Internal debt and welfare [original]

Received: 8 February 2021

Accepted: 22 December 2021

DOI: 10.1111/jpet.12567

ORIGINAL ARTICLE

Internal debt and welfare

Zarko Y. Kalamov

School of Economics and Management,

University of Technology Berlin, Berlin,

Germany

Correspondence

Zarko Y. Kalamov, School of Economics

and Management, University of

Technology Berlin, Straße des 17. Juni

135, 10623 Berlin, Germany.

Email: [email protected]

Abstract

This paper analyzes how multinational firms' internal

debt financing affects high‐tax countries. It uses a dy-

namic small open economy model and takes into account

that internal debt impacts both the multinational firms'

investment decisions and the government's tax policy.

The government has incentives to redistribute income

from firm owners to workers. If the government's redis-

tributive motive is not too strong, internal debt reduces

welfare in the short term by decreasing tax revenues.

However, debt financing stimulates capital accumulation

and exerts a positive long‐term welfare impact.

1|INTRODUCTION

Multinational enterprises (MNEs) shift a large proportion of their profits to tax havens. In 2015

more than $600 billion, or 36% of multinationals' worldwide profits, were shifted (Tørsløv et al.,

2018). Internal debt serves as one of the main channels of international tax planning and

accounts for 25%–30% of the shifted profits (Beer et al., 2020; Heckemeyer & Overesch, 2017).

Hence, in its initiative on base erosion and profit shifting, the OECD calls for, inter alia,

measures to address base erosion through internal debt (OECD, 2013,2015). Moreover, the

number of countries applying thin‐capitalization rules (TCRs; i.e., rules that limit interest

deductibility) increases over time (Merlo & Wamser, 2015).

Here, I analyze the welfare effects of internal debt in the short and long run. I show that

these effects are not necessarily negative. Furthermore, they may be nonmonotone, with ne-

gative short‐and positive long‐term welfare implications.

J Public Econ Theory. 2023;25:196–224.196

wileyonlinelibrary.com/journal/jpet

This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and

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From 1996 to 2012, the number of countries applying TCRs increases from 24 to 61 (Merlo & Wamser, 2015). Also,

21 countries made the rules stricter, and only six countries relaxed them.

This paper builds a dynamic small open economy model. There is one high‐tax (nonhaven

or host) country that hosts a national firm and a subsidiary of a foreign‐owned MNE. Workers

supply labor that is perfectly mobile between the national and multinational sectors. The MNE

invests mobile capital in the host country, and capital adjustment is subject to installation costs.

Because of installation, it takes time for new investment to augment the firm's capital stock.

The MNE's headquarters can channel equity financing to its subsidiary as internal debt through

a financial center located in a tax haven. The host country government uses a TCR to restrict

such behavior. Moreover, it chooses a time‐invariant corporate tax rate and redistributes in-

come from firm owners to workers.

First, I study the short‐and long‐term welfare implications of allowing for some internal

debt use. The short term differs from the long term because installation of new investment

prohibits the MNE from adjusting its capital stock immediately. The results are, in general,

ambiguous. However, if the government's redistributive motive is sufficiently weak, welfare

declines unambiguously in the short term and increases in the long term. The intuition is the

following. A TCR relaxation stimulates profit shifting and lowers the MNE's cost of capital for

a given statutory tax rate. The increase in profit shifting reduces the tax revenues directly,

while the cost of capital effect stimulates investment and may increase the optimal tax rate. In

the short term, the capital stock adjusts slowly because new capital installation takes time.

Hence, welfare declines if the change in the optimal tax rate cannot compensate for the loss of

tax revenues (which is the case for a sufficiently weak redistributive motive). In the long

term, capital accumulates, which increases welfare to a level that is ultimately higher than its

initial level.

Second, I analyze the optimal internal debt restriction as well as the timing of its benefits

and costs. Similarly to the case of a TCR relaxation, the optimal TCR balances short‐term

marginal costs and long‐term marginal benefits.

Furthermore, a numerical simulation of the model looks at the welfare effects of increasing

the TCR from zero to its optimal level. It shows that the negative short‐term effects may be

long‐lived. Moreover, when the government has strong redistributive motives, the numerical

analysis finds positive short‐and negative long‐term welfare changes. This case emerges when

the optimal tax rate increases strongly following the reform and the long‐term capital stock

declines.

Nonmonotone welfare effects emerge due to the dynamic nature of the MNEs' responses to

TCR reforms, which is supported by the empirical literature. Weichenrieder and

Windischbauer (2008) and Buslei and Simmler (2012) analyze the short‐term effects of two

reforms in Germany from 2001 and 2008, respectively. Weichenrieder and Windischbauer

(2008) look at the impact on the capital stock of subsidiaries of foreign‐owned MNEs in

Germany 2 years after the 2001 reform, while Buslei and Simmler (2012) analyze investment of

the same type of firms 1 year after the 2008 reform. Both papers do not identify any significant

effects on the capital stock and investment, respectively. Moreover, Harju et al. (2017) measure

the real effects of a 2014 TCR reform in Finland through its impact on output in the 2 years

following the reform. They do not find any significant effects.

However, in accordance with my results, the empirical literature finds significant long‐term

real effects of debt financing. Buettner et al. (2008) analyze the long‐term impact of TCR on

investment using a panel data set of German multinationals' affiliates in 36 countries. They find

statistically and economically significant adverse effects of both the implementation and

tightening of TCRs. Moreover, Buettner et al. (2018) find significant negative long‐term impacts

of TCRs on the MNEs' capital stock and the capital stock's tax rate sensitivity in high‐tax

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197

countries. In addition, De Mooij and Liu (2018) use panel data of MNEs operating in

34 countries over 2006–2014. They find that a TCR introduction doubles the tax rate sensitivity

of investment. Furthermore, Blouin et al. (2014) show that TCRs imposed on affiliates of US

MNEs lower the overall firm valuation as measured by Tobin's

. Because Tobin's

is a good

predictor of investment (Erickson & Whited, 2000; Philippon, 2009), the results of Blouin et al.

(2014) also suggest a long‐term impact of TCR on investment. Furthermore, Suárez Serrato

(2019) studies the long‐term real effects of elimination of tax haven use by US multinationals

and finds negative investment and employment effects. While Suárez Serrato (2019) cannot

distinguish between different profit‐shifting channels, his results are consistent with this pa-

per's predictions.

Therefore, my results highlight the importance of the timing of policy reforms' empirical

evaluation. For example, a long‐run analysis of the reforms analyzed by Weichenrieder and

Windischbauer (2008), Buslei and Simmler (2012), and Harju et al. (2017) might produce

different outcomes.

Furthermore, the paper's results have the following policy implications. Consider, for ex-

ample, a reform that restricts the TCR in a country. The reform is likely to raise tax revenues in

the short term at the cost of adverse long‐term investment effects. Hence, policymakers may

need to complement such reforms with other measures that stimulate investment. Moreover,

the observed growth in the use of TCRs (Merlo & Wamser, 2015) may be attributed to pol-

icymakers maximizing short‐term objectives. This may happen owing to political economy

reasons. Foremny and Riedel (2014) find evidence that local business taxes' growth significantly

slows in election years and significantly increases in the year after an election. A possible

explanation of the results is that shortly before (after) an election, policymakers care more (less)

about reelection and are more (less) likely to put a higher weight on their policy's short‐run

impact. This paper's results suggest that TCR policies may also involve a conflict between the

short and long term. Hence, if political economy considerations affect the choice of corporate

taxes, they may also impact the setting of TCRs.

Moreover, this paper contributes to the theoretical literature on the welfare implications of

internal debt, which finds conflicting results. The two seminal papers are by Hong and Smart

(2010) and Haufler and Runkel (2012) and both studies consider static models. First, Hong and

Smart (2010) find that (some) internal debt is unambiguously welfare‐improving for a small

open high‐tax country. I show that the results of the static model of Hong and Smart (2010)

hold in the long term but might be reversed in the short term. Second, Haufler and Runkel

(2012) find in a two‐country model with a fixed capital supply and no redistributive motive by

the government that zero internal debt is optimal (from the social planner's perspective).

my model, the short‐term capital stock is fixed due to its adjustment costs. In the absence of a

strong redistributive motive, welfare is decreasing in internal debt in the short term. Thus, the

Haufler and Runkel (2012) result also holds in the short term of a one‐country model with

elastic capital supply.

