Labour Income Uncertainty, Taxation and Public Good Provision

Abstract

This article examines optimal nonlinear income taxation, commodity taxation and public good provision under income uncertainty in a moral hazard framework. Uniform commodity taxation and the Samuelson rule for public good provision are desirable under similar conditions as in the conventional tax model. Deviations from these rules is warranted if one can encourage effort by subsidising certain goods and overproviding public goods. We also determine a rule for the optimal marginal income tax rate and provide some numerical simulations. Conditions for the validity of the solution procedure used in this class of models, the first-order approach, are also explored. Uncertainty is a key component of many important real-world decision-making processes. Consider for example an individual's decision to acquire specific skills through education. Educational investments must be made well before the resolution of uncertainty related to the returns to skill. Thus the tax system, which affects the net returns of different skill levels, has a potentially large impact on educational decisions, skill attainment and productivity. A progressive tax system offers insurance to workers by redistributing income from the lucky to the unlucky. Other forms of social insurance, such as unemployment and health insurance, work in a similar manner. A well-known problem in the design of optimal income tax under uncertainty, or any insurance mechanism, is asymmetric information between the government and individuals. Income is partly due to individual effort and partly due to luck, but the planner can only observe realised income, not effort. The optimal redistribution scheme is a balance between providing the workers with adequate incentives to acquire skills and sufficient insurance. Mirrlees (1974) was the first to examine the design of optimal redistributive income tax under income uncertainty. This moral hazard model, later used, among others, by Varian (1980), Tuomala (1984) and Low and Maldoom (2004), is an alternative to the more well-known adverse selection model of Mirrlees (1971), where income dispersion arises from differences in innate skill levels. The moral hazard model is perhaps most appealing in the tax context when effort is interpreted as an ex ante decision on educational investment. Alternatively, one can interpret the discussion as a general analysis of social insurance.1 Income tax is only one element, albeit an important one, in the design of optimal government redistributive policy. Indeed, recent optimal tax literature has devoted a lot of attention to the use of other instruments, such as commodity taxation, minimum