ESSAYS IN THE MICROECONOMICS AND ECONOMETRICS OF RATIONAL EXPECTATIONS (IDENTIFICATION, EQUILIBRIUM, OPTIONS, FUTURES)

This thesis consists of four essays on the definition, existence and properties of rational expectations equilibria. The first essay investigates the existence and optimality properties of a general equilibrium model with futures securities. Although an equilibrium need not always exist, a main finding of this paper is that, generically, an equilibrium does exist in these models, given a side condition on the number of commodities. Furthermore, it is shown that generically, in a model with two states, all equilibria will be Pareto efficient. The second essay provides an analysis of identification for nonlinear rational expectations models. Conditions on the information matrix are given which are necessary and sufficient for identification. Further, a moments based condition for identification is given. In addition to identification criteria, my main findings are: (1) unlike the case of linear rational expectations, perfectly anticipated exogenous variables need not necessarily lead to lack of identification in nonlinear rational expectations; (2) if a rational expectations model has nonunique rational expectations, then the identifiability of the model can depend on which of these expectations obtains. The third essay considers whether identification is a common or rare phenomenon in nonlinear models. For a broad class of models, the set of (globally) identified models is shown to be dense. Within a slightly less general class it is shown that there is an open and dense set of non-identified models, and consequently, that the set of non-identified models is nowhere dense. The implications of these results for macroeconomics are considered. The final essay investigates the existence and optimality properties of a general equilibrium model with options securities. An example is given of a model with options securities in which equilibrium does not exist. Although equilibrium need not always exist, a main finding of this essay is that, generically, an equilibrium does exist in these models. Futhermore, an example is given in which the (unique) competitive equilibrium of an options securities model is not Pareto optimal. Although equilibrium need not always be Pareto optimal, this essay proves that, generically, all equilibria will be Pareto efficient