Can a data-rich environment help identify the sources of model misspecification?

This paper proposes a method for detecting the sources of misspecification in a DSGE model based on testing, in a data-rich environment, the exogeneity of the variables of the DSGE with respect to some auxiliary variables. Finding evidence of non-exogeneity implies misspecification, but finding that some specific variables help predict certain shocks can shed light on the dimensions along which the model is misspecified. Forecast error variance decomposition analysis then helps assess the relevance of the missing channels. The paper puts the proposed methodology to work both in a controlled experiment - by running a Monte Carlo simulations with a known DGP - and using a state-of-the-art model and US data up to 2011.