Limiting Profit Shifting in a Model with Heterogeneous Firm Productivity

1 Introduction

With growing financial integration, multinational companies have increasingly shifted profits abroad to reduce their tax payments. Profit shifting is an effective method to lower tax payments: Egger, Eggert, and Winner (2010) find that multinationals pay over 50% less taxes than similar domestic firms in high tax countries.^[1] Governments have reacted. With the help of targeted changes to the tax code they have tried to secure their respective tax bases.

One such measure are thin capitalization rules, which aim at reducing profit shifting via internal debt.^[2] In the last years, many countries have restricted the deduction of interest payments for tax purposes to a certain percentage of earnings, that is, they have implemented a general “interest cap” (Table 1 in Langenmayr, Haufler, and Bauer 2015).^[3] In Italy, for example, interest expenses (net of interest income) can only be deducted if their value is less than 30% of earnings before interest, taxes, depreciation and amortization (EBITDA). Such rules are not restricted to borrowing from affiliates, but comprise all kinds of debt finance. Due to non-discrimination rules, they apply to many or all corporations, even if they are not active internationally.

The benefit of such a broad thin capitalization rule is that it effectively limits profit shifting via debt finance. However, such broadly applicable regulations also have disadvantages. They are badly targeted, as they also apply in cases that have nothing to do with profit shifting.^[4] In extreme cases, it is even possible that tax payments accrue under such rules even if the firm makes a loss.^[5]

As a second example, consider documentation requirements for transfer prices. Transfer pricing is often seen as the main profit shifting channel (Heckemeyer and Overesch 2013). As a countermeasure, many countries require detailed documentation from firms to justify their transfer prices for all international transactions within the firm (Lohse and Riedel 2013; Beer and Loeprick 2014). Preparing these documentations causes substantive administrative costs, especially as many countries do not have materiality thresholds (OECD 2013). Thus, these documentation requirements also affect firms who are active internationally, but do not engage in profit shifting, for example because they are only active in countries with similarly high tax rates. Further costs arise as firms hire consultants or choose inefficient strategies to comply with the regulations. For example, under a thin capitalization rule, firms may abstain from internal debt financing even when it would otherwise be optimal (e.g. for investments by affiliates who face high interest rates), and transfer pricing documentation requirements may deter firms from international expansion.

In this paper, I model such regulations to limit profit shifting, incorporating that they also impose costs on those firms that do not engage in such activities.^[6] I use this model to analyze the effects of limiting profit shifting on welfare and on the aggregate sum of profits shifted abroad. Firms in the model are heterogeneous in their productivity and compete under monopolistic competition. Including heterogeneous productivity is crucial to this analysis of limiting profit shifting, as it allows to model that the effects of this specific tax policy differ among firms with different productivity levels.

The key result of the model is that strengthening a limitation on profit shifting does not necessarily lead to less profit being shifted abroad on aggregate. As the costs of such regulations force some firms out of the market, there is less competition, so that the remaining firms become more profitable. It is therefore possible that the absolute amount of profits shifted abroad increases, even though only a smaller percentage of profits can be transferred. Furthermore, additional firms may start to shift profits abroad.

Regulations to limit profit shifting have further effects, besides the ambiguous effect on the amount of profits shifted itself. As such rules force some firms to exit the market, consumers have fewer varieties from which to choose, which implies a welfare loss. The overall welfare effect depends on the market situation: If firms have high market power, it is best if governments do not limit profit shifting possibilities. If firm productivity is very heterogeneously distributed, the government should limit profit shifting, as relatively many firms engage in profit shifting activities to begin with.

Limiting profit shifting is also more likely to be favorable if the costs of profit shifting are relatively low. As such costs have fallen during the last decades due to increasing global integration, this result is in line with the empirical evidence of increased regulation against profit shifting presented above.

