Dynamic Contracting with Persistent Shocks

In this paper, we develop continuous-time methods for solving dynamic principal-agent problems in which the agent's privately observed productivity shocks are persistent over time. We characterize the optimal contract as the solution to a system of ordinary differential equations and show that, under this contract, the agent's utility converges to its lower bound|immiserization occurs. Unlike under risk-neutrality, the wedge between the marginal rate of transformation and a low-productivity agent's marginal rate of substitution between consumption and leisure will not vanish permanently at her first high-productivity report; also, the wedge increases with the duration of a low-productivity report. We apply the methods to numerically solve the Mirrleesian dynamic taxation model, and find that the wedge is significantly larger than that in the independently and identically distributed (i.i.d.) shock case.Persistent Information, Principal-agent Problem, Private Information, Optimal Taxation

Stochastic optimal growth with a non-compact state space

This paper studies the stability of a stochastic optimal growth economy introduced by Brock and Mirman [J. Econ. Theory 4 (1972)] by utilizing stochastic monotonicity in a dynamic system. The construction of two boundary distributions leads to a new method of studying systems with non-compact state space. The paper shows the existence of a unique invariant distribution. It also shows the equivalence between the stability and the uniqueness of the invariant distribution in this dynamic system.

Stochastic optimal growth with a non-compact state space

This paper studies the stability of a stochastic optimal growth economy introduced by Brock and Mirman [Brock,W.A., Mirman, L., 1972. Optimal economic growth and uncertainty: the discounted case. Journal of Economic Theory 4, 479–513] by utilizing stochastic monotonicity in a dynamic system. The construction of two boundary distributions leads to a new method of studying systems with non-compact state space. The paper shows the existence of a unique invariant distribution. It also shows the equivalence between the stability and the uniqueness of the invariant distribution in this dynamic system.Stochastic growth; Stochastic dominance; Monotonic operator; Global stability

When can we do better than autarky?

This paper provides a necessary and sufficient condition for the existence of nonautarkic contract in a risk sharing model with two-sided lack of commitment. Verifying the condition takes just one Guassian elimination of a matrix.

When can we do better than autarky?

This paper provides a necessary and sufficient condition for the existence of nonautarkic contract in a risk sharing model with two-sided lack of commitment. Verifying the condition takes just one Guassian elimination of a matrix

Borrowing Constraint as an Optimal Contract

We study a continuous-time version of the optimal risk-sharing problem with one-sided commitment. In the optimal contract, the agent's consumption is non-decreasing and depends only on the maximal level of the agent's income realized to date. In the complete-markets implementation of the optimal contract, the Alvarez-Jermann solvency constraints take the form of a simple borrowing constraint familiar from the Bewley-Aiyagari incomplete-markets models. Unlike in the incomplete-markets models, however, the asset buffer stock held by the agent is negatively correlated with income.Borrowing constraint, limited commitment

Unemployment Insurance with Hidden Savings

This paper studies the design of unemployment insurance when neither the searching effort nor the savings of an unemployed agent can be monitored. If the principal could monitor the savings, the optimal policy would leave the agent savings-constrained. With a constant absolute risk-aversion (CARA) utility function, we obtain a closed form solution of the optimal contract. Under the optimal contract, the agent is neither saving nor borrowing constrained. Counter-intuitively, his consumption declines faster than implied by Hopenhayn and Nicolini [4]. The efficient allocation can be implemented by an increasing benefit during unemployment and a constant tax during employment.hidden savings, hidden wealth, repeated moral hazard, unemployment insurance.

Shared Rights and Technological Progress

We study how best to reward innovators whose work builds on earlier innovations. Incentives to innovate are obtained by offering innovators the opportunity to profit from their innovations. Since innovations compete, awarding rights to one innovator reduces the value of the rights to prior innovators. We show that the optimal allocation involves shared rights, where more than one innovator is promised a share of profits from a given innovation. We interpret such allocations in three ways: as patents that infringe on prior art, as licensing through an optimally designed ever-growing patent pool, and as randomization through litigation. We contrast the rate of technological progress under the optimal allocation with the outcome if sharing is prohibitively costly, and therefore must be avoided. Avoiding sharing initially slows progress, and leads to a more variable rate of technological progress.Cumulative Innovation, Patent, Licensing, Patent Pool, Litigation

Optimal auditing and insurance in a dynamic model of tax compliance

We study the optimal auditing of a taxpayer's income in a dynamic principal-agent model of hidden income. Taxpayers in our model initially have low income and stochastically transit to high income that is an absorbing state. A low-income taxpayer who transits to high income can under-report his true income and evade his taxes. With a constant absolute risk-aversion utility function and a costly auditing technology, we show that the optimal auditing mechanism in our model consists of cycles. Within each cycle, a low-income taxpayer is initially unaudited, but if the duration of low-income report exceeds a threshold, then the auditing probability becomes positive. That is, the tax authority guarantees that the taxpayer will not be audited until the threshold duration is reached. We also find that auditing becomes less frequent if the auditing cost is higher or if the variance of income is lower.Tax compliance, tax auditing, stochastic costly state verification

Optimal auditing and insurance in a dynamic model of tax compliance

We study the optimal auditing of a taxpayer’s income in a dynamic principal- agent model of hidden income. Taxpayers in our model initially have low income and stochastically transit to high income that is an absorbing state. A low-income taxpayer who transits to high income can underreport his true income and evade his taxes. With a constant absolute risk-aversion utility function and a costly and imperfect auditing technology, we show that the optimal auditing mechanism in our model consists of cycles. Within each cycle, a low-income taxpayer is initially unaudited, but if the duration of low-income reports exceeds a threshold, then the auditing probability becomes positive. That is, the tax authority guarantees that the taxpayer will not be audited until the threshold duration is reached. We also find that auditing becomes less frequent if the auditing cost is higher or if the variance of income is lower.Tax auditing ; Taxation