Additionally, the paper examines two extensions of the model. The first extension considers

a time‐varying statutory tax rate and shows that all results remain qualitatively unchanged. The

second extension endogenizes the domestic firm's capital stock, which is shown to be declining

in the TCR. The reason is that, by stimulating investment by the MNE, internal debt exerts a

Haufler and Runkel (2012) also find that local governments choose to allow for debt financing. However, this is a

race‐to‐the‐bottom result. Thus, debt financing makes each country worse‐off.

198

KALAMOV

positive effect on wages, and hence lowers both labor and capital demand in the domestic

sector. While this extension is analytically intractable, numerical analysis shows that the long‐

term welfare effects of TCR relaxation may be negative (owing to its negative impact on

domestic capital).

This paper is related to the literature on the implications of profit shifting for nonhaven

countries' welfare. All in all, there is no consensus on whether tax havens are good or bad. On

the one hand, eliminating tax havens is beneficial to nonhaven countries if it improves public

good provision (Haufler & Runkel, 2012; Slemrod & Wilson, 2009) or if it removes the secrecy

of firm ownership (Weichenrieder & Xu, 2019). On the other hand, eliminating tax havens may

have an ambiguous impact on nonhavens' welfare if it intensifies the tax competition among

the high‐tax countries (Johannesen, 2010) or if it is only partial and lowers competition among

the remaining havens (Elsayyad & Konrad, 2012). Some profit shifting may benefit high‐tax

countries if it raises the optimal tax rates of low‐tax jurisdictions (J. Becker & Fuest, 2012).

Moreover, international tax planning may be good for nonhavens if MNEs' organizational form

responds to tax discrimination (Bucovetsky & Haufler, 2008), if governments respond to tax

planning by changing their tax enforcement strategies (Chu, 2014), or in the presence of

lobbying by the owners of immobile capital (Chu et al., 2015). Peralta et al. (2006) find possible

beneficial welfare effects of profit shifting among nonhaven countries when the MNE also

chooses the location of its productive subsidiary. Choi et al. (2020) find that some profit shifting

may mitigate inefficiencies of MNE production and thus benefit consumers in high‐tax

countries.

This paper differs from the remaining literature by developing a dynamic model that dif-

ferentiates between the short‐and long‐term effects of profit shifting. It is also the first to derive

nonmonotone welfare effects of profit shifting.

Moreover, closely related are Gresik et al. (2015,2020) who analyze, in a static model, the

interrelation of internal debt and transfer pricing. They analyze the case where transfer price

manipulation is so aggressive that it eliminates the benefits of Foreign Direct Investment (FDI).

In such cases, setting a restrictive TCR is the optimal policy that discourages MNEs from

investing in the country.

This paper is also related to the literature on dynamic tax competition. Wildasin (2003)is

the first to show that the government of a dynamic small open economy chooses a positive

time‐invariant tax on capital, while Wildasin (2011) extends the analysis to two mobile factors

of production. Moreover, Wildasin (2003) shows that mobile capital taxation may benefit im-

mobile factors of production in the short run even if it is harmful in the long run. Thus, he

derives nonmonotone welfare effects of capital taxation. This paper extends the seminal

Wildasin (2003) framework to study profit shifting. By doing so, I show that profit shifting may

also exert similar nonmonotone effects.

Finally, this paper is related to the recent literature that studies the real effects of profit

shifting. Suárez Serrato (2019) finds that eliminating profit shifting to tax havens lowers in-

vestment, employment, and wages of affected US multinationals with negative spillover effects

to other firms. Alvarez‐Martinez et al. (2018) find profit shifting to have positive effects on

Furthermore, Desai et al. (2006a) find empirical evidence that high‐growth firms are more likely to operate in tax

havens. Desai et al. (2006b) explain this result theoretically in a model, where tax haven use raises the return on

investment.

Additionally, this literature analyzes the interaction between tax competition and economic growth (see, e.g.,

D. Becker & Rauscher, 2013; Köthenbürger & Lockwood, 2010).

KALAMOV

199

investment and gross domestic product (GDP) in the European Union (EU), the United States,

and Japan (these effects are, however, insufficient to compensate for the loss in tax revenues).

Buettner et al. (2008,2018) and De Mooij and Liu (2018) find negative effects of internal debt

restrictions on investment by MNEs' subsidiaries, while De Mooij and Liu (2020) find similar

effects for restrictions on transfer price manipulation. Klemm and Liu (2019) show that profit

shifting may stimulate investment in both high‐and low‐tax countries. The present paper

contributes to this literature by linking the real effects of profit shifting to welfare in the short

and long term.

The rest of the paper is structured as follows. Section 2presents the model. Sections 3and 4

derive the optimal tax policy and the welfare effects of internal debt, respectively. Section 5

presents the extensions, and Section 6concludes.

2|THE MODEL

I consider a dynamic model of a small open high‐tax country akin to the static framework of

Hong and Smart (2010). There are two types of infinitely lived agents in the economy: workers

and a representative entrepreneur. The economy produces a single homogeneous good in

two firms (sectors): a domestic firm owned by the entrepreneur and a foreign‐owned subsidiary

of a multinational firm. Workers supply one unit of labor, which is fully mobile between the

national and multinational sectors.

The domestic sector employs labor input

and fixed entrepreneurial capital

produce the homogeneous good.

Suppressing the exogenous capital stock, the domestic

production technology is given by

L()

d,where

G>0>

LLL

, where the subscript denotes a

partial derivative. Thus, labor has positive, but diminishing marginal product. Denote the

time‐invariant statutory tax rate as

,theperiod

labor employed by the national sector as

and the period

wage rate as

Then, the after‐tax profit of the entrepreneurial firm in

period

πτGL wL=(1−)( ( ) −)

Ddd

(1)

In each period, the entrepreneur maximizes the after‐tax profit (1) over the labor input L

which results in the labor demand equation

Lw()=

Ltt

d(2)

The MNE's subsidiary is modeled similarly to Turnovsky and Bianconi (1992) and Wildasin

(2003). It uses the constant returns to scale technology FKL(, )

m, where

is the capital stock,

the labor input, and F(

)

⋅has positive but diminishing marginal products. The firm has an

initial capital stock

K(0) =

. The initial capital stock is fully equity financed by the parent,

either through new equity issues or retained earnings.

Table 1summarizes the definitions of all variables and parameters in the model.

I relax the assumption of a time‐invariant tax in Section 5.

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KALAMOV

TABLE 1 List of variables and parameters

Variable/parameter Name

LL(

)

md Labor input in multinational (domestic) firm

)

Capital stock of multinational (domestic) firm

FKL(,

)

mMNE production function

KL(,)

dd Domestic production function

tWage rate

Interest rate

Statutory tax rate

πtDPeriod

after‐tax profit of domestic firm

MNE's net profit in period

πt

MNE's net cash‐flow in period

MNE's equity value

MNE's quantity of equity shares

MNE's share price

DtDividend payment

tRetained earnings

Internal debt level

Thin‐capitalization rule

Crb(

)

Deadweight costs of internal debt

II(

)

ttdMNE's (domestic firm's) investment

CI C I()( ( )

)

ddMNE's (domestic firm's) capital adjustment cost functions

1Adjustment speed

XX(

)

WE Consumption of workers (entrepreneur)

Tax revenues

Period

welfare

Weight of entrepreneur's consumption in welfare

iFG,=,

Share of capital in the production function

FG=,

Degree of substitutability between capital and labor in

F()⋅

Degree of substitutability between capital and labor in

(

)

⋅

Marginal cost parameter in

CI(

)

Marginal cost parameter in

Crb(

)

ψBBz b

,,,,=,

21 22 12

Constants determining capital transition path in Section 5.2

ζi,=1,

iAdjustment speed parameters in Section 5.2

Returns to scale of

FKL(,

)

min Section 5.2

Returns to scale of

KL(,)

in Section 5.2

Abbreviation: MNE, multinational enterprise.

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201

The MNE operates a financial center in a tax haven country with a zero corporate tax rate.

It can lower the tax liability of its productive subsidiary by channeling a part of the equity

financing through the financial center, which in turn provides internal debt,

,tothesub-

sidiary at an exogenous world interest rate

. The government constrains internal debt not to

exceed an exogenous proportion

[0, 1[∈

of the capital stock, that is,

BbK

≤

Following

Hong and Smart (2010), Mardan (2017), and Gresik et al. (2017), the MNE incurs costs for

using internal financing. Specifically, internal debt creates deadweight costs similarly to

external debt (Gresik et al., 2017; Hong & Smart, 2010). These costs may arise because the

MNE needs to hire lawyers to structure internal debt in accordance with tax law (Gresik et al.,

2017). As in Hong and Smart (2010), the deadweight costs are specified as CrBKK()

B∕,where

′>0, ″>0

BBfor

and

CC(0) = ′(0) = 0

These costs are, without loss of gen-

erality, not tax‐deductible.

