition simplified and used to derive an expression for the asset price:

Pt=1

1 + rE[Pt+1] + E[Dt+1] + ϵt+b

a+bρ−qt

a+bγσ2

Pt+1 +σ2

Dt+1 (12)

The expression in equation (12) gives the share price Ptas a function of the number

of shares outstanding qt. As expected, the expression indicates that a buybacks (i.e.

a reduction in qt) leads to higher share prices. This result is in line with the price

Chapter 4 115

behaviour that is normally assumed, cf. the introduction on share repurchasing in

Section 1.1.

Equation (12) can be used to determine the optimal repurchasing by the firm. From

the first order condition of the firm’s maximisation problem as in equation (9), we

obtain qt:

qt=(a+b) (E[Pt+1] + E[Dt+1] + ϵt) + bρ

2γσ2

Pt+1 +σ2

Dt+1 (13)

Inserting qtinto the price expression we get:

Pt=1

2 (1 + r)E[Pt+1] + E[Dt+1] + ϵt+b

a+bρ(14)

3.4.1. Steady state

To obtain a fully parameterized expression for the current prices, we determine the

expected price at t+ 1 as well as the variance of the price. For this, we first consider

the expected price and shares outstanding in the steady state. In the steady state

E[Pt+s]≡¯

P, and E[qt+s]≡¯q, ∀s≥1. Furthermore E[ϵt+s]=0,∀s≥1 by definition.

For simplicity, we assume that in the steady state the dividend payments are normally

distributed, i.e. Dt+s∼N¯

D, σ ¯

D. In combination with the optimal number of shares

outstanding in equation (13), equation (14) reduces to the following expression for the

steady state price:

P=1

1+2r¯

D+b

a+bρ(15)

Inserting the state state expected price into the expression for Ptas in equation (14)

we find:

Pt=1

1+2r¯

D+b

a+bρ+ϵt

2 (1 + r)(16)

At this point only the steady state price variance remains unknown. By noticing

that the only source of uncertainty for future prices is ϵt, the variance of Ptin steady

state can be derived directly from the price expression in equation (16).

σ2

P=1

4 (1 + r)2σ2

ϵ(17)

And finally, inserting the steady state expected price and the price variance into the

expression for the optimal number of shares outstanding, we get a fully parameterized

expression for the shares outstanding:

qt= ¯q+(a+b)ϵt

2γσ2

P+σ2

D(18)

Chapter 4 116

¯q=a+b

γσ2

P+σ2

D

1 + r

1+2r¯

D+b

a+bρ(19)

By comparison of equation (18) with equation (16) it is clear that the optimal number

of shares outstanding is proportional to the price level.

4. Observations from the static model

In equilibrium, the firm determines the number of outstanding shares (qt) according

to equation (18). The corresponding market price for the firm’s shares (Pt) is given by

(16). We make the following observations:

Observation 1. In equilibrium, the firm maximises market capitali ation (Ptqt)by

letting the number of shares outstanding (qt)compensate for the impact of volatility

on the share price.

As investors are risk averse the volatility of the payout reduces their utility from

investing in the risky asset such that a higher volatility shifts their investment decision

towards the risk free asset. Hence, increased volatility leads to lower share prices

and lower market capitalisation of the firm. However, by choosing the number of

shares outstanding optimally, the firm can counteract the negative impact of volatility

on prices. To see this, note that the optimal strategy for qtremoves the standard

deviations σ¯

Pand σ¯

Dfrom the equilibrium share price in equation (16) (in contrast

to (12) where both parameters are present). The model indicates that the optimal

strategy of the firm is to select the number of shares outstanding that minimises the

negative effect of volatility on the share prices. This is reflected in the optimal number

of shares outstanding (18), which shows how firms take the degree of risk aversion (γ)

as well as the variance of prices in mean prediction (σ2

ε) into account: The greater the

risk aversion and price uncertainty (in terms of variance of the prediction error), the

lower the number of shares outstanding.

Managing the volatility of one’s own share price is thus identified as a new and

additional motivation for share buyback activities. In our model, it emerges as a central

motivation from the assumption of risk-aversion in investor preferences. However, as

our modeling abstracts from many of the other motivations (as reviewed in Section

2.2), we cannot discuss the relative importance of this motivation.

Observation 2. When investors switch from group Bto A, the optimal response of

the firm is to reduce the number of shares outstanding.

When investors move from group Bto group A,bis reduced in (19) while (a+b)

remains constant. The overall effect is therefore to reduce qt. The intuition behind

this finding is as follows: Due to the positive systematic misperception of future prices

(ρ > 0) the B-type investors increase the share price. Hence, when investors switch

from group Bto group A, share prices ought to drop. However, the firm can partially

mitigate share price decline by buying back shares. In other words, when the number

of investors who systematically overestimate future prices (b) is reduced, the optimal

response of the firm is to reduce the number of shares outstanding and thereby force

a increase in prices.

Chapter 4 117

[Figure 4 about here.]

Figure 4 (A) compares the price and market cap for different compositions of A

and Bunder optimal shares outstanding. The repurchase dampens the negative price

effects occurring from the decline in band the subsequent decrease in investor price

predictions. That is, when investors realise the assets are overvalued and updates their

individual valuation, the best response of the firm is to repurchase its shares. The

implications of this observation in the case of stranded assets is clear: As investors

updates their beliefs about the future asset value in light of the potential stranding

and shift expectations to future share prices accordingly, the optimal response of the

firm is to buy back shares.

Observation 3. If the realisation of the prediction error εtis large and positive, the

model prescribes the best response as an increase in the number of shares outstand-

ing. Likewise, high systematic prediction error ρleads to a higher number of shares

outstanding.

The share price increases with both pricing errors εtand ρ, and so does the market

capitalisation of the firm. However, the model indicates that in the case of large and

positive errors it is optimal for the firm to increase the number of shares outstanding,

and hence sacrifice some of the price increase in return of more shares to improve the

market capitalisation. The optimal response is illustrated in Figure 4 (B) and 4 (C).

Here share prices and market capitalisation are plotted as functions of the realisation

of the prediction error (εt) and the systematic misperception of future share value (ρ)

among B-type investors.

The mechanisms presented in Observation 2 and 3 are fundamentally similar. The

changes in the composition of type Aand Binvestors (Observation 2), and changes in

the realisation of prediction error εt(Observation 3) both lead to changes in demand

for the firm’s shares. Hence, the two observations imply a similar logic for the optimal

response of the firm: the firm can maximize market capitalisation by responding to

changes in total demand by changing the supply of the share.

