4 Tax competition in the presence of trade unions

Do trade unions trigger or relax capital tax competition?

Nelly Exbrayat^y, Carl Gaigné^z: and Stéphane Riou^x{

September, 2011

Abstract

We analyze the impact of labor market rigidities on tax competition between two imperfectly integrated countries. Following a shift from a competitive to a unionized labor market in both countries, the capital tax can be adjusted upward in the country with the less rigid labor market, whereas the capital tax is always adjusted downward in the country with the more rigid one. Moreover, by reducing the labor cost di¤erential between countries, trade liberalization gives rise to tax and welfare convergences. Finally, when all of the labor markets are unionized and unions’ preferences di¤er, we show that the majority of capital is invested in the

‘low-wage and high-tax’country. Nevertheless, for asymmetric labor market regimes (competitive vs. unionized), the spatial pattern may be partially agglomerated in the unionized country.

Keywords: Tax competition, trade unions, capital mobility, trade integration.

JEL Classi…cation: F12, F16, H25

We wish to thank Simone Moriconi, Kristian Behrens and Gilles Duranton for their useful comments and suggestions. We would also like to thank the participants of the VIIth RIEF Doctoral Meetings in Rennes, the 8th Public Economic Theory meeting, the CORE spatial economic seminar, the GATE seminar, the WZB seminar, the FUNDP seminar, the 24th meeting of the JMA, the COMPNASTA workshop, and the Public Economic Group seminar of ENS-Cachan.

yUMR CNRS GATE Lyon-Saint-Etienne, Jean Monnet University, Saint-Etienne.

zINRA, UMR 1302, SMART, Rennes.

xUMR CNRS GATE Lyon-Saint-Etienne, Jean Monnet University, Saint-Etienne.

{Corresponding author. Stéphane Riou. E-mail: stephane.riou@univ-st-etienne.fr. Address: GATE Lyon-Saint-Etienne, 6 rue basse des rives 42023 Saint-Etienne, cedex 02, France.

1 Introduction

In this paper, we analyze the impact of labor market rigidities on tax competition between two imperfectly integrated countries. Speci…cally, we address the two following questions.

First, do unionized countries impose higher or lower capital taxes than non-unionized ones? Second, when countries di¤er with respect to their labor market rigidities and compete in taxation, what is the tax competition outcome and where do …rms locate?

Indeed, there are strong arguments for introducing labor market imperfections in a tax competition analysis. Various examples suggest that governments adjust their corporate tax rates to compensate for changes in labor market legislation. In 1998, the United Kingdom introduced a national minimum wage for the …rst time (National Minimum Wage Act 1998) and, at the same time, decided to make signi…cant corporate tax cuts.

In May 2007, the US Congress approved the …rst increase in the federal minimum wage in nearly a decade (Fair Labor Standards Act 2007), but President Bush and Senate Republicans made business tax breaks a condition for supporting this minimum wage increase.¹ Such a strategy has been also adopted by some Canadian provinces after increases in the minimum wage level (e.g., British Columbia in 2001, Ontario in 2003).

The possible existence of such a compensation policy has been empirically tested by Mittermaier and Rincke (2010). Using data on 16 Western European countries during the period from 1982 to 2005, they provide empirical evidence that countries with relatively high labor costs tend to set lower corporate income tax rates. According to their estimates, a one-standard deviation increase in the unit labor cost di¤erential decreases the statutory tax rate by 7.3 to 7.5 percentage points.

The empirical evidence also suggests that one has to account for the level of trade integration when investigating the in‡uence of labor market rigidities on …scal choices.

Indeed, it is now recognized that globalization forces a¤ect business tax policies by in- ducing higher tax base elasticities (Devereux et al., 2008; Rodrik, 1997).² Moreover, and crucially, trade integration is not without consequences for labor market outcomes. By inducing higher labor demand elasticities, trade integration may erode the bargaining power of labor vis-à-vis capital in the sharing of rents. As Rodrik notes: The reason is

1The two chambers accepted tax breaks worth $8.3 billion over a period of 10 years. The previous increase in the US minimum wage in 1996 was also associated with 4.8 billion dollars’worth of tax breaks.

2Through a panel of 21 countries between 1982 and 1999, Devereux et al. (2008) show that the relaxation of capital controls puts more intense competitive pressure upon corporate tax rates. Using data concerning 18 OECD countries over the period 1965-1992, Rodrik (1997) …nds that taxes on capital respond negatively to trade openness.

that employers and the …nal consumers can substitute foreign workers for domestic work- ers more easily - either by investing abroad or by importing the products made by foreign workers (Rodrik, 1997, p. 16). One might then wonder whether trade integration could lessen tax competition by reducing wage claims and mitigating the need for governments to compensate …rms for labor market rigidities.

