Final Report Summary - THE (Taxation, Heterogeneity and Employment)
The main objective of this project was to study the proper design of benefit and tax programs that promote employment and reduce inequality when individuals are heterogeneous in several dimensions. To do so, I had to elaborate a theoretical toolbox allowing me to solve a large class of multidimensional screening problems, with a wide range of policy-oriented applications. I have provided a set of methods that include: (i) techniques for models with “intensive” margin (i.e. decision on labour hours worked) only (Jacquet and Lehmann, 2014) and (ii) techniques for models with both “intensive” and “extensive” (decision to enter or not the labour market) margins (Jacquet, Lehmann and Van der Linden, 2013). In what follows, I present these theoretical approaches in the context of optimal tax theory, but the methodology can find applications in other setups, for instance to characterize the optimal nonlinear monopoly pricing when consumers differ in the slope and in the intercept of their demand curves.
THEORETICAL TOOLBOX
Assume, in an optimal income tax model where labor supply decisions take place along the intensive margin, that individuals belong to different groups and differ in terms of (continuously distributed) skills both within and between groups. A group is a subset of individuals with the same vector of characteristics (e.g. labor supply elasticity, level of non-labor income, etc.) except skill levels. The set of groups may be finite or infinite and may be multidimensional. Jacquet and Lehmann (2014) show that keeping the assumption of Spence-Mirrlees single-crossing (with respect to skill) among individuals belonging to the same group makes the model tractable. The method relies on the use of an endogenous pooling function. Given a reference group G0, let the pooling function be the mapping that associates to a given group G and skill level w, the skill level of individuals in G who earn the same income level as individuals of skill w in G0. One can show that individuals of different groups pooled at the same income level are characterized by the same marginal rate of substitution between pre-tax and after-tax income. Intuitively, individuals of distinct groups who earn the same income level face the same marginal tax rate. From the individual maximization program, it comes that identical marginal tax rates mean identical marginal rates of substitution. Using this equality in marginal rates of substitution, one can fully characterize an incentive-compatible allocation from its restriction to the reference group G0. This necessary condition can then be rewritten as an optimal tax formula i.e. in terms of behavioral responses, social welfare weights and income density.
This method and its developments give a path to address a large scope of policy-oriented problems for which it is crucial, but challenging, to include multidimensional heterogeneity. Examples of these problems are detailed in the “Primary applications” below. These applications concern adverse selection models in which agents take a decision along an intensive margin. In Jacquet, Lehmann and Van der Linden (2013), I present another technique to study cases when individuals are heterogeneous in several dimensions and take their decisions along both the intensive and extensive margins, using a random participation model.
PRIMARY APPLICATIONS
Under relatively weak assumptions, my theoretical toolkit can be used to introduce additional sources of heterogeneity (that are not mutually exclusive) in tax models. These models can be solved and implemented with real data. Within the course of this project, I have studied optimal income tax models that consider the following sources of heterogeneity.
First, I allow for heterogeneous income elasticities that incorporate different labor supply elasticities and different abilities to avoid taxation. My co-author and I had initially thought about deriving the optimal tax schedule when there are both skill heterogeneity and gender-specific responses in terms of labor force participation decisions. However, in terms of policy implications, the income taxation of self-employed individuals, as compared to the income taxation of employees turned out to be a more interesting case to consider. The economic literature suggests that, in Denmark and in the USA, the self-employed have larger taxable income elasticities and more opportunities to avoid taxation. Self-employed individuals are also thought to generate innovation, wealth and employment. Applying my theoretical framework in this case consists in determining how multidimensional heterogeneity (in skills, in income elasticity and in ability to avoid taxes) affects the optimal tax schedule, and in giving numerical values derived from real data to key parameters of the model (see Jacquet and Lehmann 2014).
Other sources of heterogeneity considered in this project include exogenous taxable non-labor income (an example of which could be rents perceived by landlords who have inherited the property they rent) and endogenous taxable non-labor income (for instance, some forms of capital income). The latter case also applies to the optimal joint income taxation of households when members of the household take their decisions cooperatively. I also consider the case of some exogenous non-taxable non-labor income (such as the imputed rent of owner-occupied housing).
My framework is also appropriate to allow for heterogeneous tastes in the commodity and income taxation model of Atkinson and Stiglitz (1976). The most influential application of this model is the case where different goods are interpreted as consumption at different periods. In this case, when consumption and labor enter the utility function in a separable way and when all consumers have the same sub-utility function of consumption, optimal income taxation is inconsistent with taxing savings. However, as soon as individuals vary along several dimensions, this result is challenged. In an ongoing research, the method presented in the “Theoretical toolbox” section allows me to determine the optimal income tax schedule and tax rates on savings.
