The Rationality of Expectations Formation and Excess Volatility

That dropping the rational expectations assumption opens the door to many more patterns of volatility as equilibrium phenomena is not surprising. That this continues to be so even after requiring the expectations to be formed rationally is indeed surprising. In effect, requiring the agents to form expectations rationally —in the sense of being such that they maximize at any time the likelihood of observed history— does not pin down what is an equilibrium outcome much better than allowing for arbitrary expectations, unless the agents have access to unlimited historical records or memory. More specifically, I establish, in simple deterministic overlapping generations economies, that if each agent holds rationally formed expectations in the sense that any other expectations justifying his choices imply a smaller likelihood for the history he observes with limited memory, then there are rationally formed expectations equilibria exhibiting an excess volatility that no rational expectations equilibrium can match. Moreover, from the allocation viewpoint, these new equilibria can be supported also by many other expectations (not necessarily rationally formed). Given that the limited records or finite memory case may arguably be the relevant one from a positive viewpoint, this result suggests that the possibility of excess volatility as an equilibrium phenomenon has been downplayed by the use of the rational expectations hypothesis.