To answer the above questions, we set up a model of generalized oligopoly, where two imperfectly integrated countries use capital taxation to maximize national welfare. Dif- ferent labor market regimes are considered. We start with a benchmark case, where both labor markets are competitive and labor supply is elastic. Then, we introduce rigidities arising from the presence of monopoly unions and consider two sources of asymmetry:

i) both countries are unionized, but the unions exhibit di¤erent preferences for wages;

ii) one country is unionized while the labor market is perfectly competitive in the other.

Finally, we adopt a game-theoretic approach where …rms, governments, and unions act non-cooperatively, and the governments are Stackelberg leaders.

Our main results are as follows. When trade unions share identical preferences, a shift in both countries from competitive labor markets to unionized ones causes governments to levy lower capital taxes and decreases welfare. Interestingly, this is no longer the case in the asymmetric con…gurations. Speci…cally, in the country with the less rigid labor market, the government can increase its capital tax compared to the benchmark case.

As expected, the level of trade liberalization plays a key role in these tax adjustments.

Speci…cally, a decline in trade costs reduces the labor cost di¤erential between countries and leads the governments of unionized countries to lower their business tax di¤erential.

As a result, the di¤erence in national welfare between the countries is reduced. Finally, when all labor markets are unionized and the unions’preferences di¤er, we show that the majority of capital is invested in the ‘low-wage and high-tax’country. Nevertheless, for asymmetric labor market regimes (competitive vs. unionized), the spatial pattern may be partially agglomerated in the unionized country.

Our contribution relates to di¤erent strands in the literature. Our model can be considered an extension of the literature analyzing tax competition within a ‘new economic geography’framework (Baldwin and Krugman, 2004; Gaigné and Riou, 2007; Hau‡er and Wooton, 2010; Ottaviano and Van Ypersele, 2005). Combining increasing returns with positive trade costs and countries with asymmetric market sizes, this literature shows that mobile capital would bene…t from an agglomeration rent in the larger countries, allowing their governments to set a higher level of taxation. All of these papers, however, consider perfectly competitive labor markets and inelastic labor supply.

A second strand in the literature analyzes the e¤ects of trade liberalization in an international unionized oligopoly framework. Based on the seminal paper by Brander and Spencer (1988), Naylor (1998, 1999) focuses on the impact that trade liberalization may have on the bargained wage in a monopoly trade union wage setting. In these models, reduced trade costs increase the total volume of production. Thus, unions translate the resulting higher labor demand into higher wages without reducing the number of jobs.

Lommerud et al. (2003) complete Naylor’s work by introducing the possibility of plant relocation and an asymmetry in the unionization of the labor markets. They show that, in terms of welfare, unionized labor can lose out from trade liberalization because of job losses resulting from higher wages.³ These models, however, ignore tax policy and its possible interactions with the trade unions’positions.⁴

An exception is a recent article by Hau‡er and Mittermaier (2011). They focus on tax competition to attract an outside …rm between a unionized and a non-unionized country.

An interesting result is that attracting this outside …rm with a generous tax environment may be a policy option that promotes wage moderation. In many cases, the unionized country succeeds in attracting the mobile …rm, a scenario that can be reproduced in our model of generalized oligopoly, given a restriction on the wage preferences in the unionized country. Our model di¤ers from that of Hau‡er and Mittermaier in several ways. First, we consider an additional case with two unionized countries that exhibit di¤erent wage preferences. Second, all of the …rms in our generalized oligopoly model are mobile, whatever the labor market regime in the country where the capital owners reside, whereas Hau‡er and Mittermaier (2011) consider a single incumbent …rm located in the unionized country with no possibility of relocation. In this article, we demonstrate that these alternative assumptions matter for the results.

The rest of the paper is organized as follows. In the next section, we develop the model.

In section 3, we analyze the tax competition outcome in the benchmark case, where both labor markets are competitive. In section 4, we consider a case with monopoly unions in both countries, and an asymmetric con…guration, where the labor market is unionized in only one country. Section 5 provides a welfare analysis. The last section concludes.

3These papers belong to a growing body of research. See also, Mezzetti and Dinopoulos (1991), Zhao (1995), and Lommerudet al. (2008).

