Sebastian Koehne

On the first-order approach in principal agent models with hidden borrowing and lending

is monotone in output. We also investigate a few possibilities of relaxing these requirements.

The First-Order Approach to Moral Hazard Problems with Hidden Saving

Moral hazard models with hidden saving decisions are useful to study such diverse problems as unemployment insurance, income taxation, executive compensation, or human capital policies. How can we solve such models? In general, this is very difficult. Under the conditions derived in this paper, however, we can replace the incentive constraint with the associated first-order condition. This allows the application of simple Lagrangian methods and yields a precise characterization of optimal contracts. To obtain tractable conditions for the validity of this approach, the paper draws on the concept of log-convexity. Since logconvexity, unlike convexity, is preserved under multiplication, the paper is able to separate the assumptions on the output distribution from the assumptions on the agent’s preferences in a sense, even though the interaction between these two is important for the agent’s incentives. The first-order approach is valid if the following conditions hold: a) the agent has nonincreasing absolute risk aversion (NIARA) utility, b) the output technology has monotone likelihood ratios (MLR), and c) the distribution function of output is log-convex in effort (LCDF). Finally, the paper shows how the curvature of optimal wage schemes can be used to relax the above conditions.

The First-Order Approach to Moral Hazard Problems with Hidden Saving: The Case of CARA Utility

This paper examines the first order approach to moral hazard problems in which the agent can secretly save and borrow. The paper shows that hidden saving constrains the concavity of the agents problem even for CARA utility and additively separable effort disutility in an important way: Consumption utility in the second period will be jointly concave in effort and saving if and only if the negative consumption utility is log-convex in effort. We derive two sets of sufficient conditions for the validity of the first order approach in this setup. First, we strengthen the classic approach by Mirrlees (1979) and Rogerson (1985). We obtain a second set of conditions by using the theory of total positivity (Karlin 1968).

Optimal Capital Taxation for Time-Nonseparable Preferences

This paper studies the effect of habit formation on optimal capital taxes in a dynamic Mirrleesian model. We make three distinct contributions. First, we decompose intertemporal wedges (implicit capital taxes) for general time-nonseparable preferences into a wealth effect, a complementarity effect, and a future incentive effect. Second, we provide conditions under which intertemporal wedges are positive. Third, we derive a recursive formulation of constrained efficient allocations and evaluate the quantitative impact of habit formation. In a model parameterized to the U.S. economy, habit formation reduces average intertemporal wedges by about 40 percent compared to the time-separable case. Moreover, intertemporal wedges are close to zero for the largest part of the working life.