PUBLIC GOOD PROVISION AND THE COMPARATIVE STATICS OF OPTIMAL NONLINEAR INCOME TAXATION*

Comparative static properties of the solution to an optimal nonlinear income tax problem are provided for a model in which the government both designs an income tax schedule for redistributive purposes and provides a public good optimally. There are two types of individuals, distinguished by their skill levels, who have the same quasilinear preferences for labor supply and the consumption of a private and a public good. Comparative statics are obtained for the weights in a weighted utilitarian social welfare function, the prices of the two goods, a taste parameter that measures the onerousness of working, and the skill levels.     

Optimal Nonlinear Income Taxation with Habit Formation

It has recently been shown that incorporating “keeping up with the Joneses” preferences into a prototypical two‐ability‐type optimal nonlinear income tax model leads to higher marginal tax rates for both types of agents. In particular, the high‐skill type faces a positive marginal tax rate, rather than zero as in the conventional case. In this paper, agents’ utility functions are postulated to exhibit “habit formation in consumption” such that the prototypical two‐ability‐type optimal nonlinear income tax model becomes a dynamic analytical framework. We show that if the government can commit to its future fiscal policy, the presence of consumption habits does not affect the standard results on optimal marginal tax rates. By contrast, if the government cannot precommit, the high‐skill type will face a negative marginal tax rate, while the low‐skill type’s marginal tax rate remains positive.     

Fair Income Tax

In a model where agents have unequal skills and heterogeneous preferences over consumption and leisure, we look for the optimal tax on the basis of efficiency and fairness principles and under incentive-compatibility constraints. The fairness principles considered here are: (1) a weak version of the Pigou–Dalton transfer principle; (2) a condition precluding redistribution when all agents have the same skills. With such principles we construct and justify specific social preferences and derive a simple criterion for the evaluation of income tax schedules. Namely, the lower the greatest average tax rate over the range of low incomes, the better. We show that, as a consequence, the optimal tax should give the greatest subsidies to the working poor (the agents having the lowest skill and choosing the largest labour time).     

Optimal Income Taxation With Quasi-Linear Preferences Revisited

Properties of the optimal income tax for quasi-linear in leisure preferences are studied. With utilitarian or maxi-min objectives, closed-form solutions are obtained. Bunching occurs over intervals where the second-order incentive condition is binding. Whether this occurs depends solely on the skill distribution. The patterns of consumption and tax rates in the nonbunched range are independent of whether the second-order incentive constraints are binding. Bunching at the bottom can also occur if a non-negative constraint on incomes is binding for some households. The pattern of marginal tax rates depends on the skill distribution and whether it is truncated.     

Majority Voting over Publicly Provided Goods, Redistribution, and Income Taxation

Federal, state, and many local governments make decisions that involve taxation, redistribution, and provision of public goods. Positive models to study these issues encounter the well‐known problem that majority‐voting equilibrium (MVE) may fail to exist in such multidimensional models. In this paper, with reasonable restrictions on preferences, I provide sufficient conditions for the existence of an MVE in a model with linear income tax and government expenditure policies that affect individual labor/leisure choices. My majority‐voting result takes account of the possibility that low‐skill individuals will drop out of the labor force under some tax and expenditure configurations.     

The impact of changing skill levels on optimal nonlinear income taxes

The impact of changing an individual's skill level on the solution to a finite population version of the Mirrlees optimal nonlinear income tax problem with quasilinear-in-leisure preferences is investigated. It is shown that it is possible to sign the directions of change in everyone's optimal consumptions and optimal marginal tax rates in response to such a change.     

Optimal Redistribution with Heterogeneous Preferences for Leisure

This paper examines the properties of the optimal nonlinear income tax when preferences are quasi–linear in leisure and individuals differ in their ability and their preferences for leisure. The government seeks to redistribute income. It can perfectly observe the level of endogenous income but cannot observe either ability or preferences. The heterogeneity of preferences leads to problems of comparability between individual utilities which challenge the design of redistributive schemes. We analyze the consequences of adopting a utilitarian social welfare function where the government is allowed to give different weights to individuals with different preferences. Under this particular social objective and given the quasi–linearity of preferences, we are able to obtain closed–form solutions for the marginal tax rates and to examine the progressivity of the tax system according to the weights used.     

