By Alexander Kriwolsky
This paper shows how to identify the structural shocks of a Vector Autoregression (VAR) while simultaneously estimating a dynamic stochastic general equilibrium (DSGE) model that is not assumed to replicate the data-generating process. It proposes a framework for estimating the parameters of the VAR model and the DSGE model jointly: the VAR model is identified by sign restrictions derived from the DSGE model; the DSGE model is estimated by matching the corresponding impulse response functions.
Starting with Galí (1999), VAR models have been used to test various predictions of DSGE models, in particular the sources of business cycle fluctuations. The empirical strategy has, however, been put in doubt by a series of recent papers, foremost Chari, Kehoe, McGrattan (2008), Fernández-Villaverde, Rubio-Ramírez, Sargent and Watson (2007) and Christiano, Eichenbaum and Vigfusson (2006).
The paper above goes further. Instead of estimating one model using restrictions from the other, it estimates both the VAR and the DSGE models jointly. Is this the way to end this debate? Does this imply that we get better estimates?