DSGE model are estimated assuming that structural shocks exist. We challenge this assumption. First, we show that forcing the existence of a non-existing structural shock produces downward bias in the estimated internal persistence of the structural model, both in the AR and in the behavioral parameters. Second, we show how distortions can be reduced by allowing the covariance matrix of the structural shock to be rank deficient. Finally, we revisit the empirical evidence of the estimated Smets and Wouters (2007) model and find that government, price and wage markup are non fundamental shocks.
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