5. Dynamic model with overlapping generations

The previous section showed the optimal response of the firm to a given changes in

parametric values in a static setting, e.g. for a positive fixed number of Binvestors, who

systematically overestimate future prices. However, according to the Efficient Market

Hypothesis irrational investors with false expectations ought not to exist: Rational

investors would take advantage of the arbitrage opportunity the irrational investors

create such that the irrational investors will loose money to them and eventually

disappear from the market. De Long et al. (1990) show in a dynamic setting that this

assumption does not hold when the irrational investors introduce additional risk to the

payoffs of the investment in the risky asset. In our model, the volatility is independent

of the number of type Binvestors, however, as we will show in the following it still

leads to a persistent number of investors with false expectations. In analogy to the

original paper of De Long et al. (1990), we analyse the dynamic properties of the model

by introducing the overlapping generations structure (OLG): Investors of generation

tallocate their wealth among the assets at time tand consume their entire realised

wealth in period t+ 1 where a new generation investors take over. The purpose of

the OLG model is to show the persistence in the presence of investors with systematic

Chapter 4 118

overestimation of prices (b > 0) by showing that despite their false beliefs they perform

better in terms of return on investments. To this end we endogenize the relative shares

of investors in groups Aand B. To simplify notation, let µbe the share of type B

investors in total investors, i.e µ=b

a+b. Furthermore, let µdevelop over time according

to the following rule:

µt+1 = max 0,min 1, µt+ξ∆RB−A

t (20)

where the flow rate between group Aand Bis determined by the flow parameter ξ

and the difference in realised return between group Band A, i.e. ∆RB−A

t=RB

t−RA

Equation (20) implies that the share of Binvestors among the total investors is between

0 and 1, and grows when the Binvestors earned a greater return than Ainvestors in

the previous period and vice versa. If the flow parameter ξis close to zero, the rate of

change in investor composition is slow, hence, it is reasonable to assume that investors

do not consider the change of investor composition while forming expectations to next

period’s prices. This means, we can use all expressions for investment in risky assets λA

and λB

t, price Ptand shares outstanding qtas derived in previous sections. To show

the persistence of B-type investors in the market, i.e. investors who systematically

overestimate future prices are persistently present in the market, we look for a stable

value of µtdifferent from zero. A value is considered stable if an increase in µtwill lead

to an expected drop in µt+1 and likewise, a decrease in µtleads to an expected increase

in µt+1. To find such stable value we analyse the expected excess return E[∆Rt] given

as a function of µt. Equation (11) gives the difference in wealth invested in the risky

asset:

λB

t−λA

t=Ptρt

γσ2

P+σ2

D(21)

The return on wealth for investor i∈A∪Bis given directly from the definition in

equation (2):

t=wi

t+1 −wi

t=Pt+1 +Dt+1

−(1 + r)λi

t+r(22)

This gives the following excess return of the B-type investors:

∆RB−A

t= (Pt+1 +Dt+1 −Pt(1 + r)) ρt

γσ2

Pt+1 +σ2

Dt+1 (23)

In the steady state, the expectation of the excess return conditional on time tis

found by using the expressions for ¯

Pand Pt:

Eth∆RB−A

ti=1 + r

1+2r¯

D−rρµt

1+2r−ϵt

2ρ

γσ2

P+σ2

D(24)

Chapter 4 119

and the unconditional expectations to the excess return in the steady state:

Eh∆RB−A

ti=(1 + r)¯

D−rρµtρ

(1 + 2r)γσ2

P+σ2

D(25)

The expected excess return is a function of µt. Given that ¯

D,γ,r,µtand the

volatility are all positive parameters, it is necessary that ρ > 0 and (1 + r)¯

D > rρµt

for the expected excess return to be positive. Hence for Binvestors to exist, they need

to systematically overestimate future prices. Underestimation of prices will lead to

negative excess return, leading to all Binvestors disappearing from the market. We

restrict our analysis to the case with positive systematic prediction error, i.e. ρ > 0.

When µt= 0 the excess return is given by:

Eh∆RB−A

ti(0) = (1 + r)¯

Dρ

(1 + 2r)γσ2

P+σ2

D>0 (26)

This means that if all investors are of type A, i.e. have correct expectations to future

prices on average, the expected excess return of a B-type investor entering the market

is positive. When µt= 1 the excess return is given by:

Eh∆RB−A

ti(1) = (1 + r)¯

D−rρρ

(1 + 2r)γσ2

P+σ2

D(27)

which may be greater or smaller than 0 depending on the parameter values. The ex-

pected excess return as given in equation (25) is a linear (hence monotone) decreasing

function of µt, which means that if the expected excess return for µt= 1 is positive,

there is for all values of µta positive expected excess return of Binvestors. Thus,

according to the rule of development in equation (20) µtis expected to increase until

it reaches 1, i.e. all investors are B-type investors. If, on the other hand, the expected

excess return for µt= 1 is negative, we find a stable point µs:

Eh∆RB−A

ti(µs) = 0 (28)

=⇒0 = (1 + r)¯

D−rρµs(29)

=⇒µs=1 + r

ρ(30)

The analysis shows that B-type investors, who systematically overestimate future share

prices, persist in the market. This leads us to the following observation:

Observation 4. If investors use observed returns to form their expectations to future

prices, such that they change investor group depending the excess return, then the

model predicts that investors who systematically overestimate prices will persistently

exists in the market. The share of investors with systematically wrong expectations are

Chapter 4 120

given as:

µ∗= min 1 + r

ρ,1(31)

For any reasonable (positive) value of the risk free rate r, the term 1+r

ris much

greater than 1. This means that the systematic misperception ρmust be much larger

than the the expected dividend payments for the share of investors with systematic

overestimation of prices, µ∗, to fall below 1. In other words, as long as the systematic

misperception is not far greater than the dividend payments, all investors will belong

to group Band overestimate future prices.

5.1. Comparison to the case of fixed share supply

To understand the relative importance of the existence of buyback schemes, i.e. the

ability of firms to adjust the supply of shares, we can compare the model results

with an equivalent model in which the number of shares outstanding is fixed at level

qf. While assuming that qfis the number of shares outstanding that maximise the

market capitalisation in expectation, redoing all steps of calculation as in the base

model, leads us to the following results: First, when the supply of shares is fixed, the

price variance is four times larger (double volatility) as compared to the case where

the firm do buybacks:

σ2

Pf=1

(1 + r)2σ2

ε(32)

Second, the excess return of investors with systematic misperception of future prices

is given by:

Eh∆RB−A

f,t i=D−µρρ

2γσ2

Pf+σ2

D(33)

which leads the share of investors who systematically overestimate future prices:

µ∗

f= min ¯

ρ,1(34)

[Figure 5 about here.]