OTHER APPLICATIONS
Besides the applications presented in the previous section, this project also answered three applied economic questions which had been so far neglected in the tax literature. The first question concerned the determination of the optimal tax schedule which satisfies equality of opportunity over the entire earnings distribution. In Boadway, Brett and Jacquet (2014), I use my theoretical toolkit to derive optimal tax policies under equality of opportunity. Dworkin (1981) argues that there is a cut between the (genetic and social) characteristics of a person’s environment, for which she should not be held responsible for, and those for which she should be. This distinction and Dworkin’s responsibility-sensitive arguments have been largely discussed in the egalitarian literature in philosophy, but have also been exploited in the economic literature, which has proposed distinct normative approaches to the compensation-responsibility dyad. In Jacquet and Van de gaer (2011) and Jacquet and Van de gaer (2014), we compare optimal tax profiles using criteria from the social choice literature and the usual criteria of the optimal income literature. In Boadway, Brett and Jacquet (2014), we propose a new specification for the government’s objective function when the government puts emphasis on the compensation principle. We build up on Roemer (1998)’s approach regarding this principle since we assume a weighted sum of utilities of the worst-off within each preference group. However, we differ by allowing the government to have a varying attitude towards persons of different preferences by possibly attaching distinct weights on individuals with distinct preferences for leisure. We study how the tax schedule is modified with these weights and relate our weights to those implicitly used in the existing literature.
The second question addressed in this project concerned the use of workfare when labor supply is simultaneously modeled along the participation margin (decision to enter or not the labor market) and the intensive margin (i.e. people decide on their labor hours). In Brett and Jacquet (2014), I study the optimality of workfare in a model where the behavioral responses occur along the extensive margin. The previous literature has studied the optimality of workfare when labor supply is along the intensive margin. With the same co-author, I am currently extending this study to check the validity of these previous results when labor supply decisions take place simultaneously along intensive and extensive margins.
The third and final question consists in examining how the recommended tax system is modified when distortions arise from labour market imperfections. In the literature on optimal redistributive taxation à la Mirrlees, non-employment or unemployment, if any, is synonymous with non-participation. It simply arises from a preference for leisure. However, in reality, some people remain jobless despite they do search for a job at the market wage. To account for the presence of such involuntary unemployment (which is an important source of inequality), a recent literature departs from the assumption of perfect labor markets. In this context, inefficiencies arise from labor supply (as in the standard model) but also from the following channel. Taxes alter the outcomes of the wage bargain and hence affect labor demand. In turn, labor demand has an impact on search and matching frictions and thus on unemployment. The introduction of matching frictions is a natural way to include involuntary unemployment. Matching frictions induce that employers and employees get a positive surplus when they match. The sum of these surpluses (the “total surplus”) has to be shared. This is typically done through bargaining. The two most popular solutions to this bargaining problem are the Nash and the proportional Kalai solutions. Several contributions have derived optimal tax schedules under matching frictions and Nash bargaining. In Jacquet, Lehmann, and Van der Linden (2014), we adopt the alternative assumption of proportional bargaining à la Kalai. Compared to the Nash approach, the link between the income tax and the labor market equilibrium is changed, which affects the design of the optimal income tax in a substantial way.
THEORETICAL TOOLBOX
Assume, in an optimal income tax model where labor supply decisions take place along the intensive margin, that individuals belong to different groups and differ in terms of (continuously distributed) skills both within and between groups. A group is a subset of individuals with the same vector of characteristics (e.g. labor supply elasticity, level of non-labor income, etc.) except skill levels. The set of groups may be finite or infinite and may be multidimensional. Jacquet and Lehmann (2014) show that keeping the assumption of Spence-Mirrlees single-crossing (with respect to skill) among individuals belonging to the same group makes the model tractable. The method relies on the use of an endogenous pooling function. Given a reference group G0, let the pooling function be the mapping that associates to a given group G and skill level w, the skill level of individuals in G who earn the same income level as individuals of skill w in G0. One can show that individuals of different groups pooled at the same income level are characterized by the same marginal rate of substitution between pre-tax and after-tax income. Intuitively, individuals of distinct groups who earn the same income level face the same marginal tax rate. From the individual maximization program, it comes that identical marginal tax rates mean identical marginal rates of substitution. Using this equality in marginal rates of substitution, one can fully characterize an incentive-compatible allocation from its restriction to the reference group G0. This necessary condition can then be rewritten as an optimal tax formula i.e. in terms of behavioral responses, social welfare weights and income density.
This method and its developments give a path to address a large scope of policy-oriented problems for which it is crucial, but challenging, to include multidimensional heterogeneity. Examples of these problems are detailed in the “Primary applications” below. These applications concern adverse selection models in which agents take a decision along an intensive margin. In Jacquet, Lehmann and Van der Linden (2013), I present another technique to study cases when individuals are heterogeneous in several dimensions and take their decisions along both the intensive and extensive margins, using a random participation model.
PRIMARY APPLICATIONS
Under relatively weak assumptions, my theoretical toolkit can be used to introduce additional sources of heterogeneity (that are not mutually exclusive) in tax models. These models can be solved and implemented with real data. Within the course of this project, I have studied optimal income tax models that consider the following sources of heterogeneity.
