DSGE models are typically estimated assuming the existence of certain primal shocks that drive macroeconomic fluctuations. We analyze the consequences of estimating shocks that are "non-existent" and propose a method to select the primal shocks driving macroeconomic uncertainty. Forcing these non-existing shocks in estimation produces a downward bias in the estimated internal persistence of the model. We show how these distortions can be reduced by using priors for standard deviations whose support includes zero. The method allows us to accurately select primal shocks and estimate model parameters with high precision. We revisit the empirical evidence on an industry standard medium-scale DSGE model and find that government and price markup shocks are innovations that do not generate statistically significant dynamics.