A method is presented for solving a certain class of hierarchical rational expectations models, principally models that arise from Stackelberg dynamic games. The method allows for numerical solution using spectral factorization algorithms, and estimation of these models using standard maximum likelihood techniques.

Methods are presented for solving a certain class of rational expectations models, principally those that arise from dynamic games. The methods allow for numerical solution using spectral factorization algorithms, and estimation of these models using maximum likelihood techniques.

How should a government use the power to commit to ensure a desirable equilibrium outcome? In this paper, I show a misleading aspect of what has become a standard approach to this question, and I propose an alternative. I show that the complete description of an optimal (indeed, of any) policy scheme requires outlining the consequences of paths that are often neglected. The specification of policy along those paths is crucial in determining which schemes implement a unique equilibrium and which ones leave room for multiple equilibria that depend on the expectations of the private sector.

We consider the large class of dynamic games in which each player’s actions are unobservable to the other players, and each player’s actions can influence a state variable that is unobservable to the other players. We develop an algorithm that solves for the subset of sequential equilibria in which equilibrium strategies are Markov in the privately observed state.

We analyze commitment to employment in an environment in which an infinitely lived firm faces a sequence of finitely lived workers who differ in their ability to produce output. A worker’s ability is initially unknown to both the worker and the firm. A worker’s effort affects the information on ability conveyed by his performance. We characterize equilibria and show that they display commitment to employment only when effort has a persistent but delayed impact on output. In this case, by providing insurance against early termination, commitment to employment encourages workers to exert effort, thus improving the firm’s ability to identify workers’ talent. The incentive value of commitment to retention helps explain the use of probationary appointments in environments in which there is uncertainty about individual ability.

This paper develops new recursive methods for studying stationary sequential equilibria in games with private monitoring. We first consider games where play has occurred forever into the past and develop methods for analyzing a large class of stationary strategies, where the main restriction is that the strategy can be represented as a finite automaton. For a subset of this class, strategies which depend only on the players’ signals in the last k periods, these methods allow the construction of all pure strategy equilibria. We then show that each sequential equilibrium in a game with infinite histories defines a correlated equilibrium for a game with a start date and derive simple necessary and sufficient conditions for determining if an arbitrary correlation device yields a correlated equilibrium. This allows, for games with a start date, the construction of all pure strategy sequential equilibria in this subclass.