Inertia of Forward-Looking Expectations

Macroeconomic variables exhibit inertia. On the face of it, such inertia sits uncomfortably with the behavior of rational, forward-looking agents who form expectations on the basis of the best information available at the time. Christopher Sims (2003, sect. 8) offers a three-fold taxonomy of attempts to rationalize inertia. The first is the idea of Robert Lucas (1973) and Edmund Phelps (1970) that agents face a signal extraction problem, so that their actions react only partially to shifts in fundamentals due to the residual uncertainty. The second is the sticky expectations approach of N. Gregory Mankiw and Ricardo Reis (2002), where otherwise rational and forward-looking agents receive information with some delay. The third is the rational inattention approach favored by Sims himself, where agents with informationprocessing constraints choose the optimal coarsening of their information (Sims, 2003). Our approach is a variation on the signalextraction theme but has implications for the sticky-expectations and rational-inattention approaches. As explained recently by Michael Woodford (2003), the original contribution of Lucas (1973) had limited success in explaining the persistence of macroeconomic aggregates due to the feature that the underlying fundamentals are fully revealed after a delay of one period. Without this simplifying feature, however, the complexity of the problem increases rapidly as expectations of others’ expectations become relevant in one’s calculations (Robert Townsend, 1983; Phelps, 1983). Tractability aside, the approach holds much promise. When agents are differentially informed, events in the distant past are “more common knowledge” than events in the recent past. Not only has enough time elapsed for the agents to ascertain the facts in the distant past, but more importantly, enough time has elapsed for each agent to be more confident that other agents have ascertained the facts. When common knowledge is important (as in coordination problems, for example) events in the distant past take on significance. Paradoxically, the farther the agents peer into the future, the farther they must look into the past to establish the informational platform for their actions. To an outside observer, the aggregate action betrays all the outward signs of adaptive expectations. In order to demonstrate this principle in a transparent way, we employ other drastic simplifications but do not assume that realizations are revealed after a delay of one period. We thereby preserve the nontrivial nature of dynamic, higher-order beliefs and show how persistence arises as a natural consequence of the original Lucas and Phelps insight.