Time scales of the low-carbon transition: A data-driven dynamic multi-sector growth model

Codina, Oriol Vallès; Semmler, Willi Article Time scales of the low-carbon transition: A data-driven dynamic multi-sector growth model Journal of Economics and Statistics Provided in Cooperation with: De Gruyter Brill Suggested Citation: Codina, Oriol Vallès; Semmler, Willi (2024) : Time scales of the low-carbon transition: A data-driven dynamic multi-sector growth model, Journal of Economics and Statistics, ISSN 2366-049X, De Gruyter Oldenbourg, Berlin, Vol. 244, Iss. 3, pp. 169-200, https://doi.org/10.1515/jbnst-2023-0040 This Version is available at: https://hdl.handle.net/10419/333280 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. 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If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. https://creativecommons.org/licenses/by/4.0/ Oriol Vall` es Codina* and Willi Semmler Time Scales of the Low-Carbon Transition: A Data-Driven Dynamic Multi-Sector Growth Model https://doi.org/10.1515/jbnst-2023-0040 Received June 3, 2023; accepted January 10, 2024 Abstract: This paper employs a dynamic multi-sector growth model with changing technology to study the relevance of the price and quantity dimensions involved in the technical substitution of carbon-intensive technology, that is, the low-carbon transition. For the framing of the transition, the stylized market dynamics by Flaschel and Semmler (1987. “Classical and Neoclassical Competitive Adjustment Processes.”The Manchester School 55 (1): 13–37) are used, who propose a cross-dual out-of-equilibrium adjustment process. The major empirical challenge to identify the adjustment speed for quantities and prices is to empirically estimate sector-specific adjustment coefficients. The transition speed is estimated for seven carbon-intensive sectors in six high-income economies (Germany, France, Italy, Netherlands, Japan, and the US) using a mixed-effects varying-slopes model on EU KLEMS data. Directed technical change is enforced by a revenue-neutral, pro-active fiscal policy of a tax–subsidy form, which has the effect to greatly accelerate the phase-out of carbonintensive technology and the phase-in of green technology. The speed of green substitution that allows decarbonization is then evaluated analytically and computationally along four policy and time dimensions: cost advantage, a percentage tax on carbon-intensive output, a green subsidy rate, and initial investment ratios. Though the tax itself has an impact on the speed of decarbonization, it is significantly improved by green subsidies and green investments. The cost advantage of the green over the carbon technology is shown to have a negligible impact on decarbonization speed by itself. Without ambitious fiscal policy, especially in the form of green The authors thank the referees, Christian Proaño, Alfred Greiner, and Peter Winker, Duncan Foley, Mark Setterfield, Anwar Shaikh, and other colleagues at the New School and the UCL Institute for Innovation and Public Purpose, as well as the panel attendees of 25th Forum for Macroeconomics and Macroeconomic Policies and the 2021 Eastern Economic Conference, for their helpful comments and insights. *Corresponding author: Oriol Vall` es Codina, Department of Economics, University of Leeds, Leeds University Business School, Maurice Keyworth Building, Leeds, LS2 9JT, UK, E-mail: [email protected]. https://orcid.org/0000-0002-1361-8243 Willi Semmler, NewSchoolforSocialResearchDepartmentofEconomics,NewYork,NY,USA;andUniversity of Bielefeld, Universitätsstraße 25, Bielefeld D-33615, Germany, E-mail: [email protected] Journal of Economics and Statistics 2024; 244(3): 169–200 Open Access. © 2024 the author(s), published by De Gruyter. This work is licensed under the Creative Commons Attribution 4.0 International License. investment support, this substitution process appears to be too slow to reach decarbonization in a timely manner. Keywords: low-carbon transition; complex dynamical systems; cross-dual dynamics; structural change; fiscal policy; carbon pricing JEL Classification: C63; O25; O41; Q55 1 Introduction According to the latest landmark reports by the UN Intergovernmental Panel on Climate Change (IPCC), global net emissions must decrease by 45 per cent by 2030, requiring a formidable structural change of the economy toward decarbonization in order to avoid climate catastrophes in the form of increasingly extreme heatwaves, wildfires, droughts, flooding, mass extinctions of species, sea-level rises, and changes in the direction of oceanic currents. Consensus among economists favors carbon pricing, either as a tax or a cap-and-trade system, as the most cost-efficient policy instrument in order to curb emissions in line with the Paris Agreement of keeping world temperature rise by 2 °C. At the current moment, very few countries are pricing carbon emissions high enough to meet climate targets (UNEP 2020). As the scale and urgency of the climate crisis intensifies and becomes more evident, its actual effectiveness to curb emissions (as well as its social regressiveness) is perceived as too low in light of the empirical evidence available (Ball 2018; Green 2021; Lilliestam, Patt, and Bersalli 2021; Narassimhan et al. 2018; Teixidó, Verde, and Nicolli 2019; Tvinnereim and Mehling 2018; Rosenbloom et al. 2020). While many countries and jurisdictions have already adopted or are in the process of introducing various schemes