4Most of the papers on unionized oligopoly with two countries assume an active …rm in each country and an outside …rm that the governments attempt to attract. As mentioned by Hau‡er and Wooton (2010), this leads to the comparison of discrete equilibrium allocations and speci…c scenarios that are di¢ cult to generalize.

2 Model

The economy consists of two countries, labeled i = H; F. The variables associated with each country will be subscripted accordingly. Because our focus is on the impact of labor market imperfections on tax policies, we control for any other exogenous advantages by assuming that the two countries have identical market sizes and technologies. We denote by l the mass of workers/consumers living in each country. Each individual works and consumes in the country she lives in. Moreover, each resident is endowed with k units of capital that she/he inelastically supplies. Thus, there are 2lk units of capital in the economy, and capital is internationally mobile. Finally, the government of each country is benevolent and maximizes the total welfare of its residents by levying a lump-sum tax or subsidy on capital (ti), based on the source principle, and a lump-sum tax or subsidy on workers ( _i).⁵

2.1 Preferences

To make the model analytically tractable, we assume that all of the residents share the same quasi-linear utility function.⁶ Speci…cally, a consumer residing in country i solves the following problem:

M ax

x^d_i;l^s_i

u_i a x^d_i

2 x^d_i +z

2(l_i^s)² (1)

s:t: y_i = x^d_ip_i+z (2)

where x^d_i denotes the consumption of the manufactured good, z the consumption of the numéraire, l^s_i the labor supply and >0 is a measure of the preference for leisure. The variabley_i is the net income, which depends on the status of the individuals in the labor market:

y_i = z+rk+w_il_i^s _i for employed workers (3) y_i = z+rk+b_i for unemployed workers

5The assumption of lump-sum taxation is commonplace in the tax competition literature based on economic geography models (see Ottaviano and van Ypersele, 2005; Hau‡er and Wooton, 2010). The reason is that introducing an ad valorem tax would not qualitatively change our results but would require numerical simulations to solve the model. Furthermore, many existing subsidy schemes take a lump-sum form (Hau‡er and Mittermaier, 2011).

6Although the income e¤ect is erased with a quasi-linear utility function, Dinopoulos et al. (2007, p.22) show that this type of preferences behaves reasonably well in models of international trade.

with z being the numeraire endowment of each worker, w_i the national wage, and r the world net return to capital. Thus, rk denotes the individual net income of capital whilew_il^s_i is the individual labor income.⁷ Finally, b_i are unemployment bene…ts for each unemployed individual, which are assumed to be exogenous. It should be noted that the numeraire is unproduced, costlessly tradable and the initial endowment z is large enough for individual consumption of the numéraire to be strictly positive at the market outcome.⁸

2.2 Technology and market structure

We consider n …rms producing a homogeneous good with increasing returns to scale and behaving as Cournot competitors. Although new trade theory with capital mobility typically focuses on trade in di¤erentiated products, it is convenient from an algebraic standpoint to assume that manufacturing …rms produce a homogeneous good. Even in the presence of trade costs, trade arises because markets are imperfectly competitive (Brander and Krugman, 1983). Furthermore, the economic geography e¤ects uncovered under monopolistic competition and di¤erentiated products are qualitatively the same as under oligopolistic competition with a homogeneous product (Gaigné and Wooton, 2011;

Hau‡er and Wooton, 2010; Thisse, 2010).

Similarly to Ottaviano and van Ypersele (2005), the marginal labor requirement in the manufactured sector equals zero. The production of the manufactured good requires a …xed amount f of labor units and one unit of capital.⁹ Shipping the manufactured good is costly. Speci…cally, …rms incur a trade cost of > 0 units of the numeraire per unit of good shipped between the two countries. We assume that the product markets are segmented and that the labor markets are national. Each …rm determines a quantity speci…c to the country in which it sells its output and wages can di¤er from one country to another because workers are internationally immobile. Hence, quantities, prices, and wages are speci…c to each country but interdependent because of capital mobility.

7Hence, residents are both workers and capital owners. This assumption is standard in the tax competition literature, even in the presence of unemployment (see Ogawaet al., 2006; Fuest and Huber, 1999; Richter and Schneider, 2001).

8The model can easily be extended by introducing a second sector producing the numeraire under constant returns and perfect competition, using a speci…c factor that is in …xed supply.

9As we will show in section 3, we abstract from wage adjustments arising from quantity variations under these assumptions. Together with the assumption of …rm mobility, this implies that wages are directly related to the relative attractiveness of a country.

