On the Solution and Application of Rational Expectations Models with Function-Valued States

David Childers
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David Childers: Yale University

No 807, 2016 Meeting Papers from Society for Economic Dynamics

Abstract: 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 a potentially infinite-dimensional function of infinite-dimensional objects. To overcome this difficulty, I provide methods for characterizing and numerically approximating the equilibria of dynamic, stochastic, general equilibrium models with function-valued state 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, most importantly, 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.

Date: 2016
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Persistent link: https://EconPapers.repec.org/RePEc:red:sed016:807

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