Why are the data at odds with theory? : growth and (re-)distributive policies in integrated economies

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Economics Department

Why are the Data at Odds with Theory? Growth and (Re-)Distributive Policies

in Integrated Economies

G u n t h e r Re h m e

ECO No. 99/43

EUI WORKING PAPERS

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European University Institute 3 0001 0038 8078 0 © The Author(s). European University Institute. version produced by the EUI Library in 2020. Available Open Access on Cadmus, European University Institute Research Repository.

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EUR O PEAN UNIVER SITY INSTITUTE, FLO R ENCE ECONOMICS DEPARTMENT

EUI Working Paper ECO No. 99/43

W h y are the Data at Odds with Theory? Growth and (Re-)Distributive Policies

in Integrated Economies GUNTHER REHME

WP 330

EUR

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No part of this paper may be reproduced in any form without permission of the author.

European University Institute Badia Fiesolana I - 50016 San Domenico (FI)

Italy © The Author(s). European University Institute. version produced by the EUI Library in 2020. Available Open Access on Cadmus, European University Institute Research Repository.

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W h y are the Data at Odds with Theory?

Growth and (Re-)D istributive Policies

in Integrated Economies*

Giinther Rehme

Technische Universitàt Darmstadt?

7 December 1999

Abstract

Many theoretical models show that redistribution causes low growth. However, cross-country regressions often suggest that growth is posi tively related to redistribution. This paper analyzes that puzzle in an open economy framework. Am ong other things it is shown that tax com petition and the danger o f capital outflows leads optimizing, redis tributing governments to pursue high growth, no redistribution policies in technologically similar economies. However, if a redistributing gov ernment’s economy is technologically superior, it is shown that it may attract foreign owned capital, have relatively higher G D P growth and may redistribute. Both results imply that in a cross-section o f countries one would observe a positive association between growth and redistribu tive transfers.

Keywords: Growth; Redistribution; Tax Com petition; Capital M o

bility

JEL Classification: 04, H21, D33, C72, C21, F21

* Earlier versions o f this paper circulated under the title ’Grab’ the Capital and Grow. Th e present version is based on chapter 3 o f my dissertation defended at the European University Institute. I would like to thank Tony Atkinson, James Mirrlees, Robert Waldmann and Robert K. von Weizsacker for stimulating suggestions and helpful advice. I have also benefited from discussions with Berthold Herrendorf, Ed Hopkins, Akos Valentinyi, and Thomas Werner. O f course, all errors are my own. Financial support by the Deutscher Akademischer Austauschdienst (D A A D ), grant no. 522-012-516- 3, is gratefully acknowledged.

t Correspondence: T U Darmstadt, FB 1/VW L 1, Schloss, D-64283 Darmstadt, Germany.

phone: +49-6151-162219; fax: 4-49-6151-165553; E-mail: rehme@hrzpub.tu-darmstadt.de

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1 Introduction

In policy discussions and in the theoretical literature it is often argued that high redistributive taxes cause capital outflows and low growth. For instance, Alesina and Rodrik (1994) and others have shown that polit ical objectives leading to policies favouring the non-accumulated factor of production (e.g. labour) imply low growth in closed economies. How ever, researchers are often surprised to find that redistributive transfers are significantly positively related to growth in cross-country growth re gressions. See, for instance, Perotti (1994) or Sala-i-Martin (1996).

This paper offers an explanation of the puzzle. It is shown that redistributing governments which face high capital mobility or which attempt to stop capital outflows before tackling distributional issues will pursue policies that are indistinguishable from, that is, observation- ally equivalent to high growth policies. This holds in an environment where foreign governments might benefit from the outflow o f domestically owned capital and if the economies involved are technologically similar. If a redistributing government’s economy is technologically superior, it is shown that it may attract foreign owned capital, have relatively higher growth and may redistribute resources to the non-accumulated factor of production. Both results imply that in a cross-section o f countries one would observe that growth correlates positively with redistributive transfers.

Suppose the government faced the redistribution-capital-outflow- low-growth problem and that stopping capital outflows was good for growth. Then in a world, in which capital was - perhaps only weakly - mobile, it might deal with the problem in two reasonable ways. First, the government could act sequentially. It might prefer not to tolerate capital outflows at all. After having secured the maximum possible size of the capital stock, it might then, and only if feasible, redistribute capital. Second, it could solve the problem simultaneously. It might strictly prefer to redistribute at the expense of losing some capital. In this paper the sequential solution method is referred to as the New Left approach (N L ) and the simultaneous solution as the Old Left approach (O L ).

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Clearly, the intertemporal welfare implications of N L and OL would in general be very different. As capital outflows may entail job losses and downward pressure on wages, electorates of redistributing (left-wing) governments appear to have increasingly favoured solving redistributive issues along the lines of N L over the last couple of years. However, this paper concentrates on both approaches by analyzing the border case where N L and O L lead to the same policies. That is given in a situa tion when capital mobility is perfect. The assumption of perfect capital mobility is often used as an analytical device. However, in the context o f long-run growth, it may also reflect that relocation costs o f capital, including technological knowledge, are negligible compared to the income stream that may be derived from operating the stock somewhere else. It is in this sense that the assumption of perfect capital mobility should be understood in this paper.1

In the model the accumulated factor of production is identified with capital and the non-accumulated factor of production with labour. I build on Alesina and Rodrik by analyzing optimizing governments that tax the capital owners’ wealth. The tax scheme is meant to represent a broad class of tax arrangements and is to be interpreted as a metaphor for many kinds o f redistributive policies.2 In order to focus on distributional conflicts the agents are assumed to be represented by governments that are either entirely pro-capital ( ’right-wing’), or completely pro-labour ( ’left-wing’).3 A ll governments respect the right of private property.4

Under the source principle all types o f income originating in a coun try are taxed uniformly, regardless of the place of residence of the in

’ The assumption creates indeterminacies that are interesting from a theoretical point o f view. A t the end o f this introduction I will point out how the results would be affected if one assumed imperfect capital m obility and N L policies.