An optional tax system

The model is of choice of hours worked and net of tax income by workers who vary in their skill levels. All workers face the same initial linear income tax schedule. We construct a set of linear income tax schedules, differeing in their degree of progressivity, and then allow each worker to choose under which schedule he shall be taxed. No worker is worse off under the option, and no worker pays less tax. Most workers are better off, and pay more tax. Hence, the optional tax system Pareto dominates the initial tax system.     

Flat tax? Maybe not a bad idea after all

This work studies the actual degree of progressivity in the Italian tax and transfer system and examines possible reforms towards the optimum. It analyzes the distribution of personal income and effective tax rates across the Italian population, computing income and tax liabilities from survey data, and studies the optimal level of progressivity. To this end, it uses a model developed in Heathcote et al. (2017) with heterogeneous agents where skill investment and labor supply are endogenous and the government provides a public good under a balanced budget. All the main tradeoffs that shape optimal progressivity appear: the presence of inequality in initial conditions and imperfect private insurance push for positive progressivity, whereas labor supply and skill investment call for regressivity. The model suggests a drastic reduction in progressivity under both the baseline and the alternative specifications. In particular, it calls for substantial reductions in marginal tax rates above approximately 0.25 times the mean income along with increased tax rates at the lower end of the income distribution. These reforms may be approximated by a flat tax at 29% under the baseline and at 32.5% under the alternative specification, holding the required positive level of progressivity constant.     

Optimal time-consistent fiscal policy under endogenous growth with elastic labor supply

We explore the implications of incorporating an elastic labor supply in an endogenous growth economy when characterizing the time-consistent Markov policy. We consider two policy instruments: an income tax rate and the split of government spending between consumption and production services. The Markov-perfect policy implies a higher income tax rate and a larger proportion of government spending allocated to consumption than those chosen under a commitment constraint on the part of the government. As a consequence, economic growth is slightly lower under the Markov-perfect policy than under the Ramsey policy. Under the Markov and Ramsey optimal policies, a higher weight of leisure in households' preferences leads to a lower optimal income tax rate and a lower proportion of public resources devoted to consumption. We also show that the policy bias that would arise when imposing a Markov policy designed ignoring the presence of leisure in the utility function would lead to a significant welfare loss.     

Tax Competition, Capital Mobility, and Public Good Provision Within a Trading Block

The authors examine a two–country general–equilibrium model of a two–country trading block where governments through tax policies attract mobile capital and provide an imported public consumption good. Within this framework the authors examine, among other things, how preferences over the public good and the size (population) of a country affect the Nash or cooperative equilibrium values of income tax rates in the two countries. The analysis identifies sufficient conditions under which (i) the Nash/cooperative equilibrium income tax rates are strategic substitutes or complements, and (ii) the Nash equilibrium income tax rates may be greater than the cooperative rates.     

Is commodity taxation unfair?

In a model where agents have unequal skills and heterogeneous preferences about consumption goods and leisure, this paper studies how to combine commodity taxes and non-linear income tax. It proposes a particular social welfare function on the basis of fairness principles. It then derives a simple criterion for evaluating the social welfare consequences of various tax schedules. Under the proposed approach, the optimal tax should have no commodity tax for some range of consumptions, and income redistribution would feature high subsidies to the working poor. It is also shown that, even when the income tax fails to be optimal, commodity taxes may not improve social welfare.     

Voting over selfishly optimal tax schedules: Can Pigouvian tax redistribute income?

This paper studies pairwise majority voting over selfishly optimal nonlinear income tax schedules proposed by a continuum of individuals who differ in privately observable skills and make consumption comparisons, which creates a negative positional externality. It shows that the tax schedule preferred by the median skill type will win the voting contest. Given a reference consumption defined as the average consumption in the population, all skills face the same Pigouvian tax rate in the utilitarian optimum, whereas in selfish optima high skills face a Pigouvian tax rate larger than that facing low skills, generating a novel income redistributive effect. Under a constant elasticity of labor supply, two more results are obtained. First, for Pareto, Champernowne, Weibull, and lognormal skill distributions, the selfishly optimal tax schedule facing high (low) skills tends to be more progressive when the bottom‐skill's (top‐skill's) status concern intensifies. Second, it identifies the conditions under which, in the voting equilibrium, high skills face higher marginal tax rates while low skills face lower ones than what they face in the utilitarian optimum.     

