Equity-efficiency implications of a European tax and transfer system

Reducing economic disparities across the region and assisting vulnerable states have long been on the policy agenda of the European Union.¹ The debt crisis of 2008 highlighted the importance of this goal and provided the impetus for deeper fiscal integration in the EU. An ambitious interpretation of deeper fiscal integration involves implementing a common tax and transfer system (see, e.g, Casella 2005; Fuest and Peichl 2012). Nevertheless, shifting tax and transfer authorities to the EU level is not free of classical equity-efficiency considerations. To the best of my knowledge, a normative treatment of the issue in a Mirrleesian framework does not yet exist in the literature.

This study simulates three optimal income tax scenarios in a Mirrleesian framework for 24 EU countries and quantifies the implications of implementing these tax scenarios. I use gross hourly earnings data from 2014 wave of the EU Structure of Earnings Survey (SES) in order to calibrate the model. In the benchmark scenario (scenario 1, S1), every country maximizes its own welfare over separate budget constraints. In the case of a European tax and transfer system (scenarios 2 and 3), the social planner maximizes the total welfare in the EU with respect to a common budget constraint. For this scenario, two different possibilities are considered. In scenario 2 (S2), the EU is treated as a single country and, hence, the same tax scheme is applied everywhere. In scenario 3 (S3), the social planner is able to condition the taxes to the country of residence (“tagging”).²

The analysis begins by investigating the outcomes at the EU level. I find that both scenarios involving a common tax and transfer system yields welfare improvement compared to the benchmark. On the other hand, more than two-thirds of the agents become worse off. Whereas S2 leads to a contraction in total output up to 2.65%, efficiency implications of S3 are sensitive to the assumption regarding the income effects on labor supply. Specifications with and without income effects produce an expansion by 1.53% and a contraction by 0.62% respectively.

As a next step, the implications of three scenarios on the economic outcomes by country are explored. In both S2 and S3, countries exhibiting relatively higher mean in the wage rate distribution (all of the Western and some of the Northern European countries) transfer resources to the other countries and become worse off. Transfers are higher in an S3 scenario. In relative terms, Denmark transfers the most resources in both S2 and S3 (around 13% and 24% of its total gross income respectively). S2 implies higher labor distortions for almost every country, explaining the aggregate decline in total output. In S3, compared to the benchmark, high-mean countries are distorted more and low-mean countries are distorted less. Yet, the social planner is able to extract higher labor effort from high-mean countries when the utility function incorporates income effects. When the utility function does not allow for income effects, higher distortion in high-mean countries directly translates into lower total output. As a result, implication of S3 on aggregate output is dependent on the specific form of the utility function.

The national tax schedules are analyzed in order to understand the changes in welfare distributions within individual countries. In low-mean countries, those with the lowest income benefit the most from cross-country transfers of S2 and S3. In countries with a high mean and low standard deviation (e.g., Sweden), distortion and average taxes on the rich rise sharply in S2 compared to the benchmark, making them the worst off in terms of indirect utility. On the other hand, countries with high mean and high standard deviation (e.g., Germany) exhibit higher overall marginal taxes in the benchmark. Therefore, S2 does not lead to a significant shift in the marginal tax rate schedule. In such countries, the poor are the worst off in S2 because they must share the tax revenues with the poor in low-mean countries. In S3, the latter effect dominates and leads to a disproportional decline in the indirect utility of the poor in all high-mean countries.

S2 and S3 demonstrates the significant losses that high mean countries have to bear for a European tax and transfer system. In order the limit the extent of the direct losses, I investigate a more restrictive scenario. Social planners of S2 and S3 solve their problem with an additional constraint, that is, linearly aggregated social welfare must not be lower than the benchmark in any country. Together with the new constraint, the social planners ensure that a certain fraction of the individuals in transferring countries is better off as a result of the integrated European tax system. In this scenario, S2 does not yield an improvement in social welfare and, hence, it is not investigated in detail. S3, different than the full optimum, implies lower optimal marginal income taxes for every country. While about half of all Europe is better off and there is sizable output expansion in S3 compared to benchmark, increase in total welfare is restricted to 1%.

The remainder of this paper is organized as follows. Section 2 briefly discusses the related studies and the contribution of this study. Section 3 formalizes the social planner’s problems in the three scenarios. Section 4 introduces the two specifications used for the utility function. Subsequently, the calibration procedure is explained. The EU-level, country-level and within-country results are presented. Finally, Sect. 5 concludes.

