Christopher Sleet

Optimal Taxation with Private Government Information

The Ramsey model of fiscal policy implies that taxes should be smooth in the sense of having small variances. In contrast, empirical labour tax processes are smooth in the sense of being random walks; they provide prima facie evidence for incomplete government insurance. This paper considers whether private government information might lie behind such incomplete insurance. It shows that optimal incentive compatible policies exhibit limited use of state contingent debt and greater persistence in taxes and debt, and it argues that they are better approximations to empirical fiscal policies than those implied by the Ramsey model. The paper also establishes that optimal incentive compatible allocations converge to allocations such that the governments incentive compatibility constraint no longer binds. Generally, these limiting allocations are ones in which the government is maximally indebted. Their credibility and the interaction of incentive compatibility and credibility is briefly discussed. Copyright 2004, Wiley-Blackwell.

Optimal taxation with endogenously incomplete debt markets

Abstract Empirical analyses of labor tax and public debt processes provide prima facie evidence for imperfect government insurance. This paper considers a model in which the governments inability to commit to future policies or to report truthfully its spending needs renders government debt markets endogenously incomplete. A method for solving for optimal fiscal policy under these constraints is developed. Such policy is found to be intermediate between that implied by the complete insurance (Ramsey) model and a model with exogenously incomplete debt markets. In contrast to optimal Ramsey policy, optimal policy in this model is consistent with a variety of stylized fiscal policy facts such as the high persistence of labor tax rates and debt levels and the positive covariance between government spending and the value of government debt sales.

On Credible Monetary Policy and Private Government Information

Credible and optimal monetary policies are considered in environments in which the government observes a signal that is correlated with the state of the economy. When the signal is public information it is optimal for monetary policy to be conditioned upon it. The extent to which such conditioning should occur when the signal is the private information of the government depends upon the governments incentives to misrepresent information. It is shown that in some cases the Ramsey policy is incentive compatible, in others it is not. In the latter cases, policy must be constrained to be incentive compatible. This may result in “penalty phases” along the equilibrium path following apparent “mistakes” by the policy maker; it may result in the optimal monetary policy making no use of the signal. Journal of Economic Literature Classification Numbers: C73, E52, E58.

Markov Perfect Equilibria in Industries with Complementarities

Summary. This paper considers the existence and computation of Markov perfect equilibria in games with a “monotone” structure. Specifically, it provides a constructive proof of the existence of Markov perfect equilibria for a class of games in which a) there is a continuum of players, b) each player has the same per period payoff function and c) these per period payoff functions are supermodular in the players current and past action and have increasing differences in the players current action and the entire distribution of actions chosen by other players. The Markov perfect equilibria that are analyzed are symmetric, not in the sense that each player adopts the same action in any period, but rather in the sense that each player uses the same policy function. Since agents are typically distributed across many states they will typically take different actions.The formal environment considered has particular application to models of industries (or economies) in which firms face costs of price adjustment. It is in this context that the results are developed.

Endogenously Incomplete Markets: Macroeconomic Implications

Endogenously incomplete models derive restrictions on asset trading from primitive constraints on the enforcement and monitoring technologies available to societies. They have been applied to a wide variety of macroeconomic problems. This essay reviews some of these applications and the models that underpin them.

On the Computation of Value Correspondences for Dynamic Games

Recursive game theory provides theoretic procedures for computing the equilibrium payoff or value sets of repeated games and the equilibrium payoff or value correspondences of dynamic games. In this paper, we propose and implement outer and inner approximation methods for equilibrium value correspondences that naturally occur in the analysis of dynamic games. The procedure utilizes set-valued step functions. We provide an application to a bilateral insurance game with storage.

Tasks, Talents and Taxes

A large positive literature emphasizes the role of technological change in driving the demand for skill and talent. We consider the normative implications of such tech- nical change for policy design.

The Dual Approach to Recursive Optimization: Theory and Examples

We bring together the theories of duality and dynamic programming. We show that the dual of an additively separable dynamic optimization problem can be recursively decomposed using summaries of past Lagrange multipliers as state variables. Analogous to the Bellman decomposition of the primal problem, we prove equality of values and solution sets for recursive and sequential dual problems. In non-additively separable settings, the equivalence of the recursive and sequential dual is not guaranteed. We relate recursive dual and recursive primal problems. If the Lagrangian associated with a constrained optimization problem admits a saddle then, even in non-additively separable settings, the values of the recursive dual and recursive primal problems are equal. Additionally, the recursive dual method delivers necessary conditions for a primal optimum. If the problem is strictly concave, the recursive dual method delivers necessary and sufficient conditions for a primal optimum. When a saddle exists, states on the optimal dual path are subdifferentials of the primal value function evaluated at states on the optimal primal path and vice versa.We bring together the theories of duality and dynamic programming. We show that the dual of a separable dynamic optimization problem can be recursively decomposed. We provide a dual version of the principle of optimality and give conditions under which the dual Bellman operator is a contraction with the optimal dual value function its unique fixed point. We relate primal and dual problems, address computational issues and give examples.

Dynamic labor contracts with temporary layoffs and permanent separations

Summary. We study the implications of optimal dynamic contracts in private information environments for fluctuations in effort and employment across time and productivity states. To this end, we incorporate temporary layoffs and permanent separations as well as on-the-job effort variations into a dynamic model of moral hazard. We consider two different “commitment” environments. In a “full commitment” environment, although the firm can temporarily lay a worker off, neither party can dissolve the contractual relationship once it has been initiated. On the other hand, in a “limited commitment” environment, both parties can dissolve the relationship at the beginning of any period in order to pursue an outside option.We use our model to study the implications of optimal contracts for incentives, employment histories, layoffs and separations across full information, full commitment and limited commitment settings. We compute solutions to the relevant principal-agent problems, endogenously determining the set of states in which separations occur and the domain of the firms value function, as well as the value function itself.