On the undesirability of commodity taxation even when income taxation is not optimal

An important result due to Atkinson and Stiglitz (1976) [Atkinson, A.B., Stiglitz, J.E., 1976. The design of tax structure: Direct versus indirect taxation. Journal of Public Economics 6, 55–75.] is that differential commodity taxation is not optimal in the presence of an optimal nonlinear income tax (given weak separability of utility between labor and all consumption goods). This article demonstrates that this conclusion holds regardless of whether the income tax is optimal. In particular, given any commodity tax and income tax system, differential commodity taxation can be eliminated in a manner that results in a Pareto improvement. Also, differential commodity taxation can be proportionally reduced so as to generate a Pareto improvement. In addition, for commodity tax reforms that neither eliminate nor proportionally reduce differential taxation, a simple efficiency condition is offered for determining whether a Pareto improvement is possible.     

Optimal mixed taxation,credit constraints,and the timing of income tax reporting

We study optimal income and commodity tax policy with credit‐constrained low‐income households. Workers receive an even flow of income during the tax year, but report their incomes and make tax payments (receive transfers) at the end of the year. They spend their disposable income on multiple commodities over the year. We show that differentiated subsidies on commodities can be optimal even if the Atkinson–Stiglitz Theorem conditions apply. When the optimal policy leaves low‐income households with binding credit constraints, it may be optimal to subsidize differentially the good that they consume in higher proportion. Uniform subsidies would also relax the credit constraint, but would be more costly to the government since they would equally benefit unconstrained households. Numerical examples suggest that commodity tax differentiation increases with basic needs and with the interest rate at which government borrows.     

Externalities and optimal taxation

This paper reexamines the optimal tax design problem (income and commodities) in the presence of externalities. The nature of the second–best, and the choice of the tax instruments, are motivated by the informational structure in the economy. The main results are: (i) environmental levies (linear or nonlinear) differ in formula from Pigouvian taxes by the expressions for the optimal tax on private goods; (ii) externalities do not affect commodity tax formulas (linear and nonlinear) for private goods; (iii) externalities do not affect the income tax structure if commodity taxes are nonlinear and affect it if commodity taxes are linear; and (iv) a general income tax plus strictly Pigouvian taxes are sufficient for efficient taxation if individuals of different types have identical marginal rates of substitution (at any given consumption bundle).     

Optimal human capital policies under the endogenous choice of educational types

This study examines optimal human capital policies under nonlinear labor and capital income taxes in the presence of consumption value of education in a two‐period setting. We show that when individuals can choose educational types differing by the relative importance of consumption value and production value, education subsidies for low‐type individuals should not equal an efficient level that offsets distortions induced by nonlinear taxes on labor and capital income. Our findings imply that education policy does not restore efficiency, or the Diamond–Mirrlees production efficiency theorem fails. Moreover, capital income taxation is optimal, which means that the Atkinson–Stiglitz theorem breaks down.     

Optimal tax theory: A synthesis

Necessary conditions for optimal taxation are derived (i) when taxes are constrained to be linear, (ii) when the form of taxation is unconstrained, (iii) when some commodities are subject to nonlinear taxation, the remainder to proportional taxation. Among the results obtained are several that help to determine upon which commodities the tax system ought to bear most heavily. In particular, a criterion for the effect of commodity taxes in the presence of an optimal income tax is found. The paper concludes with a general principle of simple form for optimal economic policies of all kinds.     

On Optimal Commodity Taxes When Consumption Is Time Consuming

This paper studies the problem of optimal taxation of commodities when consumption is a time‐consuming activity. This is done under two distinct preference separability assumptions: between goods and labor supply, and between goods and leisure. It argues that with the labor separability, the traditional uniform taxation results of optimal tax theory continue to hold. With leisure separability, on the other hand, consumption time is a major ingredient of optimal tax rates. However, the relationship between consumption time and optimal tax rates depends crucially on the representation of the economy. In representative consumer economies, time differences determine the pattern of optimal tax rates so that goods whose consumption take more time are subjected to higher tax rates. When individuals have different earning abilities, redistributive, incentive, and efficiency considerations also come into play resulting in a complex relationship. The paper derives formulas for optimal commodity taxes in this case on the basis of three different tax structures: linear commodity taxes in combination with linear and nonlinear income taxes, and nonlinear commodity taxes in combination with nonlinear income taxes.     