of carbon pricing, exponential growth of carbon emissions has steadily kept apace without substantial changes, both nationally and internationally (Narassimhan et al. 2018; Pretis 2022). Last but not least, carbon prices required to effectively decarbonize in time may be so high that are politically unfeasible, especially for low-income countries and low-income households in high-income economies. In the face of potentially immense climate risks, the relevant policy issue may be then not so much of generic intertemporal costs versus benefits of mitigating climate change, as critically noted by Stern, Stiglitz, and others in recent contributions (Kattel et al. 2018; Stern 2022; Stern and Stiglitz 2021, 2022). Critics of the social-cost-of-carbon approach highlight that its estimates vary greatly due to a high sensitivity to model assumptions and parameters (especially concerning the discount rate and the uncertainty of future damages on the economy). Further, integrated assessment models lack transparency due to its large number of equations, uncertain parameters, and 170 O. Vall` es Codina and W. Semmler model parts. Much is still insufficiently understood (Pindyck 2013): in this context, considering the large uncertainties involved, intertemporal cost–benefit analyses may not give sufficient guidance. This paper contributes to the alternative targetconsistent approach, favored by Stern and Stiglitz, to address instead the pressing issue of how much time the structural transition from carbon to renewable energy may take and, most importantly, whether fiscal policy should focus on the technology side of market dynamics in order to speed up this process of technological substitution to meet the Paris Agreement targets in time –in particular, whether carbon pricing is enough for speeding up such a process or green investments are further needed. This paper also contributes to the endogenous-growth literature on directed technical change toward decarbonization where this question was also posed by Acemoglu et al. (2012, 2016), Golosov et al. (2014) and which generally supports tax– subsidy policy mixes, with subsidies targeting low-carbon R&D innovation. Instead of addressing technical change as either raising increasing the capital-to-labor ratio (i.e., capital deepening) or raising total factor productivity, our framework differs in modeling decarbonization as the dynamic substitution of carbon-intensive processes (such as fuel-based cars or fossil energy) by less carbon-intensive ones (such as electric cars or solar energy) within specific industries (such as automotive manufacturing or energy production) in an input–output setup. Our dynamical framework allows to explicitly capture the time dependency of such technical substitution on particular policy dimensions. Although some authors still consider carbon pricing as the only and most cost-efficient policy instrument available (Blum et al. 2019), others use the existing academic work and empirical evidence to call for amorediversified policy portfolio that also includes regulations, R&D subsidies, central-bank financial support, finance instruments, and public investments (Braga, Semmler, and Grass 2021; Carnevali et al. 2020; Jenkins et al. 2020; Semmler et al. 2021; Teixidó, Verde, and Nicolli 2019). While this paper finds some support for carbon pricing to accelerate the low-carbon transition in broad agreement with the literature, the effective carbon prices required to attain the Paris Agreement targets in time appear so high that they should be accompanied in particular by substantial publicly supported direct investment in green infrastructure and technology, as fiscal instruments and subsidies on the green transition show a multiplicative effect on the speed of the low-carbon transition. For the goal of evaluating the critical role of fiscal policy in accelerating the sectoral low-carbon transition, this paper employs an original computational method that re-purposes the classic theoretical literature in micro-economic adjustment processes (Hicks 1939, 1947; Flaschel 2010; Jorgenson 1960; Mas-Colell 1986; Morishima 1981) to build data-driven dynamical input–output models of multisector growth with green process innovation and fossil-fuel process extinction Low-Carbon Transition Time Scales 171 within specific industries (Flaschel and Semmler 1987, 1992). This literature explores the stability of competitive economies by considering its complex price-quantity dynamics out of equilibrium through specific sector-level adjustment processes in the form of stylized facts as dynamical laws of motion. Each of such adjustment processes underlying a stylized law of motion can be characterized by its corresponding sector-specific reaction coefficient, which, resembling state-of-the-art machine-learning approaches, can be empirically calibrated using real training data to yield a data-driven dynamical system (Brunton and Kutz 2022; Vall` es Codina 2023). In contrast to existing highly aggregated approaches like integrated assessment modeling, this novel, data-driven, sector-oriented method is highly transparent in its abstract simplicity: instead of the formulation of market dynamics by excess demand functions, the baseline cross-dual dynamics in prices and quantities rely on imbalances of supply and demand moving prices (the Walrasian law of excess demand) and differences between prices and costs (deviations in profitability) driving quantities (the