Induction and the Ramsey policy

Abstract

We examine the classic policy problem of Ramsey (1927) modeled as an infinitely repeated game (Stokey, 1991) between the government and the private sector where the private sector consists of a continuum of identical households. We assume that the private sector is boundedly rational in the sense that its behavior is dictated by a forecasting scheme which is ‘inductive’. Instead of assigning a particular forecasting scheme to the players, we let each player choose one from a class of ‘inductive’ forecasting schemes. By focusing on the actions dictated by forecasting schemes selected by the player, we identify the Ramsey policy as the unique solution of the game where players do not discount future payoffs. When players discount future payoffs, the Ramsey policy is the only solution which is robust against small changes in the discount factor in the neighborhood of one (Kalai, Samet, and Stanford, 1988). If we modify the model so that the private sector incurs memory costs in forecasting the action of the government, we obtain that the only equilibrium outcome is to play the Ramsey outcome every period.