2For a similar argument and examples of what other redistributive mechanisms the tax scheme may capture see Alesina and R odrik’s paper.

3The logic o f the m odel would be the same if governments attached different social weights to the workers’ and capital owners’ welfare.

4Expropriation o f capital is ruled out since it is not common in the real world. For an early m odel studying the distributional conflict between capital owners and workers as a dynamic game see Lancaster (1973) and the literature ensuing from that paper. © The Author(s). European University Institute. version produced by the EUI Library in 2020. Available Open Access on Cadmus, European University Institute Research Repository.

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come recipients. In the paper the governments adopt the source principle for the taxation of internationally mobile wealth.5 Furthermore, the in vestors can costlessly shift their assets to the country offering the highest return on capital.

For given policies the open economy market equilibrium is char acterized by balanced growth and the return on capital is always equal across countries. That is what one would expect in a highly integrated world where investors can costlessly shift capital. However, depending on the public policy the level of G D P may be very different across countries. If capital flight occurs, a country may loose its entire productive capital stock so that no G D P is generated and the workers ’starve’ . These styl ized features of the model serve to bring out sharply the long-run effects, capital flight may have for an economy.

The governments of otherwise identical economies are taken to en gage in tax competition.6 A right-wing government wants to maximize the domestic capital owners’ income and does not care about the do mestically installed capital stock. In contrast, a left-wing government wants a high level and growth of GDP, because wages and redistribution depend positively on the overall capital stock. Therefore, the left-wing government does everything to prevent capital flight. It wishes to attract ( ’grab’) as much domestically or foreign owned capital as possible.

For similar, that is, equally efficient economies I show that in equi librium there is no room for redistribution. Thus, even two left-wing governments do not redistribute in the optimum. The intuition for the result is the following: For redistribution a left-wing government has to set high taxes, which imply a low return to capital, inducing capital flight. The resulting decrease in welfare is so high that a left-wing government is better off if it does not redistribute. Compensation is given by stopping any capital relocation and securing high enough wages.

5This may be justified by the observation that in a non-cooperative environment with very high capital mobility, and absent any problems arising from transfer pricing, governments may not be able to monitor their residents’ wealth perfectly.

6Tax com petition has been studied in numerous papers such as, for instance, G or don (1983), W ilson (1986), Wildasin (1988), or Sinn (1990).

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I f two right-wing governments compete in taxes, there is an infinite number o f Nash equilibria in which the capital owners never pay more or less than the growth maximizing tax rate. That is due to the fact that if the opponent happens to choose the G N P growth maximizing tax rate in equilibrium, the domestic right-wing government is indifferent what to choose since its problem has already been solved by its opponent. As a consequence there is almost surely capital flight for one country, in which the workers will ’starve’, but the capital owners will be quite well off, because they derive income abroad.

If a domestic left-wing and a foreign right-wing government com pete, the equilibrium is unique, because the left-wing government wants to ’grab’ capital and pursue a high tax, high wage policy. But high taxes drive out capital. Thus, the left-wing government will always try to un dercut its opponent’s tax rate in order to attract capital. In equilibrium both choose the growth maximizing tax rate.7 The equilibrium capital allocation is indeterminate, but the occurrence of capital flight is of mea sure zero. Interestingly, in such a situation one economy’s workers may be better off under a right-wing than under a left-wing policy.

I f two left-wing governments compete in taxes, both choose the growth maximizing policy as well. The effects of redistributive concerns are competed away for fear of capital flight. Hence, for similar countries, distributive preferences alone do not lead to non-maximal growth rates.

If the countries differ in technology, the efficient economy’s govern ment can always guarantee a higher after-tax return on capital and find more productive capital located in its economy than an inefficient econ omy’s one. A left-wing government in a technologically superior economy is able to redistribute and have higher G D P growth than its opponent. The amount of redistribution is limited by the tax choices o f its oppo nent and its efficiency advantage. But because of capital relocation from

7This paper’s results complement those in Rehme (1997). For instance, when economies are technologically similar and linked by imperfect capital mobility, an O L government knows it cannot offer a better return to capital than the growth maximizing one. It then decides to let capital flow out and redistribute the capital that remains in the country. Capital outflows might be prevented, however, if the government pursued a N L policy.

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abroad, there are more resources for redistribution and the level o f G D P and its growth are higher when capital mobility is very high than under the optimal left-wing policy in a closed economy. Clearly, the capital relo cation effect is highest when capital mobility is perfect. For these reasons an efficient economy’s left-wing government would want very high capital mobility. Furthermore, it would generally have a relatively stronger in terest in innovation (superior technology) than a right-wing government as that enlarges redistributive freedom.

To generalize the results suppose capital mobility was not perfect. Then in a market equilibrium the returns to capital would not be the same across countries for given policy. For similar countries the tax competition equilibria would all be unique because o f the costs to capital relocations or due to a N L policy, which strictly attempts to prevent capital outflows. Furthermore, in a technologically superior economy the policies would be qualitatively the same if the government was O L and perfect capital mobility prevailed or was N L and capital mobility was imperfect. Thus, all the essential qualitative results would hold if there was imperfect capital mobility and the government pursued a N L policy. From this I conclude the following:

A hypothetical comparison of possible matches o f public policies implies that a right-wing policy is always growth maximizing in the model. A n efficient economy’s left-wing policy does not necessarily max imize growth, but it induces capital flight (outflow) for an inefficient

economy’s opponent. Thus, hypothetically distributing resources towards

labour may be bad for notional, maximum growth.