Like in the base model with buybacks, the model with fixed supply of shares suggests

that investors with systematic overestimation of prices will persistently be present in

the market. However, for any reasonable level of interest rates the inequality 1+r

r>1

holds, hence, by comparison of the two models (equations (31) and (34)) we find that

the number of Btype investors will be larger when the firm can adjust the number of

shares outstanding.

Observation 5. If the firm deploys an optimal buyback strategy, its stable share of

investors who systematically overestimate future share price value will be larger than

in case the firm keeps a fixed number of shares outstanding.

Chapter 4 121

Figure 5 (A) illustrates this result.

Taking an active role to control the number of shares outstanding affects the share

price of the firm in two ways: It reduces the price volatility and elevates the number of

investors who systematically overvalue the share. Though these two effects generally

suggest a higher market capitalisation, the firm can do better with a fixed number of

shares outstanding under certain conditions, specifically when the systematic misper-

ception of future prices is small. Figure 5 (B) shows the steady state market capitali-

sation as a function of the systematic price misperception of investor type B. Except

for low levels of systematic misperception, the market capitalisation of the firm that

controls the number of shares outstanding is higher than the market capitalisation for

a firm with fixed supply of shares.

Observation 6. When a share of investors holds beliefs about the future that leads

to a large, systematic overvaluation of share prices, the firm can increase its market

capitalisation by buying back its shares.

Our model indicates that active management of shares outstanding is particularly

beneficial when the systematic misperception of future prices is substantial.

Regardless of whether the firm controls the number of shares outstanding or keeps

the number fixed, the steady state share price is equal to the risk-free intrinsic value

of the share ¯

D/r, as long as there are A type investors (µt<1, i.e. share of Btype

investors are below its upper limit). In this case, neither the number of investors with

false expectations nor the size of the systematic prediction error affect the steady state

share price. A marginal decrease in the size of the systematic overestimation of future

prices is compensated by an equivalent increase in the number of investors sharing the

belief in the overestimation such that no changes to the steady state price occurs. The

finding is a result of the investor type flow mechanism in equation (20) from which the

equilibrium share of investors is determined as the point where expected excess return

is zero. If the steady state share price included a risk term, i.e. steady state prices

diverged from the risk-neutral valuation, it would be possible for the Btype investors

to earn a higher return by taking on more risk. Hence, according to the definition of

the equilibrium, the share valuation has to be risk-free.

This finding implies that as long as the share of investors with false expectations

falls below 1, changes in investor beliefs do not lead to changes in the steady state

prices and steady state market capitalisation. Accordingly, changes in the systematic

overestimation of group Binvestors do not trigger changes in the steady state number

of shares outstanding and share repurchases are only a useful tool for accommodating

price changes around the steady state (i.e. variations caused by the common estimation

error ϵt). However, it should be noted that in equilibrium, the steady state market

capitalisation of a firm who actively controls the number of shares outstanding will be

higher than in case it kept the number fixed, because the steady state number of shares

outstanding differs. In figure 5, panel B, the curves indicating market capitalisation

are flat for values of the systematic misperception ρthat lead to a share of Btype

investors less than maximum (µt<1).

In conclusion, engaging in buyback schemes and actively controlling the number

of shares outstanding reduce price volatility, increases the number of investors who

overestimate future prices and as long as the misperception of future share prices is

sufficiently large it leads to higher market capitalisation of the firm.

Chapter 4 122

6. Conclusion

In this paper we investigate the role of share repurchasing schemes for firm value when

investors form diverging beliefs regarding future share prices. Such divergence may be

present in the case of fossil fuel companies, for which the risk of becoming stranded

assets is not adequately reflected in market prices.

The substantial amount of wealth spent on share buyback programs underlines its

popularity as a tool for shareholder remuneration. The data presented in Figure 2C

show the increasing popularity of buybacks in the fossil fuel sector. A co-integration

relationship between mean buyback rate and an index for awareness about sustain-

ability issues in finance indicate that growing awareness among investors could be a

potential motivation for buybacks in the sector. Distributing revenues through share

repurchase programs is in itself not necessarily problematic. On one hand, it could be

a sign that fossil fuel firms recognizes that they have no good investment opportunities

for the future and increasing payout is a way to let investors redistribute their funds to

more profitable businesses. On the other hand, fossil fuel firms could directly finance

green innovation. One of the main criticisms of buybacks schemes is that it leads to

under-investment and this may impede greening the fossil fuel sector. However, this

paper points at a completely different kind of issue:

Through a optimal portfolio choice model with market clearing, we show that if

investors are risk-averse, firms can deploy an optimal buyback strategy to maximise

their overall valuations. Specifically, we study share buyback as a strategic reaction

of the firm to a revaluation of its share price by a fraction of its investors. By ad-

justing the number of shares outstanding, firms can influence the share prices and

market capitalisation, and mitigate potential valuation effects occurring from changes

in shareholder expectations. In the context of divestment, the model indicates that

firms can dampen negative price effects caused by divesting shareholders selling off

their shares. Finally, we show that share repurchasing can contribute to sustaining

overestimation of future prices, leaving a persistent share of investors to have false be-

liefs about future share value. Under certain parametric conditions all investors appear

to systematically overestimate future prices.

Given the fossil fuel sectors’ extensive engagement in share buybacks, this mecha-

nism could yield an important contribution to investors’ failure to perform an accurate

valuation of potentially stranded assets. While buybacks cannot prevent revelation of

the firm value in the long run, it provides a plausible explanation how market forces

could veil the true value of fossil fuel assets. By maintaining an overvaluation, buy-

backs could contribute to the inflation of the carbon bubble. The larger the bubble, the

greater the risk that stranded assets causes macro-financial instability. Overvaluation

will eventually become a problem.

Acknowledgements

We thank participants of 6th International Symposium on Energy and Finance Issues

as well as our colleagues at the Potsdam Institute for Climate Impact Research for the

insightful discussion of the early versions of the paper.

Chapter 4 123

Disclosure statement

The authors report there are no competing interests to declare.

Funding

The research for this study was funded by the German Federal Ministry of Education

and Research (BMBF), research grant 01LN1703A, which we gratefully acknowledge.

Data availability statement

The data that support the findings of this paper were derived from the following public

domain resources, listed under references and cited in the paper where appropriate:

•Smith (2011): Fig. 2 (A)

•Lehofer (2023): Fig. 2 (B), Fig. 3 (A), and the co-integration test

•Google Trends (2023): Fig. 1, Fig. 3 (A) and the co-integration test

In addition, data sets can be provided directly from the authors upon requests.