classical law of excess profitability). While this dynamic process can also show asymptotic convergence to equilibrium as a rest state, cross-dual dynamics in its simplest form can generate complex oscillations of prices and quantities around their long-run equilibrium values. Keynesian dual short-run dynamics, which further stabilize classical oscillations, can also be explored (Vall` es Codina 2023): see Table 1 for a stylized illustration of the two types of dynamics. This paper focuses on cross-dual dynamics. By running a large number of simulations, our stylized, data-driven approach is able to rigorously assess the sensitivity of our results to the relevant parameters at play, in contrast to other methods that only focus on a limited number of parameter variations. Our theoretical framework provides a time scale and shows how fiscal policy and instruments speed up decarbonization of the economies as required by international agreements taking advantage of the complex, self-organizing dynamics of structural change of the market system. The paper is organized as follows. Section 2 describes the dynamical model of multi-sector growth. Section 3 analytically evaluates how fiscal policy impacts the Table :Classification of micro-economic adjustment processes (Morishima  and Goodwin ). Cross-dual Walrasian Law of Excess Demand If demand d i is above (below) supply x i , price p i rises (falls) Classical Law of Excess Profitability If price p i above (below) cost i ,aquantity x i rises (falls) Dual Oligopolistic Markup Pricing If price p i above (below) cost i , price p i falls (rises) Inventory Adjustment If demand d i is above (below) supply x i , quantity x i rises (falls) aIn this literature, “costs”include capital costs in the form of normal profits. 172 O. Vall` es Codina and W. Semmler profitability and growth differentials involved in the speed of decarbonization with respect to four relevant parameters: the carbon–green ratio in capital intensity, the carbon tax, the green subsidy, and the initial carbon–green ratio in investment. Once empirically calibrated with EU KLEMS and WIOD input–output data, Section 4 finally presents computer simulations of specific policy scenarios of the low-carbon transition, as well as a synthetic dataset of 14,250 observations for relevant ranges of the policy parameters, targeting seven specific target carbon-intensive sectors, “Electricity, gas, steam, and air conditioning supply”(D), “Manufacture of coke and refined petroleum products”(C19), and “Mining and Quarrying”(B), in five of the six high-income economies. Appendix B shows first an example for illustrative purposes of the dynamics of the model with seven-sector US 2003 input–output data and synthetic adjustment coefficients and then empirically extracts cross-dual adjustment coefficients for six high-income economies (Germany, France, Japan, Italy, Netherlands, and the US) using a mixed-effects model with varying slopes on EU KLEMS data. 2 A Multi-Sector Growth Model of the Low-Carbon Transition 2.1 Constant-Technology Cross-Dual Dynamics The pioneering work of Morishima (1981) and Goodwin (1983) contributed an early classification of microeconomic adjustment mechanisms (Table 1) and a thorough study of their dynamics, using Lyapunov functions and gradient processes, of particular impor-tance as it highlights the complex dynamical relation between microand macroeconomic adjustment processes (Flaschel et al. 1997). As Flaschel notes (1997), the first two adjustment processes are a description of a proportional autocontrol mechanism through cross-effects between prices and quantities, which Morishima identified as cross-dual dynamics (Morishima 1981). The Flaschel–Semmler cross-dual model of multi-sector growth under linear production (without fixed capital investment) 1 and constant technology describes complex price p i and quantity x i oscillations over time around the equilibrium values of Nprices p* (a row vector) and Nquantities x(a column vector) of the Sraffa–von 1Circulating capital on those models represents the use of intermediate goods in production. In the specific context of energy investments, the assumption of circulating capital is quite stringent; the existence of fixed capital and depreciation may impact the econometric estimation and simulations. This is addressed by works by Bródy as well as Flaschel and Semmler (Bródy 1970; Flaschel and Semmler 1986). Low-Carbon Transition Time Scales 173 Neumann system (Table 2) (Sraffa 1960; Von Neumann 1945). Production is linear, with matrix Aas inputs and matrix Bas outputs, with positive values. 2 By the Perron–Frobenius theorem, unique positive equilibrium values p* and x* solve for the positive gross rate of return or expansion rate R> 1. The expansion rate Ris the inverse of the unique largest positive real eigenvalue of the matrix of input– output coefficients A/B, equilibrium prices p* are its associated positive row eigenvector, and equilibrium output x* is the associated positive column eigenvector: p*B is the equilibrium unit revenue and Rp*Ais the equilibrium unit cost p*Ain relation to the expansion rate R(that is, costs including normal profits): 3 1+r*=R=pBx pAx (1) As in the Goodwin model of capital accumulation (1982), the coupled price and quantity oscillations of cross-dual dynamics are of the Lotka–Volterra predator–prey form, but in this, case profits (prices) play the role of the prey and profit-seeking investment (quantities) plays