However, in terms of observable comparisons, either an optimizing, left-wing government chooses the growth maximizing tax rate in simi lar countries against any opponent or it has a more efficient economy, distributes resources towards labour and has a higher observed G D P growth than its opponent, no matter whether right or left-wing. But then redistributive transfers should correlate positively with growth in cross-country growth regressions.

Thus, the paper’s main insights are the following: In the model op timizing governments do not find it optimal to tolerate capital outflows

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in order to ’pay for’ redistribution, leading to low growth. In that sense high factor mobility (globalization) ’disciplines’ national policies. How ever, globalization also offers opportunities by allowing a higher level of redistributive transfers and higher growth when an economy is techno logically superior. But then the association between growth and redis tribution should be observed as being positive in cross-country growth regressions. The results suggest that political objectives may be less important for redistribution than technological opportunities.

The paper is organized as follows: Section 2 presents the model set-up, derives the closed economy equilibrium and briefly presents the optimal policies. Section 3 analyzes tax competition among governments. Section 4 concludes.

2 The Model

Consider a two-country world with a domestic and a foreign country. De note variables in the foreign country by a (* ). There are many identical, immobile individuals in each country, who are all equally patient. The capital owners do not work, but they invest; the workers never save and just consume their entire wages.8 Both groups derive logarithmic utility, defined o n S s R U { - o o } , from the consumption of a homogeneous, mal leable good that is produced in the two countries. Foreign and domestic output are perfect substitutes in consumption. Following Barro (1990) aggregate production is carried out according to

Yt = A K ta G}~a L)~ a where K t = u tkt + (1 - wt*)jfc;, (1)

8In an endogenous growth framework Bertola (1993) has shown that agents whose initial income derives from labour (capital) only will not find it optim al to save (to work). A s a shortcut o f that result I assume that workers never save, and supply labour inelastically. The capital owners do not work, accumulate capital and decide where to install their capital. Thus, the model set-up is reminiscent o f Kaldor (1956), where different proportions o f profits and wages are saved. However, in Kaldorian models growth determines factor share incomes, whereas in endogenous growth models the direction is rather from factor shares to growth.

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a € (0,1) and Yt is output produced in the home country. K t is an index of the domestically productive capital stock, and kt (fct*) is the (broad) capital stock, including disembodied technological knowledge, owned by domestic (foreign) capitalists and G t are public inputs to production.9 Furthermore, L t = 1, so that labour is supplied inelastically. The foreign country has the same technology and technological differences are due to A, which is an efficiency index, reflecting cultural, institutional and technological development. I f both countries are equally efficient ( A — A*) the economies are called similar, because they may well be different in terms o f institutional or cultural development. I f A A* the economies are called different.

The variable u)t denotes the fraction of real capital at date t owned by domestic capitalists allocated to the home country. The rest is located abroad. The model allows for the case that all o f the domestically owned capital is located abroad by assuming wt € [0,1]. That serves to bring out sharply any effects, capital flight may have for an economy.10 Throughout the analysis I abstract from problems arising from depreciation o f the capital stock.

T h e P u b lic S ector. In both countries wealth is taxed and redis tributed at constant rates. The governments adopt the source principle for wealth taxation. The domestic tax rate r is levied on domestic wealth

u tkt and foreign wealth (1 — w(*)fc*. Analogous definitions hold for the foreign country.11 The government faces the following balanced budget constraint

r K t = G t + \ rK t (2)

9For growth models which interpret knowledge as just another capital good used in production see Frankel (1962) or Romer (1986). For an up-to-date discussion of these models see, for instance, Aghion and Howitt (1998).

10Thus, the capital stocks are perfectly mobile across countries in the m odel which is meant to capture very long time horizons.

11 Differential taxation o f foreigners and residents in a similar set-up has been an alyzed in Rehme (1995). The results there suggest that tax discrimination m ay lead to non-steady state equilibria or similar results as in this paper.

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where the LHS depicts the tax revenues and the RHS public expenditures. The workers receive X rK t as transfers and G t is spent on public inputs to production.

T h e P r iv a t e S ector. The firms are owned by domestic and foreign capital owners, who rent capital to and demand shares of the firms. They take public inputs to production parametrically. Perfect competition and profit maximization entail that the domestic firms pay each factor of production its marginal product

r = fjj£ = (3)

= = v (r, X )K t = (1 - a ) A [ ( l - A )r ]1_a /f( , L t = 1 V<. (4) Equation (3) implies that the return on foreign and domestic capital is constant and equal in the domestic country since k and k* are perfect substitutes in production. Notice that the wages grow with the aggregate capital stock. For fixed K t the pre-tax return on capital and the wage rate are increasing in r and decreasing in A. Thus, redistribution lowers pre-tax factor rewards for given capital.

The workers derive utility from consuming their entire wages and government transfers. They do not invest and are not taxed by assump tion. Their intertemporal utility is given by

In C™ e~ptdt where C™ — 7/(t, X )K t + XrKt- (5)

The capitalists choose how much to consume or invest, they have perfect foresight, and take prices and policy as given. As they may invest in either country they determine where to allocate their capital stock. By assumption perfect capital mobility prevails so that it is costless to send and install capital abroad. Furthermore, physical capital is taken to be entirely collateralized by tradeable stocks at each point in time. The capitalists maximize their intertemporal utility according to the following

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programme

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s.t. kt = ( r ~ T)ujtkt + (r* - r * ) ( l - u t)kt - C* , 0 < ut < 1,

fc(0) = ko, fc(oo) — free.