The productive subsidiary's interest costs in period

amount to

. These interest costs also

equal the net profit generated by the financial center. Define the net profit of the MNE's

subsidiary in period

as its gross profit,

FK L wL(, )−

tttt

, minus the interest costs, dead-

weight costs, and tax payments. Then, the sum of the subsidiary's and financial center's net

profits in period

is equal to

() [() ]

πFKL wL rB C rB KK τFKL wL rB rB

¯=,−−−()−,−−+.

ttttttBttt t

ttttt

Mmm mm

∕

(3)

The profit π

¯t

can either be used to pay dividends

or held as retained earnings

to finance

new investment.

The MNE augments the capital stock in period

, at the rate

such that the amount of

investment is

Assuming, without loss of generality, that capital does not depreciate, the

capital stock evolves according to

˙=

ttt (4)

Moreover, the firm incurs convex capital adjustment costs CIK()

, where

Csgn{ ′}=

ICsgn{ }, ″>0

, and CC(0) = ′(0) = 0. Convex adjustment (or installation) costs were initially

formalized by Hayashi (1982), and represent the internal costs caused by disruption within the

firm due to (dis)investment (House & Shapiro, 2008). Furthermore, adjustment costs are re-

quired to explain the firm‐level data on investment dynamics (Bloom, 2009; Cooper &

There are two types of TCRs: safe harbor rules and earnings stripping rules. A safe harbor rule limits the debt‐to‐

capital ratio, while an earnings stripping rule allows the deductibility of interest expenses up to a certain proportion of

the company's EBITDA. The restriction

on internal debt represents a safe harbor rule, following the modeling choice

of Hong and Smart (2010), Haufler and Runkel (2012), Haufler et al. (2018), and Gresik et al. (2020).

An alternative cost function, consistent with the use of a safe harbor rule, is CBKK()

B∕. Because the interest rate is

exogenous in this model, the two functions lead to the same results. In a model with an endogenous interest rate, the

choice of a cost function may affect the results.

The assumption of two different types of capital: an exogenous stock,

, employed in the domestic sector, and an

endogenous stock,

, employed in the multinational sector, follows Hong and Smart (2010) and Haufler and

Runkel (2012).

A dot indicates a time derivative.

202

KALAMOV

Haltiwanger, 2006).

Therefore, to install

units of capital, the firm needs additional CIK()

units of output (Turnovsky, 1997, p. 57).

The (costly) installation is crucial to the model because it creates a delay from new in-

vestment to capital stock adjustment. While the firm can respond immediately to any shock in

period

with a change in investment

, this new investment must be installed and can only

augment the capital stock in period

dt+

Thus, the total costs of investment in period

are ICIK

(

+())

ttt

. The firm finances these

costs through retained earnings

and new equity issues

, where

is the price of equity

and

denotes the stock of existing equity in period

Subtraction of the capital adjustment costs from the net profit π

¯t

gives the net cash‐flow

generated by the MNE's subsidiary in period

π,t

()

[() ]

πFKL wL I CI K C rB KK

τFKL wL rB

=,−−(+ ()) −()

−,−−.

tttttttt

Bttt

ttttt

Mmm

∕

(5)

Denote the value of equity in period

qE=

. The objective of the firm is to

choose the optimal paths of IL,

ttm,and

to maximize

subject to the TCR constraint

BbK

≤

.Thevalueofequity

is given by (see Supporting Information Appendix Afor a

derivation)

πedt=

trt

M−

∞

(6)

Thus, the value of the subsidiary in period 0 is the present value of its future net cash‐flow,

discounted at the interest rate

Equations (5) and (6) are generalized versions of the

equations for net cash‐flow and firm value in the model of Wildasin (2003) in the presence of

internal debt.

Denote the MNE's optimal internal debt level as

and the associated debt‐to‐capital ratio as

ˆt.

In the absence of a TCR, the firm's choice would be given by

Crb

′(ˆ)=

B; that is, where the

marginal costs equal the marginal tax benefits. The optimal value

is time‐invariant because of the

time‐invariant tax rate. Hence, any TCR above

would not be binding. However, Proposition 3

later shows that the government's optimal choice of

lies strictly below

and is, thus, binding.

Therefore, in the remaining analysis, we only focus on the case of a binding TCR:

bb=<

Supporting Information Appendix Bderives the MNE's optimal paths of

and L

, which

satisfy the following equations:

[() ]

ICrbτCrbCICIrIFKL τ

˙=1

″(1 −)+ ( )+ ( )+ ′()(−)−,(1−)

tBtttKt

tm(7)

Additionally, the convex costs are standard in models of small open economies facing perfectly elastic capital supply

and are necessary for the existence of nondegenerate dynamics (Turnovsky, 1997).

One difference between the static model of, for example, Hong and Smart (2010), and the dynamic model is in the

formal representation of the cost of capital. In the static model, firms maximize the after‐tax profit, where the cost of

capital enters negatively as

−

. In the dynamic model, we differentiate between investment and capital. The firm

maximizes the discounted future cash‐flows (Equation 6), which depend negatively on the investment costs

ICIK(+ ())

ttt

, while the cost of capital (required return on equity) is captured by the discount factor

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203

FKL=(, ).

tLt

(8)

Equation (8) equates the marginal product of labor to its marginal cost, while (7)de-

termines the optimal change in investment over time,

˙.Theright‐hand side of (7)givesthe

difference between the costs of new investment and its marginal product. Note that in

steady‐state capital is constant,

˙=0

, and, according to (4),

I=0

. Hence, if a shock in-

creases the marginal costs of investment, the right‐hand side of (7) becomes positive. In this

situation, the firm disinvests (I<0

t) and to reach steady state, investment must increase to

zero, that is, I

˙>0

Finally, the labor market must clear in each period

. Thus, we require

LL+=1

(9)

The model is in steady state when

˙=˙=0

. Denote steady‐state variables with a tilde. The

steady state is characterized by

FKL rbτCrb

(, )= (1 −)+ ( )

1−

∼

(10a)

FKL GL w(, )= ( )=

∼∼

∼

(10b)

LL+=1,

∼∼

(10c)

I=0



(10d)

The labor demand equations (2) and (8) together with the labor market clearing condition

(9) define the labor inputs

LL,

as well as the wage rate

as implicit functions of the capital

stock,

t. Denote these functions as

LLKLLKwwK(), (), (

)

ttt

tt tt

mm dd

≡≡≡

. Totally differ-

entiating (2), (8) and (9) with respect to

LLw,,

ttt

md , and

tgives

=−+>0, =−,=

+>0

LL LL

LL LK

LL LL

mdm

∂

(11)

To interpret (11), note that with a constant returns technology, capital and labor are comple-

ments in production, that is, F>0

LK . Thus, an increase in the capital stock makes labor more

productive, which raises the demand for labor in the international sector (

LK>0

∂

∕∂

). The

wage rate must increase to balance the labor market ( wK>

∂

∕∂ ), which lowers the demand

for labor in the national sector.

Next, I derive the comparative dynamic effects of a change in the tax rate in period 0 on the

capital stock in periods

, where

≥. Following Wildasin (2003), Supporting Information

Appendix C proves the following result:

Lemma 1. Suppose the government changes the tax rate

in period 0and keeps it

constant for all future periods.Then,the change in the capital stock in periods

≥is

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KALAMOV

τe=(1−)0,

tμt

∂

∂≤

∼

(12)

where

is the speed of convergence to steady state and is determined by

−−

2<0

τFGK

CF G

24(1−)

″(+ )

KK LL

LL LL

∼

(13)

while

τ∂

∕∂

∼

is the change in the steady‐state capital stock,given by

FrbF G

τFG

=(−)( + )

(1 −)<0

KLLLL

KK LL

∂

∼

(14)

Proof. See Supporting Information Appendix C.

□

According to Equation (12), in the period of the tax change (

=0), the capital stock remains

unchanged. The reason is that the capital stock cannot adjust immediately. When

becomes

large, the exponential term in (12) vanishes and the change in the capital stock approached the

negative long‐term effect,

Kτ<

0∂

∕∂

∼

. The speed of convergence is μ1



. If there are no capital

adjustment costs, that is, C()=0⋅, then μ−

1→

∞

and adjustment is instantaneous. This is the

special case of a static model. The higher the change in the marginal adjustment costs, C″, is,

the slower is the rate of adjustment

. Lastly, the comparative dynamic effects on the labor

inputs and the wage rate in periods

≥follow from (11) and (12).