the role of the predator (Gandolfo 1971, ch. III.3). In the baseline model of cross-dual adjustment, industry market prices, relative quantities, and profitability gravitate around their equilibrium values, ultimately determined by the technological structure in line with the von Neumann–Sraffainput–output model (Sraffa1960;Von Neumann 1945). Normal growth, around which industry growth gravitates, is zero, focusing on out-of-equilibrium dynamics of relative prices and quantities. Following the law of excess demand, market prices pwill decline (rise) if supply Bx is greater (smaller) than demand: ˙ p p () T =−δp[B−RA]x=δp ⎡ ⎢ ⎣RAx ⏟⏞⏞⏟ demand −Bx ⏟⏞⏞⏟ supply ⎤ ⎥ ⎦(2) Table :Sraffa–von Neumann equilibrium (Sraffa; Von Neumann ). Equality of supply and demand Bx*=RAx* Uniform profitability p*B=Rp*A 2These matrices are “augmented”in the sense that they also incorporate labor supply and its price, the wage rate. While the general form of the matrix of outputs B captures joint production, the simpler case of single production is assumed in the remainder of this paper for convenience, so that B is the identity matrix. 3R, thus, can be considered the “maximum expansion rate”(see also Shaikh (2016)), associated to equilibrium profitability r* when wages are zero and there is no consumption from capital income, that is, all profit is re-invested. 174 O. Vall` es Codina and W. Semmler Following the law of excess profitability, quantity x i will rise (decline) if unit revenues pB are greater (smaller) than unit costs times R,RpA, since capital will flow out of the sectors with below-normal profitability into the sectors with above-normal profitability: ˙ x x=+δx[B−RA]TpT=δx[BTpT ⏟⏞⏞⏟ revenue −RATpT ⏟⏞⏞⏟ cost ](3) where ˙ x xis the column vector of the growth rates in relative quantities, ˙ p pis the row vector of the growth rates in relative prices, and δ p and δ x are diagonal matrices with Npositive adjustment coefficients (so they can also be understood as vectors). Cross-duality in its simplest form may give rise to dynamic stability, yet not necessarily the conventional “asymptotic”convergence to competitive economic equilibrium to the single-point rest state with uniform profitability across sectors of production (Flaschel and Semmler 1987). In contrast, cross-duality generally reflects the classical theme of dynamic gravitation as envisioned by the great classical economists (Adam Smith, David Ricardo, Karl Marx, and John Stuart Mill), that is, of ceaseless overand undershooting of sectoral prices, quantities, and profitability around their long-run equilibrium “natural values”as centers of gravity determined by Leontief linear technology (Dum´ enil and L´ evy 1987; Goodwin 1983; Sraffa 1960). 4 A stylized description of the classical industry cycle is as follows: if an industry shows above (below) profitability, profit-seeking firms flow in (out), raising (lowering) supply with respect to demand until the latter is above (below) the former, triggering an increase (decrease) in prices through the Walrasian mechanism to adjust the supply–demand imbalance, but also lowering (raising) industry profitability, closing the cycle, and starting anew. In contrast, the Keynesian tradition focuses instead on short-run dual dynamics (see Table 1), characterized by imperfect competition, oligopolistic markup pricesetting, and barriers to capital entry, while investment operates within a longer time scale (Morishima 1981; Semmler 1984). In the short run, oligopolistic firms set prices as markups over costs, while varying supply through inventories in response to demand conditions. Classical cross-dual dynamics can thus be considered unsatisfactory in the short run, suggesting dynamic adjustments without cross-effects between prices and quantities where price and quantity movements may even be independent of each other for a while, what Morishima termed “dual dynamics” (Flaschel et al. 1997; Morishima 1981). As an illustrative example of classical gravitation, constant-technology dynamics are simulated for the 2003 US direct requirements matrix with seven sectors 4See also Foley (2003); Shaikh (2016). Low-Carbon Transition Time Scales 175 (Figure 1). 5 The nature of the linear-response model can be appreciated in Figure 2, which shows the same stylized dynamics as a scatterplot in a two-dimensional plane. In this case, the xaxis refers to the imbalance in quantities and prices (as excess unit profits), and the yaxis corresponds to the change in prices and quantities, so that all observations for a specific industry will be located on a line with the slope of its corresponding adjustment coefficient. Such general systems of micro-economic adjustment processes can be re-purposed as highly stylized dynamic macroeconomic models of multi-sector Figure 1: Constant-technology dynamics for the 2003 US direct requirements matrix, seven sectors. Dashed horizontal lines indicate equilibrium values for profitability r*, prices p*, quantities x*, and aggregate growth g* = 0(as the model deals with relativeprices and quantities). Each coloredline refers to the time evolution of market prices, quantities, profitability, and growth for each of the seven sectors. Oscillations vary in amplitude and frequency depending on the adjustment parameters chosen. 