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The power family, also known as the family of constant relative risk aversion (CRRA), is the most widely used parametric family for fitting utility functions to data. Its characteristics have, however, been little understood, and have led to numerous misunderstandings. This paper explains these characteristics in a manner accessible to a wide

We study Pareto optimal tax and education policies when human capital upon labor market entry is endogenous and individuals face wage uncertainty. Though optimal labor distortions are history-dependent, i.e. depend on income and education, simple policy instruments can yield the desired distortions: a single nonlinear labor income tax schedule combined with income-contingent loans. To take the model to the (US) data, we simplify the model to a binary education decision (graduating from college or not). We find that for low and intermediate incomes the labor supply decision of college graduates should be distorted more heavily than for individuals without a college degree. As a consequence, the optimal student loan repayment schedule increases in income for this range. This result holds along the Pareto frontier. We compare the second best to a situation where loan repayment is restricted to be independent from income and find significant welfare gains.

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In this chapter, I review empirical and theoretical literature on taxation of intergenerational transfers (estates, bequests, inheritances, inter vivos gifts) and wealth. The main message may be summarized as follows. Empirical evidence on bequest motivations and responses to estate taxation is spotty and much remains be done, but what we know points in the direction of (1) mixed motives (2) heterogeneity of preferences and (3) importance of retaining control over wealth. These patterns are important for normative analysis of taxation toward the top of the distribution. Theoretical work should further focus on understanding implications of inequality of inherited wealth: the topic that has been neglected in the past, even though it is closely related to — more carefully studied, but arguably much less important in practice — externalities from giving. Potential externalities from wealth accumulation

We analytically and quantitatively examine a prominent justi…cation for capital income taxation: goods preferred by those with high ability ought to be taxed. We study an environment where commodity taxes are allowed to be nonlinear functions of income and consumption and …nd that, when ability is positively related to a preference for a good, optimal marginal commodity taxes on this good may be regressive: i.e., declining with income. We derive an analytical expression for optimal commodity taxation, allowing us to study the forces for and against regressivity. We then parameterize the model to evidence on the relationship between skills and preferences and examine the quantitative case for taxes on future consumption (saving). The relationship between skill and time preference delivers quantitatively small, generally regressive capital income taxes and would justify only a fraction of the prevailing level of capital income taxation.

In this paper I discuss the role a progressive income tax system and a redistributive pay as you go (PAYGO) social security system can play in insuring and reallocating idiosyncratic as well as aggregate risk. I also argue that the underlying source of market failures generating such a role for government intervention may be crucial when determining the normative consequences of such social insurance.

Abstract The prominent but unproven intuition that preference heterogeneity reduces redistribution in a standard optimal tax model is shown to hold under the plausible condition that the distribution of preferences for consumption relative to leisure rises, in terms of …rst-order stochastic dominance, with income. Given familiar functional form assumptions on utility and the distributions of ability and preferences, a simple statistic for the e¤ect of preference heterogeneity on marginal tax rates is derived. Numerical simulations and suggestive empirical evidence demonstrate the link between this potentially measurable statistic and the quantitative implications of preference heterogeneity for policy. Lockwood: Harvard University, lockwood@fas.harvard.edu; Weinzierl: Harvard University and NBER, mweinzierl@hbs.edu. We are grateful to Robert Barro, Rafael di Tella, Alex Gelber, Caroline Hoxby, Louis Kaplow, Narayana Kocherlakota, Erzo F.P. Luttmer (the editor), Greg Mankiw, David Moss, Eric Nelson, Julio Rotemberg, Dan Shoag, Aleh Tsyvinski, Glen Weyl, Danny Yagan, anonymous referees and seminar participants at Harvard and Michigan for helpful comments and suggestions on earlier versions of this paper. We especially appreciate insightful suggestions on the formal analysis of section 1 by one of the referees for this Journal.

This paper studies an optimal taxation problem in a dynamic economy inhabited by individuals subject to two uncorrelated idiosyncratic shocks: on their productivity (as in Kocherlakota, 2005) and on their short-term subjective discount factor. We characterize incentive compatible Pareto optimal allocations in a multidimensional screening model where agents have to report truthfully the realizations of both shocks. We then construct the tax system implementing such allocations in a competitive equilibrium. The planner is interested in redistribution and its policy consist of a tax function nonlinear in labor and capital income. We analyze two cases, each of them considering a particular form of bounded rationality: in the first one, some individuals are myopic and discount future payoffs at a higher rates than far-sighted. In the second application, some individuals display hyperbolic discounting and systematically change their plans for the future, regretting ex-post for their lack of commitment power. We show that the marginal tax on capital income consists of several elements, combining incentive compatibility and bounded rationality considerations. The optimal tax is a decreasing function of both the fraction of short-sighted individuals and the intensity of myopia/hyperbolic discounting. Our results are not driven by the planner’s paternalism, but by