3|THE GOVERNMENT

Following Hong and Smart (2010), the government's objective is to redistribute income from

the entrepreneur to workers. It transfers the tax revenues in a lump‐sum way to the workers.

The workers do not save and their consumption, XtW, equals the total income:

XwT=+

ttt

W(15)

where

TτGL wL τFK L wL rbK=(( )−)+ ( ( , )−−)

ttttttttt

dd mm

denotes the tax revenues. The

entrepreneur also does not save and its consumption Xt

is given by

Xπ=

ED (16)

The government maximizes the welfare function XβX

ttt

for

[0, 1]∈

, where

strictly less than one represents preferences for redistribution of income to workers.

The government uses the same discount rate

as the multinational firm. This assumption is

based on the result from small open economy models with private savings that the time

discount rate equals the steady‐state interest rate (Turnovsky, 1997). Thus, the government

chooses the tax rate to

KALAMOV

205

edtmax Ω

τtrt

−

∞

(17)

taking into account the impact of taxation on the capital stock K

∂

∕∂ , as well as the functions

LKLK(), (

)

tttt

, and

)

. Denote this tax rate as

. It is implicitly determined by

τFrb βGL wL τL

FrbK

*(−)=(1−)()−−(1 −*)

+(−),

rμKK

rμ

rμK

−

∼∼ ∼

∼

∂

∼













(18)

where the term wτ<

0∂

∕∂

∼

is defined in Equation (D.5) in Supporting Information Appendix D.

The left‐hand side of (18) gives the marginal costs of an increase in the tax rate, which lowers

the MNE's mobile capital stock. The marginal benefits are on the right‐hand side of (18). The

term in the first row gives the marginal increase in welfare from additional redistribution from

the entrepreneur to workers. It is positive for

strictly less than one (and a not too negative

effect of the tax on the wage rate). The term in the second row of (18) arises due to the dynamic

adjustment of the capital stock and is initially derived by Wildasin (2003). The slow adjustment

of the capital stock following a tax rate increase creates quasirents during the transition period

to a new steady state. Since the multinational firm is not owned by the domestic residents, the

government has an incentive to tax these rents and distribute them to workers. This term is

greater, the slower the adjustment rate is, that is, the closer

is to zero. In the case of an

immediate adjustment, μ−

1→

∞

, there are no quasirents, and the second row of (18) vanishes.

Section 4discusses the long‐and short‐term effects of a change in profit shifting, as mea-

sured by the proportion of internal debt,

. It shows that the dynamic economy may behave in a

qualitatively different way from the static one.

4|EFFECTS OF INTERNAL DEBT

As discussed in Section 1, the existing theoretical literature disagrees on the desirability of

internal debt. To address this issue, I first study how, starting from a situation without debt

financing, a small permanent relaxation of the TCR affects the optimal tax rate

, the long‐

term capital stock

∼

, and welfare. Second, I derive the optimal TCR.

Consider first how allowing for some debt financing affects the optimal tax rate and the

long‐term capital stock. The impact on

∼

is positive if the user cost of capital goes down (and

vice versa), where the user cost is determined by the right‐hand side of Equation (10a).

Proposition 1. Suppose that,starting from

,the government allows internal debt by

a TCR relaxation

b>0in period 0.

(a)If the economy is static (μ−

1→

∞

), and the government has a redistributive motive,

that is,

[0, 1[∈,then

The derivation of (18) is relegated to Supporting Information Appendix D.

206

KALAMOV

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dτ

db τ

*>0, <0, if *<1

∼

(19)

(b) Suppose the economy is dynamic with

μ]−,0[

∈∞

.Then,there exists a value

ˆ[0, 1[∈such that for

β[ˆ,1]∈,the following results emerge:

dτ

*>0, >0

∼

(20)

For

β<ˆ

,both the changes in

and

∼

are ambiguous.

Proof. See Supporting Information Appendix E.

□

In both cases in Proposition 1, the introduction of internal debt may raise the optimal

statutory tax rate. The intuition is that a higher level of

lowers the marginal costs of taxation

by reducing the capital stock's tax rate sensitivity. However, the tax rate change is, in general,

ambiguous, as

also affects the marginal benefits of taxation.

The capital stock effect depends on whether the higher

lowers the user cost of capital by

more than the increase in the statutory tax rate raises it. In the case of a static model (part

(

a) of

Proposition 1), the latter effect dominates for τ*<1

∕.

However, when the convergence to

steady state is not immediate, and the government's redistributive motive is sufficiently weak,

that is,

β[ˆ,1]∈, the net effect on the user cost is negative. Hence, the capital stock is higher in

the new equilibrium (part

(

)

of Proposition 1). The change in

∼

is undetermined for lower

values of

The intuition behind this ambiguity is the following. In a static model, the only benefit of

taxation is its redistributive effect. However, in a dynamic model, the taxation of quasirents is

an additional benefit. When

is close to unity (part

(

)

of Proposition 1), the redistributive

motive is weak, and taxation of quasirents is the primary motive for taxation. Hence, the two

cases considered above analyze the two extreme situations of

(

a) only a redistributive motive

and

(

)

a predominant motive to tax quasirents.

How does the capital stock effect reverse its sign, as the convergence changes from im-

mediate to not immediate, that is, as

changes from μ−

1→

∞

to μ>−

∞

? Note that for

μ−

1→

∞

, the results from part

(

)

converge to zero as the quasirents disappear. Similarly, at

β1

→

, the results from part

(

a) converge to zero, as the redistributive motive vanishes.

Suppose we start from the situation μβ−,

1→∞ →

, where the effect on the capital stock is

zero. Then, adding a redistributive motive would lead to a decrease in the capital stock (part

(

a)), while adding a motive to tax quasirents would lead to an increase in the capital stock (part

(

)

). If we add both motives, then the change in the capital stock is positive for

β[ˆ,1]∈and

ambiguous otherwise.

The condition

τ*<1

∕

is sufficient for the derivation of the results in Proposition 1

(a)

. Note, however, that the

results derived later in Propositions 2and 3do not depend on

τ*<1

∕

To prove the convergence results, calculate the limits of Equations (E.11) and (E.14) in Supporting Information

Appendix Efor

β1

→

, and the limits of (E.16) and (E.19) for

−

1→

∞

. All four equations converge to zero.

KALAMOV

207

Thus, Proposition 1highlights the role that the convergence rate plays for the relationship

between the TCR and the capital stock. Only a small deviation from the case of immediate

convergence may affect the capital stock change qualitatively.

I turn next to the impact of profit shifting on welfare. In the case of immediate convergence,

the model collapses to the static setting of Hong and Smart (2010), and the welfare implications

are also identical. Thus, a TCR relaxation, starting from

, unambiguously increases

welfare if

and does not affect welfare if

(for a formal statement of this result and a

proof, see Lemma 2 in Supporting Information Appendix F). The reason is that this reform

allows for more redistribution via a higher statutory tax rate

In the dynamic setting, one can distinguish between two effects: the short‐term impact (i.e.,

the change in

) and the long‐term impact (i.e., the change in

∼

). While the relationship

between internal debt and welfare is, in general, ambiguous, one special case leads to un-

ambiguous results.

Proposition 2. Suppose the economy is not static,that is,

μ]−,0[

∈∞

.Also,starting

from

,the government allows internal debt by a TCR relaxation

b>0in period 0.

Then,there exists

β[0, 1[∈

such that for

β[,1]∈

,welfare decreases in the short term

and increases in the long term:

Ω<0

ββ

[,1]∈(21)

Ω>0

ββ[,1]

∼

∈

(22)

For

β<,both the short‐and long‐term welfare effects are ambiguous.

Proof. See Supporting Information Appendix F.

□

Proposition 2states that, for a sufficiently weak redistributive motive, the short‐term wel-

fare effect is unambiguously negative, while the long‐term welfare change is positive. Hence,

welfare may respond nonmonotonically to an increase in profit shifting. The intuition is the

following. In the short term, the capital stock is fixed, and the only welfare effects come from

the direct negative impact of

on the tax revenues and the change in the statutory tax rate.

Moreover, the tax rate increase does not compensate for the direct loss of tax revenues in period

0 for a sufficiently high

, and welfare declines. During the transition period, the capital stock

increases (see Proposition 1), which raises welfare. In the long term, the positive impact of

more investment overcompensates the initial negative welfare change. Hence, in the long term,

welfare improves.

