Borys Grochulski

Risky Human Capital and Deferred Capital Income Taxation

We study the structure of optimal wedges and capital taxes in a dynamic Mirrlees economy with endogenous distribution of skills. Human capital is a private, stochastic state variable that drives the skill process of each individual. Building on the findings of the labor literature, we construct a tractable life-cycle model of human capital evolution with risky investment and stochastic depreciation. In this setting, we demonstrate the optimality of (a) a human capital premium, i.e., an excess return on human capital relative to physical capital, (b) a large intertemporal wedge early in the life-cycle, and (c) a non-zero intratemporal wedge even at the top of the skill distribution at all dates except the last date in the life-cycle. The main implication for the structure of optimal linear capital taxes is the necessity of deferred taxation of physical capital. The average marginal tax rate on physical capital held in every period is zero in present value. However, expected capital tax payments do not equal zero in every period. Necessarily, agents face negative expected capital tax payments early in the life-cycle and positive expected capital tax payments late in the life-cycle.

Optimal risk sharing and borrowing constraints in a continuous-time model with limited commitment☆

We study a continuous-time version of the optimal risk-sharing problem with one-sided commitment. In the optimal contract, the agentʼs consumption is a time-invariant, strictly increasing function of a single state variable: the maximal level of the agentʼs income realized to date. We characterize this function in terms of the agentʼs outside option value function and the discounted amount of time in which the agentʼs income process is expected to reach a new to-date maximum. Under constant relative risk aversion we solve the model in closed-form: optimal consumption of the agent equals a constant fraction of his maximal 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.

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 agents consumption is non-decreasing and depends only on the maximal level of the agents 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.

On the Optimality of Ramsey Taxes in Mirrlees Economies

In this paper, we show that a simple, linear capital tax---the kind used in the Ramsey analysis---can be optimal in a Mirrlees economy with private information. We extend the Mirrlees approach to optimal taxation by studying taxes side-by-side with another institution, rather than in isolation. We consider an implementation in which agents use unsecured credit and personal bankruptcy to obtain insurance. Taxes are levied to fund government expenditures. An optimal tax system consists of lump-sum taxes and a simple Ramsey tax on wealth. In Mirrlees private information environments, optimal capital taxes do not have to be complicated.