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Equation (7) is the dynamic budget constraint of the capitalists who earn

ruitkt income at home and r * ( l — cj t)kt income abroad. The necessary first order conditions for the problem are given by equations (7), (8), (9) and

where is a positive co-state variable representing the instantaneous shadow price of one more unit of investment at date t. Equation (10a) equates the marginal utility of consumption to the shadow price o f more investment, (10c) is the standard Euler equation which relates the costs of foregone investment (LHS) to the discounted gain in marginal utility (RHS) and (lOd) is the transversality condition for the capital stock which ensures that the present value of the capital stock approaches zero asymptotically. Equation (10b) describes the capital allocation decision, which takes a ’bang-bang’ form and is given by

The capitalists’ allocation decision is extreme in that they immediately

capital is higher. Thus, relative to any planning horizon the speed of

U ' - n t = 0

Ht(r

-

r)kt -

p ( (r* -

r)kt =*

0

fit = PtP ~ Pt

[(r ~

r)cjt +

(r* - r * ) ( l - wt)] lim

ktfite~pt =

0. (10a) (10b) (10c) (lOd) (r — r ) > (r* — r * ) (r — t) = (r* — t*) (r — t) < (r* —t*) . ( H )

shift their assets (capital) to the country where the after-tax return on

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capital relocation is short in the model. Notice that even if the after tax returns are equal one may observe u = 1 or 0.12 These features are compatible with the observation that international return differentials induce capital relocations in the direction indicated above.13 For u E

[0,1] equations (10c) and (11) imply

7 = M — p, where M = max(r — t, r* — r * ) . (12) Hence, the capitalists’ consumption grows at a rate that depends on the after-tax returns in the two countries. Note that it is possible that growth is completely determined by the foreign after-tax return when all the domestic capital ’bangs’ into the foreign country.

2.1 Market Equilibrium

In the closed economy w — 1 , K t = kt. From the budget constraints the steady state market equilibrium is characterized by balanced growth with 7 — (r — r ) — p and r = c*j4[(1 - A )r]1_Q. The growth maximizing policy is given by

f = [ a ( l — a )z l]“ , A = 0. (13)

The relationship between taxes and growth in a closed economy can be read off from Figure 1, p. 29.

Substitution o f the growth maximizing (t, A) combination yields

f — t = f (pr^)- The effect of an increase in efficiency on the maximum growth rate is given by d(^~r) = (p r^ ) p j where ^ = f[a A }~ 1 > 0. The fact that a more efficient economy may have higher maximum growth

and higher taxes in the model is due to the positive externality public services exert on production.

12Some authors such as Lancaster (1973) analyze investment bang-bang problems and simply define indeterminacies away. A n indeterminacy may, however, contain qualitatively valuable information as is shown in this paper.

13For examples o f capital relocations because o f return differentials see Ruffin (1984). © The Author(s). European University Institute. version produced by the EUI Library in 2020. Available Open Access on Cadmus, European University Institute Research Repository.

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For the derivation o f the two-country market equilibrium and given arbitrary tax rates concentrate on the domestic economy first. Divide (7) by kt, and use the fact that in steady state 7* is constant. Rear ranging and taking time derivatives yields 7 = 7* and constant. Also, substituting 7 for 7* in (7) establishes that C * = pkt as the capitalists’ instantaneous consumption in steady state. Hence, in the open economy the domestic capitalists’ consumption grows at the same, constant rate as their capital stock. The total wealth of the domestic capitalists at any point in time is kt and the budget constraint satisfies equation (7). For given w, lo* the world resource constraint is given by

kt + kt = (r + n )K t + (r* + 77') K ’t - G t - G\ - C * - C f - C f - C f where K t — u>kt + (1 — u)*)ht, K t = u)*k't + (1 — ui)kt, G t —(1 — A) r K t

and = (1 — A* )r * K t since the governments run balanced budgets. The production functions imply Yt = r K t + r}Kt and Yt* = r * K t + r fK t-

From the private sector optimality and the steady state conditions the world resource constraint satisfies

'ykt + 7*fc( = (r - r ) K t + ( r * - r * )K t - pkt -

pht-In equilibrium G D P ( = Yt so that G D P must grow at the same rate as output. From the production function it follows that output Yt must grow at same rate as K t since G t grows at the same rate as K t. Then the evolution of the domestic economy is determined by the growth rate of the aggregate, domestically productive capital stock which is given by

r _ K t = -ywe^kn + 7*(1

-K t ueVko + (1 - ' 1 ’

Let a (r ) = r — r, b(r*) = r* — r* and M = max (a (r ), 6(r * )) and notice that the max(-) expressions are symmetric. Thus,

7 = M — p = 7*.

Hence, the capital income component of G N P grows at equal rates across

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countries. That property o f the model is realistic for highly integrated economies in which the capital owners can costlessly shift their capital. But then the aggregate capital stock in (14) grows at

This follows since if there is capital flight (u> = 0,w* — 1) all capi tal is shifted abroad implying K t = 0 and T( = 0. In all other cases the aggregate capital stock grows at the same rate as the capital income com ponent of GNP. In general, G N P and G D P grow at the same rate in the model. Empirically the these growth rates do not seem to be significantly different. (See, for instance, Barro and Sala-i-M artin (1995), chpt. 11.2.) The balanced growth property o f highly integrated economies may look a bit surprising, as the investors act in an extreme way. However, their investment behaviour is such that fiscal and return discrepancies among the economies are immediately ’arbitraged’ out, exerting a smoothing effect on the growth rates. In the model any alteration in return differ entials induces instantaneous convergence to a new steady state. But if there is capital flight, one would not observe balanced growth.