5Parameters for the sample simulation are given in the Appendix A: the input–output (Table 4) and the synthetic adjustment parameters that are manually selected Table 6. Equilibrium values for prices, quantities, and the expansion rate are given in Table 5 of the Appendix A. 176 O. Vall` es Codina and W. Semmler carbon and green processes but also their initial output ratio σ 0 that corresponds to the initial investment in green technology. 3.2 Carbon Phase-Out/Green Phase-In with Tax–Subsidy Policy The target-consistent path approach for carbon pricing first imposes time targets for the duration of the low-carbon transition as given, established by policy-makers following the advice of the climate science. The welfare problem of the policy maker thus consists of finding the required policy set (τ,ρ,σ 0 ) given carbon phase-out time target t*, that is, a percentage carbon tax rate τon real carbon output xc, raising a tax revenue of τxc 10 is that is added to green investment xgat subsidy rate ρ, starting from initial investment ratio σ 0 ) to phase out carbon, σt/ σat target value  σwithin duration time t/t*, with associated carbon emissions  E: σ0+∫ t* 0 ˙ σt(τ,ρ)dt= σ(15) Taking advantage of the cross-dual adjustment dynamics, the policy maker employs the tax–subsidy mix to expand the profitability and growth differentials between the green and carbon processes. Instead of taxing carbon content as in carbon pricing, the tax levied is on the volume produced by the carbon-intensive process, as in Mittnik and Semmler (2022). Green and carbon outputs using the tax–subsidy mix (where the hat notation distinguishes the variable with and without policy) thus becomes:  xc t=xc t−τxc t=xc t(1−τ)  xg t=xg t+ρτxc t=xc t(σt+τρ) Output proportion with tax–subsidy policy τ,ρbecomes:  σt= xg t  xc t =σt+τρ 1−τ(16) Profitability for the carbon and green sectors internalizes the tax–subsidy policy: 1+ rc t=pc txc t(1−τ) κc txc t =1+rc t () (1−τ)(17) 1+ rg t=pc txc t(σt+τρ) θκc txc tσt =1+rc t () 1+τρ σt θ(18) 10 The relation between the tax on carbon output τand carbon price πis τ=επ pc. Low-Carbon Transition Time Scales 183 While the negative contribution of tax τis linear on the carbon sector, its positive effects on green profitability depend on the fraction τρ σt, i.e., they are the largest when carbon output is much larger than greenoutput (σ t ∼0), that is, at the beginning of the introduction of the policy, and they are multiplied by cost advantage θ. The profitability differential once the policy is introduced can be then computed in terms of cost advantage θ, output proportion σ t , and tax rate τ: 1+ rc t 1+ rg t =σtθ(1−τ) σt+τρ =θ(1−τ) 1+τρ σt (19) which shows how a tax–subsidy policy can reinforce cost-induced profitability and growth differentials (when θ< 1) or even offset them (when θ> 1). Growth rate differential with policy τ,ρwith and without policy can be compared: 1+ gg t 1+ gc t =1+gg t 1+gc t +τρ σt [] 1 1−τ(20) Onceagain,theadditivepresenceoftheratioτρ σtshows that the policy to direct technical change toward decarbonization is the most effective at the earliest stages of the phase-in (i.e., σ t ∼0) when the subsidy rate is nonzero. This result, confirmed by the simulations, shows the relevance of green subsidies (ρ> 0) in kickstarting and mobilizing private funds for decarbonizing the economy, in line with recent studies (Deleidi, Mazzucato, and Semieniuk 2020; Heine et al. 2019; Semmler et al. 2021). However, a tax rate τon real output alone can already accelerate substantially the phase-out of the carbon sector without any green subsidies ρ= 0, even if green cost advantage is lower (θ>1),although there is no guarantee decarbonization may occur in time to achieve the UN IPCC targets. 4 Simulation Results 4.1 Specific Policy Scenarios of the Low-Carbon Transition The simulations can be conceived as a computational, stylized “thought experiment” to identify what are the policy dimensions most relevant in the domain of the lowcarbon transition, that is, whether carbon prices or green investment. Simulations study the phase-out of the carbon process and phase-in of the green process within particular carbon-intensive industries by time t*, of relative capital intensities θ, under a carbon tax rate τ, a green subsidy rate ρ, and initial investment ratio σ 0 . The specific carbon-intensive industries targeted for substitution are “Manufacture of coke and refined petroleum products”(C19), “Electricity, gas, steam, and air conditioning supply”(D), and “Mining and Quarrying”(B), which feature positive adjustment coefficients for seven sectors in five of the selected countries: Germany, 184 O. Vall` es Codina and W. Semmler France, Italy, Japan, and the Netherlands. Apart from this one-offprocess of substitution, no other forms of technological change occur as the growth model operates on constant technology. 