This paper is part of the literature that combines models of heterogeneous firm productivity, which are commonly used in international trade theory since Melitz (2003), with the analysis of tax policy. A first part of this literature studies competition for internationally mobile firms (Davies and Eckel 2010; Haufler and Stähler 2013; Baldwin and Okubo 2014). Baldwin and Okubo (2009a) and Bauer, Davies, and Haufler (2014) analyze tax-cut-cum-base-broadening tax reforms, and Pflüger and Suedekum (2013) study entry subsidies in the context of firm heterogeneity. Becker (2013) and Bauer and Langenmayr (2013) consider the interaction between taxes and foreign direct investment. Closest to this paper, Krautheim and Schmidt-Eisenlohr (2011) study profit shifting in a model with monopolistic competition among heterogeneous firms. In their model, the most productive firms shift all of their profits to a tax haven. In contrast, this paper analyzes the case when the government has a second instrument at its disposal, namely regulations that limit profit shifting. Due to such regulations, firms can only partially shift profits abroad.

A different line of literature examines specific policy measures to limit profit shifting. Hong and Smart (2010) consider if the presence of tax havens is desirable from the perspective of high-tax countries. In an extension they consider the case that the high-tax country imposes thin capitalization rules. Haufler and Runkel (2012) focus explicitly on thin capitalization rules, but in contrast to this paper, the firms’ internationalization decision is not endogenous in their model. Instead, they assume that only some firms are active internationally, and firms are otherwise identical.

This paper is structured as follows. The next section introduces the reader to the model and derives a first result on the aggregate amount of profits shifted abroad. Section 3 analyzes the optimization problems of the two countries in more detail. Some numerical simulations in Section 4 clarify the theoretical results. Section 5 concludes.

2 Model

The model consists of two countries, the “home market” and the “tax haven.” The tax haven is small; all production takes place in the home market. The economy of the home market comprises two sectors. One of them is a numeraire sector that produces a homogeneous good with a single factor (labor) under perfect competition using a technology with constant returns to scale. The final good in this sector is freely traded, its price is normalized to unity. In the second sector, firms with heterogeneous productivity manufacture differentiated goods under monopolistic competition.^[7] The cost of production consists of constant, firm-specific marginal costs ai and fixed production costs c. Marginal costs of all potentially active firms follow a Pareto distribution in the interval [0,1].^[8] The cumulative distribution function of marginal cost is given by

The Pareto distribution implies that higher values of ai are more likely than lower values, i.e. that relatively few highly productive firms exist. Firms are more heterogeneous when the shape parameter γ is lower.^[9]

Firms in the differentiated goods sector compete under Dixit–Stiglitz monopolistic competition: Each firm offers a product that is, from the consumers’ point of view, only imperfectly substitutable by other goods. Therefore, firms have some market power. Consumers’ preferences are given by

X I and XN represent the quantities consumed of the differentiated and numeraire goods, respectively. XG is a public good, financed by tax revenue, and enters the utility function weighted by a factor β > 1. μ shows the importance of the differentiated goods relative to the numeraire good. Θ is the set of all differentiated goods. The Dixit–Stiglitz parameter σ can be interpreted as the (constant) elasticity of substitution.

Maximizing the utility function [2] subject to the budget constraint, the demand for a particular variety of the differentiated good is given by

where pi is the price of variety i, and P is the CES price index. Aggregate demand for XI is thus given by XI=μP.

Firms facing this demand function maximize their profits. Therefore, they set their prices as a constant mark-up over marginal cost,

The price is higher if the elasticity of substitution is lower, i.e. if firms have more monopoly power.

Thus, pre-tax profits of firms are given by the following equation, with the second equality taking optimal price and quantity decisions into account^[10]

The most efficient firms (i.e. the firms with the lowest marginal cost ai) are the most profitable.

Profits are taxed at a constant marginal rate tH in the home country. However, firms have the possibility to shift profits to the tax haven, where the profit tax rate tX is lower than in the home country (0 < tX < tH < 1).^[11] To shift profits, firms have to incur a fixed cost, f. As the cost of profit shifting is fixed, only the most profitable firms choose to shift their profits abroad (see Krautheim and Schmidt-Eisenlohr 2011).