First, I allow for heterogeneous income elasticities that incorporate different labor supply elasticities and different abilities to avoid taxation. My co-author and I had initially thought about deriving the optimal tax schedule when there are both skill heterogeneity and gender-specific responses in terms of labor force participation decisions. However, in terms of policy implications, the income taxation of self-employed individuals, as compared to the income taxation of employees turned out to be a more interesting case to consider. The economic literature suggests that, in Denmark and in the USA, the self-employed have larger taxable income elasticities and more opportunities to avoid taxation. Self-employed individuals are also thought to generate innovation, wealth and employment. Applying my theoretical framework in this case consists in determining how multidimensional heterogeneity (in skills, in income elasticity and in ability to avoid taxes) affects the optimal tax schedule, and in giving numerical values derived from real data to key parameters of the model (see Jacquet and Lehmann 2014).
Other sources of heterogeneity considered in this project include exogenous taxable non-labor income (an example of which could be rents perceived by landlords who have inherited the property they rent) and endogenous taxable non-labor income (for instance, some forms of capital income). The latter case also applies to the optimal joint income taxation of households when members of the household take their decisions cooperatively. I also consider the case of some exogenous non-taxable non-labor income (such as the imputed rent of owner-occupied housing).
My framework is also appropriate to allow for heterogeneous tastes in the commodity and income taxation model of Atkinson and Stiglitz (1976). The most influential application of this model is the case where different goods are interpreted as consumption at different periods. In this case, when consumption and labor enter the utility function in a separable way and when all consumers have the same sub-utility function of consumption, optimal income taxation is inconsistent with taxing savings. However, as soon as individuals vary along several dimensions, this result is challenged. In an ongoing research, the method presented in the “Theoretical toolbox” section allows me to determine the optimal income tax schedule and tax rates on savings.
OTHER APPLICATIONS
Besides the applications presented in the previous section, this project also answered three applied economic questions which had been so far neglected in the tax literature. The first question concerned the determination of the optimal tax schedule which satisfies equality of opportunity over the entire earnings distribution. In Boadway, Brett and Jacquet (2014), I use my theoretical toolkit to derive optimal tax policies under equality of opportunity. Dworkin (1981) argues that there is a cut between the (genetic and social) characteristics of a person’s environment, for which she should not be held responsible for, and those for which she should be. This distinction and Dworkin’s responsibility-sensitive arguments have been largely discussed in the egalitarian literature in philosophy, but have also been exploited in the economic literature, which has proposed distinct normative approaches to the compensation-responsibility dyad. In Jacquet and Van de gaer (2011) and Jacquet and Van de gaer (2014), we compare optimal tax profiles using criteria from the social choice literature and the usual criteria of the optimal income literature. In Boadway, Brett and Jacquet (2014), we propose a new specification for the government’s objective function when the government puts emphasis on the compensation principle. We build up on Roemer (1998)’s approach regarding this principle since we assume a weighted sum of utilities of the worst-off within each preference group. However, we differ by allowing the government to have a varying attitude towards persons of different preferences by possibly attaching distinct weights on individuals with distinct preferences for leisure. We study how the tax schedule is modified with these weights and relate our weights to those implicitly used in the existing literature.
The second question addressed in this project concerned the use of workfare when labor supply is simultaneously modeled along the participation margin (decision to enter or not the labor market) and the intensive margin (i.e. people decide on their labor hours). In Brett and Jacquet (2014), I study the optimality of workfare in a model where the behavioral responses occur along the extensive margin. The previous literature has studied the optimality of workfare when labor supply is along the intensive margin. With the same co-author, I am currently extending this study to check the validity of these previous results when labor supply decisions take place simultaneously along intensive and extensive margins.
The third and final question consists in examining how the recommended tax system is modified when distortions arise from labour market imperfections. In the literature on optimal redistributive taxation à la Mirrlees, non-employment or unemployment, if any, is synonymous with non-participation. It simply arises from a preference for leisure. However, in reality, some people remain jobless despite they do search for a job at the market wage. To account for the presence of such involuntary unemployment (which is an important source of inequality), a recent literature departs from the assumption of perfect labor markets. In this context, inefficiencies arise from labor supply (as in the standard model) but also from the following channel. Taxes alter the outcomes of the wage bargain and hence affect labor demand. In turn, labor demand has an impact on search and matching frictions and thus on unemployment. The introduction of matching frictions is a natural way to include involuntary unemployment. Matching frictions induce that employers and employees get a positive surplus when they match. The sum of these surpluses (the “total surplus”) has to be shared. This is typically done through bargaining. The two most popular solutions to this bargaining problem are the Nash and the proportional Kalai solutions. Several contributions have derived optimal tax schedules under matching frictions and Nash bargaining. In Jacquet, Lehmann, and Van der Linden (2014), we adopt the alternative assumption of proportional bargaining à la Kalai. Compared to the Nash approach, the link between the income tax and the labor market equilibrium is changed, which affects the design of the optimal income tax in a substantial way.