11 At the current moment, green energy is increasingly outcompeting carbon energy: the cost of green energy can be considered to be between 0.7 and 1.1 times the cost of carbon energy –this is the range of values chosen for θ, which can also be thought to internalize a carbon price (IRENA 2020). For OECD economies, the current share of final energy consumption in renewable sources over carbon sources is around 5 % (Upadhyaya 2010), which is the benchmark value that is taken for the initial output ratio σ 0 in the simulations, which can also be increased by the issuance of green bonds. For simplicity, target carbon–green output ratio is  σ=1, which implies that the low-carbon transition is successfully achieved when green output is equal to carbon-intensive output. Each timestep can be considered as one year, given the time dimension included in the adjustment coefficients, which were computed from yearly data. Specific simulations of the low-carbon transition for particular policy scenarios under different chosen parameters in order to obtain a first qualitative, stylized comparison of their impact on carbon phase-out and green phase-in. For each of the selected policy scenarios and target industries, Figure 3 shows the time of carbon phase-out and green phase-in, i.e., the duration of the low-carbon transition when target output ratio is 1, highlighting that, although a percentage tax on carbonintensive volumes substantially accelerates decarbonization, it should be accompanied by green investment in order to effectively meet the 2018 UN IPCC targets, as carbon taxes alone may be too high to be politically feasible. While the flagship UN Emissions Gap Report of 2021 recently urged the pledging nations to halve carbon emissions in the next 8 years, the simulation results are compared with slightly less drastic duration targets for decarbonization of the 2018 UN IPCC report of 2018 (Masson-Delmotte et al. 2018): 16 years for a 66 % chance of avoiding a temperature increase of 1.5 °C, 23 years for a 50 % chance of avoiding a temperature increase of 1.5 °C, 51 years for a 66 % chance of avoiding a temperature increase of 2 °C, and 65 years for a 50 % chance of avoiding a temperature increase of 2°C Each row of Figures 4–7 shows the simulated trajectories of prices, quantities, profitability, and growth rates for all industries (the full list of industries is given in 11 As investment has the effect of increasing labor and capital productivity over time, the constanttechnology assumption is obviously very strong in the long run: in this sense, the simulation results should be understood more qualitatively than quantitatively, as they only aim to answer how policy can speed up carbon phase-out in time, in particular, whether only carbon pricing will be enough to curb emissions in time or instead more ambitious fiscal policy is required. Low-Carbon Transition Time Scales 185 Figure 5: Scenario simulation of the low-carbon transition: only carbon pricing. Despite an extreme carbon price (θ= 0.1), carbon pricing alone is not able to successfully increase the profitability differential of the green process enough to speed up the substitution process even below 150 years. The vertical dashed line indicates the moment where the green process takes over the carbon process, i.e.,  σ=1. Figure 4: Scenario simulation of the low-carbon transition: no policy. Driven by lower production costs alone, profitability and growth differentials are not large enough to decarbonize in a hundred years. The vertical dashed line indicates the moment where the green process takes over the carbon process, i.e.,  σ=1. 186 O. Vall` es Codina and W. Semmler Figure 7: Scenario simulation of the low-carbon transition: tax–subsidy mix. Only a combination of carbon taxes and green subsidies can accelerate decarbonization to reach UN IPCC targets in time. The vertical dashed line indicates the moment where the green process takes over the carbon process, i.e.,  σ=1. Figure 6: Scenario simulation of the low-carbon transition: only percentage carbon tax. A percentage carbon tax directly impacts growth (rather than profitability), speeding up decarbonization closer to, but still far from, UN IPCC targets. The vertical dashed line indicates the moment where the green process takes over the carbon process, i.e.,  σ=1. Low-Carbon Transition Time Scales 187 Table 7 in Appendix C). Each column corresponds to a different industry under decarbonization, where the carbon-intensive and the green processes are highlighted with less alpha transparency and larger width in red and green than the other industries, respectively. The vertical dashed line indicates the moment where the output of the green process overtakes the output of the carbon-intensive process. As they share the same price, the trajectory of the price of the carbon-intensive process is identical to the green one. However, it is the two bottom rows, showing the industry trajectories of profitability and growth rates, which are the most informative, as they highlight the differentials between the carbon and green processes regulated by fiscal policy that make decarbonization feasible: while the profitability differential is regulated by the cost advantage parameter θ(on which carbon pricing operates), the tax–subsidy scheme operates over the growth rate differential, progressively increasing it from scenario 2 to scenario 4. The specific scenarios are the following: 1. No policy (Figure 4), with a very high initial investment ratio of 25 % and very high cost advantage for the green process (θ= 0.7). Although this is a very favorable scenario for a fast technical substitution in absence of policy, profitability and growth differentials are not large enough as induced by lower production costs alone so that the fastest green phase-in takes place in around 250 years, for German mining and quarrying. For three industries, decarbonization time exceeds the maximum time of 500 years. 2. Only carbon pricing (Figure 5), with carbon pricing inducing an extremely high cost advantage for the green process (θ= 0.1), an initial investment ratio in line with the current empirical evidence. Even with an extreme carbon price, carbon pricing alone is not able to successfully increase the profitability differential of the green process enough to speed up the substitution process even below 150 years for any of the studied industries and below 500 years for Italian Mining and Quarrying and Japanese Electricity Production. 