A vast literature explores and analyzes the different possibilities of deeper fiscal integration in Europe.³ This study is the first to estimate optimal Mirrleesian schemes for a European tax and transfer system. The analysis of “tagging” (S3), which considers 24 EU countries as subgroups, and the “linear country welfare improving scenario” have not yet been pursued within the discussion on a European tax and transfer system. A number of studies that investigate the implications of a potential EU-wide labor income taxation system, albeit via different methodologies, are discussed in detail below.

Recently, a growing literature evaluates the distributional outcomes of different policies across the EU via micro-simulation approach using EUROMOD. Paulus et al. (2017), for example, analyzes the consequences of fiscal consolidation measures implemented following the financial crisis of 2008. See Figari et al. (2015) for a detailed discussion of the micro-simulation approach for policy analysis.⁴

Closest to the purpose of this paper among the micro-simulation literature, Bargain et al. (2013b) and Dolls et al. (2013) study the redistributive and stabilizing effects of implementing a common tax and transfer scheme in the euro area. By using household level data from EUROMOD, the authors construct a European tax and transfer system as the weighted average of the observed national tax and transfer systems. In a next step, they compare the results of the hypothetical scenario to the observed scenario. In this study, I abstract from the stabilizing effects and take a normative approach to evaluate equity-efficiency implications of different scenarios at the optimum. Conceptually, S2 of this study is equivalent to the European Tax and Transfer System discussed in Bargain et al. (2013b) and Dolls et al. (2013). I find that the optimal tax scheme of S2 is more distortive than almost every nationally optimal tax scheme. Thus, resulting implications on (in particular) efficiency for individual countries are different than Bargain et al. (2013b) and Dolls et al. (2013), where a centralized tax system is assumed to be the weighted average of existing national tax schemes. In S2 of this study, for example, labor supply falls in most of the countries, both with and without income effects.

Kopczuk et al. (2005) studies optimal world redistribution. For a Cobb–Douglas utility function with given parameters and an average flat tax rate, they estimate the ability distributions of 118 countries that matches empirical Gini coefficients and mean incomes. In a next step, they adjust the parameters of the utility function to minimize the squared errors between empirical PPPs and to match the average labor supply. Finally, they estimate a flat tax rate and a constant demogrant to approximate the optimal world redistribution.

More relatedly, Seelkopf and Yang (2018), relying on the methodology in Kopczuk et al. (2005), constructs an optimal EU-wide income taxation system. I estimate fully non-parametric optimal European tax schemes, contrary to the flat tax rate combined with a demogrant in Seelkopf and Yang (2018), whose EU-wide tax system corresponds to S2 with income effects in this study. Solving for non-parametric schemes allows me to thoroughly investigate the changes in the within-country distributions of welfare (see Sect. 4.3.3). Notable insights are as follows. In S2, richer are the worst off in high-productivity countries with low standard deviation (e.g., Sweden), whereas poorer are the worst off in high-productivity countries with high standard deviation (e.g., Germany). Redistributive benefits of an integrated tax system for poor countries, however, always come at the expense of the poor in high-productivity countries in S3. Moreover, in Seelkopf and Yang (2018), poorer countries experience a decline in labor distortions and EU-level labor supply remains the same. With the non-parametric tax schemes, I find that marginal income taxes increase especially for the lower part of the distribution in poorer countries, where a high fraction of the population is located, as a result of S2. Consequently, income weighted marginal taxes increase for majority of the countries in S2, including the poorer ones, and there is a sizable contraction in total output.

Additionally, different from Seelkopf and Yang (2018), this study recovers the ability distributions over the micro data (SES) and applies empirical PPPs directly to the observed wage rates. Because the construction of PPP-adjusted wage rates in this study does not require any prior assumptions, results can be obtained via different preference specifications. Section 4.3.2 showcases that there are considerable differences between results for utility specifications with and without income effects for S3.

In the optimal income tax literature initiated by Mirrlees (1971) and Akerlof (1978) was the first to argue that conditioning taxes on observable characteristics (tags) that are correlated with earnings ability would improve the performance of taxation.⁵ As emphasized above, this study is the first to consider “tagging” for the discussion of a centralized European tax and transfer system. The common practice in the literature of “tagging” is to compare the outcome of the tagged scenario (S3) to the pooled scenario (S2). See, for example, Cremer et al. (2010) and Bastani et al. (2013) among others. Evaluating an EU-wide tax system with tagging by country of residence provides a natural framework to compare the tagged scenario (S3) to the separate maximization (S1). I find that the optimal marginal income taxes increase with “tagging” compared to separate maximization for the groups with higher mean.