In reality, many regulations limit profit shifting. Such regulations have to target the means of profit shifting, i.e. transfer pricing or internal financing structures. Due to limited information, the government cannot fully differentiate between legitimate intra-firm transactions and profit shifting. It thus has to use broader rules that also hinder activities other than profit shifting.^[12] A first example is thin capitalization rules, which dictate that only interest expenses of up to a certain fraction of profits can be subtracted from earnings for tax purposes for all firms. On the one hand, this limits the possibilities for profit shifting via debt. On the other hand, it increases all firms’ financing costs, as they have to comply with these rules or face higher tax rates, also if they did not intend to shift profits abroad. A second example is transfer pricing documentation requirements, which apply to all firms that are active internationally, also when they operate only in countries with similar tax rates.

In the model, the government of the home country can impose such regulations, which limit the maximum percentage of profits α that firms are able to shift abroad. This, however, imposes costs on all firms. These costs can be interpreted in manifold ways: Firms may choose inefficient strategies to comply with the regulations, or have to hire costly consultants. Transfer pricing requirements imply significant administrative costs. If thin capitalization rules are used, financing costs may rise. As many regulations (such as the Italian thin capitalization rule, see fn. 4) apply to all firms, such costs arise even if the firm does not engage in profit shifting activities. Thus, limits on profit shifting imposes costs on all firms, as they have to comply with the regulations, e.g. find different sources of financing if internal debt is limited by a thin capitalization rule.^[13] To represent all these different costs, every firm in the model bears an additional cost of (1−α)τ. The parameter τ scales the severity of the burden, which also depends on the strictness of the limitation on profit shifting, 1−α. While this cost is the same across firms in absolute value, it is highest for low-productivity firms in relative terms. It thus captures in a simplified way the empirical observation that tax compliance costs are highly regressive: Slemrod and Blumenthal (1996) present survey evidence that the tax compliance cost per employee is about $1,200 for firms with less than 1,000 employees, but only about $60 for firms with over 40,000 employees.^[14]

Due to the fixed costs of production and profit shifting limitations, not all potential firms are productive enough to be in business. A zero-profit condition determines the cut-off value aτ, that is, the cost coefficient of the least productive firm in the market:

Solving this condition for aτ yields

If the tax rate in the home country or the cost of the limitation on profit shifting is higher, fewer firms are in the market. More firms are active in larger markets (as measured by μ). For α=1 eq. [7] collapses to the case without a limitation on profit shifting.

Every firm can incur a fixed cost f to shift some of its profits abroad.^[15] As the most profitable firms have the most to gain from avoiding taxes, and given that the cost of profit shifting is fixed, only firms with marginal costs below a level aP shift profits abroad. This cut-off is determined by the following indifference condition, which already takes into account that fixed costs c and the burden of the limitation on profit shifting (1−α)τ have to be borne in both cases:^[16]

The left-hand side of eq. [8] represents the case in which the firm pays taxes only in the home country. On the right-hand side, it shifts profits into the tax haven. As the cost of profit shifting, f, is fixed, the firm always shifts as much of its profit abroad as is possible. It is assumed that the cost of profit shifting is not deductible from the firm’s taxable base.^[17]

Inserting eq. [5] for the profits, the marginal cost level aP is given by

Firms with marginal costs under aP shift as much of their profits as possible abroad; the other firms (with marginal costs ai∈[aP,aτ]) prefer to pay taxes on all profits in the home country, as the costs of profit shifting are – for them – too high relative to their earnings. A higher tax rate in the home country or a lower tax rate abroad induce more firms to shift profits abroad. Note that aP depends only indirectly (via the price index) on the costs that profit shifting limitations impose on all firms.

The cut-off values aτ and aP depend on the price index. Using the definition of the price index and combining it with eqs [4] and [7], the equilibrium value of the price index is

Lastly, let us consider optimal quantities of the numeraire good XN and the public good XG. Demand for the numeraire good is given by XN=I−μ, whereby income I consists of labor income L and profit income. The public good is financed by tax revenue T, XG=T. Thus, optimal quantities of the numeraire and the public good depend on aggregate profits and their taxation.