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Chapter 4 126

Appendix A. Buyback data for co-integration analysis

For co-integration test we use the mean buyback rate reported by Lehofer (2023), who

calculates the rate based on the gas, coal and oil firms in the Refinitiv Universe of

Fossil Fuel Industry. The sample excludes firms in China and India, as these coun-

tries restricts buybacks through regulation and also, the smallest firms comprising 10

percent of the total market capitalisation. From the final sample reported by Lehofer

(2023), we remove outliers defined as firms that bought back more than 25 percent

of market cap in one quarter. The identified outliers are the two companies, Shawcor

Ltd and Sunoco LP.

Appendix B. Parameter values

[Table 2 about here.]

Appendix C. Extended model solution

This appendix contains the derivation of the solutions to the expanded model that

includes the market portfolio as an investment option. We extend the base model

with the an additional investment opportunity for the investors: the risky market

portfolio which represents all risky assets available for investment excluding the firm

share. In this way, the investors can choose between the risky firm share, the risky

market portfolio, and the risk free assets. By distinguishing between investment in

the risky share of the firm and the risky market portfolio, we can investigate the

pricing mechanism of the specific share, when there exists other risky investment

opportunities. As in the base model, at time tthe investor iholds wealth wi

t. The

investor selects λi

tof her wealth to invest in the risky assets i.e. the firm share, κi

in the risky market portfolio and the rest of the wealth 1 −λi

t−κi

tin the risk free

assets. The market portfolio is bought for the price PM

tand is sold for PM

t+1 in the

next period. For simplicity, we assume no dividends will be paid in the two periods

and the risk-free rate ris given exogenously. The investors optimisation problem can

now be described as:

max

λi

t,κi

ˆwi

t+1 −γ

2σ2

t+1 (C1)

where

ˆwi

t+1 =wi

t(1 + r) + λi

t ˆ

t+1

−(1 + r)!+κi

t PM

t+1

−(1 + r)!(C2)

σ2

t+1 =λi

σ2

Pt+1 +κi

2σ2

t+1 +2λi

tκi

PtPM

σP,P M(C3)

∀i∈A∪B. The problem of the firm as well as the market clearing condition remains

as described in the base model. Following the same steps as with the base model,

we derive expressions for share prices and the optimal number of shares outstanding

Chapter 4 127

around the steady state. The investors choose their investment in the risky asset λt

and the market portfolio κtby solving the optimization problem given in equation

(C1).

From the two first order conditions we obtain an expression for the share of wealth

invested in the risky asset. The first order condition with respect to λi

t+1

−(1 + r)!−γλi

σ2

Pt+1 −γκi

PtPM

σP,P M= 0 (C4)

FOC with respect to κi:

t+1

−(1 + r)!−γκi

2σ2

t+1 −γλi

PtPM

σP,P M= 0 (C5)

By isolating κiin equation (C5) and inserting the expression into (C4), we optain the

following expression for λi:

λi

t=Ptˆ

t+1 −Pt(1 + r)−σP,P M

σ2

t+1 ˆ

t+1 −PM

t(1 + r)

γ σ2

Pt+1 −σ2

P,P M

σ2

t+1 !(C6)

Assuming there are ainvestors in group Aand bin group Bwith the expectations

to future prices of the risky assets as in equation (4) and (5), respectively, the market

clearing condition for the risky share simplifies to:

qtPt=X

i∈A

Ptˆ

t+1 −Pt(1 + r)−σP,P M

σ2

t+1 ˆ

t+1 −PM

t(1 + r)

γ σ2

Pt+1 −σ2

P,P M

σ2

t+1 !

j∈B

Ptˆ

t+1 −Pt(1 + r)−σP,P M

σ2

t+1 ˆ

t+1 −PM

t(1 + r)

γ σ2

Pt+1 −σ2

P,P M

σ2

t+1 !

(C7)

From this expression it is easy to derive the price:

Pt=1

1 + r E[Pt+1] + εt−σP,P M

σ2

t+1 ˆ

t+1 −PM

t(1 + r)+b

a+bρ−qt

a+bγ σ2

Pt+1 −σ2

P,P M

σ2

t+1 !!

(C8)

The expression for Ptcan be used to determine the optimal repurchasing by the firm.

The firms maximisation as in equation (9), gives the following first order condition

Chapter 4 128

with respect to qt:

1 + r E[Pt+1] + εt−σP,P M

σ2

t+1 ˆ

t+1 −PM

t(1 + r)+b

a+bρ−2qt

a+bγ σ2

Pt+1 −σ2

P,P M

σ2

t+1 !!= 0

(C9)

which leads to qt:

qt=

(a+b) E[Pt+1] + εt−σP,P M

σ2

t+1 ˆ

t+1 −PM

t(1 + r)!+bρ

2γ σ2

Pt+1 −σ2

P,P M

σ2

t+1 !(C10)

Inserting qtinto the price expression we get:

Pt=1

2(1 + r) E[Pt+1] + εt−σP,P M

σ2

t+1 ˆ

t+1 −PM

t(1 + r)+b

a+bρ!(C11)

E[Pt+1] = 1

2(1 + r)(E[Pt+2] + E[εt+1]−σP,P M

σ2

t+2

(ˆ

t+2 −ˆ

t+1(1 + r)) + b

a+bρ) (C12)

Next, we determine the expected prices in the following period. To do so, we assume

steady state in which E[Pt+s]≡¯

P,E[PM

t+s]≡¯

PMand E[qt+s]≡¯q, ∀s. Furthermore

E[εt+s]=0,∀sper definition. Furthermore, the variances and covariance of the prices

are constant across all periods. This gives the following expression for the steady state

price:

P=1

2(1 + r)(¯

P−σP,P M

σ2

(¯

PM−¯

PM(1 + r)) + b

a+bρ) (C13)

⇒¯

P=1

1+2r(σP,P M

σ2

(r¯

PM) + b

a+bρ) (C14)

Inserting the steady state expected price in into the expression for qtand current

price Pt(equations (C10) and (C11), respectively) we find:

qt=

(a+b) (r+ 1) σP,P M

σ2

PMPM

t−¯

1+2r+2

1+2r

a+bρ!+ (a+b)εt

2γ σ2

P−σ2

P,P M

σ2

PM!(C15)

Pt=εt

2(1 + r)+bρ

(1 + 2r)(a+b)+σP,P M

2σ2

(PM

t−¯

1+2r) (C16)

Chapter 4 129

At this point only the steady state price variance remains unknown. By noticing

that the only source of uncertainty for future prices of the firm share is εtand PM

t, we

derive the variance of Ptin steady state directly from the price expression in equation

(C16). First consider the covariance of the asset price and the price of the market

portfolio:

σP,P M=Cov Ps, PM

s=Cov "σP,P M

2σ2

s, PM

s#+Cov εs

2(1 + r), PM

s

=σP,P M

2σ2

σ2

PM+1

2(1 + r)σϵP M=σP,P M

2+1

2(1 + r)σϵP M

(C17)

⇒σP,P M=1

(1 + r)σϵP M(C18)

The derivation above and implies that the covariance between the prices of the asset

and the market portfolio equals the discounted covariance between the prediction error

and the price of portfolio. From equation (C16) we find the share price variance:

σ2

P=1

(1 + r)2σ2

ε+σ2

P,P M

4σ2

+ 2 1

2 (1 + r)

σP,P M

2σ2

σϵP M

(1 + r)2σ2

ε+1

(1 + r)σϵP M2

4σ2

(1 + r)

(1 + r)σϵP M

2σ2

σϵP M

4 (1 + r)2 σ2

ε+3σ2

ϵ,P M

σ2

PM!(C19)

And finally, inserting the steady state expected price and the price variance into the

expression for the share price in steady state optimal number of shares outstanding,

we get a fully parametrized expression for the share price, Pt:

Pt=εt

2 (1 + r)+bρ

(1 + 2r) (a+b)+σϵ,P M

2 (1 + r)σ2

PMPM

t−¯

1+2r(C20)

Chapter 4 130

Lkewise, we get the expression for the optimal number of shares outstanding, qt:

qt=1 + r

2γ σ2

P−σ2

P,P M

σ2

PM!(2bρ

1+2r+ (a+b) εt

1 + r+σP,P M

σ2

PMPM

t−¯

1+2r!

=1 + r

2γ(1

4 (1 + r)2(σ2

ε+3σ2

ϵ,P M

σ2

)−1

(1 + r)2

σ2

ϵ,P M

σ2

)

· 2bρ

1+2r+a+b

1 + r εt+σϵ,P M

σ2

PMPM

t−¯

1+2r!!

=2 (1 + r)2

γ σ2

ε−σ2

ϵ,P M

σ2

PM! 2 (1 + r)bρ

1+2r+ (a+b) εt+σϵ,P M

σ2

PMPM

t−¯

1+2r!!

(C21)

Here, ¯

PMis the expectation to next period’s price of the market portfolio in the

steady state.

Pt=εt

2(1 + r)+bρ

(1 + 2r) (a+b)+σϵ,P M

2σ2

PMPM

t−¯

1+2r(C22)

qt=(1 + r)3

γ σ2

ε−σ2

ϵ,P M

σ2

PM! 2bρ

1+2r+a+b

1 + r εt+σϵ,P M

σ2

PMPM

t−¯

1+2r!! (C23)

The results of equation (C22) and (C23) indicates that the observations 1-3 made from

the basemodel also holds for the extended model. In addition, we make the following

observation:

Under the assumption that the asset price is positively correlated with market prices

(σϵ,P M>0), the best response to an increased expectation to the market portfolio

return (i.e. either ¯

PMincreases or PM

tdecreases) is to reduce the number of shares

outstanding.

As market portfolio offers better returns on investment compared to the firm’s share,

we would expect a shift in investment from the firm to the market portfolio, which

would reduce the share price of the firm. To mitigate the drop in prices, the firm can

buyback its shares.

Chapter 4 131

ADF test xtytzt

Test statistic: 5.23 -1.724 -3.644

p-value: 1.0 0.419 0.0038

Null-hypothesis: accepted accepted rejected

Conclusion: non-stationary non-stationary stationary

Table 1. Test results of the ADF tests for awareness (xt), buyback rate (yt) and the residuals obtained from

the Engle-Granger methods (zt). The optimal number of lags for the test is chosen by the Aikaike information

criterion. The reported p-values are Mackinnon’s approximate p-values (Mackinnon 1990). The ADF test cannot

reject the existence of a unit root for Xtand Ytbut rejects for zt.

Chapter 4 132

Parameter Value

r 0.04

γ1.8

D0.05

σ2

D0.02

ρ0.1

εt0.0

σ2

ε0.02

a+b1

b0.5

Table 2. Values used for generating Figure 4 and 5, unless otherwise specified in the figures.

Chapter 4 133

2010 2012 2014 2016 2018 2020

Year

100

150

200

250

Index

Google search indexes

stranded assets

sustainable investment

ESG investment

sustainable finance

fossil fuel divestment

Figure 1. Search indexes for search terms related to greening the financial sector. Source: Google Trends

(2023)

Chapter 4 134

1976 1978 1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004

Year

20%

40%

60%

80%

100%

(A) Payout type as percentage of total payout

Buybacks

- All public US

Dividends - All public US

Q1 2010

Q1 2011

Q1 2012

Q1 2013

Q1 2014

Q1 2015

Q1 2016

Q1 2017

Q1 2018

Q1 2019

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1e10

) Fossil fuel buybacks

0.10%

0.20%

0.30%

0.40%

0.50%

Total buybacks

Mean buyback ratio

Figure 2. Dividend payments and share repurchases in US and in the fossil fuel sector. Panel (A): The share

of total payout of US publicly traded companies. Source: Smith (2011). Panel (B): shows total buybacks in USD

and the mean buyback rate, calculated as the mean buyback to market cap ratio, for the fossil fuel industry.

Source: Lehofer (2023).

Chapter 4 135

2010 2011 2012 2013 2014 2015 2016 2017 2018 2019 2020

Year

0.2

0.4

0.6

0.8

1.0

index

(A) Google search index and mean buyback ratio

Search index

Buyback

0.2 0.4 0.6 0.8 1.0

Search index

0.1

0.2

0.3

0.4

0.5

Mean buyback ratio

(B) Scatterplot

2010 2012 2014 2016 2018 2020

Year

−0.1

0.0

0.1

0.2

0.3

0.10%

0.20%

0.30%

0.40%

0.50%

Bu−back) a) pe(ce%tage of ma(ket cap

Figure 3. Co-integration relationship between mean buyback rate in the fossil fuel sector and sustainable

finance awareness.

Chapter 4 136

0.0 0.2 0.4 0.6 0.8 1.0

Share of B-type investors,

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.45

Price and Market Cap

(A) Market cap as a f(nction of in)estor mix

Price

Market cap

−0.15 −0.10 −0.05 0.00 0.05 0.10 0.15

In)estor o(t ook,

0.0

0.1

0.2

0.3

0.4

0.5

0.6

Price and Market Cap

(B) Market cap as a f(nction of in)estor o(t ook

Price

Market cap

0.0 0.2 0.4 0.6 0.8 1.0

S+stematic misperception,

Price and Market Cap

Price

Market cap

1.0

1.5

2.0

2.5

3.0

Shares o(tstanding

Price

Market Cap

Shares o(tstanding

0.5

1.0

1.5

2.0

2.5

3.0

3.5

Shares o(tstanding

Price

Market Cap

Shares o(tstanding

Price

Market Cap

Shares o(tstanding

Figure 4. The optimal number of shares outstanding, share price and market cap as a function of share of

investors in group A(Panel A), the realisation of εt(Panel B), and the systematic prediction error ρof group

Binvestors (Panel C). Values used to construct the figure available in Appendix B.