Relatedly, Kessing et al. (2020) split the districts of the US into two groups (large metropolitan and other regions) in order to study the trade-off between enhanced redistribution and efficiency enhancing migration. Their model incorporates an extensive margin migration decision and, therefore, the region of residence functions as an endogenous tag. This study assumes immobile workers and considers country of residence as an exogenous tag.⁶

A longstanding argument in the theory of fiscal federalism is that redistributive taxation should be carried out at the central level due to the mobility of the taxpayers (see, e.g., Oates 1999). On the other hand, a connected body of the literature embeds multiple layers of governments into the Mirrleesian optimal income tax model and, more relevant for the EU, analyzes optimal tax policies and public goods provision when workers are immobile.⁷ See Boadway and Keen (1993), Aronsson and Blomquist (2008) and Aronsson (2010). The analysis in this paper does not consider public goods provision, but adds to this literature by quantifying the welfare and equity-efficiency implications of centralized vs. decentralized solutions in an applied example.

There is a set K of N countries in the economy. Each country k constitutes a fraction \( s_{k} \), that satisfies \( \sum _{k \in K} s_{k} = 1 \), of the total population. Countries are populated by an immobile unit continuum of agents who differ with respect to their wage rates (abilities), w. In each country k, wage rates are distributed with density \( f_{k}(w) \) over the same support \( [{\underline{w}}, {\overline{w}}] \).⁸

Agents derive utility over the same separable preferences that are a function of consumption, c(w) , and labor supply, \( l(w) = \frac{z(w)}{w} \), where z(w) corresponds to gross income:Disutility of labor supply satisfies usual convexity conditions, that is \( v^{\prime }(.)>0 \), \( v^{\prime \prime }(.)>0 \). Properties of u(.) differ across specifications.

In each of the three tax scenarios, the social planners employ a social welfare function G(.) . Note that specific form of G(.) varies according to the choice of u(.) in order to satisfy the diminishing marginal utility of consumption principle. The social planners have access to a non-linear income tax instrument, T(z(w)) , that satisfies: \( z(w) - c(w) = T(z(w)) \). The information structure of the model is standard. When choosing the optimal tax schedule, the social planners are able to observe z(w) but not w. Hence, incentive compatibility constraints must be employed in order to ensure that each agent reveals his or her true ability type. In what follows, by using the first-order approach, incentive compatibility constraints are replaced by a law-of-motion that describes how the utilities of different ability types change at the optimum.⁹

In S1, the social planner solves a standard Mirrlees problem for each country separately according to its individual budget constraint. Therefore, this benchmark scenario excludes the possibility of cross-border transfers. At the same time, the social planner observes the differences in the probability distributions of the agents in each k (\( f_{k}(w) \)) and can differentiate the tax schemes across countries.¹⁰

The problem of the social planner in S2 is technically identical to S1. The only difference is that the probability distribution function used in S2 (\( f_{P}(w) \)) is obtained by pooling the populations of different countries. In other words, the social planner treats the entire population as a single country in S2. Note that, by construction of the problem, budget constraints of the countries are also pooled. Hence, transfers between countries are possible. However, the social planner does not exploit the information on differing probability distributions across countries and, therefore, applies the same tax scheme to every country.

In order to construct the probability distribution of the pooled population, the individual probability distributions of various countries are scaled by their population shares and then the resulting probability distributions across countries is summed (see Eq. (7)). As a result, a single wage rate distribution (that integrates to one) is obtained in which any wage bin represents the probability interval of the pooled population.¹¹

S3 is conceptually similar to S2. The social planner maximizes the weighted sum of the welfares of all countries over a common budget constraint. This implies that cross-border transfers are possible. The difference in the notations of S2 and S3 stems from the notion that the social planner recognizes the differences in the probability distributions of the agents across countries while optimally choosing the tax schedules.¹² Therefore, the social planner is able to condition the law-of-motion between indirect utilities of the agents to an observable tag: the country of residence (see Eq. (10)). As a result, the final optimal tax schemes may differ across countries.

The countries’ individual probability distributions in S3 (\( f_{k}^{\prime }(w) \)) are different than those of S1 (\( f_{k}(w) \)). This reflects the social planner’s need of taking the population shares into account while optimally designing the country-specific tax schedules. To construct \( f_{k}^{\prime }(w) \), it suffices to scale countries’ probability distributions by their population shares. Note that, integration of the resulting probability distributions yields countries’ population shares, that is \( \int _{w \in W}f_{k}^{\prime }(w) = s_{k} \). Hence, the new probability of any wage bin in a given country incorporates both the probability of drawing that particular country and wage bin.¹³ Probabilities of wage bins with the densities of S1 (\( f_{k}(w) \)), on the other hand, represents only the conditional probabilities (e.g., conditional on being in a country).