To look at this in more detail, consider the tax base in both countries (i.e. aggregate profits without deducting the burden imposed by the limitation on profit shifting). These are for the home country (Π) and tax haven (Π∗), respectively:

The tax base in the home country, eq. [11], can be interpreted as the sum of all profits (i.e. the tax base without any profit shifting, μσ) less the profits shifted to the tax haven (the second term) and aggregate fixed costs.

What determines how much profit is shifted abroad on aggregate? The tax base in the tax haven rises if the tax difference between the two countries increases. It falls if firms have higher costs to shift profits (higher f) or if the demand for differentiated goods in the home market is lower (lower μ). If profit shifting limitations impose a greater burden, the tax base is lower, as there are fewer firms in the market. The tax base in the haven is also smaller if the firms are more heterogeneous (lower γ).

Importantly, it is not always the case that a limitation on profit shifting leads indeed to less profit being shifted abroad on aggregate. Differentiating eq. [12] with respect to α, it becomes clear that counteracting effects are at work:

The first term reflects the effects on the intensive margin, that is, the change in the amount of profit each firm shifts abroad. First, there is a direct effect ∫0aPπidGa, as a change in α changes the percentage of profits that each firm is allowed to shift abroad. Second, there is an indirect effect: By strengthening a limitation on profit shifting (lowering α), the government crowds some firms out of the market. For the remaining firms, the market becomes less competitive, thus rendering them more profitable. Thus, possibly, if the increase in profitability is strong enough, these firms shift more profits abroad despite the profit shifting regulation. The second term captures an effect on the extensive margin, that is, on the number of firms that shift profits. As all active firms become more profitable, it is possible that firms that did not shift profits abroad before start to do so after it is strengthened.^[18] The following proposition summarizes these effects.

This result is driven by the market exit of some small firms, which occurs because of the compliance costs associated with regulations limiting profit shifting. To gauge the likelihood that such costs force some firms out of the market, let us consider some real-world numbers: In a survey of mid-sized US firms, Slemrod and Venkatesh (2002) find average tax compliance costs of $243,942. In a different sample, Blumenthal and Slemrod (1995) show that about 40% of compliance costs arise due to regulations concerning foreign-source income and are thus directly related to measures against profit shifting. There is also evidence that corporate tax compliance costs fall disproportionally on small firms (Sandford et al. 1989; Slemrod and Venkatesh 2002). For example, even the smallest firms in Slemrod and Venkatesh (2002) sample (firms with less than $5 million assets) report compliance costs of $105,467. Considering even smaller firms (less than 250 employees), Foreman-Peck, Makepeace, and Morgan (2006) find that tax compliance costs bear most heavily on the profitability of the smallest firms. In total, it is plausible that measures against profit shifting force some firms out of the market.

A numerical simulation in Section 4 will shed some more light on this result. First, however, I derive and discuss the conditions that determine the optimal tax rates and limitation on profit shifting in the following section.

3 Optimal Tax Policies

4 Numerical Analysis

4.1 Simulation of Proposition 1

The theoretical model has shown that it is not clear that a regulation that limits profit shifting always succeeds in its aim of decreasing the amount of profits that is shifted to a tax haven (see Proposition 1). In the following, numerical simulations will illustrate this. Their results are shown in Figure 1.

The graphs clarify how the tax policy of the home country affects the aggregate amount of profits shifted abroad. It compares the aggregate value of profits shifted abroad in the case with a limitation on profit shifting (dark plane) and without such a limitation (light plane). The optimal response of the tax haven (i.e. the optimal tX) is taken into account.

Figure 1:

Aggregate profits shifted abroad, with a limitation imposed (dark plane) and without such a limitation (light plane). Parameter values: L=1,μ=0.5,β=3,f=c=0.1,γ=1.5,σ=2. On the left, τ=0.1, on the right, τ=0.5.

On the two axes with the independent variables are tH and α, which constitute the home country’s tax policy. The graph in the benchmark case without a limitation on profit shifting (i.e. the light layer) is independent of α, which is drawn on the right-hand axis. Aggregate profits in the tax haven go to zero if either α→0 or tH→0, as then there is either no possibility or no incentive to shift profits abroad. Note, however, that this does not allow any inference about welfare.

