Approximating Time Varying Structural Models with Time Invariant Structures

The paper studies how parameter variation affects the decision rules of a DSGE model and structural inference. We provide diagnostics to detect parameter variations and to ascertain whether they are exogenous or endogenous. Identification and inferential distortions when a constant parameter model is incorrectly assumed are examined. Likelihood and VAR-based estimates of the structural dynamics when parameter variations are neglected are compared. Time variations in the financial frictions of Gertler and Karadi's (2010) model are studied.