Optimal top marginal tax rates under income splitting for couples

This paper provides formulas for optimal top marginal tax rates when couples are taxed according to income splitting between spouses, consumption is taxed, and the skill distribution is unbounded. Optimal top marginal income tax rates are computed for Germany using a dataset that includes the tax returns of all German top taxpayers. We find that the optimal top marginal tax rate converges to about 2/3 and convergence obtains at income levels that are substantially higher than those currently subject to the actual top tax rate.     

Poverty alleviation and tax policy

This paper examines public good provision and tax policy—optimal non-linear income taxation and linear commodity taxation—when the government departs from purely welfarist objective function and seeks to minimise poverty. This assumption reflects much policy discussion and may help understand some divergences of practical tax policy from lessons in optimal tax analysis. In contrast to Atkinson and Stiglitz (J. Public Econom. 6 (1976) 55), it may be optimal to use differentiated commodity tax rates, including the taxation of savings, even if preferences are separable in goods and leisure. The optimal effective marginal tax rate at the bottom of the distribution may be negative, suggesting that wage subsidy schemes can be optimal. Finally, optimal provision of a public good is analysed under poverty minimisation.     

AN APPROXIMATION FOR THE OPTIMAL LINEAR INCOME TAX RATE

This paper derives a convenient method of calculating an approximation to the optimal tax rate in a linear income tax structure. Individuals are assumed to have Cobb-Douglas preferences and the wage rate distribution is lognormal. First, the optimal tax rate is shown, for a general form of social welfare function, to be the smallest root of a quadratic equation involving a welfare-weighted average wage rate. Second, an approximation to this average is derived for an isoelastic social welfare function. This average depends on the degree of inequality aversion of the welfare function and the coefficient on consumption in individuals' utility functions. Calculations show that the method performs well in comparison with standard simulation methods of computing the optimal tax rate.     

Tax policy in the presence of emigration

This paper investigates the relationship between utilitarianism and horizontal equity in models of income taxation in particular and self-selection in general. An example involving well-behaved individual preferences is constructed in which a maximization of a utilitarian social welfare function leads via income taxation to horizontal inequities. Sufficient conditions for utilitarianism to bring horizontal equity are derived. The results are applied to the question of whether income tax credits are an appropriate way to treat differences in family size.     

Fairness in tax compliance: A political competition model

This paper analyzes the political economy of income redistribution when voters are concerned about fairness in tax compliance. We consider a two‐stage model where there is a two‐party competition over the tax rate and over the intensity of the tax enforcement policy in the first stage, and voters decide about their level of tax compliance in the second stage. We find that if the concern about fairness in tax compliance is high enough, a liberal middle‐income majority of voters may block any income redistribution policy. Alternatively, we find an equilibrium in which the preferences of the median voter are ignored in favor of a coalition formed by a group of relatively poor voters and the richest voters. In this equilibrium income redistribution prevails with no tax enforcement.     

Optimal income taxation with tax avoidance and endogenous labour supply

I determine the optimal income tax schedule when individuals both choose endogenously their labour supply and have the possibility of avoiding paying taxes. Considering a convex concealment cost function, I propose a formula for the optimal marginal tax rate, that generalizes the formula of the standard Mirrlees model to the case of tax avoidance. I also show that the results obtained by Casamatta (2021) in the fixed income case hold true when labour supply is endogenous: with a low enough marginal cost of avoidance, it is optimal to let some taxpayers, located in the interior of the skill distribution, avoid taxes.     

The optimal taxation of unskilled labor with job search and social assistance

In order to explore the optimal taxation of low-skilled labor, we extend the standard model of optimal nonlinear income taxation in the presence of quasi-linear preferences in leisure by allowing for involuntary unemployment, job search and an exogenous welfare benefit. In trading off low-skilled employment against work effort of higher skilled workers, the government balances distortions on the search margin with those on work effort. Higher welfare benefits typically reduce taxes paid by low-skilled workers and raise marginal tax rates throughout the skill distribution.