Wages and International Tax Competition∗ Sebastian Krautheim†

Tim Schmidt-Eisenlohr‡

October 2014 Abstract

We introduce wage bargaining and private information into a model of profit shifting and tax competition between a large and a small country. Shifting profits to the small country not only reduces a firms’ tax bill but also creates private information on profitability, altering the wage bargaining in favor of the firm. This additional shifting incentive makes the tax base of the large country more elastic and leads to higher outflows, lower wages, higher firm profits and lower equilibrium tax rates. Tax rates alone no longer determine the direction and the extent of profit shifting. JEL: F23, H25, H73 Keywords: tax competition, profit shifting, wage bargaining, private information ∗

We would like to thank Pamela Bombarda, Mike Devereux, Daniel Dreßler, Carsten Eckel, Peter Egger, Ben Ferrett, Clemens Fuest, Giorgia Maffini, Andreas Haufler, Eckard Janeba, Marko Koethenbuerger, Udo Kreickemeier, Frank St¨ahler as well as seminar and conference participants at the American Economic Association Meetings 2013, CREST Workshop on Economic Integration and Labor Markets, CBT Summer Symposium 2011, Loughborough University, University of T¨ ubingen, ZEW Mannheim, University of Namur, CESifo Public Sector Economics Area Conference, Humboldt University Berlin and ETH Zurich for fruitful discussions and comments. Any remaining errors are our own. Schmidt-Eisenlohr acknowledges financial support from the ESRC (Grant No RES -060-25-0033) and CESifo, Munich. † Faculty of Business Administration and Economics University of Passau, 94030 Passau, Germany. E-Mail: [email protected]. ‡ Economics Department, University of Illinois at Urbana-Champaign, 214 David Kinley Hall, 1407 W. Gregory, Urbana, Illinois 61801, USA. E-Mail: [email protected].

1

Introduction

Globalization has changed the economic playing field in many ways. A key case in point are multinational firms that can substantially reduce their tax payments by shifting profits across jurisdictions. Through transfer pricing, internal loans and royalty payments, they can allocate revenues from high-tax to low-tax jurisdictions and thereby undermine the ability of nation-states to tax incomes generated within their borders. At the same time, it has been argued that multinational firms are in a better position when bargaining with their workers. Their ability to relocate production to another country, for example, can be a credible threat to limit wage demands.2 In this paper, we show that the relationships between multinational firms, governments and workers may be more interrelated than previously thought. In particular, we demonstrate that profit shifting can be a means not only to reduce tax payments but also to lower wages. The idea is straight-forward: workers know more about what is going on in their production location than in other parts of the multinational firm. When a multinational firm shifts profits to a lowtax jurisdiction, this does not only reduce its tax bill but also generates opacity for workers who no longer know for certain how much surplus is generated by their work.3 When firms bargain with workers over wages this informational advantage leads to a rent for the firm in the form of lower wages paid to workers. In a recent case of a large mining company in South Africa that received wide-spread media attention, the Alternative Information and Development Centre, a South African NGO promoting social justice, argues that exactly this happened: “The problem of transfer pricing – companies moving a part of their profits to countries with low or no tax on profits – isn’t only about escaping taxes. It is even more a matter of wage evasion. For every R100 million 2

See e.g. Eckel and Egger (2009). As shown in a literature in accounting, finance and management discussed below, this can be the case even if workers observe the public financial accounts of the firm. 3

1

successfully moved to a subsidiary on Cayman Island, British Virgin Island or Barbados, a company escapes R28 million (if paying the full SA 28% tax on profits). But in addition, R72 million disappear from the wage bargaining process.” (AIDC (2014a)).4 Another example, discussed in Zhao (1998), is the case of Saint Gobain, a French multinational company that shifted profits to Switzerland to save taxes and to improve its bargaining position with labor unions.5 Systematic evidence for this behavior is harder to come by as large parts of multinational accounts are non-public. As a matter of fact, most of the information in the South African case was only revealed in the context of a large investigation into the death of 44 mine workers that were killed during the Marikana miners’ strike in 2012. To study this issue formally, we develop a model where workers and firms bargain over wages and profit shifting generates private information about production costs. While we focus on the case of workers, the analysis should be easily generalizable to other setups with multiple stakeholders and private information.6 This paper adds to the literature in three ways. First, we propose a model in which profit shifting creates opacity and thereby reduces bargained wages in a setup with rational expectations; that is, all actors have full information about 4

See AIDC (2014b) for further details and background information. “A widely cited example is Saint Gobain (a French company, its main product being glass). In the 1960s it operated in more than ten countries. It also established a holding company in Switzerland for all subsidiaries outside France. Swiss law allowed revenues earned from foreign manufacturing to be subjected to favourable tax rates. Thus, the holding company bought from its subsidiaries at low prices and sold to customers at high prices. Profits were thus taken in Switzerland. Moreover, Saint Gobain could show the labour unions in different countries that its subsidiaries were not profitable. See International Federation of Chemical and General Workers Union Bulletin, June-July 1969; Business Europe, 11 April 1969; Business International, 18 April 1969.”(Zhao (1998), p. 818). 6 The basic idea is closely related to work by Desai and Dharmapala (2006) and Desai et al. (2007) who study multinational firms and argue that it is important to jointly analyze the interactions between different stakeholders. Both papers focus on governments, shareholders and managers. Desai and Dharmapala (2006) provide empirical support for this by showing that the quality of corporate governance affects profit shifting behavior at the firm level. 5

2

the game ex-ante and the only information asymmetry is about the realization of the shock ex-post. Second, we show that for exogenously given tax rates, the presence of wage bargaining under private information can increase the tax rate elasticity of tax revenues. Third, we provide a full solution to the tax game between governments and show that taking effects from relevant third parties on profit-shifting into account can be crucial. In our setup the optimal choices of governments change and tax rate differences are no longer sufficient to predict the direction or the extent of profit shifting. In the model, there are three stakeholders: the government, firm owners and workers. Firms are located in a ‘large’ country but can decide to shift profits to a ‘small’ country that typically has a lower tax rate. Different from existing models of international tax competition, the profit shifting decision of the firm does not only affect its tax bill, but also impacts the wage bargaining with workers. This provides an additional rationale for profit shifting: the wage incentive. We show that accounting for the wage incentive has important effects on tax competition between the governments in both countries, as it distorts their best response functions. For a given tax rate of the other country, the large country faces higher outflows of the tax base and chooses to set a lower tax rate while the small country sets a higher one. We show that the introduction of the wage incentive leads to a lower equilibrium tax rate of the large country, reflecting the increased competitive pressure it faces. For extreme parametrizations, the large country becomes so concerned about outflows of tax base that it sets a lower tax rate than the small country. In this case, profits are shifted in the opposite direction than usual: from the low-tax to the high-tax country. While reasonable parametrizations do not generate this result, it nevertheless illustrates the general point that controlling for additional shifting incentives is key when determining the effect of tax differences on profit shifting behavior. A key contribution of our paper is to provide a micro-foundation for the 3

effect of profit shifting on the firm-worker interaction. The main idea is that profit shifting can create some private information on the realization of a cost shock (here: the cost of an intangible asset) that the firm owners can exploit in the wage bargaining with workers. Technically, we apply the Neutral Bargaining Solution proposed by Myerson (1984) for bargaining under incomplete information. We derive parameter restrictions for which private information through profit shifting indeed leads to a lower expected wage rate of shifting firms. This micro-foundation provides a clear mechanism ruling the interaction between firm owners and workers, which then feeds back into the interaction between firm owners and the government. The modeling of the micro-foundation is quite general and could be adjusted to other settings where asymmetric information between management of the firm and a third stakeholder matter. One example would be managing and non-managing shareholders as in Desai et al. (2007). One may think that observing profits cannot be that difficult and that hiding information from workers should therefore not be feasible. In addition to the examples given above, research in accounting, finance and management provides evidence that managers indeed manipulate reported income to affect wage bargaining. Among other things, it finds that managers withhold favorable information and promote bad news to improve their standing in the wage bargaining with workers.7 The result that multinationals can use profit shifting to reduce wages appears to contradict results from the international trade literature, which finds that multinationals on average pay higher wages (see e.g. Aitken et al. (1996)). Note, however, that our model does not feature any of the key ingredients that 7

See, for example, Chung et al. (forthcoming) who analyze Korean firm level data. They find that the firms facing strong unions have a lower disclosure frequency than other firms. Moreover, firms facing strong unions tend to withhold good news during the negotiations with unions and only gradually release it afterwards. Related papers with similar findings are Hilary (2006), DeAngelo and DeAngelo (1991) and Kleiner and Bouillon (1988).