In contrast to the convergence property the capitalists’ allocation decision has important consequences for the instantaneous levels of out put, consumption and the aggregate capital stock.14 From (7) and (12) the capital owners’ instantaneous consumption in steady state is C * =

pkt = pk^e7t, and similarly for the workers’ instantaneous consump tion one gets C™ = (v + At) K t = (p + At) (uk0 + (1 - uj*)k^) e7' when there is no capital flight. For both groups consumption depends on the after-tax return on capital. If a country experiences capital flight, aggre gate production breaks down completely in the model and the workers must ’starve’ . The capital owners, however, survive, because they derive

14For instance, Barro and Sala-i-M artin (1995), chpt. 11.1, mention that the dis tinction between G D P and G N P may be important in some cases. For example, in the state o f W yom ing there exists a significant difference between G N P and G DP, because a substantial fraction o f capital inputs in that state are owned by residents of other states.

{

7 : for V ta, tu* s.t. w ^ 0 A 0 : if u = 0 A w* = 1. uj* ^ 1 (15)

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income abroad and can consume foreign goods.

2.2 The Government

The domestic government maximizes the intertemporal utility of its na tional clientele. For simplicity, it is assumed to be either entirely pro capital ( ’right-wing’) or completely pro-capital ( ’left-wing’ ).15 The capi tal owners’ welfare is

so that the model’s right-wing government is only concerned about growth

of the capital owners’ wealth.

The welfare of the workers is given by

which is not a proper function, since for given M the u ’s may be indeter minate. Notice that V 1 is increasing in 7 and so in M . As M implicitly determines uj and w*, any left-wing policy must try to optimize M . Thus, a left-wing government would also try to maximize growth. More impor tantly, however, the left-wing government wants to secure a high capital stock as that raises wages and provides the basis for redistribution. It will want to avoid any situation that leads to capital flight. As the investors’ capital allocation is extreme, one may say that for a given growth rate the left-wing government wants to ’grab ’ capital.

T h e G o v e rn m e n t in a C losed E conom y. Respecting the right of private property, the governments choose r and A > 0 in order to max

15The welfare measures are derived in Appendix A .T h e paper’s qualitative results would not change if the government represented the agents’ welfare in different pro portions. In the model shifting relatively more political power (social weight) to capital would always imply higher growth. For a formal argument see Appendix B.

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Vta, u>* s.t.

u 7

^ 0, w*

^

1

w —0, u>* = 1, © The Author(s). European University Institute. version produced by the EUI Library in 2020. Available Open Access on Cadmus, European University Institute Research Repository.

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imize their clientele’s welfare.16 The optimal left-wing policy is derived in appendix B and is given by

If p > [(1 — a )A ]° then:

t — p, A = 1 - ^ . (18)

P

If p < [(1 — a ) A ] “ then:

r [ 1 — a ( l — a )A r~ a] = p (l — a ), A = 0 . (19) The (t, A) combination solving these equations is denoted by f and A.

The right-wing government is only concerned about capital income in the model. Maximizing (16) it chooses the growth maximizing tax rate t and does not redistribute. Under the left-wing policy f > f when A > 0 so that growth is not maximized in general as can be visualized using Figure 1, p. 29. Thus, a redistributing government (A > 0) trades off growth against redistribution at a point such as f , A > 0. However, the conditions for redistribution and positive growth are restrictive in the model.

L e m m a 1 For positive growth the income share of (broad) capital must be sufficiently large (a > under a redistributing, left-wing policy.

The lemma is proved in Appendix C and is useful below.

3 Tax Competition

W hat happens to the optimal, closed economy policies if governments have to decide in a two-country world with capital mobility and the gov ernments cannot coordinate their policies? This is a relevant question for

I6Notice that the condition A > 0 restricts the governments in such a way that even a right-wing government does not tax workers. In that sense even a right-wing government is ’nice’ to the workers. A negative A would effectively amount to a tax on wages. © The Author(s). European University Institute. version produced by the EUI Library in 2020. Available Open Access on Cadmus, European University Institute Research Repository.

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countries where full tax harmonization is not feasible. As a consequence governments may engage in tax competition. (For a similar point see, for instance, Sinn (1990) or Bovenberg (1994).) I model tax competition as a two-stage game and assume that the governments move simultaneously, but before the private sector. The strategies o f the governments are the choices o f taxes and redistribution. The governments and the private sector agents move simultaneously. Furthermore, both economies have the same initial capital stock k0 = k^, and are equally efficient, A = A*,

unless stated otherwise. Solving backwards requires a government to maximize (16) or (17) taking its opponent’s choice o f (r * ,A * ) as given. Thus, each government’s problem is to choose taxes and redistribution so that

r, A = argmax { V*\given r*, A *} , j — l,r.

The problem cannot be handled simply by differentiation of the objective function since VJ depends on 7 and so M . Recall M = m ax(r — r, r* — r * ) which is a continuous function, but not differentiable everywhere. I will now analyze each government’s problem in turn.

3.1 Tax competition among similar economies

Consider the domestic, non-redistributing right-wing government. As the welfare measure V r is increasing in 7 and only the growth rate depends on taxes the right-wing governments’ problem reduces to choosing r such that

r = argmax {M ; given r*, A *} . (20)

Thus, it wants to maximize M , given r*, A* and given the optimal, private sector uj and u*. Recall that a (r ) = r — r and b(r*) = r* — r*, and notice that b is independent of r. Then M = max(a, b) and a is a continuous function o f r. But for given r* the function b is as well, because a constant

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is a continuous function of a variable x. Then

M ( r ) = max (a (r ), 6(r * )) a (r ) + 6(t*)

2

a (r ) - 6(r * )

2

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which may be differentiable under certain conditions.17 (See Figure 2, p. 29.) For similar economies notice that f = r*. Suppose the foreign right or left-wing government sets t* ^ r * , then b < b where b = r* — r *. As a consequence there is some r G [t,*, r*] where a > b, because at r,*, r* the functions a and b intersect. From Figure 2, the domestic right-wing government will choose r G (r,*, r*). But then M is differentiable and ^ = r T — 1 = 0 and so r = f is an optimizing response o f the domestic right-wing government.