The operating pro…ts of a …rm located in country i are given by

i =pixii+ (pj )xij

wherex_iiis the quantity that the …rm supplies to domestic consumers, x_ij is the quantity it sells to foreign consumers and p_i is the price prevailing in country i. Thus, its net pro…ts are expressed as follows:

i = _i f w_i r_i t_i (4)

where r_i is the rental rate of capital in country i. In the long run, r_i is equalized across countries due to capital mobility.

2.3 Labor market regimes

We consider two types of wage setting regimes: competitive and unionized labor markets.

The latter regime induces a higher wage than the competitive wage, thereby generating unemployment. Three types of unionized labor market models are currently considered in the literature on trade unions: the monopoly union model, the wage bargaining model and e¢ cient bargaining models (see Oswald, 1985). Here, we choose the …rst alterna- tive, where the labor market is dominated by a monopoly union that sets a wage for all

…rms in the country, subject to the labor demand function.¹⁰ This combination of linear Cournot oligopoly and monopoly unions is commonplace in the literature.¹¹ The union’s preferences are characterized by the following Stone-Geary-type utility function:

U_i = (w^u_i w) ⁱ(L^d_i)^{1 i} (5)

where w^u_i is the nominal wage rate set by the union in country i, L^d_i the level of em- ployment in country i, and w the reservation wage rate.¹² As emphasized by Cahuc and Zylberberg (1991), the objective function above is a simple way of considering that unions are concerned with both wages and employment, and it avoids assigning an arbi- trary value to the preferences of unions. Hence, the parameter _i 2 (0;1) represents the relative importance of wages over employment for the trade union in country i.

10The assumption that workers are shareholders would be problematic for the two other types of models.

In this case, both parties would negotiate on behalf of the same interest.

11Examples are Bughin and Vannini (1995), Lejour and Verbon (1996), Leahy and Montagna (2000), Lommerudet al. (2003), Naylor (1998, 1999), Straume (2003), Richter and Schneider (2001), and Leite- Monteiroet al. (2003) and Hau‡er and Mittermaier (2011).

12It is assumed that unions have perfect information about the labor demand function.

2.4 Governments

Governments maximize the welfare of their residents by non-cooperatively choosing the tax on capital (ti) and on employed workers ( _i). Taxes exist only for the purpose of redistributing income and we disregard e¢ ciency considerations of public good provision (Persson and Tabellini, 1992). Given the one-to-one correspondence between …rms and capital, the budget constraint is given by:

t_in_i+ _il_i^e=b_il^u_i (6)

where l_i^e is the number of employed workers, whereas l_i^u is the number of unemployed workers. Inserting (2) and (3) in (1) and after rearranging, we obtain the aggregate welfare in each country:

W_i =lS_i+rkl+l_i^eh w_il_i^s

2(l_i^s)² _ii

+l^u_ib_i+constant (7) where Si denotes the consumer’s surplus. The national welfare is the sum of six terms:

total consumer surplus, capital income, labor income, disutility from labor, labor tax income, bene…ts to unemployed residents and a constant equal to the total endowment of the numeraire. Therefore, the maximization program of the government is closely related to labor market performance. When the labor market is competitive, l_i^u = 0 and l_i^e = l, while l^u_i > 0 and l^e_i < l (with l_i^u+l^e_i = l) under labor market imperfections. When the wage is higher than the competitive wage, we obtain L^d_i = l^s_il_i^e, where l_i^s stands for the labor units supplied by each worker so that

l^e_i =L^d_i=l^s_i.

3 Tax competition with competitive labor markets

We …rst describe the tax competition outcome in a benchmark case without labor market imperfections. The model consists of a sequential game with perfect information, where the players are workers, …rms and governments. In the …rst stage, the two governments simultaneously and non-cooperatively choose a lump-sum tax or subsidy. In the second stage, capital owners choose the location of their capital investment and in the last stage

…rms and residents make their respective production, consumption and labor allocation choices. The game is solved by a sub-game perfect Nash equilibrium, involving backward induction beginning at the last stage.