Chapter 4 137

0.0 0.2 0.4 0.6 0.8 1.0

Share of B-type investors,

−0.04

−0.02

0.00

0.02

0.04

0.06

0.08

0.10

Expected excess return

(A) Excess return for B

-type investors

With buybacks

Without buybacks

Stable point

0.0 0.2 0.4 0.6 0.8 1.0

Systematic misperception,

Market cap

(B) Market cap with and without buybacks

0.0

0.2

0.4

0.6

0.8

1.0

Stable share of B-type investors

MC with buybacks

MC without buybacks

* with buybacks

* without buybacks

Figure 5. Panel (A): The expected excess return as a function of the share of group Binvestors, µ, in the case

where the firm can control the supply of shares (”With buybacks”) and where the supply is fixed (”Without

buybacks”). The stable values of µis given by equations (31) and (34). Panel (B): The steady state market

capitalisation of the firm who controls shares outstanding (”MC with buybacks”) and the firm who keeps a

fixed number of shares outstanding (”MC without buybacks”). The stable share of investors who systematically

overestimate future prices, µ∗, is determined endogenously by equations (31) and (34). Values used to construct

the figure are available in Appendix B.

Chapter 4 138

Chapter 5

Synthesis and Outlook

5.1 Summary

To meet the targets of the Paris Agreement, investments in mitigation need to be

scaled-up worldwide. However, mobilising the sufficient financial resources is a

challenge.

In this thesis, I explore the role of financial market failures in the green transi-

tion. I examine mechanisms through which financial market failures contribute to

suboptimal allocation of funds through inefficient pricing of financial assets. To this

end, I rely on equilibrium models designed to investigate the financial market fail-

ure under a specific set of market condition. The core contribution is an improved

understanding of the underlying mechanisms that lead to inefficient allocation of

capital during the green transition.

A central theme in the thesis is under-investment in clean energy capital and

over-investment in fossil fuel related capital. The findings indicate that financial

market imperfections have the power to cause such suboptimal allocation through

mispricing of financial contracts and assets. The inefficient pricing is a result of in-

formational asymmetry between the financiers and the firms seeking to have their

projects financed.

The findings suggest that policies that aim to reduce uncertainty about the future

profitability of firms are suitable for addressing the financial market failures. Hence,

policies that clearly can be translated into an effect on future revenue streams for

the fossil fuel related businesses, as well as for the clean energy substitutes, will fare

better with respect to reducing the price inefficiencies, compared to those who leave

market participants in uncertainty.

In this chapter, I will first synthesise the main findings (Section 5.2). Then I will

discuss the benefits and drawbacks of the methods applied in the chapters (Section

5.3), and finally, provide an outlook for future research on the topic (Section 5.4).

139

Chapter 5 140

5.2 Main findings

In this section, I summarise the main findings of the three chapters and discuss their

implications for policies aiming to facilitate the green transition. Three aspects will

be included: first, the over-investment in fossil fuel capital, and under-investment

in mitigation efforts. Second, the implied cost of the transition, and third, the role of

uncertainty.

5.2.1 Suboptimal allocation

Financial market failures have the power to distort allocation of financial resources.

For the green transition, this means under-investment in mitigation and over-investment

in fossil fuel related capital.

Despite focusing on different aspects of the economic impact of financial market

failures, the three previous chapters all highlight the problem of allocation. Chapter

2 shows that financial market failures interact with financial openness in small open

economies, causing adverse effects on the allocation of capital: After the introduc-

tion of policies aimed at reducing carbon emissions, the capital stock of the fossil

fuel energy sector remains higher than it would in the frictionless setting, while the

investments in new clean energy stay lower. Chapter 3 shows that financial market

failures lower the project value of wind power plants, reducing the feasible level of

installed wind power capacity. In Chapter 4, fossil fuel firms can take advantage of

false beliefs of one group of investors and use buybacks to secure higher asset value,

i.e. over-investment causes inefficiently high asset prices.

5.2.2 The cost of the green transition

The suboptimal allocation of financial resources induced by financial market failures

has real consequences for the transition by increasing the costs.

Financial market failures drive up the cost of capital for green alternatives, which

means the marginal costs of substituting fossil fuel with clean alternatives increase

more than assumed under a fixed interest rate regime. As a result, financial market

failures will drive up the costs of the green transition.

This finding is discussed in Chapter 2 that presents the estimated welfare costs of

different policy schemes, with and without financial frictions. Financial frictions in-

crease the welfare costs. Because substitution with clean energy becomes expensive

under the presence of frictions, the frictions shift the mitigation from a reduction in

emission intensity to a down-scale of economic activity, which implies large welfare

losses for households.

In Chapter 3, welfare costs are not explicitly discussed, however, a similar issue

appears from the results. Under market-based remuneration of wind power plants,

Chapter 5 141

the carbon price has to be very high in order to support the political targets for in-

stalled renewable energy capacities. While the pass-through of the carbon price to

the revenues of the wind power plants is limited for high levels of wind capacity, the

pass-through of the carbon price to the consumer price remains relatively high. This

means that if the carbon price was high enough to sufficiently support the capacity

targets, the consumers are likely experiencing high costs of electricity. Faced with

large electricity costs, consumers may wish to scale down on consumption, which

could imply a loss of welfare. Even if the reduction is through efficiency, invest-

ment in efficiency would reduce the budget available for other consumption pur-

poses. While the problem of the pass-through exists even without financial market

failures, the failures exacerbate the problem by increasing the cost of capital, and

consequently, lowering wind power project values while pushing up the required

carbon price needed to support targets.

In Chapter 4, over-investment in fossil fuel assets implies a lower cost of capital

for the fossil fuel sector. Lower costs of capital render more projects feasible, and

as a result, we can expect more fossil fuel related projects to be undertaken, while

green alternatives may find it harder to compete. To counteract these effects, poli-

cies intended to reduce carbon emission need to send strong signals of the future

profitability, e.g. carbon prices have to be higher, with potentially greater distortive

effects on short-term welfare.

Hence, financial market frictions have implications for climate policy interven-

tions. These will be discussed in the next section.