Moreover, Proposition 1helps explain the reasons for the choice of an infinite horizon framework in this paper. A

two‐period model, where profit shifting adjusts in period one and capital adjusts in period two, could also derive results

similar to Proposition 1(b

)

. First, while such a model would be simpler to analyze, it would not allow the static

economy to emerge as a special case. Second, it would not allow us to study the speed of convergence and show that

even a very fast but not immediate transition can change the static results qualitatively.

208

KALAMOV

However, the welfare effects of allowing for internal debt are, in general, ambiguous. This is

partially a direct consequence of the gradual capital stock transition. Furthermore, the speed of

convergence affects the tax rate's response to a change in internal debt, which also impacts the

capital stock transition.

Thus, a small deviation from the case of immediate convergence may reveal a qualitatively

different short‐term welfare effect. The reason is the following. If

declines, the transition

period shortens. As μ−

1→

∞

, the short term vanishes as its length converges to zero. Hence,

the short term cannot be observed in a static model. Thus, in the static model, the initial

condition

K=0

is not observed, while the capital stock reacts fully to policy changes and

reaches immediately its steady‐state value

∼

. However, for any nonimmediate convergence, the

initial condition

K=0

enters the model and allows us to observe the short‐term effect

(whose sign depends on the value of

Moreover, Proposition 2converges to Hong and Smart's (2010)resultasμ−

1→

∞

.Thatis,asthe

speed of convergence becomes infinite, the positive long‐term welfare effect at

becomes zero

(because the quasirents disappear and the optimal tax rate is

τ*=0

). Furthermore, in this case,

also approaches zero, such that (22) is positive for any

. To see this, note that the static welfare

effect is a special case of (22), when μ−

1→

∞

. Moreover, (21)cannotbeobservedasμ−

1→

∞

because the initial condition

K=0

does not hold in this (degenerate dynamic) case.

The existing empirical evidence points to a nontrivial short‐term adjustment period. Em-

pirical estimates of the speed of convergence lie between

μ=−0.0

and

μ=−0.

(Turnovsky, 2002). Furthermore, as discussed in Section 1, the analyses of three different TCR

reforms in Germany and Finland do not find real effects for periods of up to 2 years (see Buslei

& Simmler, 2012; Harju et al., 2017; Weichenrieder & Windischbauer, 2008). However,

Buettner et al. (2008,2018) and De Mooij and Liu (2018) find significant adverse long‐term

effects of TCRs on the investment of MNEs' subsidiaries. Moreover, Suárez Serrato (2019) finds

that after the access to a tax haven is prohibited to US multinationals, employment of the

exposed firms gradually declines for at least 10 years until it settles at a new level (see fig. 8 of

Suárez Serrato, 2019).

Thus, the short‐term effects may last at least 2 years, and full adjust-

ment may take at least a decade.

Moreover, the case of a weak redistributive motive is not unrealistic for the choice of the optimal

corporate income tax rate. When

,welfare

equals the jurisdiction's national income:

wTπ

=++

. Thus, in this situation, the government maximizes national income. This as-

sumption is common in the literature on corporate taxation (see, e.g., Bond & Samuelson, 1989;

Janeba, 1995;Wildasin,2003). Furthermore, policymakers often motivate corporate tax reforms on

inter alia efficiency grounds, instead of redistribution motives. For example, the European Com-

mission's proposal for the implementation of a common consolidated corporate tax base (CCCTB) in

the EU motivates it partially by stating that “It is equally important to also stimulate growth and

economic development in the internal market by facilitating cross‐border trade and corporate in-

vestment”(European Commission, 2016, p. 12).

Suárez Serrato (2019) also finds that investment immediately declines following the reform. This result is consistent

with the theoretical model presented here, as only the capital stock is fixed in period zero. However, investment

changes immediately following an increase in internal debt, that is, Ib Kb

˙>

∂

∕∂ ∝ ∂ ∕∂ .

However, market regulation is a notable example where governments put a higher weight on consumer surplus

relative to firm profits. Regulators may wish to protect consumers on the grounds of, for example, asymmetric

information or firm market power (see, e.g., Campbell et al., 2010, for the case of financial products regulation).

KALAMOV

209

In addition, even though both Hong and Smart (2010) and Proposition 2predict a positive

long‐term welfare change, the intuition behind these results is different. On the one hand, in

Hong and Smart (2010), the capital stock declines. Nevertheless, welfare increases are due to

the increase in the statutory tax rate. On the other hand, in Proposition 2, both the tax rate and

the capital stock increase.

Next, I derive the optimal TCR. Suppose that the government maximizes the discounted

sum of welfare (17) over

and

Proposition 3. The optimal TCR

satisfies bb

<*<

for

and

*=0

for

When the government chooses

in time period zero,it faces a strictly positive initial

time period t

[

0, *]of negative welfare effects

bedtΩ<0

trt

−

∂

∂(23)

Proof. See Supporting Information Appendix G.

□

Thus, if the government has some redistributive motives, it chooses a positive TCR but

allows for less internal debt than the MNE would find optimal. Moreover, the marginal costs of

higher internal debt occur in the short term, while its marginal benefits emerge later.

The latter result is independent of

. The welfare effects in Proposition 2depend on

because of how it impacts

τd

*∕. However, since welfare is maximized over the statutory tax

rate, the optimal tax rate's reaction to internal debt,

τd

*∕, does not affect the optimal TCR.

Consequently,

does not matter for the sign of the short‐term welfare impact of internal

financing, when the government chooses

optimally.

How do Propositions 1–3compare to Hong and Smart (2010)? Hong and Smart (2010)

find a positive welfare impact of some internal debt in a static small open economy. Pro-

positions 2and 3show that the result of Hong and Smart (2010) continues to hold in the

long term of the dynamic model but may be reversed in the short term because of the capital

stock's gradual adjustment. Moreover, the negative relationship between the TCR and the

capital stock, that Hong and Smart (2010) find, may be reversed in a dynamic model, as

shown in Proposition 1

(

)

Additionally, in the static model, in the absence of costs of internal debt, the case

characterized by zero optimal tax rate and undefined optimal TCR,

*[0, 1]∈(see

Equation 16 and the proof of Proposition 4in Hong & Smart, 2010). However, the same case in

the dynamic model predicts

τ*>0

(owing to the taxation of quasirents) and

*=0

. The reason

for zero optimal TCR is (i) the government can use only one instrument to tax optimally the

quasirents and (ii) there are costs of positive internal debt.

Owing to the Envelope theorem, it does not matter whether the government chooses

and

simultaneously or

sequentially.

The choice of zero TCR in the absence of redistributive motives,

*(=1)=0

, does not, however, imply that

necessarily close to zero for

close to but strictly less than one. Specifically, for

and C′>

B, we have bb

<*<

However, a reduction in the marginal deadweight costs raises both

and

, such that, keeping

, we have

bblim *=lim

ˆ=

′′

CC00

→→

(as in Hong & Smart, 2010). On the other hand, keeping C′>

B, an increase in

lowers the

benefits of internal debt such that blim *=0

1→.

210

KALAMOV

However, Propositions 1and 2deliver unambiguous results only for two special cases. To

gain intuition regarding the results away from the special cases, Section 4.1 calibrates the

model.

4.1 |Simulation

To simulate the model, denote first the domestic technology as

KL(,)

, with

defined in

Section 2as the exogenous entrepreneurial capital stock. Production is characterized by

CES functions: FKL aK a L GK L aK a L(, )=( +(1−) ), ( , )=( +(1−))

FχFχGϕGϕmmdddd

χϕ

11with

χϕ,<

and aa,]0,1[

∈. Oberfield and Raval (2021) estimate an elasticity of substitution

for the US manufacturing sector between 0.5 and 0.7. However, using international data

Karabarbounis and Neiman (2014) find an elasticity of substitution of 1.25. I set

χϕ==−0.

which produces an elasticity of substitution equal to 0.83 (the elasticity is defined as

(1 −

)

∕

for

xχϕ=,

). Moreover, the share of capital is one‐third: aa= = 0.33

FG . The world interest

rate is

r=0.0

and the weight of entrepreneurs in the welfare function may take three different

values:

= 0.9, 0.95, 0.975. The adjustment cost function as well as the cost of debt are

quadratic:

CI cI c C rb c rb c()=0.5 , >0; ( )=0.5 ( ), >0

BBB22

It remains to choose three exogenous parameters: the cost parameters

cc,

, and the capital

stock

. They are fixed such that the model matches empirical observations on the tax rate

internal debt

, and the speed of convergence

. First, Buettner et al. (2016) estimate the

average

and

in 36 countries over the period 1996–2004 and get τb=0.34, =0.279(see

Table 2in Buettner et al., 2016). Second, empirical studies of the speed of convergence find

estimates as low as 2%, while standard calibrations of economic models yield values between

6% and 20% (Ortigueira & Santos, 1997). Moreover, there is evidence that the 2% empirical

estimates are downward biased (Turnovsky, 2002). In the benchmark case, I target a speed of

convergence of 6%, that is,

μ=−0.0

1and vary this estimate in the sensitivity analysis. Thus,

cc,

, and

are set such that the model predicts

μ=−0.0

1and optimal policies

τb

*=0.34, *= 0.279. The resulting parameter values are reported in Panel A of Table 2.

