Robust Conditional Predictions in Dynamic Games: An Application to Sovereign Debt

Abstract

We study the problem of an outside observer who, based on observations on a particular economic setting, tries to make an inference about the set of equilibria where the economy could be; our aim is to obtain robust predictions conditional on equilibrium history for dynamic policy games. Our main result is a characterization of “equilibrium consistent outcomes”: outcomes of the game in a particular period, that are consistent with a subgame perfect equilibrium conditional on an equilibrium history. We focus on a model of sovereign debt as in Eaton and Gersovitz (1981); but, our methodology can be readily applied to other dynamic policy games as in models of capital taxation or monetary policy. For this model, we characterize the set of equilibrium consistent debt prices. While the upper bound is the price in the optimal Markov equilibria, the lowest equilibrium consistent price is both positive and backward looking. In our baseline case, where output is continuous or there is a public randomization device, the last opportunity cost (the amount of debt just repaid, the conditions under which that debt was repaid, and how much debt was issued) is a sucient statistic of the set of equilibrium consistent prices. When income is discrete or there are no randomization devices available, the whole history could determine equilibrium consistent prices; whether or not a particular event in history matters for equilibrium consistent prices today depends on the likelihood and the length of that particular history. We finally link the set of equilibrium consistent outcomes with the predictions of a Bayesian econometrician who is uncertain about the prior over outcomes.