4

typically give rise to the multinational wage premium, in particular differences in productivity. Our results are perfectly consistent with multinationals paying higher wages, but suggest that wages may be lower than they would be in the absence of profit shifting. The structure of the model is as follows. In the large country there is a monopolistically competitive sector with firms producing differentiated products making positive surpluses. A standard wage bargaining setup implies that in equilibrium these surpluses are shared with workers before the remainder (profits) is taxed by the government. Production requires labor and an intangible input which is produced at a random cost. When the intangible is produced in the large country, workers observe the realization of the cost and take its value into account in the wage bargaining. Firms can pay a cost of creating an affiliate in the small country. When the production of the intangible takes place in this affiliate there is a positive probability that the realization of the cost shock is private information of the firm. Such private information alters the wage bargaining in favor of the firm: transferring the production of the intangible to an affiliate in the small country results in an expected net transfer from workers to the firm, creating the wage incentive for shifting. Moreover, the firm can use royalty payments for the use of the intangible to shift its profits to the small country, potentially reducing its tax bill. This creates the (standard) tax incentive for profit shifting. We first show formally that our setup does create an additional shifting incentive and analyze its determinants. We find that a higher probability of creating private information through shifting leads more firms to do so. An interesting corollary to this result is that the introduction of wage bargaining into the model has in and by itself an ambiguous effect: while a higher bargaining power of workers strengthens the wage incentive, it weakens the tax incentive for the simple reason that less profits remain with the firm if workers have a high bargaining power. This latter effect mirrors a result in Riedel (2011) and also 5

relates to the results of Schindler and Schjelderup (2012). The former effect, to our knowledge, is new to the tax competition literature. We then look at the decision of governments in the large and the small country, which are assumed to maximize welfare of their citizens.8 We first analyze a key determinant of optimal choices of governments in the tax game: the own-tax elasticity of tax revenue. To do so, we decompose this elasticity into a direct- and a tax base effect and show that for the large country the own-tax elasticity increases when the tax incentive gets stronger, while the opposite holds for the small country. This implies that the introduction of private information through shifting increases the competitive pressure on the large government. Next, we turn to the best response functions of both countries. We compare these to the benchmark case without the wage incentive for profit shifting. It turns out that the best response functions of both countries are distorted, meaning that the introduction of the third stakeholder into the analysis alters the optimal strategies of governments setting their tax rates. The key feature here is that the best response function of the large country is shifted downwards over the whole support, while the one for the small country is shifted upwards. It is interesting to note that the large countries’ best response now allows for cases where the large country undercuts the small country. This is a direct implication of the additional shifting incentive: even if both countries set the same tax rate, some firms would still shift profits to reduce their expected wage payments. To reduce outflows beyond this point, the large country would have to undercut the small one. Note, however, that for reasonable parameterizations undercutting by the large country is not an equilibrium outcome. Finally, we combine the different elements and derive the equilibrium of the tax game in closed form. This allows us to show formally that the introduction of the wage incentive leads to higher outflows, lower wages, higher firm profits and lower equilibrium tax rates. 8

The framework allows for revenue maximization as a special case.

6

This paper is related to several strands of literature. First, it contributes to the research on profit shifting behavior of multinational firms. Several empirical studies have shown that multinationals indeed use profit shifting to reduce their tax payments.9 Theoretical work in this area has mainly focused on the question how profit shifting can allow firms to reduce their tax payments and how, and to which extent, this limits the ability of governments to raise taxes.10 An notable exception is Zhao (1998) who studies how a multinational firm may use transfer pricing to affect wage bargaining at the subsidiary level but does not consider taxation. Several papers study tax competition with labor market frictions. Ogawa et al. (2006) and Eichner and Upmann (2012) consider tax competition in the presence of unemployment. Haufler and Mittermaier (2011) analyze tax competition for foreign direct investment (FDI) under labor unionization. Exbrayat et al. (2012) extend their setup to two unionized countries with all firms being mobile. Egger and Seidel (2011) study the interrelation of fair wages, trade costs and tax competition and show that more rigid labor markets lead to lower equilibrium tax rates. Closest to our paper, Riedel (2011) suggests a model of tax competition featuring wage bargaining. Her paper differs from ours in that there is no additional shifting incentive and the equilibrium of the tax game between governments is not derived. Instead, she focuses on the case of identical tax rates and analyzes the different implications of separate accounting and formula apportionment. None of these papers features the wage incentive for profit shifting present in our model. The paper also relates to a recent literature on tax competition with heterogeneous firms. Our modeling approach is closest to Mongrain and Wilson 9

See among others Swenson (2001), Altshuler and Grubert (2003), Clausing (2003), Desai et al. (2004), Bernard et al. (2006) and Huizinga et al. (2008). 10 See e.g. Elitzur and Mintz (1996), Haufler and Schjelderup (2000), Janeba (2000), Mintz and Smart (2004), Peralta et al. (2006) and Bucovetsky and Haufler (2008).

7

(2011) in that we assume heterogeneity in fixed rather than variable costs.11 The idea that a multinational firm can use its presence in different jurisdictions to reduce its wage bill has been studied previously. Eckel and Egger (2009) analyze a setting where multinational firms with production plants in two countries face local wage bargaining in both locations. In case of a strike in one location, the firm can compensate a part of the production loss by importing from the other location. This improves the outside option of the firm and thereby lowers equilibrium wages. While Eckel and Egger (2009) consider the location of production, we focus our analysis on a different feature of multinational firms: their ability to shift profits across jurisdictions. In showing how this additional channel affects wage bargaining, we complement the existing literature on multinationals and wage bargaining. The basic idea of our wage mechanism is also related to the concept of ‘tunneling’ where majority owners can exploit differences in the ownership structure of a business group by shifting surplus to the entity where they receive the largest fraction of profits. Bertrand et al. (2002), for example, provide evidence for this activity in India. This mechanism is very different to our paper where the division of surplus is determined through bargaining. In recent work, based on this paper, Siegloch and Simmler (2013) provide empirical support for key implications of our model using German firm level data. Their preliminary results show that there is a positive correlation between reported profits before wages (total observable surplus) and unionization. In line with our model this correlation disappears for multinational firms, possibly due to profit shifting. Moreover, for multinationals higher unionization brings along higher internal debt (a measure for profit shifting), while it does not for purely domestic firms. They also show that an increase in the average wage paid in an industry (e.g. driven by a positive technology shock) translates 11 For other ways of introducing firm heterogeneity see also Baldwin and Okubo (2009), Davies and Eckel (2010), Krautheim and Schmidt-Eisenlohr (2011) and Haufler and St¨ahler (2013).

8

into higher wages for purely domestic firms, while it does not affect wages of multinationals. Overall, these results are consistent with the prediction of our model that multinational firms facing a stronger bargaining power of workers use profit shifting to reduce their wage bill.12 There is ample empirical evidence for a positive relationship between wages and profits.13 Moreover, Budd and Slaughter (2004), Budd et al. (2005) and Martins and Yang (2014) provide evidence that within multinational firms rentsharing also takes place across national borders. Budd et al. (2005) and Martins and Yang (2014) show that higher profits in the headquarter are shared with workers in the foreign affiliates. It is of interest to note that both papers do not find robust evidence for rent-sharing in the opposite direction: higher affiliate profits have no significant effect on wages in the headquarters. This asymmetry is consistent with our model: to the extent to which shifted surpluses are not detected by workers, they should not affect domestic wages. The rest of the paper is structured as follows. The next section outlines the model and analyzes the determinants of the cutoff cost level. Section 3 introduces the tax game between the large country and the small country and presents the best response functions. The equilibrium of the tax game as well as the main results of the paper are derived in Section 4. Section 5 extends the analysis to bargaining with private information. Section 6 concludes. 12

Unfortunately, a first draft of their paper is not yet available. Results are, however, available upon request from the authors. 13 See for example Blanchflower et al. (1996), Van Reenen (1996) and Hildreth and Oswald (1997) and references therein. In line with these earlier findings, Helpman et al. (2012), who analyze detailed matched firm-worker data from Brazil, find that most of the wage inequality within sectors and occupations is driven by wage differences between firms rather than by wage differences within firms.

9

2

The Model

We consider two countries: a ‘large’ country that is endowed with a unit mass of workers and a ‘small’ country with a zero mass of workers.14 Labor is the main input in production. All production of consumption goods takes place in the large country. Each worker inelastically supplies one unit of labor. There are two sectors, one producing varieties of a differentiated good and one producing a homogeneous good used as the numeraire.

2.1

Preferences

The workers in the large country are all identical and share the same quasilinear preferences over the two consumption goods and a public good provided by the government: Z U = E lnQ + β G + q0

with

σ−1 σ

qi

Q=

σ  σ−1

di

,

(1)

I

where qi is the quantity consumed of variety i and I is the set of available varieties. The elasticity of substitution between varieties is given by σ > 1. Q represents utility from consumption of a basket of differentiated goods. G is the quantity of a public good provided by the government. The consumption of the numeraire good is given by q0 . E and β are parameters with 0 < E < 1 < β. The parameter β represents marginal utility from the public good. Setting β > 1 assures that the government has an incentive to provide the public good also when the distortion from tax competition is introduced. Demand for one particular variety i can be derived as: qi =

p−σ i Q. P −σ

14

(2)

For a detailed discussion of the main assumptions see also Krautheim and SchmidtEisenlohr (2011).

10

We denote the price of variety i by pi and the welfare based price index by P .15

2.2

Firm problem

Technology - homogeneous goods sector: In the homogenous good sector one unit of output is produced using one unit of labor. As standard in the literature, we only consider equilibria in which the homogeneous good is produced. Then, the differentiated goods sector is too small to accommodate all workers. Technology - differentiated goods sector: There is a fixed and exogenous measure of firms in the differentiated good sector of size one, which are owned by consumers in the large country. All firms have the same labor input requirement per unit of output of a. To produce, a firm requires an intangible input. This can for example be thought of as management services, intellectual property rights or financial services. We assume that these inputs can be generated within the firm at a stochastic fixed cost F . For simplicity we assume that there are only two realizations of this random variable: with probability φ the world is in state 0 and F = 0, with probability 1 − φ state 1 occurs and F = f > 0. Wages: As one unit of the numeraire good is produced using one unit of labor, the wage in the homogeneous good sector is one. In the differentiated good sector, workers and firms bargain over wages. The outside option for workers is employment in the homogenous good sector. Firms’ outside option is no production which leads to zero variable profits. 15