3.1 Product, labor and capital market outcomes (stage 3)

Given (1) and (2), the individual demand for the manufactured good is given byx^d_i =a p_i. Hence, the inverse individual demand for the manufactured good in countryi is given by p_i = a Q_i=l with Q_i = n_ix_ii+n_jx_ji, n_i being the number of …rms located in country i (with n₁ +n₂ = n). In addition, maximizing (4) with respect to x_ii and x_ij yields the following quantity choices in equilibrium: x_ii =lp_i and x_ij =l(p_j ). The market clearing condition for the manufactured good in each country, given bylx^d_i =n_ix_ii+n_jx_ji, gives the equilibrium price prevailing in each country:

pi = a+ n_j

1 +n (8)

The price in country iincreases with trade barriers because the local …rms are more pro- tected against foreign competition, and with the number of …rms located abroad because, in this case, the local competition is less intense. At these equilibrium prices and quanti- ties, the operating pro…ts made by …rms located in countryi are described as follows:

i = a+ n_j 1 +n

2

l+ a+ n_i 1 +n

2

l (9)

Moreover, we assume that the trade cost is non-prohibitive. Put di¤erently, we focus on cases where trade costs are su¢ ciently low to ensure that each …rm exports into the foreign market (xij > 0 and x_ji > 0) regardless of their spatial distributions. Formally, this condition is given by:

< trade a=(1 +n)

We now turn to the labor market outcome. By inserting the budget constraint (2) into the resident’s utility function (1) and maximizing the resulting expression with respect to l^s_i, we obtain the equilibrium individual labor supply in countryi:

l_i^s=w_i= (10)

such that the total supply of labor units is given by lw_i= . Our approach di¤ers from existing models of trade and location with tax competition where labor supply is inelastic.

In our framework, individual labor supply depends upon wages and the disutility of labor.

The national demand for labor units, related to the labor requirement and the number of

…rms, is given by:

L^d_i =f n_i

The labor market clearing condition yields the equilibrium wage rate in country i for a given location of …rms:

w_i^cc =f n_i=l (11)

where the superscript^ccindicates that the labor markets are competitive in both countries.

Intuitively, the competitive wage prevailing in a country is a decreasing function of the number of workers and an increasing function of the number of …rms located in the country.

Capital market clearing implies that there are n = 2lk (up to the integer problem) oligopolistic …rms.¹³ However, the …xed cost of entry, i.e. the cost of acquiring the one unit of capital needed for production, is endogenous in our framework. Because there are positive pro…ts at the current price of capital, capital owners bid up the price of capital until pro…ts are zero. In other words, the equilibrium rental rate in each country is determined by a bidding process for capital, which ends when no …rm can earn a strictly positive pro…t at the equilibrium market price. This yields

r_i = _i f w_i^cc t^cc_i : (12)

3.2 Location of capital (stage 2)

The location of capital is governed by the spatial di¤erence in net returns to capital (12), evaluated at equilibrium prices (8) and wages (11). Let0 1 stand for the share of capital in country H.¹⁴ A spatial equilibrium 2 (0;1) is such that no unit of capital can induce a higher return by being invested in another country. Formally, an interior equilibrium arises at ^cc 2(0;1)when H( ^cc) f w_H^cc( ^cc) t^cc_H = _F( ^cc) f w_F^cc( ^cc) t^cc_F. Solving this equality with respect to ^cc yields

cc = 1 2

(1 +n) (t^cc_H t^cc_F) 4nl ²+ 2 f²(1 +n)n=l:

The location equilibrium is primarly the result of three mechanisms. The …rst is standard, and known in the economic geography literature as a pro-competitive e¤ect.

When a country hosts new …rms/capital, existing domestic …rms face more competitors in their domestic market and fewer in the foreign one. Thus, the domestic price falls, and the foreign price rises (see 8). Domestic sales generate more revenues than foreign

13Indeed, given that each …rm must use one unit of capital and the amount of capital is exogenous and equal to2lk, the number of …rms is exogenous and equal to2lk.

14Hereafter, the terms ‘capital’ and ‘…rms’ are indi¤erently used, as a …rm needs one capital unit to produce.

sales because of the trade cost (see 9), so that this e¤ect acts as a dispersion force. The pressure on the cost of labor induced by the agglomeration of …rms is the second force a¤ecting the international allocation of capital. Indeed, the attractiveness of the country with the …scal advantage is moderated for high …xed requirements of labor (f) and high disutility from labor ( ). In this case, the …scal advantage is counteracted by a strong wage pressure that entices …rms to relocate. Finally, the location choice is a¤ected by the tax wedge. Unsurprisingly, a unilateral rise in capital taxation in a country leads to an out‡ow of capital from this country (d ^cc=dt^cc_H <0). Speci…cally, the tax base elasticity in each country (de…ned as "^cc_i = d ^cc=dt^cc_H:t^cc_H= ^cc) has an interesting property: it is increasing with trade integration (d"^cc_i =d < 0). Indeed, observe from (8) that prices become less and less sensitive to the spatial distribution of …rms as trade costs decrease.