5.2.3 Uncertainty

The risk associated with inventions and technological change is large at best and

completely unknown at worst, causing innovative projects to face higher cost of cap-

ital through higher premiums. Uncertainty is in itself not a source of market failure,

but the uncertainty needs to be priced correctly. Under perfect capital markets, pol-

icy interventions aimed to reduce uncertainty about the profitability of clean and

polluting firms would therefore appear inefficient and distortive, even if they were

a tool to effectively align the flow of funds with the targets of the green transition.

However, financial market failures distort the pricing of risk.

This finding appears from the three chapters in which uncertainty is a dominat-

ing theme. In Chapter 2 and 3 uncertainty about the future return on capital drives

the premium on debt, distorting the cost of capital and the allocation of funds. In

Chapter 4, uncertainty about future asset value is a precondition for firms to be

able to take advantage of buybacks and for some investors to maintain false beliefs.

Hence, it is through uncertainty, financial market failures cause over-investment in

fossil fuel related assets (Chapter 2 and 4) and under-investment in clean energy

(Chapter 2 and 3).

Chapter 5 142

Since the existence of uncertainty is the root of the problem of inefficient allo-

cation, climate policies that aim to reduce uncertainty are well-suited for overcom-

ing the issues of financial market failures. Because of financial market failures, risk-

reducing measures may be both effective and efficient. This finding supports the

arguments brought forward in related literature: Brunner et al. (2012) state that in-

vestors prefer long-term predictability of the policy. Battiston et al. (2021) argue that

for the financial sector to enable the green transition, the policy signal needs to be

credible in the perception of market players and investors. Likewise, a review study

by Polzin et al. (2019) finds that policies that effectively incentivise renewable energy

investments reduce the risk while increasing the return.

In Chapter 2 and 3 of this thesis, I focused on the use of carbon pricing as the

main policy instrument for guiding the green transition. While a carbon price in-

creases the market price of energy and hence lead to higher return on renewable

energy capital, it improves the risk-return profile only indirectly. Subsidies to re-

newable energy producers are clearly the most direct way of incentivising invest-

ment. Chapter 2 shows that combining the carbon tax policy with direct subsidies

may lead to significant short-term welfare gains compared to a stand-alone carbon

tax. Furthermore, as discussed in Chapter 3, feed-in tariffs can almost completely

remove uncertainty in the revenue stream of the wind power plants.

The results of this thesis show that policy commitment is a necessary — but not

sufficient — condition for the policy to effectively attract investment. The policy also

has to translate into an attractive risk-return profile of the clean energy. Removing

market risk of wind power reduces the impact of financial frictions, however, such

policy schemes imply that the market risk is borne by the government instead of

the market agent. Hence, consideration of risk-reducing policies opens a new set of

questions that are outside the scope of this thesis: For instance, how much of the

risk should the government take, and will the government be able to price the risk

correctly?

5.3 Method and models

Each of the chapters relies on modelling as a tool to investigate the topic. In this

section, I will discuss the limitations of the models.

5.3.1 Exclusion of other taxes

Chapter 2 presented a New-Keynesian DSGE model, developed to capture specific

characteristics of developing countries. The model included features that are stan-

dard in the New-Keynesian modelling framework including price rigidity, and fea-

tures that are standard in small open economy models, incl. a real exchange rate

and the covered interest parity condition. However, in addition, I included energy as

Chapter 5 143

an input to production, which is a feature known from environmental business-cycle

models. Finally, I also added financial market frictions.

The decision to include specific features in the modelling framework holds sig-

nificance, but equally crucial is the decision to exclude certain ones. For instance,

in the DSGE model presented in Chapter 2, all taxes besides the carbon tax, were

excluded. According to the ’double dividend hypothesis’, using the carbon tax rev-

enue to reduce distortionary taxes, such as income tax, could lead to overall positive

welfare effects. While the hypothesis has been contested (see e.g. Van Der Ploeg

2023) other distortionary taxes could have been included to get a broader idea of the

possible uses of the carbon tax revenue.

5.3.2 Whose frictions?

In Chapter 2 and Chapter 3 I used the costly state verification framework to model

financial frictions. In these chapters, the cost of capital and optimal leverage ra-

tio depend on the equity position of the firm. However, there is an alternative way

of modelling financial market failures through the costly state verification problem,

which is to let the restrictions in the lending be related to the balance sheet of the

financial intermediator, i.e. ‘the bank’, instead of the balance sheet of the firm (see

e.g. Gertler & Karadi 2011).

When the value of the assets of the bank decline, its equity position diminishes.

This increases the riskiness of the lending, and the bank needs to reduce the loan

quantities. This way of modelling financial market failures is often applied in the

literature on macro-financial instability, as presented in Chapter 1. Placing the con-

straint on the banks’ balance sheet implies that policies aiming to incentivise lend-

ing should address the equity position of the banks. Therefore, climate policies

should be supported by monetary policies or macro-prudential regulation in order

to address the climate-related risk that may lead to financial instability.

If — on the other hand — the financial market failure is related to the balance

sheet of the borrower, i.e. the firm, solid business models are important: Borrowing

becomes constrained because the risk of the firms’ return on capital does not sup-

port additional lending. This view implies that policies addressing financial market

failures should aim to resolve uncertainty about the borrower’s profitability, as ar-

gued in this thesis.

There is significant scientific debate about where the friction lies (see e.g. Mian

& Sufi (2015) who outline the different views and explore the role of household bor-

rowers in the financial crisis 2007-2009). I adopt in this thesis the view that it is the

risk of the borrower that drives the failures. This view is most clearly highlighted in

Chapter 2 and 3 where the costly state verification framework is applied to the bal-

ance sheet of the firm. However, also in Chapter 4 this view is employed: in Chapter

4, uncertainty about future profitability of the firm allow investors to form wrong

Chapter 5 144

beliefs about the future value.

The reason for the choice lies in the focus on the allocation of funds between

clean and dirty investments and the role of climate policies in driving the allocation.

The mechanisms and drivers behind macro-financial instability are out of scope of

this thesis.

5.3.3 Predicting the future

In terms of novelty, the neural network-based model presented in Chapter 3, is per-

haps the most prominent. The strength of the model lies in being based on real

market data. However, this may also be a weakness, as using empirical models for

forecasting has its drawbacks.

For forecasts to be accurate, observed distributions have to remain informative

of the future. Market developments may have significant impact on the ability of

past prices to reflect those of the future. For instance, new transmission capacities to

neighbouring regions or development of demand-side technologies could alter the

electricity market conditions. Hence, there is value in comparing the results with

outputs from other types of models, e.g. large scale energy system models used for

generating price distributions. An example is Jåstad et al. (2022), who study the dis-

tributions of return on renewable energy technologies in Norway in 2040.