3. Only percentage carbon tax (Figure 6), with a 2.5 % percentage tax on carbonintensive output, an initial investment ratio in line with the current empirical evidence, and similar cost advantage θ= 0.9. By directly impacting growth rather than profitability, the substitution process substantially speeds up to bring decarbonization in around 100 years, which is still considerably beyond the Paris Agreement targets. 4. Tax–subsidy mix (Figure 7), with a 2.5 % percentage tax on carbon-intensive output and 50 % subsidy rate, an initial investment ratio in line with the current empirical evidence, and similar cost advantage θ= 0.9. By using only half of the tax revenue raised from taxing carbon-intensive output (ρ= 0.5), decarbonization time finally falls within the 2018 UN IPCC targets, showing the multiplicative effect of green investment to accelerate decarbonization. 188 O. Vall` es Codina and W. Semmler 4.2 General Role of Fiscal Policy Parameters in Accelerating the Low-Carbon Transition While the simulation results of the former section already highlight that it is more convenient to use fiscal policy to impact on growth directly rather than profitability, a more systematic computational analysis of the policy space can be conducted using the empirically calibrated growth model to complement the comparative-statics analysis of Section 3. In this section, 14,250 simulations are computed for specific ranges of the four policy parameters at stake in order to investigate how the duration of decarbonization t* depends on them: the range for relative cost advantage θis (0.7, 1.1), the range for the percentage tax rate τis (0, 0.24) (i.e., the share of carbonintensive volume that is taxed), the range for the green subsidy rate ρis (0, 1), and the range for the initial output ratio is (0.1, 0.25). The industries studied are “Manufacture of coke and refined petroleum products”(C19) for Germany, France, Italy, and Netherlands, and “Electricity, gas, steam and air conditioning supply”(D) for Japan. Table 3 shows the regression results of the dependence of decarbonization speed on the four policy parameters as regressors, which is highly significant for all of them and with a very high R2value. In this context, the regression slopes for each policy parameter correspond to the magnitude of their impact on decarbonization speed: the percentage tax on carbon-intensive output bears the largest impact on speed, around 10 times higher than the subsidy rate (which is expected, as ρmultiplies τin the model) and the initial output ratio. Since the latter have very different upper thresholds, respectively, 1 and 0.25, green subsidies are thus expected to bear a four-time impact on the speed of decarbonization compared to the initial output ratio. Most strikingly, Table :OLS regression results for decarbonization speed /t* with respect to the four policy parameters: initial investment ratio σ  , cost advantage θ, tax rate τ, and subsidy rate ρ. Dependent variable Independent variable Constant σ  θτρ Speed /t*.*** −.*** .*** .*** −.*** (.)(.)(.)(.)(.) Observations , Residual std. error . (df = ) R. Fstatistic ,.*** (df = ;) Adjusted R. Note: *p<.;**p<.; ***p<.. Low-Carbon Transition Time Scales 189 the impact of cost advantage θis almost negligible, casting severe doubt on the feasibility of carbon pricing alone as an effective tool to decarbonize in time. Following these results, the most effective fiscal strategy would dispense with making firms internalize carbon prices in production and focus instead on a high percentage tax rate on real carbon-intensive output (as in sales), accompanied by substantial green investment, both in the form of a single large initial investment σ 0 and green subsidies ρ. Keynesian dual dynamics addressing mark-up pricing can be used to properly assess to what extent firms pass on the carbon tax to customers. For the illustrative sake of clarity, Figure 8 shows the dependence of decarbonization speed 1/t* (i.e., the inverse of the duration of decarbonization time) for a Figure 8: Impact of parameters on decarbonization speed for sector C19, Germany, for many values of the tax rate. When the tax rate is the dependent variable, the different lines correspond to different values of the subsidy rate. Horizontal dashed lines correspond to the necessary speed to meet the IPCC targets. 190 O. Vall` es Codina and W. Semmler specific sector (C19, Germany) with respect to each parameter, for different values of the tax rate. In agreement with the regression results, the figure shows a very robust linear dependence of decarbonization speed on the tax rate τ. The relationship between speed and subsidy rate ρis more complex, indicating a multiplicative interaction with the tax rate: linear at low tax rates and logarithmic at high tax rates, showing that green subsidies are most effective when carbon taxes are the highest. In contrast, cost advantage θand initial investment ratios have negligible impacts on decarbonization speed within their respective domains. The impact of carbon pricing on decarbonization speed is relevant only if carbon prices are so high that θis closer to zero. For instance, the top-left panel shows that, for a cost advantage θ= 0.8 and an initial output ratio