Avoiding Nash inflation: Bayesian and robust responses to model uncertainty

In his 1999 monograph The Conquest of American Inflation Tom Sargent describes how a policymaker, who applies a constant-gain algorithm in estimating the Phillips curve, can fall into the grip of an induction problem: concluding on the basis of reduced-form evidence that the trade-off between inflation and output is more favorable than it actually is. This results in oscillations between periods of disinflation and reflation. The problem arises because the policymaker is naive about possible misspecification, her role in creating that misspecification, and its role in policy design. In particular, while her use of a constant-gain algorithm admits the possibility that her model may be misspecified, she does not take this into consideration when designing policy. In this paper, we relax this assumption. We derive five policy rules which treat possible misspecification in three different ways. First, the linear-quadratic Gaussian (LQG) rule exhibits the familiar pattern of escape dynamics described by Sargent. We show a rule that takes uncertainty seriously, but in a Bayesian fashion, does no better. Finally, we consider three rules that are robust in the sense of Knight. The robust rules do a worse job than the LQG approach, and sometimes a lot worse. This is so even though the induction problem faced by the policymaker provides a prima facie case for being robust. We conclude that there appears to be no obvious tool that can be applied mechanically to alleviate the induction problem. A corollary of this finding is that Sargent's story for the inflation of the 1970s is robust to relaxing a key assumption in the original monograph.