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.     

Viewpoint: Innovations in the theory and practice of redistribution policy

Abstract We present a survey of key results from second‐best optimal redistribution theory and their implications for tax‐transfer policy. The core results include the Corlett‐Hague theorem, the Deaton conditions, the production‐efficiency theorem, the Atkinson‐Stiglitz theorem, and the Mirrlees‐Saez characterization of the optimal non‐linear income tax system. These have been augmented in recent years by optimal participation tax rates, the implications of involuntary unemployment, the use of unconventional instruments, such as minimum wages, in‐kind transfer, and workfare, and the optimal taxation of capital income and bequests.     

Taxation of capital income in overlapping generations economies

Whether capital income should be taxed in overlapping generations economies is vividly discussed. It is shown that intergenerational lump‐sum taxes cannot implement the Golden Rule allocation when agents have private information on their earnings potential. Hence, the seminal Atkinson–Stiglitz result that optimal income taxation pre‐empts any role for indirect taxation cannot be interpreted to imply that capital income taxation (affecting intertemporal relative prices) should not be taxed. Specifically, capital income should unambiguously be taxed in small open economies, and the optimal tax rate depends inversely on the elasticity of total savings to disposable income and the after‐tax rate of return.     

Optimal mixed taxation,public goods and the problem of high-skilled emigration

The optimal income tax model under the threat of migration of Simula and Trannoy (J Public Econ 94:163–173, 2010; Soc Choice Welf 39(4):751–782, 2012) is extended to include indirect taxes and public goods. This enables us to conclude that: (1) optimal income tax rates are higher than in the absence of indirect taxation, and may be positive at the top of the skills distribution; (2) indirect taxes, à la Corlett and Hague, may help mitigate the loss of redistributive capacity arising from income taxation caused by migration threats; (3) migration encourages the provision of the public goods preferred by the most productive workers; (4) optimal tax and public goods provision policies against the emigration of the highly-skilled are connected through the conditions for Pareto efficiency; (5) if the number of potential migrators is large, it may be desirable to violate classical tax rules to retain the most able in the home country; (6) when migration costs are exogenously given and utility is weakly separable, Simula and Trannoy’s results are restored; (7) if migration costs are endogenous, the Atkinson and Stiglitz theorem breaks down and the taxation of country-specific goods becomes desirable, even if utility is strongly separable.     

Trade,environment, and income inequality: An optimal taxation approach

In a small open economy, how should a government pursuing both environmental and redistributive objectives design domestic taxes when redistribution is costly? And how does trade liberalization affect the economy's levels of pollution and inequalities, when taxes are optimally and endogenously adjusted? Using a general equilibrium model under asymmetric information with two goods, two factors (skilled and unskilled labor), and pollution, this paper characterizes the optimal mixed tax system (nonlinear income tax and linear commodity and production taxes/subsidies) with both production and consumption externalities. While optimal income taxes are not directly affected by environmental externalities, conditions are derived under which under‐ or over‐internalization of social marginal damage is optimal for redistributive considerations. Assuming that redistribution operates in favor of the unskilled workers and that the dirty sector is intensive in unskilled labor, simulations suggest that trade liberalization involves a clear trade‐off between the reduction of inequalities and the control of pollution when the source of externality is only production; this is not necessarily true with a consumption externality. Finally, an increase in the willingness to redistribute income toward the unskilled results paradoxically in less pollution and more income inequalities.     

Optimal nonlinear income taxation with learning-by-doing

This paper examines a two-period model of optimal nonlinear income taxation with learning-by-doing, in which second-period wages are an increasing function of first-period labour supply. We consider the cases when the government can and cannot commit to its second-period tax policy. In both cases, the canonical Mirrlees/Stiglitz results regarding optimal marginal tax rates generally no longer apply. In particular, if the government cannot commit and each consumer's skill-type is revealed, it is optimal to distort the high-skill type's labour supply downwards through a positive marginal tax rate to relax an incentive-compatibility constraint. Our analysis therefore identifies a setting in which a positive marginal tax rate on the highest-skill individual can be justified, despite its depressing effect on both labour supply and wages.     

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.     