The welfare based price index in our case takes the standard form and is given by P = 1
1−σ , where I represents the set of available varieties in the differentiated good

p1−σ di I i sector. R

11

2.3

Governments and Profit Shifting

Large country: The government in the large country sets a proportional tax tH on the profits of firms in the large country. Tax income is used to provide government services G to consumers. The government can transform one unit of the numeraire good into one unit of government services. It is assumed to maximize welfare of its own citizens. Small country: The structure of the small country is kept as simple as possible. There is no production of final goods. However, firms from the large country can set up affiliates in the small country to produce intangible inputs. The small country sets a proportional tax rate tX on profits declared by foreign affiliates in its jurisdiction. Taking the tax rate in the large country as given, the small country maximizes total revenues. Profit shifting: As discussed above, firms from the large country can open an affiliate in the small country. This requires paying a firm-specific fixed cost ci . Fixed costs are a random variable distributed uniformly between zero and one, i.e. G(c) = c with c ∈ [0, 1]. Assume that this cost is borne completely by the owners of the firm, that it is not tax deductible in the small country, and that it does not affect the surplus bargained over with workers. The government of the large country does, however, take this cost into account when setting its tax rate. A firm can outsource the production of the intangible input to its affiliate in the small country. As the production cost of these services cannot be easily verified, the affiliate can charge an amount ν ≥ 0 to the firm that is independent of its actual cost. This provides the firm with a way to avoid taxation in the large country. When the tax rate in the small country is lower, the firm has an incentive to use this mechanism to shift profits. There is a tax incentive for profit shifting. 12

Workers know the technology of the firm. In particular they are aware that the production cost of the intangible input F takes the values of zero and f with probabilities φ and 1 − φ, respectively. If all production takes place in the large country, workers can perfectly observe the realization of F . When the intangible is produced in the small country, workers may observe F only imperfectly. To keep a flexible setting, we assume that workers can observe F in the affiliate with probability η ∈ [0, 1]. That is, with probability 1 − η the cost F is private information of the firm. As we show below in more detail, a firm that has private information improves its position in the wage bargaining with workers. Hence, when the realization of the shock in the small country cannot be fully observed by workers, 1 − η > 0, there is an additional incentive for profit shifting: the wage incentive.

2.4

Timing

The timing is as follows. Step 1: Governments in the large country and the small country simultaneously set tax rates. Step 2: Firms decide whether or not to establish an affiliate in the small country. Step 3: Firms choose the number of workers N . From this point onwards, N cannot be changed unilaterally by a firm. Step 4: The fixed cost shock F is realized and revealed to the firms. It is also revealed to workers if the intangible input is produced in the large country. When the intangible is produced in the affiliate, workers observe the realization of F with probability η. Step 5: The workers and the firm bargain over wages. Step 6: Production takes place. We solve the problem by backward induction.

13

2.5

Output, surplus and profits

In step 6 production takes place. As all firms are symmetric and share the same labor productivity a, output per firm can be expressed as:16 q=

N . a

(3)

Total expenditure on the differentiated goods sector is given by E = QP . Given equation (2), the demand a firm faces takes the familiar form: q = p−σ P σ−1 E.

(4)

Together with (3) this implies that the optimal price of firm i can be expressed as a function of the optimal number of workers employed:  p=

N a

− σ1 P

σ−1 σ

1

Eσ.

(5)

Revenues of a firm can be calculated as: R = pq = N

σ−1 σ

a

1−σ σ

P

σ−1 σ

1

Eσ.

(6)

It is useful for the presentation of the results to define:17 s0 = (p − a)q = R − N

(7)

This variable corresponds to the variable profits a firm generates if it happens to pay the same wage as in the outside sector (w˜ = 1) and draws a zero cost of 16

Note that the firms only differ in their shifting costs ci . We therefore drop the index i where it causes no confusion. 17 It is convenient to define s1 and s0 such that they are the same for all firms and do not account for the firm-specific shifting cost ci .

14

producing the intangible input. Equivalently, define: s1 = (p − a)q − f = R − N − f,

(8)

as the variable profits at a wage of one generated in the state where the cost of producing the intangible is f .18 It directly follows from above that the expected surplus of a firm at wage 1 is given by: s = R − N − (1 − φ)f,

(9)

where (1 − φ)f represents the expected expenditure on the production of the intangible input. Pre-tax variable profits are given by revenues minus wage payments and minus the realization of the cost of the intangible (zero or f ): π0 = R − N w 0

(10)

π1 = R − N w1 − f.

(11)

In the next step, the wage rates in the different states of the world, w0 and w1 , are determined.

2.6

Wage bargaining

In step 5, firms and workers bargain over wages. We consider purely domestic firms and firms with an affiliate in the small country separately. The former do standard Nash-bargaining with workers under full information. The latter may generate private information through shifting intangible production to the small country. For them, we can apply the neutral bargaining solution (NBS) developed by Myerson (1984), which is a generalization of Nash bargaining to the case of private information. 18

We will see below that s0 and s1 turn out to be the surpluses the firm and workers bargain over.

15

Bargaining for non-shifters Define πH,j as the profits of a non-shifter in state j ∈ {0, 1}, where H indicates that all activity of the firm takes place in the large country. We can then write the Nash product conditional on the realization of F as: ΩH,j = [(wj − 1)N ]δ [πH,j ]1−δ ,

(12)

for j ∈ {0, 1}. As discussed earlier, the outside option of workers is to work in the homogenous good sector at a wage of unity. The outside option of the firm is zero variable profits. We can now plug in profits in the two states of the world from equations (10) and (11) and maximize with respect to w0 and w1 respectively. In doing so, we take the number of workers N as given, as it is determined at an earlier stage (step 3) and is exogenous at the time the wage bargaining takes place. This delivers the wages payed by a non-shifting firm in the two states of the world:  s0 R −1 = 1+δ = 1+δ N N   s1 R−f −1 = 1+δ . = 1+δ N N 

w0 w1

(13) (14)

The expressions nicely illustrate the two components of the wage in the differentiated goods sector. The first term reflects the worker’s outside option of a wage of unity. The second term is the bargaining power of workers times the surplus generated at a wage of unity. This corresponds to the standard result under Nash bargaining. Each party receives its outside option plus a share of the surplus that is proportional to its bargaining power. In order to later compare outcomes for shifters and non-shifters, it is useful to calculate the expected

16

wage for a domestic firm as a function of expected surplus s: f R−N − (1 − φ)δ N N s = 1+δ . N

wH = φw0 + (1 − φ)w1 = 1 + δ

(15)

Bargaining for shifters Recall that if a firm produces its intangible input abroad, with probability η there is full information and standard Nashbargaining as described above takes place. Private information is generated when workers do not observe the realization of F , which happens with probability 1 − η. In this case we apply the neutral bargaining solution (NBS).19 The NBS works as follows. If the firm and its workers do not agree on a sharing rule, the decision is taken through a random dictator game. In this case either the firm or the workers are randomly assigned to suggest a sharing rule that the other side can either accept or reject.20 As shown in Balkenborg (2006), asymmetric bargaining power can be introduced by varying the probability that workers are the dictators between zero and one. We assume that this probability takes the value of δ, the bargaining power of workers in the standard Nash-bargaining for non-shifters described above. In the absence of private information, this generates the same sharing of surplus as under standard Nash-bargaining. If the firm is the dictator it takes the full surplus. Workers, however, do not know whether surplus is high or low. If they request a wage higher than the actual surplus, the firm rejects the offer and no production takes place, implying zero surplus. Kennan (2010) shows, applied to our case, that as long as φs0 < s1 , it is optimal for the workers to take the certain payment of s1 when 19

In the exposition we closely follow Kennan (2010) who applies the NBS to wage bargaining, where the firm has private information on the surplus generated by a firm-worker match. While Kennan (2010) only considers the case of symmetric bargaining power, we build on the generalization of Balkenborg (2006) in allowing for asymmetric bargaining power. 20 For more details on the dictator game see G¨ uth et al. (1982).

17

they are the dictators. The intuition is that workers have to choose between the low surplus s1 with certainty and the high surplus s0 with probability φ. If the difference between the high and low surplus is sufficiently small (low cost f of the intangible) and the probability of the high surplus is sufficiently low (low φ), it is optimal for workers not to put the production of the firm at risk and take the low surplus s1 when they are the dictators. In our model this condition translates into f <

E (1 σ

− φ).

This implies an informational rent for the firm: even if the workers are the dictators, the fact that they do not know the realization of the shock leaves the firm with a positive expected surplus. The wage under the NBS is given by: wN BS = 1 + δ

s1 = w1 N

(16)

The wage under private information is identical to the wage with full information in state 1 in equation (14). The difference is that under private information workers always get this lower wage independently of the realization of the fixed cost shock. We can now calculate the expected wage in a profit shifting firm as: wX = η(φw0 + (1 − φw1 )) + (1 − η)wN BS = ηφw0 + (1 − ηφ)w1 s φδf = 1 + δ − (1 − η) . N N

(17)

With probability η workers observe the realization of the cost shock and receive the expected wage under Nash bargaining which is equal to wH in equation (15). With probability (1 − η) there is private information and workers receive wN BS . A comparison to the expected wage of a non-shifter in equation (15) shows how the ability of creating private information reduces the expected wage payments of a shifting firm to its workers.

18

2.7

Profits of Shifters and Purely Domestic Firms

Before moving on to the labor choice of the firm in step 3, it is instructive to consolidate the information on expected profits of shifters and purely domestic firms. We have seen above that wages are lower in firms with private information on the realization of the cost F . Therefore, expected profits of shifters and nonshifters differ. We denote expected profits of a non-shifter by πH , which are given by the bargaining power of the firm times the expected surplus as defined in equation (9): πH = (1 − δ)s.

(18)

Expected profits of shifters, πX , can be derived as: πX = (1 − δ)s + (1 − η)φδf.

(19)

Note that the difference between πH and πX is simply given by the differences in the wage bill (N times the difference between expected wages from (15) and (17)): (1 − η)φδf . This term consists of two parts. Under complete information δf represents the workers’ share of the cost of the intangible iff it takes the value of f . Under incomplete information, workers pay ‘their share’ δf even if the cost is zero leading to a de facto transfer from workers to the firm of δf . The term (1 − η)φ represents the probability that this occurs: workers do not observe the realization and the realization of the intangible’s production cost is zero. Taking the two elements together, (1 − η)φδf represents the expected transfer from workers to a shifting firm.