Moreover, Panel B of Table 2reports the values of the endogenous variables. Labor is ap-

proximately equally divided between the two sectors and the two capital stocks are also at

similar levels.

Because the model has been calibrated to yield the same optimal tax rate and TCR for

different

values, I can analyze identical reforms in each case. Suppose the economy initially

prohibits internal debt and sets

. In this case, the optimal tax rate, τb

*(=0

)

, is reported in

Panel A of Table 3and is approximately 27% irrespective of the value of

. Let there be a reform

that sets

at the optimal level,

*= 0.279

. Panel B in Table 3summarizes the impact of this

reform on the tax rate, capital stock, and welfare in each of the three cases. The statutory tax

rate increases by about 6−7 percentage points, and this effect is slightly decreasing in

However, one should keep in mind that together with

, we vary

cc,

, and

, such that in

each case, the model predicts the same optimal policy. Thus, the numerical results in Table 3

cannot be interpreted as the effect of

on optimal policy, ceteris paribus. Moreover, because

the tax rate increases by less at higher

values, the change in the capital stock increases with

In fact, at

=0.9

, the capital stock declines and at

= 0.95, 0.975

, it increases. Thus,

, which

is the threshold

value above which Proposition 1

(

)

holds, is above 0.9 in the first case, and

below 0.95 and 0.975 in the second and third cases, respectively.

KALAMOV

211

Moreover, long‐term welfare declines when

=0.9

. While this possibility is not included in

Proposition 2, it is also not excluded (the proposition only gives a special case). Thus, the static

results can be overturned even in the long run of the dynamic model. At higher

values, long‐

term welfare increases.

Furthermore, Figure 1plots the evolution of welfare relative to steady‐state welfare for

over time (with some abuse of notation, the steady‐state welfare before the reform is

labeled

in Figure 1). The case

=0.95(Figure 1b) shows monotone positive welfare effects

(that would be expected if the static model results apply in the dynamic model for all

), while

TABLE 2 Benchmark simulation

Low

Middle

High

A. Parameter values

0.9 0.95 0.975

χϕ,

−0.2

0.33

0.05

2.89 3.16 3.27

3.04 1.37 0.65

3.35 3.08 2.96

B. Endogenous variables at steady state

∼

2.95 3.24 3.37

∼

1.27 1.28 1.28

∼

0.47 0.51 0.53

0.34

0.279

μ1

−0.06

Parameter/endogenous variable constant across different

values.

Parameters chosen such that

τbμ

*=0.34, *= 0.279, = −0.0

∼is given by

−

∼

TABLE 3 Effects of a reform from

b=*=0.27

Low

Middle

High

A. Optimal tax when

τb

*(=0

)

0.269 0.273 0.275

B. Steady‐state effects of reform

Δ*

0.071 0.066 0.064

∼

−2.26 0.12 1.04

ΔΩ

∼

−0.043 0.023 0.05

212

KALAMOV

= 0.975 is consistent with Proposition 2(negative short‐and positive long‐term effects). Thus,

in the last case,

is below 0.975. Moreover, the negative short‐term impact in Figure 1c is long‐

lived and lasts around 10 years. However, for

=0.9

, the short‐term effect is positive, and the

long‐term effect is negative (Figure 1a). Thus, at lower

values, the static model results may

fail to hold in the long term even though they remain in the short term.

Figure 1illustrates the welfare effects of TCR reforms under different assumptions about

redistributive preferences, holding the optimal policy constant. However, it is also important to

understand how

affects the welfare implications of TCR reforms, holding all other exogenous

parameters constant. These effects are presented in Figure 2. It illustrates the evolution of

welfare following a reform of increasing

from zero to

for three different

values, holding

cc,

, and

at their values from the column Low

in Table 2. Thus, in the case

=0.9

, the

optimal policy is again characterized by τb

*=0.34, *= 0.279, and Figure 2a coincides with

Figure 1a. In the second case,

=0.95 changes the optimal policy to

τb

*=0.28, *=0.

Here, Figure 2b shows that the short‐and long‐term effects are positive (as in the analogous

case in Figure 1). However, the short‐term effect now overshoots the long‐term effect. Lastly,

when

= 0.975, the optimal policy is τb

*= 0.264, *=0.05

. Figure 2c reveals negative short‐

and positive long‐term welfare effects that are qualitatively similar to Figure 1c.

Moreover, Figure 3shows how the results change with the speed of convergence

, when

we keep the redistribution motive at

=0.95

. Similarly to Figure 1, here we vary

the targeted value of

, while keeping the targeted policy variables unchanged

τb

(

*=0.34, *= 0.279

)

. On the one hand, under slow convergence (

μ=−0.0

Figure 3a shows that the short‐term effects become more positive and the long‐term effects

(a) (b) (c)

FIGURE 1 Welfare effects for a change from

b=*=0.27

at time t=0for

=0.9(a),

=0.9

(b), and

= 0.975 (c)

(a) (b) (c)

FIGURE 2 Welfare effects for a change from

at time t=0for

=0.9(a),

=0.9

(b), and

= 0.975 (c), ceteris paribus

KALAMOV

213

become negative. This case seems, however, unrealistic because, as the horizontal axis shows, it

takes almost 100 years for the economy to reach its new steady state. On the other hand, fast

convergence (

μ=−0.

) results in negative short‐and positive long‐term effects. Therefore,

calibrating the model to a faster speed of convergence strengthens the case of negative short‐

term effects. However, one should again keep in mind that, in this simulation, we vary

cc,

and

to keep the optimal policy equal to its observed values and

at its target value. Hence,

Figure 3does not show the effect of changing the adjustment speed, ceteris paribus.

5|EXTENSIONS

This section presents two extensions of the model. First, I consider a time‐varying tax rate and

show that all results remain qualitatively unchanged. Second, I consider an endogenous do-

mestic capital stock. This extension becomes analytically intractable and, therefore, I analyze

its implications in a numerical analysis.

5.1 |Time‐varying tax rate

Section 4assumes a time‐invariant tax rate. In this section, I analyze whether this constraint on the

government's policy impacts the results qualitatively. To simplify the analysis, and without loss of

generality, assume that the adjustment cost function is quadratic: CI cI()=0.5

,wherec>0.

Suppose the tax rate is time‐dependent and denote the period

statutory tax as

The

first‐order conditions of the national and multinational firms are again given by (2), (7), and (8),

with the only difference that we replace the tax rate

in (7).

(a) (b)

FIGURE 3 Welfare effects for a change from

b=*=0.27

at time t=0for

=0.9

and

=−0.0

1(a) and

=−0.

(b)

By assuming a time‐varying tax rate and a constant TCR, this section introduces an asymmetry in the policy

parameters. This asymmetry simplifies the analysis and does not affect the results qualitatively. Propositions 1and 2

analyze the desirability of some internal debt and are independent of whether the TCR is time‐varying. While

Proposition 3is quantitatively affected by the assumption of a constant TCR, the bounds on the optimal TCR are not

affected by its path.

214

KALAMOV

To solve for the government's optimal tax policy in this case, one needs to determine how

investment

depends on the statutory tax rate

and the capital stock

t. Define period

investment as the function IIKτ(,

)

tttt

≡. In Supporting Information Appendix H, I derive the

first and second partial derivatives of the function I(

)

t⋅.

The government maximizes the same objective function as in Section 3. Thus, it solves

edt K IKmax Ωs.t. ˙=

τtrt ttt

−

∞

(24)

taking into account

IIKτLLKLLK=(,), = (), = (

)

tttt

ttt

mm dd

, and

wK=(

)

ttt

. The optimal

policy is summarized in the following proposition:

Proposition 4. The optimal tax rate

is a function of the capital stock

t,given by

τταKKe=+( −)



tμt

∼

(25)

where

α0

≷

is defined in Equation (I.17) in Supporting Information Appendix I,while τ



the optimal tax rate in steady state and is equal to

from Equation (18).