Suppose the foreign government sets r* = t. In that case the 6(r*)- line would be tangential to the point a and M would not be differentiable anymore. Thus, if r* = f the optimal response is indeterminate.

L e m m a 2 In similar economies the best response of a domestic right- wing government against any foreign opponent is to choose

(1) t — T i f r* < T

(2)

r G [0,1]

i f r

*

—

f

.

The indeterminacy when the opponent sets f reflects the fact that the right-wing government does not care about the aggregate capital stock and w, u* per se. It just wants to ensure that the growth rate of domestically owned capital is high enough. So when the opponent chooses the growth maximizing tax rate, the domestic right-wing gov ernment’s problem has already been solved by its foreign opponent.

17I use the following property o f the max( ) function. (See, for instance, Liedl and

Kuhnert (1992), p. 224.) Let f ( x ) and g{x) be two differentiable functions in x, then

m a x ( f ( x ) , g ( x ) ) / (x ) + g{x) 2 + f ( x ) - g (x ) 2 © The Author(s). European University Institute. version produced by the EUI Library in 2020. Available Open Access on Cadmus, European University Institute Research Repository.

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A domestic left-wing government’s problem is to find r and A such that

r, A = argmax {V l\ given r*, A * } .

Assume A = A* = 0 and suppose t* > t. From Figure 2 it is not difficult to see that if r* > t the domestic left-wing government sets r = f . If f < t* < t , it is optimal to set t — t* — e, where e is small. As t* —> f the domestic left-wing government will definitely set r = t. Thus, L e m m a 3 In similar economies the best response of a domestic left-wing government against any foreign opponent is to choose

(1) r = f if T* > f

(2) r = r* — e, if T < T* < f

(3) t = t, _{if T*}—1T.

Given the best response functions in similar economies the outcome of tax competition is as follows: For two right-wing governments and by symmetry of the problem Lemma 2 implies that there is an infinite num ber of Nash equilibria. That is due to the fact that if one player chooses

f the other player is indifferent what to choose. Qualitatively, however, that makes sense because in a world with two right-wing governments the investors will never pay more or less than f . In the Nash equilibrium the after-tax returns are equal so that capital flight may take place. P r o p o s itio n 1 I f two right-wing governments engage in tax competition in similar economies, there is an infinite number of Nash equilibria. The capitalists never pay more or less than f in either country. Capital flight is possible and there will be maximum GDP growth in at least one econ omy.

An infinite number of equilibria may appear implausible at first sight. However, it has an important economic meaning in the m odel.18

18I f one allows for equilibrium refinements à-la Selten (1975), the introduction of

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A right-wing government is not concerned about the aggregate capital stock. It just maximizes the capitalists’ income. I f the foreign opponent actually chooses the growth maximizing tax rate in equilibrium, then the domestic right-wing government’s problem is solved and it may optimally choose any tax rate. That has significant consequences for the workers in either country. Among all equilibria the one with r = t* = f is of measure zero and so quite improbable (although perhaps the most plausible.) Consider the class of equilibria where r* = f and r € [0,1] and r ^ t. Then in equilibrium one definitely observes capital flight in the domestic economy so that Y = 0 and its workers would ’starve’ . In contrast, the workers in the foreign economy would be quite well off, since all the capital would locate in their country. Hence, under right- right competition, capital flight is quite likely, the workers of one country are really badly off and the capital owners are equally well off in either economy.

I f a left-wing and a right-wing government compete in taxes the Nash equilibrium is unique. In a closed economy the domestic left-wing government chooses r > f . Lemma 2 implies that for all t ^ t the foreign right-wing government chooses r* — t. By Lemma 3 the domestic left- wing government always tries to undercut its opponent’s choice for fear of capital flight. But then the foreign right-wing government makes sure that the capitalists income is maximized by setting r* — f whereupon the left-wing government will choose r = f . As a consequence it cannot be that A > 0.

P r o p o s itio n 2 There is a unique Nash equilibrium in the right-left tax competition game with similar economies. The governments set r =

t = t* . There is no redistribution, A = 0, in the domestic left-wing government’s economy. Capital flight is almost impossible and there is maximum GDP growth in both economies.

small probabilities that the opponent plays irrationally leads to a unique trembling

hand perfect equilibrium in which both right-wing governments set f . As concerns strategic behaviour trembling hand perfection seems a superior concept to require. On the other hand, the m odel’s extrem ely large number o f equilibria may capture some qualitatively interesting economic phenomena. For that reason Nash equilibrium refinements are not considered any further.

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The objective of ’grabbing’ capital prevents redistribution in equi librium and is due to the left-wing government’s fear of capital flight. Capital ’grabbing’ and the right-wing objective of capital income maxi mization reduce the number of Nash equilibria to one. Thus, the objec tives remove a source o f indeterminacy, make capital flight quite unlikely and lead to equal G N P and G D P growth for both economies. That is so, because in equilibrium with r = r* = f , the after-tax returns will be equal and any uj,uj* combination is possible. Thus, in contrast to the closed economy, a non-cooperative environment causes the left-wing government to mimic a growth maximizing policy. Importantly, the pos sibility of capital flight for the domestic economy is o f measure zero. Hence, the workers are ex ante better off under left-right than under right-right tax competition. Proposition 1 implies that under right-right competition capital flight happens in one economy so that the workers in that country will ’starve’. As the capital allocation is indeterminate in an equilibrium with r = r* = f (Proposition 2), the workers may be better off under either a right or a left-wing government. If the capital ists happen to shift more capital into the foreign right-wing government’s economy, its workers will be better off than their domestic counterparts. That has the rather surprising implication that the workers may be better off under a right-wing government.

