Zero Expected Wealth Taxes: A Mirrlees Approach to Dynamic Optimal Taxation

In this paper, I consider a dynamic economy in which a government needs to finance a stochastic process of purchases. The agents in the economy are privately informed about their skills, which evolve stochastically over time in an arbitrary fashion. I construct an optimal tax system that is restricted to be linear in an agent’s wealth but can be arbitrarily nonlinear in his current and past labor incomes. I find that wealth taxes in a given period depend on the individual’s labor income in that period and previous ones. However, in any period, the expectation of an agent’s wealth tax rate rate in the following period is zero. As well, the government never collects any net revenue from wealth taxes. ∗This version fixes some typos in the December 2003 version. The material in this paper previously circulated as part of the manuscript, "A Mirrlees Approach to Dynamic Optimal Taxation: Implications for Wealth Taxes and Asset Prices." Feel free to contact me with comments or questions via email at [email protected]. I acknowledge the support of NSF SES-0076315. This work grew out of my joint paper with Mikhail Golosov and Aleh Tsyvinski and owes a large intellectual debt to them. I thank Barbara McCutcheon and Ivan Werning for helpful comments; the paper has also benefited from comments from participants in seminars at Penn State University, University of Iowa, Federal Reserve Bank of Chicago, University of British Columbia, Federal Reserve Bank of Minneapolis, Stanford University, and Federal Reserve Bank of Cleveland. The views expressed herein are those of the author and not necessarily those of the Federal Reserve Bank of Minneapolis or the Federal Reserve System. In this paper, I consider the following question. Suppose a government needs to finance a given stochastic process of purchases using wealth taxes and labor income taxes. What are the properties of the optimal wealth taxes? There is a great deal of literature that addresses these and related questions using a Ramsey approach: the government is assumed to be able to use only linear taxes on wealth and/or labor income. (See Chari and Kehoe (1999) for an excellent survey.) I instead use what I term a Mirrlees approach. Like Mirrlees (1971), I assume that agents differ in skills (that is, labor productivities), and that a given agent is privately informed about his skill. The government’s tax code is restricted only by the government’s informational limitations. Both the Mirrlees and Ramsey approaches are motivated by the fact that modern societies rarely use lump-sum taxes, but they differ dramatically in the way that they deal with this fact. Under the Ramsey approach, the government cannot use lump-sum taxes. Under the Mirrlees approach, the government chooses not to use lump-sum taxes. My analysis builds off a recent paper by Golosov, Kocherlakota, and Tsyvinski (2003) (henceforth, GKT). GKT consider a dynamic economy in which individual skills are private information. Skills are allowed to follow arbitrary stochastic processes; however, preferences are restricted to be additively separable between consumption and leisure. In this setting, GKT provide a partial characterization of Pareto optimal allocations. They show that in all periods, any individual’s shadow interest rate is no higher than, and typically strictly less than, the rate of return to capital. In other words, it is Pareto optimal to have a wedge between individual shadow interest rates and social shadow interest rates. GKT’s results are about wedges in Pareto optima, not taxes in an economy with decentralized trade. In this paper, I provide a partial characterization of optimal taxes in a version of GKT’s model economy. Unlike GKT, I allow for publicly observable aggregate shocks (including government purchases shocks). As in GKT, agents’ preferences are additively separable over time and between consumption and leisure. I adopt the following model of trade. I assume that agents can sell units of effective labor and rent capital to a representative firm, subject to taxes that are allowed to be arbitrarily nonlinear functions of current and past labor income, but are restricted to be linear in wealth. I construct a class of such tax systems that weakly implement the optimal allocation. The main result in my paper concerns the nature of the wealth taxes in these optimal systems. It would seem natural in this setting to use a tax system in which the wealth tax rate levied in period (t + 1) is equal to the socially optimal wedge between private and social shadow interest rates between period t and period (t+1).We know from the work of GKT that under such a system, the wealth tax would typically be positive on each person. However, following Golosov and Tsyvinski (2003a) and Albanesi and Sleet (2003), I show that this kind of tax system is suboptimal. The problem is that such a system does not have enough instruments to prevent individuals from doing a joint deviation of saving and lying. I instead design an optimal tax system that uses period (t + 1) wealth taxes that depend on period (t+1) labor income (as well as prior labor incomes). I find that under the optimal system, an individual’s expected wealth tax rate in period (t+1), conditional on his period t information and on the period (t+ 1) history of public shocks, is zero. Individuals who are surprisingly highly skilled in period (t+1) receive a subsidy that is a linear function of their wealths. Individuals who are surprisingly unskilled in period (t + 1) are taxed on their wealths. Intuitively, society needs income-contingent wealth taxes to deter the joint deviation of an individual’s accumulating too much wealth from period t to period (t + 1)