In this section, I simulate the three scenarios introduced in Sect. 3 for 24 EU member states. The difficulty of obtaining analytical results for Mirrleesian optimal income tax problems is repeatedly mentioned in the literature. However, interpreting the results of simulations for a large set of countries would be challenging without a basic understanding of the role played by the wage rate distributions. Therefore, Appendix B.1 provides examples for two imaginary countries which are intended to build intuition by utilizing a simple applied framework. Main lessons are as follows. If a country, ceteris paribus, exhibits higher mean or standard deviation, this results in higher nationally optimal marginal income taxes. As a result of “tagging”, S3, social planner finds it optimal to increase marginal income taxes of such countries in order to raise tax revenue that can be redistributed to the other countries. Even when the two countries’ taxes are nationally optimal, pooling the two countries may not necessarily lead the population weighted average of the national tax schemes.

In the rest of this section, first, the specifications used in the simulations are presented. Second, the calibration procedure for the main simulations is introduced. Third, EU-level, country-level and within-country results are respectively presented. Finally, following a brief discussion on political feasibility, a more restrictive centralized taxation scenario is pursued.

This study analyzes the equity-efficiency implications of a European tax and transfer system in a Mirrleesian setting. Using the Structure of Earnings Survey 2014 wave, three different income taxation scenarios are calibrated and simulated for 24 member states of the EU. In S1, every state discretely solves its own maximization problem. In S2 and S3, welfare in the EU is maximized with respect to a common budget constraint. In S3, the social planner can condition taxes to the country of residence whereas the social planner of S2 is restricted to apply the same tax scheme to every country. For the purpose of comparing the common tax and transfer systems to discrete maximization, S1 is considered as the benchmark while discussing the numerical results.

In spite of the increase in total welfare, more than two-thirds of the households become worse off in S2 and S3 compared to the benchmark. When the social planner is unable to differentiate the tax schemes across countries (S2), total output contracts by 2.65%. Implications of S3 on the total output is sensitive to the assumption regarding the income effects on labor supply. When the income effects are assumed away, S3 leads to a contraction by 0.62% while the specification with the income effects yields an expansion of 1.53%.

Countries with high mean transfer resources to low-mean countries. Because the size of the transfers are higher in S3 compared to S2, total welfare decreases (increases) gradually in high- (low-) mean countries when moving from S1 to S3. Pooling the populations in S2 results in a highly dispersed gross earnings distribution, leading to increased distortion (and reduced output) in almost all of the countries. In S3, on the other hand, high-mean countries contract, whereas low-mean countries expand when the income effects are assumed away. When the utility function allows for the income effects, the conclusion is reversed, explaining the contrast in the total output implications of S3.

Poorer households in low-mean countries gain the most from both scenarios involving a common tax and transfer system. Within high-mean countries, standard deviation of the wage rate distribution determines the segment of the population that experiences the highest decline in indirect utility. In countries with a low standard deviation (e.g., Sweden), the richest lose the most due to much higher taxes and distortion compared to the benchmark scenario. The poorest lose the most in countries with a high standard deviation (e.g., Germany) because of sharing the redistributive taxes with the poorest in low-mean countries. In S3, the latter effect dominates in all high-mean countries, rendering the problem as a trade-off between the poor in high- and low-mean countries.

The outcomes of S2 and S3 lays out the potential costs of an integrated tax system to the high productivity countries. It is possible to limit the costs by imposing the restriction that linearly aggregated social welfare must not decline in any country compared to the benchmark. Inferring from the size of the transfers and the fractions of individuals that become better off in every country, such a scenario seems more politically feasible compared to the full optimum case. On the other hand, with the new constraint, S2 yields a reduction in aggregated well-being, whereas S3 improves social welfare by about 1%.

The analysis in this study can be extended in multiple directions. First, it would be interesting to examine the effect of cross-country heterogeneities in redistributive preferences and labor supply elasticities on the model outcomes. Second, the assumption of immobile workers can be removed to investigate the optimal tax schedules under the trade-off between enhanced redistribution and productivity-enhancing migration as in Kessing et al. (2020). Finally, incorporating extensive margin labor supply decision to the model seems promising for future research.