of σ 0 = 0.05, a very high tax rate of τ= 0.22 = 22 % decarbonizes sector C19 within an IPCC target of 23 years for any subsidy rate, even with ρ= 0. If all carbon tax revenues are instead re-invested as green subsidies (ρ= 1), then decarbonization within the same 23 years can already be achieved with half of the tax rate, τ= 0.11. For any subsidy rate from 0 to 100 %, a tax rate of τ= 0.05 decarbonizes sector C19 within a substantially higher IPCC target time of 51 years. Many current state policy guidelines aim at decarbonizing by 2050; this would require a tax rate on real output (as in sales) between 0.06 and 0.16, depending on the subsidy rate. 5 Conclusions The transition speed toward a low-carbon economy has become a critical issue due to the increase in intensity and severity of extreme weather events in the form of increasingly severe heatwaves, wildfires, droughts, flooding, mass extinctions of species, sea-level rises, or changes in the direction of oceanic currents. Current consensus among economists considers that the market failure of climate change needs to be addressed through a rigorous analysis of the costs and benefits of climatechangemitigation.However,thetraditional theoretical frameworks (Kattel et al. 2018; Stern 2022; Stern and Stiglitz 2022) and the associated policy of carbon pricing, either as taxation or a cap-and-trade system, need complementary measures to be able to speedily resolve the “grand challenge”of climate change society faces today in the face of the potentially immense risk of climate catastrophes: If those risks are very large due to tipping points and sudden changes, a proper cost– benefit analysis with adequate discounting of future damages is very hard to undertake. Hence, this paper follows the target-consistent price path approach, which starts first from decarbonization targets as given by climate scientists and policymakers and then proceeds to compute the appropriate set of policies to achieve them. In agreement with recent contributions (Acemoglu et al. 2016; Braga, Low-Carbon Transition Time Scales 191 Semmler, and Grass 2021; Deleidi, Mazzucato, and Semieniuk 2020; Heine et al. 2019; Jenkins et al. 2020; Semmler et al. 2021; Nyambuu and Semmler 2023), this paper shows how global aggregate carbon pricing alone, although cost-efficient, is not effective enough to curb emissions in time: carbon pricing urgently needs to be accompanied by a myriad other sector-oriented fiscal policies such as setting standards through regulations, R&D subsidies, central-bank financial support in the form of green finance, and, most especially, public investment on climateoriented infrastructure and clean energy development and deployment. As to the role of the private sector, by adjusting sectoral profitability and growth differentials of carbon phase-out/green phase-in using carbon pricing and, most importantly, green investment subsidies, this paper clearly shows how fiscal policies can take advantage of the complex, self-organizing, and out-of-equilibrium dynamics of the market system: by regulating multi-sector growth in balance with the ecosystem, fiscal policy can accelerate decarbonization within specificcarbonintensive sectors to support the Paris Agreement targets. The results of the paper highlight the feasibility of fiscal policy to accelerate structural change within specific carbon-intensive industries toward the low-carbon transition and thus stabilize economic-ecosystem interactions in a timely manner. Target-consistent fiscal policies are evaluated analytically and computationally following an original empirically calibrated macroeconomic model of multi-sector growth and technical process substitution that re-purposes the classic literature on micro-economic adjustment processes to focus on the dynamic stability of competitive economic equilibrium (Fisher 2013; Flaschel 2010; Hahn 1982; Hicks 1939, 1947; Jorgenson 1960; Mas-Colell 1986; Morishima 1981). Much of this work, based on set theory, duality, and choice of technique literature in the tradition of disequilibrium theory, is mostly forgotten in the current literature on equilibrium dynamics. In this literature, the stability of the economic system is explored by considering specific adjustment processes out of equilibrium, characterized by particular reaction coefficients in the form of stylized facts as dynamical sectoral laws of motion that can be empirically calibrated. Furthermore, in contrast to aggregate approaches like integrated assessment modeling, our stylized methodology of market adjustmentprocessesishighly transparent and practical for policy purposes. Resembling state-of-the-art supervised machine-learning models, the linear adjustment coefficients of the datadriven dynamical model can be empirically calibrated with real data using a hierarchical mixed-effects linear model with varying slopes on EU KLEMS datasets, although other functional forms can be attempted in more sophisticated fashion, such as the logistic function. By running a large number of simulations, our stylized, data-driven approach is able to rigorously assess the sensitivity of our results to the relevant parameters at play, in contrast to existing methods that only 192 O. Vall` es Codina and W. Semmler Response to the Threat of Climate Change, Sustainable Development, and Efforts to Eradicate Poverty. Cambridge: Cambridge University Press. Miller, R. E., and P. D. 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