Proof. See Supporting Information Appendix I.

□

According to Proposition 4, the optimal steady‐state tax is the same as the optimal tax in the

model with a constant tax rate. The intuition is that once the economy is in a steady state, the

government finds it optimal to levy a constant tax rate, which then coincides with

. However,

during the transition period, the optimal tax may either be increasing or decreasing in the

capital stock

t(the exact relationship depends on the properties of the production and the

adjustment cost functions).

Therefore, the change in the steady‐state tax when some internal debt is allowed is identical

to the change of the time‐invariant tax rate in the main model. Hence, Proposition 1can be

derived analogously by replacing

with τ



. Moreover, the fact that policy responds identically

in the long term means that the steady‐state welfare impact of an introduction of internal debt

is the same as under a constant tax rate (i.e., Equation 22 from Proposition 2continues to hold).

The short‐term welfare effect may, however, differ. If

Kdb>

∕

∼

, then the tax rate in the period

of the shock,

τ0

, increases by less (or decreases more strongly) than τ



and vice versa if

(see Equation 25). The reverse is true in the case

Kdb<

∕

∼

. In the case of weak

redistributive preferences (

sufficiently close to one), the long‐term capital stock is increasing

in internal debt (according to Proposition 1) and, thus, the initial change in the tax rate is less

than the long‐term change if

(and vice versa if

). Irrespective of whether the initial

tax rate change over‐or undershoots the long‐term change, Supporting Information Appendix J

shows that for sufficiently high

, the short‐term welfare impact is negative under the addi-

tional assumption that the steady state is stable. Lastly, the determinants of the optimal TCR

are unaffected by the time path of the tax rate. Thus, Proposition 3holds. Proposition 5

summarizes these results, while the formal proof is relegated to Supporting Information

Appendix J.

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215

Proposition 5. In the model with a time‐varying tax rate,Proposition 1holds when one

replaces

with τ



.If the steady state is stable,Proposition 2remains qualitatively

unchanged.Proposition 3remains qualitatively unchanged.

Proof. See Supporting Information Appendix J.

□

Hence, all previous results are robust to an extension with a time‐varying tax rate.

5.1.1 |Simulation

A simulation of the model with a time‐varying tax produces the same long‐term results as the

model with a constant tax. The reason lies in Proposition 4, which states that the long‐term

optimal tax is equal to the constant optimal tax. However, the transition may differ. Figure 4

plots the path of the optimal tax rate in the benchmark situation from Tables 2and 3for each

value of

. In all three cases,

, that is, the tax rate increases over time if the capital stock

increases and vice versa (the exact values of

for each case are reported in the caption to

Figure 4). Because for

=0.9

, the capital stock declines, the tax rate initially overshoots its

long‐term change, and then declines to its new steady‐state value. In the remaining two cases,

the capital stock is increasing, and thus the initial tax rate change falls short of the long‐term

effect. Hence, the tax rate rises over time to reach τ



Figure 5shows the time path of welfare. While the long‐term effects are exactly the same as

in Table 3, the short‐term impact changes. In the case

=0.9

, the short‐term increase in

welfare is much greater than in the situation with a constant tax because of the overshoot in the

tax rate increase. Thus, it overshadows the long‐term welfare decline graphically. However,

when the tax rate initially undershoots the long‐term change (in the remaining two cases),

short‐term welfare deteriorates. Thus, the short‐term welfare effects improve (deteriorate) if the

tax rate initially overshoots (undershoots).

5.2 |Endogenous domestic capital

Even though it is a standard assumption in the TCR literature that the capital stock in the

domestic sector is immobile (see Haufler & Runkel, 2012; Hong & Smart, 2010), it is reasonable

(a) (b) (c)

FIGURE 4 Path of optimal tax τtfor a change from

b=*=0.27

at time t=0for

=0.9(a),

=0.9

(b), and

= 0.975 (c). The respective values of

are

= 0.76, 0.69, 0.6

for

= 0.9, 0.95, 0.97

respectively

216

KALAMOV

to consider the effects of tax changes on the domestic capital stock. Hence, this subsection

extends the model to study these effects.

Denote the domestic production function as

KL(,)

. In period

, the domestic firm

invests the amount

. The total cost of investment is

ICIK

(

+())

ttt

dddd

, where C(

)

d⋅is an

installation cost function with the same properties as CI()

t. Hence, the period

net cash‐flow of

the domestic firm is

πτGK L wL I C I K=(1−)( ( , ) −)−(+ ())

ttt

ttt tt

Ddddd

ddd (26)

and its capital stock evolves according to

˙=.

(27)

Similarly to the MNE, the domestic firm finances new investment via retained earnings or on

the international capital market. Following the same steps as in Supporting Information

Appendix A, we derive the domestic firm's value,

, as the discounted sum of all future cash‐

flows. The firm value‐maximizing labor demand is again determined by (2), while the equation

for optimal investment is analogous to (7) (see Supporting Information Appendix K for all

derivations). Hence, the steady‐state domestic capital stock,

∼

, is given by

KL r

(,)=

1−

∼

(28)

Together, (10a)–(10c)and(28) determine the steady‐state capital stocks, labor inputs, and wage.

Here, a change in assumptions is necessary. In the main model's simulation, I assume, following

Hong and Smart (2010), that both F(

)

⋅and

()⋅exhibit constant returns to scale. However, in the

case of an endogenous

, this assumption leads to the same indeterminacy of optimal inputs as in

the case of profit maximization of a single representative firm under constant returns to scale. To

ensure that the optimal capital and labor inputs are defined, I assume that at least one of the

production functions exhibits decreasing returns to scale. Formally, HH H−0

KK LL KL

≥,where

HFG=, and the inequality is strict for at least one sector. One can interpret decreasing returns to

(a) (b) (c)

FIGURE 5 Welfare effects for a change from

b=*=0.27

at time t=0for

=0.9(a),

=0.9

(b), and

= 0.975 (c)

The expression in (10b) represents two equations and thus we have five equations for five endogenous variables.

KALAMOV

217

scale as follows. If in addition to the mobile capital stocks

K,d, there is a third, truly immobile

capital stock used in production, then the economic rents arising due to decreasing returns are the

remuneration to this factor of production.

In this extension, Equations (2), (8), and (9) determine the labor inputs and wage rate as

functions of both capital stocks, given by

LKK LKK(, ), (, )

tttt

mddd

, and

KK(,

)

tttd

. Moreover,

the capital stocks represent two state variables. Thus, the transition following a change in a

policy parameter is not characterized by a single adjustment speed. Instead, it is determined by

two adjustment parameters. For a change in policy parameter

, where zτ

=,, we have the

following equivalent of Lemma 1:

zBe Be=+ +

tzζtzζt

∂

∼

(29)

zBψeBψe=+ +

tzζtzζt

121 222

∂

∼

(30)

where

ζζ,<

determine the speed of convergence and BBψψ,,,

zz1221 2

are constants that are

derived in Supporting Information Appendix K. Unfortunately, the model quickly becomes

analytically intractable and a derivation of results similar to those from Proposition 1is in

general not possible. Furthermore, while Supporting Information Appendix K derives the op-

timal tax rate

and TCR

(see Supporting Information Equations K.35 and K.36), a detailed

analysis of the short‐and long‐term welfare effects similar to Proposition 2is also not possible.

Therefore, I look at a numerical simulation.

5.2.1 |Simulation

The simulation in this section assumes that the production functions take the form

FKL aK a L GK L aK a L(, )=( +(1−)),(,)=( +(1−))

FχFχGϕGϕmmdddd

χν

ϵ, where

aaχϕ,,,

are as defined in Section 4, while ν

,]0,1]∈determine the returns to scale. The simulation in

Section 4considers a special case where

In this simulation, I use the same values for

aaχϕ,,,

FG as in Table 2. Initially, I simulate

the model for

. In this case,

is chosen such that the variables determining the speed of

adjustment,

ζζ,

, take plausible values (as a plausible range, I again view values between −0.1

and −0.02). This condition is satisfied for low

values. Hence, I consider the cases ν=0.

and

. Then, I simulate the model for

=0.9

. In this case,

is set once at 0.95 (to consider the

situation where the production functions are identical) and once at 0.85.

Additionally, since the returns to scale play a crucial role here, I consider for simplicity only

one

value, and set

=0.95(the middle value from Table 2). To further simplify the simu-

lation and its interpretation, set c=0

B, that is, assume there are no costs of internal debt.

