Information, VARs and DSGE Models

Abstract

How informative is a time series representation of a given vector of observables about the structural shocks and impulse response functions in a DSGE model? In this paper we refer to this econometrician’s problem as “E-invertibility” and consider the corresponding information problem of the agents in the assumed DGP, the DSGE model, which we refer to as “A-invertibility” We consider how the general nature of the agents’ signal extraction problem under imperfect information impacts on the econometrician’s problem of attempting to infer the nature of structural shocks and associated impulse responses from the data. We also examine a weaker condition of recoverability. A general conclusion is that validating a DSGE model by comparing its impulse response functions with those of a data VAR is more problematic when we drop the common assumption in the literature that agents have perfect information as an endowment. We develop measures of approximate fundamentalness for both perfect and imperfect information cases and illustrate our results using analytical and numerical examples