A Disinflation Trade‐Off: Speed Versus Final Destination

I. INTRODUCTION Whether or not expectations of inflation are rational is an open question. Rational forecasts require knowledge and information that some agents may not find worthwhile acquiring. Instead, because past inflation is a cheap and potentially informative signal about the policies of the central bank, those agents with less information may resort to extrapolation from past inflation to a greater extent than those with more information. In other words, for all agents, expectations have a rational (forward-looking) and an adaptive (backward-looking) component. Differences across agents in terms of information can lead to a separation between those who form more rational and those who form more adaptive expectations. (1) A simpler heterogeneity--agents with purely rational or with purely adaptive expectations-has been adopted in some models. (2) In that context, when a central bank is the major source of information about monetary policy, it could potentially influence the proportion of agents in each group. A natural question is: What are the central bank's preferences regarding the distribution? More specifically, does the central bank prefer many or few agents with rational expectations when introducing a monetary regime designed to reduce inflation? We will analyze the properties of a BarroGordon (1983a) model of monetary policy, in which some agents form rational and some adaptive expectations. In that setting, a higher proportion of agents with adaptive expectations generally slows down the disinflation process but, as in Sargent (1999), it also allows for a lower long-run inflation rate. An implication of this is that the central bank will prefer a higher proportion of agents who form rational expectations if it disinflates from a high level of inflation, but not so if it disinflates from a moderate or low inflation level. It is generally recognized that expectations do not adjust instantaneously to reflect the new conditions following a change in monetary regime. Instead, as in Lewis (1989), Wieland (2000), and Mankiw et al. (1987), agents, including the central bank, observe the unfolding macro developments and form estimates of the parameters that characterize the new environment. A number of interesting questions are addressed in that set-up. What is the speed and correctness of learning? Can the central bank use its control over monetary aggregates to generate observations useful in the learning process, that is, can learning be an active process? When does equilibrium have an inflationary bias? The structure of our model is simpler in the sense that the central bank has direct control over inflation and, aside from a random shock, the output response to changes in prices is clear. The simpler set-up makes the model analytically tractable and allows us to solve explicitly for steady-state inflation and a parameter that captures speed of convergence of inflation to the steady state. We can compare our results with the numerical estimates of other more complicated models, most notably that of Sargent (1999). Our explicit solution helps clarify insights about the dynamics of disinflations. Models of parameter uncertainty and learning have also addressed questions about gradual versus rapid disinflation. With results similar to ours, Balvers and Cosimano (1994) find that rapid disinflation is preferred when inflation is high, although in their framework rapid reduction in money growth is warranted to facilitate learning. In our model, rational agents are preferred because with high initial inflation, the benefit from rapid disinflation with more rational agents outweighs the cost of higher steady state inflation. Similar to Cukierman and Meltzer (1986) and Cosimano and Van Huyck (1993), in our model there is a possibility for the central bank to influence the beliefs of the population. The process of expectation formation, however, is not modeled formally, which contributes substantially to the analytical tractability of the model. …