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Set Identified Dynamic Economies and Robustness to Misspecification

We propose a new inferential methodology for dynamic economies that is robust to misspecification of the mechanism generating frictions. Economies with frictions are treated as perturbations of a frictionless economy that are consistent with a variety of mechanisms. We derive a representation for the law of motion for such economies and we characterize parameter set identification. We derive a link from model aggregate predictions to distributional information contained in qualitative survey data and specify conditions under which the identified set is refined. The latter is used to semi-parametrically estimate distortions due to frictions in macroeconomic variables. Based on these estimates, we propose a novel test for complete models. Using consumer and business survey data collected by the European Commission, we apply our method to estimate distortions due to financial frictions in the Spanish economy. We investigate the implications of these estimates for the adequacy of the standard model of financial frictions SW-BGG (Smets and Wouters (2007), Bernanke, Gertler, and Gilchrist (1999)).