Fundamental shock selection in DSGE models

DSGE models are typically estimated assuming the existence of certain structural shocks that drive macroeconomic fluctuations. We analyze the consequences of introducing nonfundamental shocks for the estimation of DSGE model parameters and propose a method to select the structural shocks driving uncertainty. We show that forcing the existence of non-fundamental structural shocks produces a downward bias in the estimated internal persistence of the model. We then show how these distortions can be reduced by allowing the covariance matrix of the structural shocks to be rank deficient using priors for standard deviations whose support includes zero. The method allows us to accurately select fundamental shocks and estimate model parameters with precision. Finally, we revisit the empirical evidence on an industry standard medium-scale DSGE model and find that government, price, and wage markup shocks are non-fundamental.