2.8

Labor Choice

Prior to wage bargaining, firms choose the number of workers N they seek to hire in step 3. Firms that do not shift profits choose the number of workers as 19

to maximize expected profits πH .21 For the case of non-shifters expected profits are given by equation (18). Using equations (6) and (9) they can be expressed as a function of the number of workers N:   1−σ σ−1 1 1 πH = (1 − δ)N N − σ a σ P σ E σ − 1 − (1 − δ)(1 − φ)f.

(20)

Maximization with respect to the number of workers gives:  N=

σ−1 σ

σ

a1−σ P σ−1 E.

(21)

Note that the only difference between equations (18) and (19) is the term (1 − η)δφf . This term is independent of the number of workers. Therefore equation (21) constitutes the optimal labor choice of both non-shifters and shifters.

3

Profit Shifting

In step 2 firms decide whether to open an affiliate in the small country and shift surplus there. At this stage the tax rates of the large and the small country are given, as these are set in stage 1. We first analyze the different shifting incentives at the firm level and compute the key variables which describe the economy for given tax rates.

3.1

Wage and tax incentives for profit shifting

Firms decide whether or not to open an affiliate in the small country based on the impact on expected after-tax profits at given tax rates. While the tax rates did not affect the choices analyzed in steps 3 to 6, they need to be taken into 21

Note that firms maximize after-tax profits. However, given the proportional tax on profits, maximizing pre-tax profits is equivalent to maximizing post-tax profits. For a clearer exposition, we can thus leave out the tax rates in the maximization problem.

20

account at this stage, as profit shifting does have an effect on which tax rate applies to pre-tax profits. Cutoff cost level: A firm with a shifting cost c trades off the benefits from shifting against its cost. We define the cutoff cost level c∗ as the cost level that equalizes expected after tax profits with and without shifting. This implies that we must have (1 − tH )πH = (1 − tX )πX − c∗ . Solving for the cutoff shifting cost and using the expressions for expected profits from above delivers: c∗ =

ρ(1 − δ)s + (1 − tX )(1 − η)φδf . | {z } | {z } tax incentive wage incentive

(22)

Here ρ = tH − tX represents the tax rate difference between the large and the small country. The left hand side of this equation represents the cost of shifting which, for the firm at the cutoff, is exactly compensated by the benefits. These benefits consist of two components, which we refer to as the tax incentive and the wage incentive for profit shifting. The tax incentive for profit shifting: The tax incentive reflects the fact that firms have to pay taxes on their share of the surplus and that the large and the small country can set different tax rates. Therefore, shifting allows the firm to reduce its tax bill, if the tax rate is lower in the small country. The wage incentive for profit shifting: From the discussion of equation (19) we know that the term (1 − η)φδf can be interpreted as the expected transfer from workers to the shifting firm. When the firm shifts, its expected pre-tax profits increase by this amount to which then the tax rate of the small county is applied. The fact that shifting leads to a lower expected wage rate, creates this additional shifting incentive which is entirely independent of the tax rate of the large country. This implies that there is a determinant of the 21

shifting decision that cannot be influenced by the policy instrument of the large country tH . We will see below that this systematically alters the incentives for the government of the large country when setting its tax rate. Impact of the wage incentive on shifting: How strong the wage incentive is depends on the probability that shifting actually leads to private information 1 − η. As this probability only affects the wage incentive, but leaves the tax incentive unaffected, we use it as a measure of the strength of the wage incentive. Instead of focussing the analysis on the extreme case of 1 − η = 1 (shifting always leads to private information), we use a more general setup with values of η reaching from zero to one. This allows us to do comparative statics on the strength of the wage incentive by analyzing changes in 1 − η. For equation (22) this implies that, holding all other variables constant, a strong wage incentive (a high 1 − η) leads to a high cutoff cost c∗ and to more shifting firms. Note that an interesting case arises for a negative tax difference (ρ < 0). Then, for a sufficiently large wage incentive, profits are shifted from the low-tax to the high-tax jurisdiction. While this typically does not occur in equilibrium, it represents an extreme illustration of the more general point that in our setup the tax difference alone is no longer a sufficient statistic to predict the direction and the extent of profit shifting.

3.2

Wage bargaining and profit shifting

The combination of wage bargaining and private information on the cost of the intangible creates the wage incentive for profit shifting in our model. A higher δ strengthens the wage incentive as it increases the value of private information of the firm. This can be seen from the expected transfer from workers to the shifting firm (1 − η)φδf . There is, however, also a direct effect of the bargaining power δ on shifting that has the opposite sign. A stronger bargaining power of workers reduces the 22

surplus that a firm receives. Given the fixed cost of shifting, this makes it less desirable for the firm to shift its profits to benefit from the tax rate difference.22 As we show later, the overall effect of wage bargaining on profit shifting and tax competition depends crucially on the relative importance of these two opposing effects.

3.3

Firm output, surplus and pre-tax profits

Before we can turn to the analysis of the tax game between the large and the small country, we need to compute the remaining equilibrium variables of the model for exogenous tax rates. Using the equilibrium value of N from equation (21) together with the expression for the price of an individual firm in equation (5), delivers the standard result of mark-up pricing over marginal costs: σ a. σ−1

p=

(23)

Since all firms share the same unit labor requirement a, they all charge the same price. With the number of firms normalized to one, the welfare based price index, as defined in footnote 15, is simply given by: P =

σ a. σ−1

(24)

With equation (4) this allows to express demand per firm as: q=

σ−1 E . σ a

(25)

Combining this with equations (6), (7) and (9) delivers surplus of a firm under 22

This direct effect of wage bargaining on the profit shifting incentive is also present in Riedel (2011).

23

full information with zero cost of the intangible as: E σ

(26)

E − (1 − φ)f. σ

(27)

s0 = as well as expected surplus of a firm: s=

We have now derived the complete equilibrium of the model for given tax rates. In the next section we endogenize the tax rates in order to analyze how the introduction of the wage incentive for profit shifting affects tax competition.

4

Tax Competition and the Wage Incentive

We have seen above how wage bargaining can affect the profit shifting decision of an individual firm when there is scope for private information. We now turn to the question how the additional shifting incentive at the firm level may affect aggregate outcomes. In particular, we ask how its presence may change the tradeoffs governments face when setting tax rates and how it may alter the strength of tax competition.

4.1

Aggregation

So far we only considered variables at the firm level. When governments set tax rates, they maximize domestic welfare and therefore take into account effects on aggregate variables like aggregate profits (the tax base), aggregate wages and the sum of shifting costs. The relevant aggregate variables in our model can be

24

calculated as:23 BH = (1 − c∗ )δs

BX = c∗ (δs − (1 − η)φδf )

ΠH = (1 − c∗ )(1 − δ)s

ΠX = c∗ [(1 − δ)s + (1 − η)φδf ] . (29)

(28)

BH and BX are total payments going to workers in excess of labor income generated with a wage of one. ΠH and ΠX are aggregate pre-tax profits of firms paying taxes in the large country and of firms paying taxes in the small country. Total shifting costs are given by: Z

c∗

C=

cdF (c) = 0

1 ∗ 2 (c ) . 2

(30)

We now have all the aggregated variables that matter for governments when setting tax rates in step 1.

4.2

Own-Tax Elasticities of Tax Revenues

As is well known, the optimal tax rate a government chooses is directly linked to the tax rate elasticity of tax revenues. We therefore begin by analyzing how the wage incentive affects this key variable. The tax revenue elasticities of the large and the small country can be decomposed into a direct effect (DE) and a tax base effect (BE). Holding the tax base constant, an increase in the tax rate increases tax revenue (direct effect). At the same time an increase in the tax rate leads to a reduction in the tax base (tax base effect). Using Leibnitz rule, the own-tax elasticities of tax revenues for the large and 23

See Appendix C for the derivation.

25

the small country can be derived as as:24 d(ΠH tH ) 1 dtH ΠH d(ΠX tX ) 1 dtX ΠX

(1 − δ)s tH 1 − c∗ (1 − δ)s + (1 − η)δφf = 1− tX . c∗ = 1−

(31) (32)

The direct effect holds the tax base constant (constant c∗ ) and captures the variation in taxes payed by each individual firm. Both for the large and the small country, the direct effect is positive and equal to unity. That is, holding the tax base constant, a one percent increase in the tax rate increases revenues by one percent. To compute the tax base effect, tax payments of a firm at the cutoff are multiplied with the change in the number of shifting firms implied by the change in the tax rate. As long as some firms are paying taxes in each country (0 < c∗ < 1), this effect always implies a loss of tax base for the country that raises its tax rate. To facilitate the interpretation, in the following we define as the t | strength of the tax base effect its absolute value. That is: |BEH | = | − (1−δ)s 1−c∗ H and |BEX | = | −

(1−δ)s+(1−η)δφf tX |. c∗

We can now analyze how the wage incentive for profit shifting affects the own-tax elasticities of the two countries. Proposition 1 A stronger wage incentive for profit shifting, measured by a higher 1 − η, implies (i) a stronger tax base effect in the large country , i.e. (ii) a weaker tax base effect in the small country, i.e. Proof: see Appendix A.1. 24

See Appendix D for details on the derivation.

26

∂|BEH | ∂(1−η)

∂|BEX | ∂(1−η)

>0

< 0.

The wage incentive affects the tax game between the large and the small country. While the additional shifting incentive makes the large country’s tax base more responsive to the tax rate, the corresponding elasticity for the small country decreases. For given tax rates of the other country, this should lead the large country to set a more aggressive (i.e. a lower) tax rate, while the opposite should hold for the small country. This conjecture is confirmed in the analysis of the best response functions in the following sections.

