Unobservable persistent productivity and long term contracts

We study the problem of a firm that faces asymmetric information about the persistent productivity of its potential workers. In our framework, a worker's productivity is either assigned by nature at birth, or determined by an unobservable initial action of the worker that has persistent effects over time. We provide a characterization of the optimal dynamic compensation scheme that attracts only high productivity workers: consumption—regardless of time period—is ranked according to likelihood ratios of output histories, and the inverse of the marginal utility of consumption satisfies the martingale property derived in [Rogerson, William P., 1985. Repeated moral hazard. Econometrica 53 (1) 69–76]. However, in the case of i.i.d. output and square root utility we show that, contrary to the features of the optimal contract for a repeated moral hazard problem, the level and the variance of consumption are negatively correlated, due to the influence of early luck into future compensation. Moreover, in this example long-term inequality is lower under persistent private information.