### New Research in Economics: Robust Stability of Monetary Policy Rules under Adaptive Learning

I have had several responses to my offer to post write-ups of new research that I'll be posting over the next few days (thanks!), but I thought I'd start with a forthcoming paper from a former graduate student here at the University of Oregon, Eric Guass:

Robust Stability of Monetary Policy Rules under Adaptive Learning, by Eric Gaus, forthcoming,Southern Economics Journal: Adaptive learning has been used to assess the viability a variety of monetary policy rules. If agents using simple econometric forecasts "learn" the rational expectations solution of a theoretical model, then researchers conclude the monetary policy rule is a viable alternative. For example, Duffy and Xiao (2007) find that if monetary policy makers minimize a loss function of inflation, interest rates, and the output gap, then agents in a simple three equation model of the macroeconomy learn the rational expectations solution. On the other hand, Evans and Honkapohja (2009) demonstrates that this may not always be the case. The key difference between the two papers is an assumption over what information the agents of the model have access to. Duffy and Xiao (2007) assume that monetary policy makers have access to contemporaneous variables, that is, they adjust interest rates to current inflation and output. Evans and Honkapohja (2009) instead assume that agents only can form expectations of contemporaneous variables. Another difference between these two papers is that in Duffy and Xiao (2007) agents use all the past data they have access to, whereas in Evans and Honkapohja (2009) agents use a fixed window of data.

This paper examines several different monetary policy rules under a learning mechanism that changes how much data agents are using. It turns out that as long as the monetary policy makers are able to see contemporaneous endogenous variables (output and inflation) then the Duffy and Xiao (2007) results hold. However, if agents and policy makers use expectations of current variables then many of the policy rules are not "robustly stable" in the terminology of Evans and Honkapohja (2009).

A final result in the paper is that the switching learning mechanism can create unpredictable temporary deviations from rational expectations. This is a rather starting result since the source of the deviations is completely endogenous. The deviations appear in a model where there are no structural breaks or multiple equilibria or even an intention of generating such deviations. This result suggests that policymakers should be concerned with the potential that expectations, and expectations alone, can create exotic behavior that temporarily strays from the REE.