4.3

Small Country Best Response

We now solve for the equilibrium of the tax game. To this purpose, we first derive the best response functions of the small country and the large country, respectively. In a next step, we then solve for the Nash equilibrium. Taking the tax rate in the large country as given, the small country maximizes total revenues V = tX ΠX , which implies the following best response function:25 tX (tH ) =

(1 − δ)s (1 − η)δφf + tH . 2((1 − δ)s + (1 − η)δφf ) 2((1 − δ)s + (1 − η)δφf )

(33)

Figure 1 illustrates numerical examples of this best response function. The tax rate of the small country is on the x-axis and the tax rate of the large country is on the y-axis. The dashed lines are the best response functions of the small country for different values of η, that is for different strengths of the wage incentive. First consider the case without wage incentive (1 − η = 0) as a benchmark. This is represented by the best response function to the left. The intercept in equation (33) is zero. Hence, in this case, the best response is always above the 45 degree line. No matter which tax rate the large country sets, the small 25

Note that there are no workers or capital owners in the small country. Hence, in the small country, revenue maximization is equivalent to welfare maximization.

27

country always undercuts. This is the standard result in the tax competition literature. The other dashed lines in the graph illustrate how the situation changes when the wage incentive is introduced. The further to the right a line, the stronger is the wage incentive for shifting. To better understand the mechanism, it is instructive to consider the best response of the small country to tH = 0. In the absence of the wage incentive, the small country cannot attract any tax base even if it sets tX = 0. With the wage incentive this changes. As firms consider both the tax and the wage benefits of shifting, some shift profits even when both countries set the same tax rate and shifting therefore takes place even in the absence of any tax benefits. That is, if the large country sets tH = 0, the small country can still attract some tax base. Revenue maximization then implies tX > 0. Figure 1 here.

4.4

Large Country Best Response

The government in the large country maximizes welfare of its citizens which is: U = U¯ + (1 − tH )ΠH + (1 − tX )ΠX + BH + BX + βtH ΠH − C.

(34)

The first term on the right hand side is a constant given by:   E − E + 1. U¯ = E ln σ U¯ consists of the utility from consuming the basket of differentiated goods, the cost of this basket E and basic labor income 1. The second and third terms in equation (34) are the profits retained by consumers of non-shifting and shifting firms, respectively. The next two terms represent surplus dependent payments

28

to workers. The final two terms are the overall utility from the consumption of the public good and the aggregate costs of surplus shifting. Taking the tax rate of the small country as given, the large country has two options. It can set a tax rate leading to some positive outflow (c∗ > 0) or it can choose a tax rate that implies zero outflows (c∗ = 0). It turns out that for low tax rates of the small country, the large country chooses option 1 (c∗ > 0). For high tax rates of the small country, it sets a rate that prevents all outflows (c∗ = 0):26

tH (tX ) =

 (β − 1)[(1 − δ)s + (1 − η)δφf ]) β − 1 − β(1 − η)δφf   + tX   (2β − 1)(1 − δ)s  (2β − 1)(1 − δ)s

if 0 ≤ tX < tk1 X

   (1 − η)δφf (1 − δ)s + (1 − η)δφf  − + tX (1 − δ)s (1 − δ)s

if tk1 X ≤ tX ≤ 1,

with tk1 X =

(35)

(β−1)(1+(1−η)δφf ) . β[(1−δ)s+(1−η)δφf ]

Figure 2 here. The best response function is illustrated graphically in Figure 2. The line the furthest to the left represents the benchmark case of 1 − η = 0, where the wage incentive is closed down. For values below tk1 X the large country sets its tax rate according to the first equation in (35), implying a higher tax rate than the small country. This leads to outflows due to the tax incentive for shifting. The large country never sets a tax rate below that of the small country. By assumption, the small country has no tax base of its own so that, in terms of outflows, the large country cannot do better than reducing outflows to zero. In the absence of the wage incentive a tax rate of tH = tX achieves this goal while keeping the highest possible tax rate. 26

We also assume that tax rates are bounded from below by zero and from above by one. In the main text we focus on cases where these corner solutions do not arise. For completeness the best response function including the possible corner solutions is derived in the Appendices E and F.

29

This changes when the wage incentive is introduced (1 − η > 0), in Figure 2 strengthening from left to right. We have seen above that with the wage incentive even for tH = tX = 0 there would be some outflows of tax base. This affects both parts of the best response function. For high values of tX , the best response function of the large country is now below the 45 degree line, implying undercutting by the large country. This is optimal because even on the 45 degree line (tH = tX ), some tax base shifts to the small country due to the wage incentive. For high values of tX , the large country prefers to reduce tax base outflows to zero. When tX becomes sufficiently small (below tk1 X ), the large country changes strategy and sets a tax rate allowing for some outflows.

5

Tax Equilibrium and the Wage Channel

We can now solve for the equilibrium of the tax game and analyze how it is affected by the wage incentive.

5.1

Equilibrium

Combing the best response functions of the small and the large country in equations (33) and (35), the equilibrium tax rates can be derived as:

Proposition 2 There is a unique equilibrium of the tax game. Equilibrium tax rates are given by: t∗H

  2(β − 1) − (β + 1)(1 − η)δφf ,0 ,1 = min max (3β − 1)(1 − δ)s   (β − 1)(1 + (1 − η)δφf ) 1 ∗ tX = min , . (3β − 1)[(1 − δ)s + (1 − η)δφf ] 2 



Proof: see Appendix A.2. 30

(36) (37)

Figure 3 here. The graphs in Figure 3 illustrate equilibria for no, an intermediate and a strong wage incentive. For the benchmark case without the wage incentive (1 − η = 0) we get a standard equilibrium with the small country undercutting the large country in the first graph. The second and third graphs illustrate the cases where the wage incentive is active and workers can only observe F with probability η = 0.5 and η = 0 of shifted surplus. Opening up the wage channel pushes the equilibrium tax rates down. In the second graph (1 − η = 0.5) the small country undercuts the large country but the equilibrium is closer to the 45 degree line, implying that competitive pressure on the large country increases but also that tax rates are more similar. These aspects will be discussed in detail below. Note that even with the maximum wage incentive (η = 0), the equilibrium tax rate of the large country is typically above the tax rate of the small country. A sufficient condition for this to be the case is δφf <

β−1 . 2β

This condition tends

to be violated when the large country has a very low incentive to tax (β → 1). In this case it matters less for the welfare maximization, whether the private or the public good is consumed. In the limit, there is no benefit from taxing firms at all, so that preventing outflows (and therefore taxation by foreigners), becomes the only government objective. In such extreme cases (for β sufficiently close to one) it is possible to have undercutting by the large country as preventing outflows becomes the dominant objective. Of course, this case only arises for somewhat extreme parameters and only mentioned here for completeness. We can now calculate the remaining equilibrium objects. Substituting the interior solutions for tH and tX from equations (36) and (37), respectively, into

31

equation (22), delivers the equilibrium cost cutoff level:27 c∗ =

β−1 [1 + (1 − η)δφf ] 3β − 1

(38)

This directly pins down the equilibrium values of BH , BX , ΠH and ΠX , as they are only functions of c∗ and parameters as derived in equations (28) and (29).

5.2

Wage Incentive and Tax Competition

We can now analyze how the wage incentive affects the equilibrium. In particular, we can answer the question how its introduction changes equilibrium tax rates and how this depends on the bargaining power of workers. The impact of a stronger wage incentive is summarized in the following proposition: Proposition 3 At an interior equilibrium with rent-sharing, i.e. t∗H ∈ (0, 1) and δ ∈ (0, 1), (i) a stronger wage incentive for profit shifting forces the gov∂t∗H < 0. (ii) This effect ∂(1−η) 2 ∗ ∂ tH is increasing in the bargaining power of workers: ∂(1−η)∂δ < 0. (iii) If the wage ∂t∗X incentive is stronger, the small country sets a lower tax rate: ∂(1−η) < 0.

ernment of the large country to set a lower tax rate:

Proof: see Appendix A.3. The introduction (and the strengthening) of the wage incentive increase the competitive pressure on the government in the large country, leading to a lower equilibrium tax rate. The intuition is clear. With the wage incentive, firms are more willing to shift because they do not only save taxes but can also reduce their expected wage bill by creating an affiliate. This makes the tax base of the large country more elastic, increasing tax competition. The proposition further shows that a higher bargaining power of workers increases the effect of the wage incentive on the large country tax rate. This is 27

Appendix G provides details on the derivation.

32

the case, because a higher δ increases the ‘expected transfer’ from workers to the firm induced by profit shifting. In other words, a higher δ leaves workers with higher wages to begin with, which consequently gives firms a stronger incentive to invest in wage reduction through shifting. Figure 4 here. The result that the small country reduces its tax rate may seem surprising in the light of the result from the section on the own-tax elasticities. There we showed that a stronger wage incentive lowers the own-tax elasticity of the small country. In equilibrium, however, this does not lead the small country to set a higher tax rate. The best response functions derived above can shed some light on this. Consider the best response functions for different levels of the wage incentive in Figure 3. The best response of the small country in equation (33) implies that for a given tax rate tH , the small country indeed increases its tax rate when the wage incentive is stronger. The negative effect of the stronger wage incentive on the best response of the large country is, however, so large that the new equilibrium tax rate of the small country is lower. Figure 4 plots the equilibrium tax rates of both countries for all values of η between zero and one. As predicted by proposition 3 they both increase in η. Finally, we can also analyze how the other equilibrium objects change with the wage incentive 1 − η.28 An inspection of equation (38), directly reveals that the cost cutoff level increases when shifting generates more private information. This decreases aggregate surplus-dependent payments to workers in non-shifting firms as their workers now represent a smaller fraction of the overall workforce. Interestingly, aggregate surplus-dependent payments to workers in shifting firms also decrease as the intensive margin (lower pay per worker) dominates the extensive margin (more shifting firms) in equilibrium in the aggregate. Lastly, aggregate profits of non-shifters ΠH decline whereas aggregate profits of shifters 28

Derivations for all results discussed in this paragraph can be found in Appendix G.