While other methods for generating return distributions may lead to different

estimations of the cost of capital and the limit to market-based wind power invest-

ment, I expect that the core finding that market conditions affect the costs remains

valid. This is because the finding builds on the structure of the electricity supply

curve, which would appear from any energy systems model with hourly dispatch.

5.4 Outlook

In conclusion, the work presented in this thesis investigates the role of financial mar-

ket failures for the green transition under specific market mechanisms. The failures

are driven by an informational asymmetry between the agents financing mitigation

investments and fossil fuel assets, and the firms, who are undertaking the real in-

vestments. The failures lead to a distortion of the allocation of financial resources

and are magnified through uncertainty in the future profitability of the firms. This

implies that climate policies that effectively reduce emissions and secure the redirec-

tion of financial flows from fossil fuel to clean energy, reduce the uncertainty about

future revenue streams.

Despite the contributions of this thesis, there are still many aspects of financial

market failures and the green transition to be discovered. In the following sections, I

propose some directions for future research.

Chapter 5 145

Cost of capital

The cost of capital is crucial for many energy economic models that aim to pro-

vide estimates of the costs of various renewable energy options (Steffen 2020) and

optimal mitigation pathways (Lonergan et al. 2023). The private economic cost of

capital provides the rate at which the future returns on investment are discounted,

hence setting it correctly is crucial for accurate estimations. It is especially impor-

tant because renewable energy technology is more capital intensive than conven-

tional thermal technology, and hence, the cost of renewable energy and its optimal

deployment are sensitive to the cost of capital (Hirth & Steckel 2016). Likewise, I find

that the cost of capital is endogenous and depends both on the policy in place and

on the market microstructure of the financial market as well as the real markets in

which the firms operate. The results presented in this thesis indicate that more re-

search on the cost of capital is needed. To gain a better understanding, two types of

research are needed:

The first type is empirical research on past experiences in the energy sector. Stef-

fen & Waidelich (2022) review research on the drivers of the cost of capital and find

only a limited number of empirical studies aiming to quantify the effect of policy

intervention. Investigation of more technologies of different maturities, a broader

geographical coverage, and the role of market conditions is required for a compre-

hensive understanding of the financing conditions resulting from different mitiga-

tion strategies.

The second type includes using the findings of the empirical research to provide

a better energy modelling framework aiming at identifying optimal mitigation path-

ways or estimating the costs of the green transition. Preferably, the cost of capital

used in such models should be endogenised to account for market failures and the

impact of market conditions and remuneration policies. This, however, may prove

to be a challenge, because such considerations require introducing risk in models

that are already computationally heavy, making them even more difficult to solve.

Information and efficient pricing of risk

The results of the research presented in this thesis indicate that reducing informa-

tional asymmetry between firms and investors would lower the impact of financial

market failures and allow for more efficient pricing of transitional risk.

Mandatory and voluntary disclosure of exposure to climate-related risks can be

used to bridge the information gap between firms and investors. Ameli et al. (2021)

argue that disclosure is in itself not enough to drive the redirection of funds from fos-

sil fuel businesses to clean energy, because first, the time horizon considered when

making financial decisions is much shorter than those of the climate-related risks,

and second, the fossil fuel related assets are so different from those of renewable en-

ergy that they are not direct substitutes from the investor perspective. Nevertheless,

Chapter 5 146

climate risk disclosure is in demand among investors (Ilhan et al. 2023), but there

is no conclusive evidence of the impact of disclosure policies on the financial con-

ditions of the firms (Wang 2023). Further empirical research on the implication of

disclosure on the cost of capital as well as the effectiveness of disclosure policies to

redirect funds appear as viable directions for further research.

Decision heuristics

The financial market failures studied in Chapter 2-4 are based on theoretical frame-

works adapted from contract theory and portfolio choice theory. While such frame-

works may provide a tractable way of modelling decisions of economic agents under

the presence of financial market failures, real life investment decisions are cluttered

by behavioural biases and heuristics (Subrahmanyam 2007).

Thomä & Chenet (2017) point to additional sources of inefficient pricing of climate-

related risk, including bounded rationality and risk models that do not account for

fat-tailed return distributions. Quantification of the impact of such behavioural bi-

ases on allocation of capital is another potential direction for further research.

The efficient market hypothesis highlights the benefit of passive investments,

and indeed placing financial resources in index funds is a popular investment strat-

egy. While a body of literature on sustainable index funds is slowly emerging (see

e.g. Mercereau et al. 2019), the literature on the role of regular passive funds is so far

limited. Wilson & Caldecott (2023) suggest that future research could aim to analyse

the impact of passive funds on the cost of capital for fossil intensive firms and the

pricing of climate risk-exposed capital.

Crises and technological change

Finally, financial market failures provide micro-foundations for macro-financial in-

stability, however, the instability literature has so far focused on the risk related to

stranded assets. Technological change through disruptive innovation can also lead

to macro-financial instability through price bubbles related to the new technology.

However, this perspective has been largely ignored by researchers (Semieniuk et al.

2021). In principle, just like a sudden write-down of fossil fuel assets could cause in-

stability, an abrupt increase in green technology could as well. Combining theories

of financial frictions and technological change could offer insights on this topic.

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Appendix A

Statement of Contributions

Chapter 2: Financial Frictions and Climate Policy in an Open Econ-

omy: Promoting a low-cost Green Transition through Clean Energy

Investments

This paper builds on the paper of Hendrik Schuldt and Kai Lessmann, 2022. The

idea for an extension of the model was developed in cooperation. I designed the

new model features, including expanding the number of sectors, introducing a retail

sector and a central bank. I integrated the new model features into the model code.

Hendrik Schuldt did all calibration except of the climate policy and foreign borrow-

ing, which I did. I performed all model simulations and visualisation, and I lead the

efforts of interpreting the simulation results. The original draft of the literature re-

view and the calibration section were written by Kai Lessmann and Hendrik Schuldt,

respectively. In addition, Hendrik Schuldt wrote the Appendix 3. I wrote the original

draft of the remaining sections and lead the review and editing efforts.

Chapter 3: There’s no bad weather, only bad prices: Market-based

wind power investments under financial frictions

I carried out the entire work for this chapter.

Chapter 4: Share Buybacks and Investor Beliefs about Carbon Risk

The idea of this paper was developed in cooperation with Kai Lessmann. I carried

out the empirical study and lead the development of the analytical model. Kai Less-

mann wrote the original draft of Section 2, I wrote the remaining sections, and per-

formed the formal analysis, data curation, programming, and visualisation.

149