C o r o lla ry 1 Under left-right tax competition in technologically similar economies (A = A* ), the workers may be better off under a right or a left-wing government.

Economically, the results suggest that in highly integrated, technologi cally similar economies political preferences per se are not very important in determining growth or the well-being of a government’s clientele.

By Lemma 3 two left-wing governments try to undercut each other.

But the process of undercutting leads to t = f = r* and no redistribu tion. © The Author(s). European University Institute. version produced by the EUI Library in 2020. Available Open Access on Cadmus, European University Institute Research Repository.

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P r o p o s it io n 3 There is a unique Nash equilibrium in the left-left tax competition game in similar economies. Both governments set r = f —

r*. There is no redistribution, A = 0 = A* in either country. Capital flight is almost impossible and there is maximum GDP growth in both

economies.

W ith perfect capital mobility redistribution is not optimal in a non- cooperative environment, even though the opponent may have the same distributive preferences. Thus, the effects of the concern for redistri bution are competed away for fear of capital flight. Interestingly, that makes two left-wing governments mimic growth maximizing policies in the model. The workers are compensated for non-redistribution by high growth o f their wage income.

3.2 Tax competition among different countries

I f a domestic right-wing government with a more efficient economy chooses its nationally optimal tax policy, it faces no constraints in doing so. No opponent can do better, if A > A* and r is set such that a — f — t > b.

Thus, a foreign right or left-wing opponent may choose anything and will experience capital flight. The efficient economy’s right-wing government has higher G D P growth than any of its opponents.

A domestic left-wing government wants to undercut its opponent’s tax rate in order to prevent capital flight. It chooses r such that a > b,

because a foreign right-wing government would choose r* if it could and a foreign left-wing government would choose that in the limit. It is an interesting question under what circumstances a left-wing government with an efficient economy chooses to redistribute. Lemma 1 tells us that for positive growth and redistribution a > | which I assume to hold. A domestic left-wing government is able to redistribute and have relatively higher G D P growth if a > b, that is, if r — r > T* ■ Under a redistributing, left-wing policy r = y r ^ [(l — oi)A\« so that

([(1 - a ) A ] « - [ a ( l - > r © The Author(s). European University Institute. version produced by the EUI Library in 2020. Available Open Access on Cadmus, European University Institute Research Repository.

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must hold. Furthermore, for redistribution r > [(1 — a)^4]°. Thus,19

i r ; ([(1 - “ M I - - [ o ( l - “ M 1 - J t > t [(1 - a )A )i

• > £

\ a ) a A

For a > | the LHS is smaller than 0.946. Letting A = x A*, x > 1, the inequality holds if a: > 1.056. Thus, in the model an efficiency advantage of, say, 6 percent is enough for a left-wing government to redistribute and to have higher G D P growth than its right-wing opponent.

P r o p o s itio n 4 A domestic left-wing government with a more efficient economy (A > A*) sets taxes so that it gets all the capital (u = l,u>* —

0), has higher G DP growth than its opponent (T > T* = 0) and may redistribute. The capital income component of G N P grows at equal rates across countries (7 = 7’ ). Furthermore, if it redistributes (A > 0),

the domestic agents are sufficiently impatient (p > [(1 — a )j4 ]i), the domestic economy is relatively efficient [A > (2^ 1) ° a A *), and the share of (broad) capital is large (a > |).

Efficiency differences induce capital flight for an inefficient economy. Theoretically, an efficient economy’s right-wing policy leads to a higher G D P growth rate than a left-wing policy, when competing with inefficient economies’ governments. The efficient economy’s left-wing government tries to get all the capital, but does not necessarily choose the growth maximizing tax rate. Thus, a hypothetical comparison o f regimes when

A > A* reveals that tax policies, favouring the non-accumulated factor of production might be bad for growth.

However, by Proposition 4 one may observe higher taxes favouring the non-accumulated factor of production and higher G D P growth than in another, less efficient economy with a right-wing government. Thus, in integrated economies it is well possible that an efficient economy’s, left-wing government distributes towards labour and grows more than

19Use the fact that P > x and x > Q implies P x > Qx.

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a less efficient economy under a right-wing policy.20 For that reason a government that wishes to redistribute is relatively more interested in having a superior technology brought about by innovations and technical progress.

The paper’s propositions are testable and hypothesize that optimiz ing governments in an integrated world would only distribute resources towards the non-accumulated factor of production, if they have an ef ficiency advantage vis-à-vis another government’s economy. Is that not the case, it is argued that a left-wing government would optimally not redistribute. But then one would observe a positive association between redistribution and growth in cross-country growth regressions when in large samples the m ajority of redistributing governments acts as shown in the paper. Hence, in the model the effect of redistributive taxation on growth in an integrated world is less an issue of political preferences, but more one o f efficiency differences.

4 Conclusion

Many theoretical models show that redistributive taxation reduces growth On the other hand, redistribution is often found to correlate positively with growth in cross-country growth regressions. This paper offers an explanation o f the puzzle.

Analyzing the growth-redistribution problem in a two-country world with capital mobility and tax competition, the possibility of capital out flows features saliently in the optimal decisions of redistributing govern ments. In the paper a left-wing government wants to attract as much capital as possible for securing high wages and for redistribution. It is concerned about the level and growth of domestic GDP. In contrast, a right-wing government only wants to maximize the national capitalists’ return on capital.

20Notice that the efficient economy’s government does this at the expense o f the inefficient economy’s workers. In that sense the workers o f an inefficient economy have to be afraid o f a ’nationalistic’ , left-wing policy abroad.

