We consider a dynamic Mirrlees economy in a life cycle context and study the optimal insurance arrangement. Individual productivity evolves as a Markov process and is private information. We use a first order approach in discrete and continuous time and obtain novel theoretical and numerical results. Our main contribution is a formula describing the dynamics for the labor-income tax rate. When productivity is an AR(1) our formula resembles an AR(1) with a trend where: (i) the auto-regressive coefficient equals that of productivity; (ii) the trend term equals the covariance productivity with consumption growth divided by the Frisch elasticity of labor; and (iii) the innovations in the tax rate are the negative of consumption growth. The last property implies a form of short-run regressivity. Our simulations illustrate these results and deliver some novel insights. The average labor tax rises from 0 % to 40 % over 40 years, while the average tax on savings falls from 20 % to 0 % at retirement. We compare the second best solution to simple history independent tax systems, calibrated to mimic these average tax rates. We find that age dependent taxes capture a sizable fraction of the welfare gains. In this way, our theoretical results provide insights into simple tax systems.

We characterize optimal taxation of foreign capital and optimal sovereign debt policy in a small open economy where the government cannot commit to policy, seeks to insure a risk averse domestic constituency, and is more impatient than the market. Optimal policy generates long-run cycles in both sovereign debt and foreign direct investment in an environment in which the first best capital stock is a constant. The expected tax on capital endogenously varies with the state of the economy and investment is distorted by more in recessions than in booms, amplifying the effect of shocks. The government’s lack of commitment induces a negative correlation between investment and the stock of government debt, a “debt overhang ” effect. Debt relief is never Pareto improving and cannot affect the long-run level of investment. Furthermore, restricting the government to a balanced budget can eliminate the cyclical distortion of investment. We thank Andrea Prat and two anonymous referees for very helpful suggestions. We also thank Emmanuel

Abstract The aim of this paper is to study how the intertemporal behavior of taxes affects the wealth distribution. The optimal-taxation literature has often concentrated on representative-agent models, in which it is optimal to smooth distortionary taxes. When tax liabilities are unevenly spread in the population, deviations from tax smoothing lead to interest rate changes that redistribute wealth. When a "bad shock" hits the economy, the optimal policy will then call for smaller or larger deficits depending on the political power of different groups. The model is applied to war financing and the introduction of a balanced-budget policy.

This paper addresses the question as to whether it is optimal to use separating or pooling nonlinear income taxation, or to use linear income taxation, when the government cannot commit to its future tax policy. We consider both two-period and in…nite-horizon settings. Under empirically plausible parameter values, separating income taxation is optimal in the two-period model, whereas linear income taxation is optimal when the time horizon is in…nite. The welfare e¤ects of varying the discount rate, the degree of wage inequality, and the population of high-skill workers are also explored. For realistic changes in these parameters, separating income taxation remains optimal in the two-period formulation, and linear income taxation remains optimal in the in…nite-horizon model.

A planner sets a lump sum transfer and a linear tax on labor income in an economy with incomplete markets, heterogeneous agents, and aggregate shocks. The planner’s concerns about redistribution impart a welfare cost to fluctuating transfers. The distribution of net asset holdings across agents affects optimal allocations, transfers, and tax rates, but the level of government debt does not. Two forces shape longrun outcomes: the planner’s desire to minimize the welfare costs of fluctuating transfers, which calls for a negative correlation between the distribution of net assets and agents ’ skills; and the planner’s desire to use fluctuations in the real interest rate to adjust for missing state-contingent securities. In a model parameterized to match stylized facts about US booms and recessions, distributional concerns mainly determine optimal policies over business cycle frequencies. These features of optimal policy differ markedly from ones that emerge from representative agent Ramsey models like Aiyagari et al. (2002). Key words: Distorting taxes. Transfers. Redistribution. Government debt. Interest rate risk. JEL codes: E62,H21,H63

We study optimal income taxes and transfers in an economy with heterogeneous agents and aggregate shocks. An optimal equilibrium determines agents ’ net asset positions, but not their absolute levels. The distribution of debt holdings across agents influences optimal allocations and taxes, but the level of government debt does not. Higher correlations of debt holdings and labor incomes imply more distortions and lower welfare. In incomplete markets economies, the government has no precautionary incentive to accumulate assets to smooth government expenditures, an outcome that implies different optimal taxes and government debt than representative agent Ramsey models like Aiyagari et al. (2002). Imposing exogenous borrowing constraints can actually increase welfare. When markets are incomplete, the government optimally responds to an increase in government expenditures by increasing taxes and decreasing transfers. These responses are persistent and history dependent.

This paper considers four different models of asset trade. In all of them, immortal agents face idiosyncratic shocks to their ability to produce output, and they can trade a single risk-free asset over time. In the first model, the risk-free asset is a privately issued one-period bond, and in the second model, it is a publicly issued one-period bond that cannot be shorted. In the third model, it is publicly issued money (a durable barren asset). In the fourth model, it is privately issued money. I prove the following theorem. Given an equilibrium in one of these economies, it is possible to pick the exogenous parameters in the other three economies so that there is an outcome-equivalent equilibrium in each of them. Moreover, in these outcome-equivalent equilibria, the agents ’ budget sets are all identical. ∗Highly preliminary- please do not cite. I thank Neil Wallace for a great conversation about this paper; I thank Adam Slawski and Hakki Yazici for their comments. I acknowledge the support of NSF 06-06695. The views expressed herein are mine and not necessarily those of the Federal Reserve Bank of Minneapolis or the Federal Reserve System. 1.

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 answers the question posed in the title within a model where agents receive idiosyncratic, wage-rate shocks that are privately observed. When the model social insurance system is comprised by the US social security and income tax system, then the maximum ex-ante welfare gain to improved insurance is equivalent to a 12.3 percent increase in consumption. We determine the reasons behind this large welfare gain. We also analyze two parametric reforms of the model social insurance system. One reform increases welfare very little, whereas the other achieves nearly all of the maximum possible welfare gain.

We show a standard model where the optimal tax reform is to cut labor taxes and leave capital taxes very high in the short and medium run. Only in the very long run would capital taxes be zero. Our model is a version of Chamley’s, with heterogeneous agents, without lump sum transfers, an upper bound on capital taxes, and a focus on Pareto improving plans. For our calibration labor taxes should be low for the first ten to twenty years, while capital taxes should be at their maximum. This policy ensures that all agents benefit from the tax reform and that capital grows quickly after when the reform begins. Therefore, the long run optimal tax mix is the opposite from the short and medium run tax mix. The initial labor tax cut is financed by deficits that lead to a positive long run level of government debt, reversing the standard prediction that government accumulates savings in models with optimal capital taxes. If labor supply is somewhat elastic benefits from tax reform are high and they can be shifted entirely to capitalists or workers by varying the length of the transition. With inelastic labor supply there is an increasing part of the equilibrium frontier, this means that the scope for benefitting the workers is limited and the total benefits from reforming taxes are much lower.