Through this e¤ect, trade integration weakens the dispersion force associated with price competition and strengthens the weight of taxes in the capital location choice.

3.3 Equilibrium tax policies (stage 1)

We now solve the …rst stage of the game and characterize the subgame perfect Nash equilibrium (SPNE, hereafter). When the labor market is competitive, the government’s budget constraint amounts to _il = t_i ^cc_i n.¹⁵ Inserting the equilibrium level of labor supply (10), prices (8) and competitive wage rates (11) in the welfare function (7), knowing that l^u_i = 0 and l_i^e=l, the objective function of each government amounts to:

W_i^cc=lS_i+ n

2r+t_i ^cc_i n+l(w_i^cc)²

2 +constant (13)

where r represents the net return to capital at the location equilibrium (r = rH( ^cc) = r_F( ^cc)) while the fourth term represents the gross total wages of residents minus their disutility from labor. The consumer surplus S_i, evaluated at the equilibrium price in countryi, is given by:

S_i = 1 2

n²[a (1 ^cc_i )]²

(1 +n)² (14)

Before proceeding further with the analysis, we isolate how each component of the aggregate welfare reacts in response to a tax variation. Let us …rst consider the e¤ect of a variation in capital taxation on the domestic consumer’s surplus. By introducing

15Because budgets have to be balanced, the policy problem faced by each government is one- dimensional: the choice of the capital tax rate determines the tax rate on workers required to satisfy the budget constraint.

the location equilibrium in (14), we can easily show that to lower prices in its domestic market, each government has an incentive to set a low tax burden on capital:

dSi

dti

= @S_i

@p_i

@p_i

@ ^cc_i

@ ^cc_i

@t^cc_i <0:

Second, the e¤ect of a marginal variation inti on the net return to capital is given by:

dr dti

= @ _i

@p_i

@p_i

@ ^cc_i

@ ^cc_i

@t^cc_i

| {z }

+

f@w^cc_i

@ ^cc_i

@ ^cc_i

@t^cc_i

| {z }

+

1?0

This expression encapsulates one direct e¤ect and two indirect e¤ects. We …rst focus on the indirect e¤ects. By inducing more price competition among …rms, a tax cut reduces the operating pro…ts. In addition, when a unilateral tax cut is enacted, the labor demand shifts upwards and the cost of labor rises. Hence, a unilateral decrease in corporate taxes gives rise to a lower gross-of-tax capital income. Nevertheless, as expected, a lower tax burden has a direct positive e¤ect on net capital income.

Depending on the sign oft^cc_i , the third term in (13) describes the capital tax revenues or the …scal contribution of workers as taxation is assumed to be redistributive. The e¤ect of a unilateral tax change on this term is ambiguous:

d(t_i ^cc_i n)

dt^cc_i = ^cc_i n+t^cc_i n@ ^cc_i

@t^c_i = ^c_in(1 "^cc_i )?0

Starting from positive capital taxation, the tax base elasticity has to be low enough to allow an increase in the capital tax to increase capital tax revenues.

Finally, we can investigate the e¤ect of the tax policy upon the labor market compo- nent of the welfare equation, that is, gross labor income minus the disutility from labor.

After substitutions and simpli…cations, we obtain:

d l(w^cc_i )²=2

dt^cc_i = f² n² 2l

@( ^cc_i )²

@t^cc_i <0

Clearly, reducing the tax burden on capital positively a¤ects the wage rate net of the disutility from labor. The mechanism at work is simple: a tax cut generates an in‡ow of capital that increases the competitive wage level.

Maximizing (13) with respect tot^cc_i , we obtain the tax on capital at the SPNE in each country:¹⁶

~t^cc_i = nl [2a (2n+ 3)]

2 (1 +n)²

~t^cc: (15)

16Hereafter, the superscript^~ will denote variables at the SPNE.

Trivial calculations reveal that ~t^cc >0, as long as > with 2a=(2n+ 3) < _trade. Below this threshold level of trade costs ( ), governments subsidize capital and tax labor income. Furthermore, capital taxes describe a J-shaped curve with respect to because d~t^cc=d T 0 when R =2. Starting from high trade costs ( ), a gradual decline in trade barriers reduces capital taxes. When trade liberalization reaches intermediate levels ( > > =2), governments subsidize capital. Hence, the subsidy level rises as trade costs decline further. Nevertheless, when trade costs reach =2, the cost for workers to …nance higher subsidies for …rms exceeds the bene…ts they enjoy from this policy.