While these costs are necessary in the main model for an interior solution of

, they are no

longer necessary in the case of endogenous domestic capital stock. The reason is that an

increase in

stimulates investment by the MNE, which raises the wage rate and thus lowers

both the labor demand and capital stock of the domestic firm (see Equations K.10–K.13 in

Supporting Information Appendix K). Therefore, even in the absence of costs of internal fi-

nancing, the optimal TCR is below 100%.

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KALAMOV

Moreover, similarly to Section 4.1, the adjustment cost functions are quadratic and given by

CI cI C I cI()=0.5 , ( )=0.5

2dd dd

. The parameters

and

are chosen such that the model

predicts optimal tax rate

τ*=0.3

and TCR

*= 0.279

, as in the main model. Table 4presents

the estimated parameters

ζζ,

, as well as the long‐term effects of a reform that changes the

TCR from

*= 0.279

in period 0.

As Panel A from Table 4shows, if the MNE's production is characterized by constant

returns to scale (

) and ν=0.

, then

is at the upper bound of the target range. Increasing

to 0.75 makes

even smaller in absolute value. At

νζ

= = 0.95,

(

) indicate very fast

(slow) convergence. Lowering

to 0.85 sets the value of

in the plausible range without

affecting

's value.

When looking at a reform of raising the TCR from zero to

, the effect on the tax rate in all

four cases is very similar to the main model. The tax rate rises by 5−6 percentage points.

However, there is now a strong positive impact on

∼

and an even stronger negative effect on

∼

. The domestic capital stock declines because of the increase in both

and

. The negative

change in the domestic capital stock furthermore leads to negative long‐term effects of the

reform (in all four scenarios). Thus, introducing an endogenous domestic capital stock may

qualitatively change the static model's welfare prediction in the long term.

Furthermore, Figure K.1 in Supporting Information Appendix Kshows the evolution of

welfare over time. In the two cases where

, welfare initially declines, then improves over

the medium term and declines again over the long term. However, in the two cases with

=0.9

, the short‐term effects are positive and the long‐term effects are negative. Therefore,

TABLE 4 Speed of adjustment and effects of a reform from

b=*=0.27

=0.9

ν=0.

ν=0.75 ν=0.95 ν=0.85

A. Calibrated parameter values

−0.1 −0.098 −0.161 −0.169

−0.024 −0.01 −0.0149 −0.083

B. Optimal tax when

τb

*(=0

)

0.283 0.28 0.277 0.29

C. Steady‐state effects of reform

Δ*

0.057 0.06 0.063 0.05

∼

2.8 3.43 23.72 8.29

∼

−10.56 −14.12 −30.42 −17.6

ΔΩ

∼

−0.25 −0.49 −3.53 −0.94

Panel A reports only the calibrated speeds of adjustment ζζ,

. The respective adjustment cost parameters are

c=2.44

c= 21.99

(ν

=1, =0.

cc= 2.49, = 46.09

(ν

=1, =0.7

), cc= 0.86, = 12.43

d(ν

= = 0.95), cc=0.99, =1.85

(ν

=0.95, =0.8

Further reduction of

makes

implausibly negative. For example, at

=0.9,

takes values around

−

0.5

(not

reported in Table 4).

KALAMOV

219

the short‐term effects of internal debt in the case of endogenous domestic capital stock depend

crucially on the form of the production technologies in each sector.

Moreover, the results in this extension may also crucially depend on other assumptions,

such as the zero domestic ownership share of the MNE, and the lack of a savings decision by

domestic workers and entrepreneurs. Further extending the model in these directions is

however beyond the scope of this paper and left for future research.

6|CONCLUSIONS

This paper addresses the real effects as well as the welfare implications of profit shifting

through internal debt. I develop a dynamic model to take explicitly into account that capital is

less mobile in the short run compared with the long run. If the government's redistributive

motive in a high‐tax country is not too strong, nonmonotone welfare effects emerge, with

negative short‐and positive long‐term effects.

Hence, policy reforms that restrict internal debt may only be beneficial in the short term.

Therefore, an important policy implication of this paper is that such reforms should also

include measures to stimulate investment. Furthermore, the observed tightening of TCR re-

strictions in many countries might be explained by policymakers prioritizing short‐term gains

over long‐term adverse effects. Analyzing such political economy considerations is an im-

portant avenue for future empirical research.

Furthermore, a numerical simulation shows that the long‐term welfare effects may be

reversed when (i) the redistributive motive is relatively strong or (ii) the domestic capital stock

is endogenous. Moreover, in the numerical analysis, TCR reforms have opposing effects on the

domestic and MNE's capital stocks. Future empirical work should quantify these effects, as well

as the effects on labor demands in both sectors.

This paper's results also contribute to the theoretical literature on internal debt and welfare.

When governments have weak redistributive motives, Hong and Smart's results hold in the

long term, but are reversed in the short term. Also, one similarity to Haufler and Runkel (2012)

emerges, even though they use a different model. A relaxation of the TCR cannot affect the

capital stock both from the social planner's perspective in a model with fixed capital supply

(Haufler & Runkel, 2012) and in the short term of a dynamic model with perfectly elastic

capital supply. Hence, the welfare effects of internal debt are qualitatively similar in both cases.

Additionally, my results highlight the importance of the timing of empirical evaluation of

TCR reforms. A reform that restricts the interest expenses' deductibility may be evaluated as

having either no or negative real effects depending on how much time has passed between the

reform and the time of analysis. The empirical literature supports this conjecture. While

Weichenrieder and Windischbauer (2008), Buslei and Simmler (2012), and Harju et al. (2017)

do not find real effects of three different TCR reforms up to 2 years after these reforms took

place, Buettner et al. (2008,2018) and De Mooij and Liu (2018) find such effects over a longer

time horizon.

Moreover, the results emerge because debt financing affects the user cost of capital. Similar

results should also hold for other profit‐shifting mechanisms if they also affect the user cost.

Such effects may emerge if, for example, the concealment costs are a function of the capital

stock. A dynamic analysis of other profit‐shifting channels is left for future research.

One limitation of the model is that it considers a single economy setting. One may argue

that in the presence of other high‐tax countries, the MNEs' global investment might remain

220

KALAMOV

unaffected by TCRs imposed by a single country. This conjecture is, however, not supported by

the existing empirical evidence. Suárez Serrato (2019) finds that eliminating US multinationals'

access to one tax haven lowers their global investment despite some shifting of investment

away from the US. Thus, the presence of other high‐tax countries may mitigate but not

overturn the theoretical results. A dynamic analysis of a multi‐country setting, probably similar

to the static model of Haufler and Runkel (2012), is thus an important agenda for future

research.

Furthermore, I do not explicitly model the households' savings and labor supply decisions,

and the government's borrowing choice. Additionally, the model assumes perfect capital

markets. However, financing frictions exist in many countries and affect both the MNE's

financing choices (Desai et al., 2004) and the optimal TCR (Mardan, 2017). Thus, an extension

with an imperfect capital market may produce new results. A model with (private and public)

borrowing, an imperfect capital market, and endogenous labor supply would likely be analy-

tically intractable, but it would allow for a quantitative evaluation of the welfare effects.

Moreover, this paper views domestic and multinational firms as price‐takers. Future work

should consider whether MNE's market power affects the welfare implications of profit

shifting.

ACKNOWLEDGMENTS

The author would like to thank Diego d'Andria, Max Franks, Andreas Haufler, Jota Ishikawa,

Christopher Ludwig, Marco Runkel, Dirk Schindler, Karl Schulz as well as participants at the

2019 ZEW Public Finance Conference in Mannheim, the 75th Annual Congress of the Inter-

national Institute of Public Finance in Glasgow, the 11th German‐Norwegian Seminar on

Public Sector Economics in Munich and the 2019 Berlin Economics Workshop on Taxation for

helpful comments. The usual disclaimer applies. This paper subsumes an earlier version that

was entitled “Not all Profit Shifting is Created Equal? An Analysis of Internal Debt”(Kalamov,

2020). Open access funding enabled and organized by Projekt DEAL.

ORCID

Zarko Y. Kalamov http://orcid.org/0000-0002-1016-3415

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SUPPORTING INFORMATION

Additional supporting information may be found in the online version of the article at the

publisher’s website.

How to cite this article: Kalamov, Z. Y. (2023). Internal debt and welfare. Journal of

Public Economic Theory, 25, 196–224. https://doi.org/10.1111/jpet.12567

224

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