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For tax competition among similar economies and no matter what distributional preferences a government has, the fear of capital flight leads to maximum growth of the capital income component of G N P in equilibrium and no redistribution takes place. That holds even though all governments might care about redistribution. The reason is that capital is good for redistributing governments. Capital flight reduces wages and the welfare loss incurred by a drop in wages outweighs the welfare gain derived from redistribution. However, political preferences do matter as regards GDP. Under right-right tax competition one economy will surely experience capital flight and its G D P will not grow. That constellation is bad for the workers. I f a left-wing government competes against any opponent, no capital flight will take place. In that sense, (re-)distributive preferences are important for a country’s non-accumulated factor o f pro duction.

If the countries are technologically different, more capital will locate in the efficient economy and it will have higher growth. If the efficient country’s government wishes to redistribute, it may to do so without loosing any capital. The amount of redistribution depends on who the opponent is and on the efficiency gap that distinguishes it from its op ponents.

From these arguments it follows that in cross-country growth re gressions one would observe a positive association between growth and redistribution.

Furthermore, the paper argues that policies that make an economy more efficient are in the interest of both domestic workers and foreign as well as domestic capital owners. In comparison to other economies redistributive taxation does not necessarily cause slower growth if op timizing governments in an integrated world engage in tax competition and a redistributing government’s economy is technologically superior.

Several caveats apply. If governments could condition on the history of the game, problems of time inconsistency might arise. The paper has not analyzed the role of tariffs. It is likely that a country that faces the danger of capital outflows will try to set up tariffs. These and other problems are left for further research.

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A

Welfare

The agents’ welfare is V r = f ‘ ln C tk e pt and V 1 = f* In C™ e pt. Let

t —* oo and use integration by parts. For this define — In C{, dv\ — e~ptdt where j = k, W . Recall that dv2 = 7^ = 7 for j — k, W and constant in steady state. Then v\ = —~p e~pt so that

In C\ e~pt dt

where Cq = pK 0 and C™ — (t) + At)K 0 and K 0 = (wfc0 + (1 — a>*)£<))• Evaluation at the particular limits yields the expressions in (16) and (17).

B

The optimal closed economy policies

Suppose the government solves max (1 — (3) V r + (3 V 1 s.t. A > 0 where (3

r, A

denotes the social weights attached to the workers’ intertemporal welfare. The first order conditions for r and A are given by

P Vr + A

(v

+ Ar)p

Vx + r

(77 + \ r)p = 0

Concentrating on an interior solution for A, simplifying and rearranging yields

g Vr + A 7t 3 Vx + T 7a

iv

+ At) p

{v

+ Ar) p (B l)

Notice that j T must be negative for the first equation to hold, so in the optimum t > t. Division of these two equations by one another yields — 'J-l and must hold in an optimum with A > 0. Since 7a = r x and 7t = r T — 1 we get (r]T + A)r x = {vx + r ) ( r T - 1) which upon multiplying out becomes f]Tr x + \rx = r Tr/x + r Tr — r)x — t. Notice r xi]T = r Tr/x and

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that ï] = j• Then Arx — rTr — ~ Lrx — T and so

^A + rx = rrT - r & r r T t

rx r x

Let

E

= (1 — a )v4 [(l - A )r] ° so that r T —

aE{

1 — A) , r x —

a E ( —r).

Then ^ = - ra-f f e -A-) = - ( 1 - A). Thus, for above

A + (1 — A) + - — — T

r\

— T

which means that E — 1 and

1 - A (B2)

For the first order condition for r note that rj =

(1

—

a)j4[(l — Ajr]1 “

=

£[(1-A)r]

=

[(l-a )y l]«

. Furthermore,r/T —

(1

- a )( 1 -

A),

r T —

a (l-A ).

Then eqn. (B2) entails

A

= 1 — so that

rj + Ar = [(1 - a )A ]i + r ^1 - j = r .

Then the first order condition for r becomes

o Vr + A _ 7 r r?T + A _ 7T r]T + A _ r

P {V + At) p t f3p 7r @p*

From above = ~ a(*i-A)-i+A = ~1 so that r = /3p. Thus,

f = /3p and A = 1 - q ) ^ ° . (B3)

PP

which is equation (18) when /? = 1. Recall that these equations hold for A > 0, that is, for /3p > [(1 — a )A ]i.

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Suppose A = 0, then the first order condition becomes ÜL V r r - 1 ( i - g ) g 0p tE a E — 1 Pp (1 — a)(3p = t— a r E

so that the solution with A = 0 is given by

(1 — a)f3p =

t

[l

—

a (l - a)Ar a]

(B4)

which holds only if f3p < [(1 — a ) A ] ° . For /3 — 1 that is equation (19) in the text. If (3 — 0, the government is right-wing and chooses

r = t. Furthermore, implicitly differentiating yields ^ > 0 and so

% = f? % < 0 under both policies. Hence, shifting social weight to labour reduces after-tax returns and growth in the model.

C

Proof of Lemma 1

Suppose the left-wing government redistributes wealth in the optimum. Then (18) holds with A > 0. I will now check under what conditions we have 7 > 0 with A > 0. If (18) holds then (1 — A ) f = [(1 - a)>4]i. Let 0 = (1 — a )A, then

f = p has to satisfy f > G » A ( •■a ) Q ° > 2 f => f ( — — ) © i > 0 " 2 f \1 - a ) \ l - a ) 3 © The Author(s). European University Institute. version produced by the EUI Library in 2020. Available Open Access on Cadmus, European University Institute Research Repository.

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Figure 1: The relationship between 7 and r in a closed economy 1

Figure 2: M (t, t*) for the domestic government and given r*

M ( r , r * ) © The Author(s). European University Institute. version produced by the EUI Library in 2020. Available Open Access on Cadmus, European University Institute Research Repository.

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