Consequently, the subsidy level for capital shrinks, and ~t^cc tends to zero when trade liberalization approaches free trade. Put di¤erently, tax competition is relaxed when trade costs reach low values.¹⁷

Given the perfect symmetry of the model, the location equilibrium is symmetric (that is, ~^cc = 1=2). Inserting it into the competitive wage (11), we get the level of wages w~^cc in each country at the SPNE:

~

w^cc_i = f n

2l w~^cc (16)

4 Tax competition in the presence of trade unions

In this section, we consider distorted labor markets and evaluate their in‡uence on the tax competition outcome. Because wages are now determined by trade unions, our model is a four-stage game, and three possible con…gurations should be considered: the union is a Stackelberg leader, the government is a Stackelberg leader, or both play Nash. In the following, we focus on the case where governments act as Stackelberg leaders (for a similar approach, see Palokangas, 1989; Fuest and Huber, 1999; Hau‡er and Mittermaier, 2011). This implies that when deciding upon its tax policy, each government is aware of its in‡uence on trade unions’wage choice and can adjust its tax policy strategically to a¤ect the wage claims. Clearly, however, there is no consensus on the most relevant sequence of events that one should consider. Thus, we evaluate the robustness of our propositions under the two alternative sequences of events in a technical appendix, where we show that all of the results are qualitatively unchanged.¹⁸ Moreover, the international di¤erences

17Interestingly, we thereby show that the J-shaped relationship between capital taxes and trade costs, which was …rst demonstrated in the tax competition literature based on NEG models with a constant wage (Ludema and Wooton, 2000; Kind et al., 2000; Ottaviano and van Ypersele, 2005; Hau‡er and Wooton, 2010), also holds when wages increase with the share of local …rms.

18The technical appendix is downloadable at http://www.gate.cnrs.fr/spip.php?article441.

in labor market institutions invite us to consider the case of asymmetric preferences for wages among trade unions. Without loss of generality, we will assume that the labor union in country F has an identical or a stronger preference for wages than the labor union in countryH ( _{F H}).

In the following subsections, we solve the previous stages where …rms make their location choices (subsection 4.1), trade unions set wages (subsection 4.2) and governments set their tax policies (subsection 4.3).¹⁹ The last subsection extends our analysis to an extreme and polar case where one country adopts a perfectly competitive labor market, while the other is distorted by the presence of a trade union.

4.1 Capital location and tax base elasticities (stage 3)

Let ^uu denote the share of capital located in country H when both labor markets are unionized. The choice of capital location is made for the given wage levels chosen by unions (w_i^uu) and corporate taxes in each country (t^uu_i ). Speci…cally, the location equilibrium arises when H( ^uu) t^uu_H f w_H^uu = F( ^uu) t^uu_F f w^uu_F . Solving this equality with respect to ^uu yields:

uu(t^uu_i ; w^uu_i ) = 1 2

(1 +n)[f(w^uu_H w_F^uu) +t^uu_H t^uu_F ]

4l ²n : (17)

Let us de…ne"^uu_i as the tax base elasticity in countryiin the presence of trade unions in both countries. We check that "^uu_i ( ) > "^cc_i ( ) when w^uu_H =w^uu_F . Indeed, following a marginal increase in t_i, the negative impact of the out‡ow of …rms on wages vanishes in the presence of trade unions. The tax base is then more reactive to a unilateral change in taxation. For the same reason, trade integration makes capital location more responsive to taxes than in the case of perfectly competitive labor markets (d"^uu_i =d < d"^cc_i =d < 0).²⁰

4.2 Equilibrium wage rates (stage 2)

In the second stage of the game, each labor union setsw_i^uunon-cooperatively to maximize (5) withL^d_i =f n ^uu_i , by anticipating capital location and taking w_j^uu, t_i and t_j as given.

Moreover, we make the standard assumption that w is equal to the competitive wage

~

w_i^cc (see. 16). The trade-o¤ for monopoly unions can be summarized as follows. While

19The product market outcome arising at the fourth stage of the game is unchanged and described in subsection 3.1.