33

ΠX increase in the wage incentive. That is, the tax base of the large country shrinks while the tax base of the small country grows when private information is more pervasive.

5.3

Rent Sharing and Tax Competition

While the above results on the impact of the wage incentive are the focus of our analysis, in this section we report results on the impact of the bargaining power of workers δ on the equilibrium. Equation (22) implies that a higher δ strengthens the wage incentive, but also has an opposing, dampening, effect on the tax incentive. The intuition behind this second effect is that when workers get a large fraction of surplus, firm profits shrink and therefore, for a given shifting cost, profit shifting for tax avoidance becomes less attractive. Which of these effects dominates? Is the overall effect of a change in the bargaining power δ on the strength of tax composition positive or negative? As the following proposition shows, the result is ambiguous and depends on the strength of the wage incentive. Define κ ≡

2(β−1) . (β+1)φf

Then:

Proposition 4 At an interior equilibrium, i.e. t∗H ∈ (0, 1), the effect of the bargaining power δ on the equilibrium tax rate depends on the strength of the wage incentive for profit shifting measured by 1−η. (i) When the wage incentive is strong enough, (1 − η > κ) an increase in the bargaining power of workers δ increases competitive pressure measured by 1 − t∗H , i.e.

∂(1−t∗H ) ∂δ

> 0. For a weak

wage incentive with 1 − η < κ the opposite holds. For 1 − η = κ the effect is zero. (ii) The tax rate of the small country is increasing in the bargaining power of workers, i.e.

∂t∗X ∂δ

> 0.

Proof: see Appendix A.4. There is a threshold value κ for the strength of the wage incentive 1 − η. If the wage incentive is weak (1 − η < κ), the direct effect of rent sharing on 34

profits dominates. Firms have a smaller incentive to shift profits when there is wage bargaining. Hence, tax competition for the large country gets weaker. The opposite holds when the wage incentive is strong (1 − η > κ). Then, firms have a stronger incentive to shift profits under rent sharing and the strength of tax competition increases in the share of surplus δ going to workers. The results in Proposition 4 are illustrated in Figure 5 where the equilibrium tax rates of the large country (solid line) and of the small country (dashed line) are plotted against δ. When the wage incentive is completely shut down (1 − η = 0), both tax rates increase in the degree of rent sharing δ. If the wage incentive is at its maximum it can happen (if 1 − η = 1 > κ) that the tax rate of the large country decreases in δ. While the general finding that the wage incentive increases tax competition should be clear, this last result only arises for very specific parameter values.

6

Conclusions

It is well known that multinational firms can reduce their tax bill by shifting profits from high-tax to low-tax jurisdictions. However, tax considerations may not be the only reason for this activity. Firms may also shift profits to another jurisdiction to reduce the information available to other stakeholders who claim a share of the surplus. In this paper, we explore this idea, analyzing profit shifting in the presence of wage bargaining. We show that firms can have an incentive to shift profits to generate opacity and thereby reduce bargained wages in a model with rational expectations; that is, all actors have full information about the game ex-ante and the only information asymmetry is about the shock realization ex-post. We show that compared to the case without private information through profit shifting, the large country may face a more elastic tax base implying tougher tax competition. We derive the equilibrium of the tax game and show that the 35

introduction of the wage incentive results in lower equilibrium tax rates, higher outflows, lower wages and higher firm profits. The analysis reveals that, when there is a third stakeholder involved, tax rates alone no longer determine the direction and the extent of profit shifting. This also has implications for empirical work. As the relevance of wage bargaining differs substantially across countries and industries, controlling for the wage incentive may be key to correctly estimate the effect of tax rate differences on profit shifting. The model could be easily extended to other cases where surplus is shared with additional stakeholders and where private information can be important. An example would be the interaction of management or managing shareholders and (minority) shareholders as discussed by Desai and Dharmapala (2006). Such extensions would generate similar omitted variable biases and should therefore be further explored in future empirical and theoretical research.

References AIDC, “Back to the negotiating table now! 2014.

Stop wage evasion!,”

http://www.aidc.org.za/programmes/political-economy/wage-

and-profits/58-aidc-back-to-the-negotiating-table-now-stop-wage-evasion, accessed October 26, 2014. , “Bermuda Connection: Profits Shifting and Unaffordability at Lomnin 1999-2012,” 2014. http://www.aidc.org.za/media-room/publications/wageand-profits/viewdownload/9-wage-and-profits/164-bermuda-connectionprofits-shifting-and-unaffordability-at-lomnin-1999-2012, accessed October 26, 2014. Aitken, B., A. Harrison, and R.E. Lipsey, “Wages and foreign ownership A comparative study of Mexico, Venezuela, and the United States,” Journal 36

of international Economics, 1996, 40 (3), 345–371. Altshuler, Rosanne and Harry Grubert, “Repatriation taxes, repatriation strategies and multinational financial policy,” Journal of Public Economics, January 2003, 87 (1), 73–107. Baldwin, Richard and Toshihiro Okubo, “Tax Reform, Delocation, and Heterogeneous Firms,” Scandinavian Journal of Economics, December 2009, 111 (4), 741–764. Balkenborg, Dieter, “Judgment-Proofness and Extended Liability in the Presence of Adverse Selection,” Frontiers in the Economics of Environmental Regulation and Liability, 2006, p. 235. Bernard, Andrew B., J. Bradford Jensen, and Peter K. Schott, “Transfer Pricing by U.S.-Based Multinational Firms,” NBER Working Papers 12493, National Bureau of Economic Research, Inc August 2006. Bertrand, Marianne, Paras Mehta, and Sendhil Mullainathan, “Ferreting Out Tunneling: An Application to Indian Business Groups,” Quarterly Journal of Economics, 2002, pp. 121–148. Blanchflower, David G, Andrew J Oswald, and Peter Sanfey, “Wages, Profits, and Rent-Sharing,” The Quarterly Journal of Economics, February 1996, 111 (1), 227–51. Bucovetsky, Sam and Andreas Haufler, “Tax competition when firms choose their organizational form: Should tax loopholes for multinationals be closed?,” Journal of International Economics, January 2008, 74 (1), 188–201. Budd, John W. and Matthew J. Slaughter, “Are Profits Shared across Borders? Evidence on International Rent Sharing,” Journal of Labor Economics, 2004, 22 (3). 37

, Jozef Konings, and Matthew J. Slaughter, “Wages and International Rent Sharing in Multinational Firms,” The Review of Economics and Statistics, November 2005, 87 (1), 73–84. Chung, Richard, Byung Hee Lee, Woo Jong Lee, and Byungcherl Sohn, “Do managers withhold good news from labor unions?,” Management Science, forthcoming. Clausing, Kimberly A., “Tax-motivated transfer pricing and US intrafirm trade prices,” Journal of Public Economics, September 2003, 87 (9-10), 2207– 2223. Davies, Ronald B. and Carsten Eckel, “Tax Competition for Heterogeneous Firms with Endogenous Entry,” American Economic Journal: Economic Policy, February 2010, 2 (1), 77–102. DeAngelo, Harry and Linda DeAngelo, “Union negotiations and corporate policy: A study of labor concessions in the domestic steel industry during the 1980s,” Journal of Financial Economics, November 1991, 30 (1), 3–43. Desai, Mihir A, Alexander Dyck, and Luigi Zingales, “Theft and taxes,” Journal of Financial Economics, 2007, 84 (3), 591–623. and Dhammika Dharmapala, “Corporate tax avoidance and highpowered incentives,” Journal of Financial Economics, 2006, 79 (1), 145–179. Desai, Mihir A., C. Fritz Foley, and James Jr. Hines, “Foreign direct investment in a world of multiple taxes,” Journal of Public Economics, December 2004, 88 (12), 2727–2744. Eckel, Carsten and Hartmut Egger, “Wage bargaining and multinational firms,” Journal of International Economics, 2009, 77 (2), 206 – 214.

38

Egger, Peter and Tobias Seidel, “Tax competition, trade liberalization, and imperfect labour markets,” Oxford Economic Papers, 2011, 63 (4), 722–739. Eichner, T. and T. Upmann, “Labour Markets and Capital Tax Competition,” International Tax and Public Finance, 2012, 19, 203–215. Elitzur, Ramy and Jack Mintz, “Transfer pricing rules and corporate tax competition,” Journal of Public Economics, June 1996, 60 (3), 401–422. Exbrayat, N., C. Gaigne, and S. Riou, “The Efects of Labor Unions on International Capital Tax Competition,” Canadian Journal of Economics, 2012, 45 (4). G¨ uth, Werner, Rolf Schmittberger, and Bernd Schwarze, “An experimental analysis of ultimatum bargaining,” Journal of economic behavior & organization, 1982, 3 (4), 367–388. Haufler, Andreas and Ferdinand Mittermaier, “Unionisation Triggers Tax Incentives to Attract Foreign Direct Investment,” The Economic Journal, 2011, 121 (553), 793–818. and Frank St¨ ahler, “Tax Competition In A Simple Model With Heterogeneous Firms: How Larger Markets Reduce Profit Taxes,” International Economic Review, 2013, 54 (2), 665–692. and Guttorm Schjelderup, “Corporate Tax Systems and Cross Country Profit Shifting,” Oxford Economic Papers, April 2000, 52 (2), 306–25. Helpman, Elhanan, Oleg Itskhoki, Marc-Andreas Muendler, and Stephen J Redding, “Trade and inequality: From theory to estimation,” Technical Report, National Bureau of Economic Research 2012. Hilary, Gilles, “Organized labor and information asymmetry in the financial markets,” Review of Accounting Studies, 2006, 11, 525–548. 39