Endogenous human capital accumulation, comparative advantage and direct vs. indirect redistribution

Recently, several papers have reexamined the so-called production efficiency theorem and the Atkinson and Stiglitz theorem on commodity taxes in the optimal taxation literature. Naito [J. Public Econ. 71 (1999) 65] showed that indirect redistribution through production distortion or consumption distortion can Pareto-improve welfare and that the two theorems do not necessarily hold when different factors are imperfect substitutes and factor prices are endogenous. On the other hand, Saez J. Public Econ. (2002) forthcoming argued that in the long run, where human capital accumulation is endogenous, the two theorems are still valid. This paper develops reasonable alternative models where individuals accumulate human capital based on their comparative advantage. The present paper shows that the production efficiency theorem is not necessarily valid and that indirect redistribution from the able to the less able such as tariffs and production subsidies can increase efficiency even when skill accumulation is endogenous.     

Optimal tax perturbations

The paper considers an economy with H households, N+1 commodities and M fixed factors with commodity taxes and government expenditures on goods and services. The paper studies under what conditions (small) Pareto improving tax changes exist, i.e., tax changes which increase the utility of each household in the economy. The basic analytical technique used is just the usual comparative statics apparatus, except that duality theory is used in order to simplify the computations. The paper derives both the changes in prices and in real incomes that are induced by (small) changes in exogenous tax variables (differential real income balanced budget incidence analysis).     

Environmental taxes with heterogeneous consumers: an application to energy consumption in France

This paper constructs a model with four groups of households who have preferences over labor supply, consumption of polluting (energy related) and non-polluting (non-energy) goods, and emissions. It quantifies the model for the French economy and computes its optimal tax equilibria under nine second-best tax regimes. We find that the redistributive role of environmental taxes requires the polluting goods to be taxed at a rate much below their marginal social damage. These goods may even require an outright subsidy if the society values equality ‘a lot’. Secondly, if environmental taxes that have an exclusively externality-correcting role, they benefit all types—although the gains are rather modest. The gains and losses become more substantial when environmental taxes have a redistributive role as well. Third, setting the environmental tax at its Pigouvian level, rather than its optimal externality-correcting-cum-redistributive level, benefits the high-income group at the expense of the low-income groups. Fourth, nonlinear taxation of polluting goods, and nonlinear commodity taxation in general, is a powerful redistributive mechanism. Fifth, introducing environmental taxes in the current French tax system, with its suboptimal income taxes, results in substantial welfare gains for the highest income group and a sizable loss for the least well-off persons.     

Relative Consumption Concerns and the Optimal Tax Mix

This paper studies the optimal tax mix (taxes on income and commodities) under asymmetric information in a two‐type model, when individuals make relative consumption comparisons. The model includes both positional and nonpositional goods, taking into account the fact that relative concerns matter for some but not for all commodities. We find that in general the whole tax system is affected by the externalities caused by the consumption of positional goods, notably also the taxes on income and on a nonpositional good. The tax rates on positional goods are higher than in the absence of status effects, reflecting their Pigouvian role. The sign of the Pigouvian part in the income tax schedule is ambiguous and depends crucially on whether status goods are complements or substitutes to leisure.     

Optimal taxation with consumption time as a leisure or labor substitute

This paper studies the optimal commodity taxation problem when time taken in consumption is a perfect substitute for either labor or leisure. It shows that while labor substitutability affects the optimal tax structure, leisure substitutability leaves the classical optimal tax results intact. In the Ramsey tax framework with linear income taxes, whether the consumers have the same or different earning abilities, labor substitutes tend to be taxed at a higher rate than leisure substitutes with the tax differential being increasing in consumption time. This is not necessarily the case when one allows for nonlinear income taxation.     

Income tax deductions for losses as insurance revisited

Kaplow (1992) shows that allowing income tax deductions for losses as partial insurance is undesirable in the presence of private insurance markets. This paper revisits the issue by considering a model that integrates Kaplow (1992) with Stiglitz (1982). We address the following question: Whether the income tax deduction for losses is part of an optimal income tax system. We show that introducing the income tax deduction for uninsured losses to complement an optimal nonlinear labor income tax will Pareto-improve welfare, provided that: (i) information is incomplete for the government as in the Stiglitz framework, and (ii) the premium for private insurance is unfair or moral hazard is present.