20Intuitively, this result is valid for all wage rigidities such that agglomeration has no impact upon the cost of labor.

choosing high wages increases the workers’ gross income, it reduces labor demand and leads more people to become unemployed as dL^d_i=dw_i^uu <0. Inserting the labor demand function into the monopoly union’s objective function, maximizing the corresponding expression with respect to w_i^uu and crossing the reaction functions, we obtain:²¹

w^uu_i = ~w^cc+ 2ln ² f(n+ 1)

i j + 1 1 _{i j}

i 1 _j

1 _{i j}

t^uu_i t^uu_j

f (18)

Several comments are in order. First, as expected, for identical levels of taxation (ti = t_j), strong preferences for wages in country i and j raise the wage in country i. Second, the wage prevailing in country i decreases with t_i and increases with t_j. In other terms, monopoly unions compensate …rms for relatively higher capital taxes in their country by setting a lower wage rate in order to keep jobs within national borders. Observe also that strong domestic (foreign) preferences for wages exacerbates (attenuates) the negative e¤ect oft^uu_i onw^uu_i . Our model thus rationalizes the empirical …nding that a part of the corporate tax burden is shifted onto labor in the form of lower wages (Arulampalam et al., 2007; Desaiet al., 2007; Felix and Hines, 2009). Third, the wage rate declines with trade integration, and it is straightforward to verify that this e¤ect is stronger in the country where the preference for wages is the highest (dw_F^uu=d > dw_H^uu=d > 0 for

F > _H).²²

Lemma 1 Assume that there are monopoly unions in each country and governments are playing as Stackelberg leaders. At the second stage of the game, the equilibrium wage in each country is increasing with the level of trade costs (dw^uu_i =d >0). This relationship is stronger in the country where trade unions have a higher preference for wages; hence trade liberalization reduces the wage di¤erential between countries.

Indeed, by increasing the labor demand elasticity to the wage rate ( @L^d_i=@w_i^uu:w^uu_i =L^d_i), trade integration forces trade unions to adopt a wage moderation policy to reduce the negative e¤ect of a high wage on labor demand and the resulting level of unemployment.

As expected, this wage adjustment is more important in the country where wage claims are the highest. Interestingly, this labor demand elasticity e¤ect illustrates Rodrik’s intu- ition thattrade increases the degree to which employers can react to changes in prevailing wages by outsourcing or investing abroad (Rodrik, 1997, p. 12-13).²³ This result is also

21At these levels of equilibrium wages, the second-order condition is veri…ed.

22This property remains valid at the SPNE (see section 4.3).

23The e¤ect of trade integration on the labor demand elasticity is well-documented (see for instance Slaughter, 2001; Hasanet al., 2007).

in sharp contrast to the relationship found by Naylor (1998), according to which wages increase with trade integration when the spatial distribution of …rms is exogenous. Thus, abstracting from the fact that high wages might deter investments, Naylor’s model cannot capture the e¤ect of trade costs on the aggregate labor demand elasticity.²⁴

4.3 Nash tax policies (stage 1)

We now solve the …rst stage of the game and characterize the SPNE. Because of distortions in the labor market, each government now faces two categories of households (employed or unemployed). The labor tax is levied exclusively on employed residents, and each national government provides bene…ts b_i to unemployed people, the number of which is given by

l^u_i =l f ^uu_i n w^uu_i

where ^uu_i is obtained by inserting (18) in (17). This creates intuitive relationships:

unemployment increases with the wage set by unions while it decreases with the number of …rms, the …xed requirement of labor and the preference for leisure. With (6) and after rearranging, the objective function of each government is:

W_i^uu =lS_i+rn

2 +t^uu_i n ^uu_i +1 2

(w^uu_i )²

l^e_i +constant (19) As in the benchmark case of competitive labor markets, the domestic wage is a decreasing function of the capital tax. However, note that the nature of this relationship is quite di¤erent because it now results from the ability of governments playing in stage 1 to a¤ect the wage choice of the trade union in stage 2. Observe also that the number of employed people is now an endogenous variable that directly responds to the tax policy.

Speci…cally, a corporate tax cut increases employment through the induced capital in‡ow (dl^e_i=dt^uu_i < 0). The other incentives to tax are similar to the benchmark case, except that the tax base elasticity is stronger.

By inserting the location equilibrium and (18) in (19) and maximizing the resulting expression with respect to t^uu_i , we get the following Nash taxes:

~t^uu_H = ~t^cc f

2w~^cc+ _H( _H; _F; ) and ~t^uu_F = ~t^cc f

2w~^cc+ _F ( _H; _F; ) (20)

24In Naylor’s model, the only channel through which trade costs a¤ect labor demand comes from the positive impact of a decline in trade costs on the total output and employment of each …rm. Within our framework, we do not capture this e¤ect because we assume that the marginal labor requirement equals zero. This assumption allows us to focus on the relationship between trade integration and wages passing through capital mobility and its impact on the labor demand.