Sluggish Inflation Expectations: A Markov Chain Analysis

A large body of recent empirical work on inflation dynamics documents that current real variables (like unemployment or output gaps) have little explanatory power for future inflation. Motivated by these findings, I explore the properties of a wide class of models in which inflation expectations respond little, if at all, to real economic conditions. In this general context, I examine Markov equilibria to games in which the relevant forcing processes are Markov chains and the central bank chooses a short- term nominal interest rate at each date subject to a lower bound. I construct a simple numerical algorithm to solve for such Markov equilibria. I apply the algorithm to a numerical example. In the example, the economy can experience long periods of what looks like secular stagnation because households believe that there is a significant risk of a crisis (that is, a sharp decline in economic activity). Within the example, there are large benefits to being able to reduce the lower bound on the short-term nominal interest rate by as little as fifty basis points.