The graphs clarify that only for some combinations of α and tH a rule which limits profit shifting actually leads to less profits being shifted abroad on aggregate. Even with relatively low costs of profit shifting regulation (left graph), a strict regulation may induce more profit shifting if the tax rate is high. If the burden is relatively high (right graph), very strict regulations to limit profit shifting may be counterproductive no matter what the tax rate is. As explained above, this happens because such regulation decreases competition in the market.

4.2 Simulation of Proposition 2

Lastly, let us consider the welfare effects, which were described in Section 3 and summarized in Proposition 2. A numerical analysis of the model confirms that it is not always optimal to limit profit shifting if this entail costs for all firms.

However, the simulations also show that if a limitation is welfare-increasing at all, then the government should set is as strict as possible, i.e. set α→0 (see the Appendix).^[21] Thus, the optimum in the model economy is always a corner solution, setting α either to 0 or to 1.

It depends on the characteristics of the economy (i.e. on parameters) whether a country chooses to prohibit profit shifting or not. Figures 2 and 3 show how market and firm characteristics influence whether profit shifting should be barred.

Figure 2:

Prohibiting profit shifting for different market characteristics. Parameter values: γ=1.5, L=1, μ=0.5,β=3 and f=τ=0.1.

Figure 2 summarizes the results of simulations comparing welfare without a limitation on profit shifting (i.e. α→1) and after its introduction for different market characteristics. These are on the one hand the elasticity of substitution, σ, which is also a measure for competition in the market, and fixed costs, c, which represent barriers to entry into the market. The darker area represents parameter constellations under which it is favorable to prohibit profit shifting.

Profit shifting should not be limited with a regulation that imposes costs on all firms if there are relatively many firms in a relatively uncompetitive market. If the elasticity of substitution is low, then it is more important for consumers to have as many firms in the market as possible. Hence, the utility loss of losing additional varieties is higher. In contrast to what might be the first intuition, this effect is stronger when many firms are in the market (low fixed costs c), because the additional fixed costs of limiting profit shifting become more important when other fixed costs are low.

Figure 3:

Prohibiting profit shifting for different firm characteristics. Parameter values: γ=1.5, L=1, μ=0.5, β=3,τ=0.1 and σ=1.5.

A further interesting aspect is the interplay of the different firm characteristics, namely fixed costs c and the costs of profit shifting, f, which is depicted in Figure 3. It is intuitive that the benefit from limiting profit shifting is smaller if few firms shift profits due to high costs f, especially because the burden imposed by regulation to hinder this falls on all firms. However, high fixed costs c make it more likely that profit shifting should be limited. If fixed costs are high, the market consists mainly of highly profitable firms, which are more likely to shift profits abroad, thus increasing the benefit of limiting profit shifting.

The degree of firm heterogeneity also influences whether profit shifting should be prohibited or not. Heterogeneity is measured by γ. High heterogeneity (a low γ) implies that the distribution of firm productivity approaches a uniform distribution, i.e. there are many firms with very high or low productivity levels.^[22] If firms are very heterogeneous, limiting profit shifting is more favorable. This is the case because with high heterogeneity, there are relatively many large, productive firms, which would shift all of their profits abroad otherwise, and relatively few small, unproductive firms, which are affected negatively (or even forced out of the market) by the regulations.

5 Conclusion

This article has analyzed the various effects and welfare implications of limiting profit shifting. It points out that regulations that aim to limit profit shifting may curb competition by forcing some firms out of the market. By rendering the remaining firms more profitable, it is possible that more profits are shifted abroad on aggregate after the introduction of a regulation that is supposed to prohibit or limit profit shifting.

In the introduction it was mentioned that such measures, e.g. thin capitalization rules, have increasingly been introduced or strengthened during the last years. The model also offers explanations for this by clarifying the effect of different parameters on the likelihood that limiting profit shifting increases welfare. It becomes clear that lower costs of profit shifting, which may have resulted from increasing financial integration, make limiting profit shifting more beneficial.