Hildreth, Andrew K G and Andrew J Oswald, “Rent-Sharing and Wages: Evidence from Company and Establishment Panels,” Journal of Labor Economics, April 1997, 15 (2), 318–37. Huizinga, Harry, Luc Laeven, and Gaetan Nicodeme, “Capital structure and international debt shifting,” Journal of Financial Economics, April 2008, 88 (1), 80–118. Janeba, Eckhard, “Tax Competition When Governments Lack Commitment: Excess Capacity as a Countervailing Threat,” American Economic Review, December 2000, 90 (5), 1508–1519. Kennan, John, “Private Information, Wage Bargaining and Employment Fluctuations,” Review of Economic Studies, 04 2010, 77 (2), 633–664. Kleiner, Morris M. and Marvin L. Bouillon, “Providing business information to production workers: Correlates of compensation and profitability,” Industrial and Labor Relations Review, July 1988, 41 (4), 605–617. Krautheim, Sebastian and Tim Schmidt-Eisenlohr, “Heterogeneous firms, ‘profit shifting’ FDI and international tax competition,” Journal of Public Economics, 2011, 95 (1-2), 122 – 133. Martins, Pedro S and Yong Yang, “Globalized Labour Markets? International Rent Sharing Across 47 Countries,” British Journal of Industrial Relations, 2014. Mintz, Jack and Michael Smart, “Income shifting, investment, and tax competition: theory and evidence from provincial taxation in Canada,” Journal of Public Economics, June 2004, 88 (6), 1149–1168. Mongrain, Steeve and John D. Wilson, “Tax Competition with Heterogeneous Capital Mobility,” IEB Working Paper 2011/25, Barcelona Institute of Economics 2011. 40

Myerson, Roger B, “Two-Person Bargaining Problems with Incomplete Information,” Econometrica, March 1984, 52 (2), 461–87. Ogawa, H., Y. Sato, and T.Tamai, “A Note on Unemployment and Capital Tax Competition,” Journal of Urban Economics, 2006, 60, 350–356. Peralta, Susana, Xavier Wauthy, and Tanguy van Ypersele, “Should countries control international profit shifting?,” Journal of International Economics, January 2006, 68 (1), 24–37. Reenen, John Van, “The Creation and Capture of Rents: Wages and Innovation in a Panel of U. K. Companies,” The Quarterly Journal of Economics, 1996, 111 (1), 195–226. Riedel, Nadine, “Taxing multi-nationals under union wage bargaining,” International Tax and Public Finance, 2011, pp. 1–23. Schindler, D. and G. Schjelderup, “Debt Shifting and Ownership Structure,” European Economic Review, 2012, 56 (4), 635–647. Siegloch, Sebastian and Martin Simmler, “Multinationals, profit shifting and wage bargaining,” November 2013. Presentation at the ZEW conference Taxing Multinational Firms. Swenson, Deborah L., “Tax Reforms and Evidence of Transfer Pricing,” National Tax Journal, March 2001, 54 (1), 7–26. Zhao, Laixun, “Labour-management bargaining and transfer pricing in multinational corporations,” Canadian Journal of Economics, 1998, pp. 817–829.

41

A A.1

Proofs of Propositions Proof of Proposition 1: Own-tax elasticity of revenue

Partial differentiation delivers: (1 − δ)s(1 − tX )φδf ∂|BEH | = tH > 0 ∂(1 − η) (1 − c∗ )2 ∂|BEX | δφf [κ1 (1 − tX ) − c∗ ] = − tX ∂(1 − η) (c∗ )2 δφf (1 − δ)s(1 − tH ) = − tX < 0 (c∗ )2 with κ1 ≡ (1 − δ)s + (1 − η)δφf . q.e.d.

A.2

Proof of Proposition 2: Equilibrium

First, note that the small country needs to attract positive inflows of tax base to generate a positive welfare level V > 0. Define the effective tax difference ρ˜ as the transformation of the tax difference ρ which takes the value of zero when outflows are zero, i.e. the cutoff c∗ = 0. The small country attracts tax base whenever ρ˜ > 0 (or, equivalently, if c∗ > 0), which is the case when: tX <

(1 − η)δφf (1 − δ)s + tH . κ1 κ1

With κ1 as defined in Appendix A.1. As long as δ > 0, for any tH > 0 there is some tax rate tX that fulfills this condition. If δ > 0 and η < 1, the small country can also attract tax base if tH = 0. Therefore, a necessary condition for an equilibrium is ρ˜ > 0. The equilibrium is determined by the intersection of equation (E.2) (tH (tX )ρ˜>0 ) with equation (33) (tX (tH )). As discussed before, there are two cases for the best response function of the

42

large country. In the following we discuss equilibrium existence for each of them separately. Case 1, tk1 X ≤ 1 First, note that in this case the tax rate of the large country ˜=0 tH in equation (F.1) is bounded from above by one as tρH (tX = 1) = 1. Given

that tk1 X ≤ 1, the tax rate of the large country tH in equation (E.2) is bounded ρ˜>0 from above by equation (F.1) for ∀tX ≥ tk1 X . Consequently, tH (tX ) ≤ 1.

Therefore, the equilibrium is either at tH = 0 if tX (tH = 0) ≤ tk2 X or it is at the positive intersection between equations (E.2) and (33). The equilibrium is unique as equations (E.2) and (33) are strictly monotonously increasing in the other country’s tax rate. Case 2, tk1 X > 1 Now, (E.2) is the best response of the large country for k2 ∀tX > tk2 X . Therefore, the equilibrium is either at tH = 0 if tX (tH = 0) ≤ tX , at

the positive intersection between equations (E.2) and (33) if the intersection is below or equal to one, or at tH = 1 if the two functions (E.2) and (33) meet at tH = 1. The equilibrium is unique as (E.2) and (33) are strictly monotonically increasing in the other country’s tax rate. q.e.d.

A.3

Proof of Proposition 3: Impact of η

The first result follows from differentiating equation (36) with respect to (1−η), which gives: (β + 1)δφf ∂t∗H =− < 0. ∂(1 − η) (1 − δ)(3β − 1)s For the second result, take the cross-derivative of t∗H with respect to (1 − η) and δ: (β + 1)φf ∂ 2 t∗H =− < 0. ∂(1 − η)∂δ (3β − 1)s(1 − δ)2 43

Differentiating (37) with respect to (1 − η) delivers: β−1 δφf [(1 − δ)s − 1] ∂t∗X = . ∂(1 − η) 3β − 1 [(1 − δ)s + (1 − η)δφf ]2 A sufficient condition for the right hand side to be negative is (1 − δ)s − 1 < 0, which is always true. We therefore have: ∂t∗X < 0. ∂(1 − η) q.e.d.

A.4

Proof of Proposition 4: Impact of δ

From equation (36), the large country equilibrium tax rate for an interior solution, i.e. t∗H ∈ (0, 1), is given by: t∗H =

2(β − 1) − (β + 1)(1 − η)δφf . (3β − 1)(1 − δ)s

This implies for the competitive pressure measured by 1 − t∗H : ∂(1 − t∗H ) 2(β − 1) − (β + 1)(1 − η)φf =− . ∂δ (3β − 1)s(1 − δ)2 Solving for η delivers the following condition: 2(β − 1) ∂(1 − t∗H ) > 0 ⇐⇒ 1 − η > = κ. ∂δ (β + 1)φf This proves (i). To build some intuition consider the extreme cases of perfect detection and zero detection. With perfect detection (η = 1) the wage incentive is closed down and we have

∂t∗H | ∂δ η=1

> 0. With a strong wage incentive (η = 0)

44

we have: 2(β − 1) ∂t∗H |η=0 < 0 ⇐⇒ φf > . ∂δ β+1 Under this parameter condition the wage channel is so strong that the sign of ∂t∗H ∂δ

flips. To prove (ii) we use equation (37). The small country equilibrium tax rate

for an interior solution, i.e. t∗H ∈ (0, 1), is given by: t∗X =

(β − 1)[σ/α + δ(1 − η)] . (3β − 1)(1 − ηδ)

Differentiating with respect to δ delivers: ∂t∗X β − 1 (1 − η)φf s + s − (1 − η)φf . = ∂δ 3β − 1 [(1 − δ)s + (1 − η)δφf ]2 It follows that: ∂t∗X s >0⇔η >1− . ∂δ φf (1 − s) To show that this holds in general consider the case of η = 0, and solve for s which implies: s>

φf . 1 + φf

(A.1)

Recall that for the Neutral Bargaining Solution to work, we imposed the condition f < ασ (1 − φ) ⇔

α σ

>

f . 1−φ

s>

From this it follows that:

f − (1 − φ)f. 1−φ

45

To check equation (A.1), we replace s by this lower bound to get: s>

φf f − (1 − φ)f > . 1−φ 1 + φf

Reformulating the second inequality delivers: 1 + φf [2 − φ] > 0 which holds always. Hence,

∂t∗X ∂δ

> 0 ∀η, δ. q.e.d.

46

B

Figures

Figure 1: Best response function of

Figure 2: Best response function of

large country for different η. Horizontal axis: small country tax rate tX , vertical axis: large country tax rate tH . η = {0; 0.5; 1}, σ = 3, α = 0.7, β = 1.05, δ = 0.5, f = 0.1 and φ = 0.4.

large country for different η. Horizontal axis: small country tax rate tX , vertical axis: large country tax rate tH . η = {0; 0.5; 1}, σ = 3, α = 0.7, β = 1.05, δ = 0.5, f = 0.1 and φ = 0.4.

(a)

(b)

(c)

Figure 3: Equilibria of the tax game for different levels of the wage incentive (a): 1 − η = 0, no wage incentive; (b): 1 − η = 0.5, intermediate wage incentive and (c): 1 − η = 1, strong wage incentive. Horizontal axis: small country tax rate tX (dashed line), vertical axis: large country tax rate tH (thick solid line). Thin line: 45 degree line. Other parameters: σ = 3, α = 0.7, β = 1.05, δ = 0.5, f = 0.1 and φ = 0.4.

