Solution of Rational Expectations Models with Function Valued States


Many variables of interest to economists take the form of time varying distributions or functions. This high dimensional functional data can be interpreted in the context of economic models with function valued endogenous variables, but deriving the implications of these models requires solving a nonlinear system for an infinite dimensional function of infinite dimensional objects. To overcome this difficulty, I provide methods for characterizing and numerically approximating the equilibria of DSGE models with function valued variables by linearization in function space and representation using basis functions. These methods permit arbitrary infinite dimensional variation in the state variables, do not impose exclusion restrictions on the relationship between variables or limit their impact to a finite dimensional sufficient statistic, and come with demonstrable guarantees of consistency and polynomial time computational complexity. I demonstrate the applicability of the theory by providing an analytical characterization and computing the solution to a dynamic model of trade, migration, and economic geography.

R&R at Econometrica

Previous versions of this paper circulated under the title On the Solution and Application of Rational Expectations Models with Function-Valued States