47

Figure 4: Equilibrium tax rates of the large country (solid line) and the small coun-

1

1

0.9

0.9

0.8

0.8

0.7

0.7

0.6

0.6 tH, tX

tH, tX

try (dashed line) as a function of the detection parameter η (horizontal axis). Our measure of the wage incentive 1 − η therefore increases from the right to the left. Other parameters: σ = 3, α = 0.7, β = 1.05, δ = 0.5, f = 0.1 and φ = 0.4.

0.5

0.5

0.4

0.4

0.3

0.3

0.2

0.2

0.1

0.1

0

0

0.1

0.2

0.3

0.4

0.5 δ

0.6

0.7

0.8

0.9

(a)

1

0

0

0.1

0.2

0.3

0.4

0.5 δ

0.6

0.7

0.8

(b)

Figure 5: Equilibrium tax rates of the large country (solid line) and the small country (dashed line) as a function of the degree of rent-sharing δ (horizontal axis). Graph (a): 1 − η = 0, no wage incentive; (b): 1 − η = 1, strong wage incentive. Other parameters: σ = 3, α = 0.7, β = 1.05, δ = 0.5, f = 0.13 and φ = 0.4.

48

0.9

1

FOR ONLINE PUBLICATION C

Aggregation Z

1

bH dF (c) = (1 − c∗ )δs

BH =

c∗ c∗

Z

bX dF (c) = c∗ (δs − (1 − η)φδf )

BX = 0

Z

1

πH dF (c) = (1 − c∗ )(1 − δ)s

ΠH = c∗

Z

c∗

πX dF (c) = c∗ [(1 − δ)s + (1 − η)φδf ] .

ΠX = 0

D

Derivation of Tax Revenue Elasticities

Using Leibnitz rule, the own-tax elasticities of tax revenues for the large and the small country, respectively, can be decomposed into the two effects:

E

1

1 ∂ dF (c) dF (c∗ ) dc∗ tH πH (a) dc − tH πH (c∗ ) dc Π dc dtH c∗ ∂tH {z } {z }| H tax base effect (BE ) direct effect (DEH ) H (1 − δ)s = 1− tH . 1 − c∗ Z

d(ΠH tH ) 1 dtH ΠH

1 = Π |H

d(ΠX tX ) 1 dtX ΠX

∂ dF (c) 1 dF (c∗ ) dc∗ tX πX (c) dc + tX πX (c∗ ) ∂tX dc Π dc dtX 0 {z } {z }| X tax base effect (BE ) direct effect (DEX ) X (1 − δ)s + (1 − η)δφf tX . = 1− c∗ 1 = Π |X

Z

c∗

Best response of large country U = U¯ + (1 − tH )ΠH + (1 − tX )ΠX + BH + BX + βtH ΠH − C.

1

FOR ONLINE PUBLICATION Partially differentiating with respect to tH , rearranging and simplifying delivers: ∂c∗ ∂U = (β − 1) (1 − c∗ ) (1 − δ)s − [(1 − δ)sβtH + (1 − η)δφf ] . ∂tH ∂tH Plugging in

∂c∗ ∂tH

(E.1)

and setting the whole expression equal to zero, we can solve for

tH (tX ): tH (tX ) =

(β − 1)[(1 − δ)s + (1 − η)δφf ]) β − 1 − β(1 − η)δφf + tX . (E.2) (2β − 1)(1 − δ)s (2β − 1)(1 − δ)s

q.e.d.

F

Derivation of kinks of large country best response function

As illustrated in Figure 6 there can be two discontinuities in the best response function of the large country which limit the range of values of tX for which the large country sets its tax rate according to (E.2). We label these points tk1 X and k1 tk2 X . In this appendix we first derive tX as defined in the main text (point at

which the large country would optimally set its tax rate such that no tax base leaves the country). The tax rate of the large country is bounded from below by zero. We derive a threshold tk2 X > 0. For any tX below this threshold, according to (E.2), the large country would set a negative tax rate, so that the non-negativity constraint becomes binding. We derive a sufficient condition for this not to occur in equilibrium. First kink at ρ˜ = 0: Define ρ˜ = 0 as the tax difference ρ for which at a given tax rate of the small country tX , firms with zero shifting costs are indifferent between shifting and not shifting, i.e. c∗ = 0. This constitutes a corner solution

2

FOR ONLINE PUBLICATION with zero outflows. Any interior solution implies ρ˜ > 0 and therefore a positive number of firms shifting profits c∗ > 0. Appendix E implies that for an interior solution the best response of the large country tH (tX )ρ˜>0 is given by equation (E.2) above. It is never optimal for the large country to set tH such that ρ˜ < 0, as ρ˜ = 0 maximizes tax income conditional on zero outflows. The optimal tax rate for the corner solution of zero outflows can therefore be found by setting equation (22) to zero and solving for tH . This delivers: ˜=0 tρH (tX ) = −

(1 − δ)s + (1 − η)δφf (1 − η)δφf + tX . (1 − δ)s (1 − δ)s

(F.1)

Now, the second order condition of the large country maximization problem is: ∂c∗ ∂ 2 c∗ ∂ 2U = − (1 − δ)s(2β − 1) − [(1 − δ)sβtH + (1 − η)δφf ] < 0. ∂t2H ∂tH ∂t2H The sign follows from the fact that

∂c∗ ∂tH

> 0 and

∂ 2 c∗ ∂t2H ∗

= 0. This implies that

the welfare function is strictly concave whenever c > 0. Thus, there are two cases: if for a given tX equation (E.2) implies ρ˜ ≥ 0, then the first order condition (condition (E.1)) can be solved for the best response function as given by equation (E.2). If (E.2), however, implies ρ˜ < 0, then the constraint ρ˜ = 0 is binding and the best response function is given by equation (F.1). To find the value of tX where the best response function of the large country changes, we solve for the intercept of functions (E.2) and (F.1) which delivers: tk1 X =

(β − 1) [1 + (1 − η)δφf ] . βκ1

Second kink at tH = 0: To find the second kink solve equation (E.2) for tH = 0, which delivers: tk2 X =

β(1 − η)δφf − (β − 1) . (β − 1)κ1 3

FOR ONLINE PUBLICATION For any value of tX ≤ tk2 X the best response function of the large country is tH = 0. Now check when the equilibrium falls into the area where tH > 0. This is the case if the best response function of the small country at tH = 0 is to the right of tk2 X . We first derive tX (tH = 0): tX (tH = 0) =

(1 − η)δφf . 2κ1

As discussed above, the equilibrium t∗H is larger zero iff tX (tH = 0) > tk2 X . This implies t∗H > 0 ⇔ φf <

2(β − 1) . (β + 1)δ(1 − η)

Under revenue maximization (β → ∞) this condition writes: t∗H > 0 ⇔ φf <

2 > 1, δ(1 − η)

where the second inequality follows from the fact that δ and η are between zero and one. The first inequality then always holds as f < ασ (1 − φ) < 1 and φ ≤ 1. Best response function large country There are two cases: First, if tk1 X ≤ 1 then the best response function of the large country is given by:

tH (tX ) =

   −   

(1−η)δφf (1−δ)s

+

(1−δ)s+(1−η)δφf tX (1−δ)s

β−1−β(1−η)δφf + (2β−1)(1−δ)s     0

(β−1)[(1−δ)s+(1−η)δφf ]) tX (2β−1)(1−δ)s

if tk1 X ≤ tX ≤ 1 k1 if tk2 X < tX < tX

if 0 ≤ tX ≤ tk2 X,

k2 with tk1 X and tX given by equations (F.2) and (F.2).

Second, if tk1 X > 1 then the best response function of the large country is given

4

FOR ONLINE PUBLICATION

Figure 6: Graphical illustration of a best response of the large country for which the non-negativity constraint of the tax rate is binding. Horizontal axis: small country tax rate tX , vertical axis: large country tax rate tH .

by:

tH (tX ) =

 n  min β−1−β(1−η)δφf + (2β−1)(1−δ)s

o

(β−1)[(1−δ)s+(1−η)δφf ]) tX , 1 (2β−1)(1−δ)s

if 0 ≤ tX ≤ tk2 X.

 0

G

if tk2 X < tX ≤ 1

Equilibrium cost cutoff level and changes of aggregate equilibrium variables with (1 − η)

From equation (22), we have: c∗ = ρ(1 − δ)s + (1 − tX )(1 − η)δφf. This can be rewritten to: c∗ = tH (1 − δ)s − tX [(1 − δ)s + (1 − η)δφf ] + (1 − η)δφf.

5

FOR ONLINE PUBLICATION Plugging in the equilibrium tax rates and simplifying delivers: c∗ =

β−1 [1 + (1 − η)δφf ]. 3β − 1

It is easy to see that the cost cutoff level increases in the strength of the wage incentive 1 − η. Other variables: Aggregate surplus-dependent payments to workers of nonshifters decrease in (1 − η): ∂BH ∂c∗ = −δs < 0. ∂(1 − η) ∂(1 − η) Surprisingly, also aggregate surplus-dependent payments to workers of shifters decrease in (1 − η), that is the negative intensive margin effect dominates the positive extensive margin effect: ∂BX ∂c∗ = −δφf c∗ + [δs − (1 − η)δφf ]. ∂(1 − η) ∂(1 − η) Note that: 1 + (1 − η)δφf c∗ = > 0. ∗ ∂c /∂(1 − η) δφf Dividing equation (G.1) by ∂c∗ /∂(1 − η) delivers: 

 ∂BX = −[1 + (1 − η)δφf ] + δs − (1 − η)δφf < 0. sign ∂(1 − η) Aggregate profits of non-shifters decrease in 1 − η: ∂ΠH ∂c∗ = −(1 − δ)s < 0. ∂(1 − η) ∂(1 − η)

6

(G.1)

Aggregate profits of shifters increase in 1 − η: ∂c∗ ∂ΠX = [(1 − δ)s + (1 − η)δφf ] + δφf c∗ > 0. ∂(1 − η) ∂(1 − η)

7