Invertibility and VAR Representations of Time-Varying Dynamic Stochastic General Equilibrium Models

I study the invertibility problem for time-varying Dynamic Stochastic General Equilibrium (DSGE) models. The question of interest is whether the shocks of a time-varying DSGE model can be recovered from an infinite time-varying VAR on the observable variables. Then I focus on DSGE models whose coefficients are driven by a Markov chain, and propose tractable methods to check their invertibility. Finally, I illustrate the validity of such methods via computations and examples. My results relate with the works of Amisano and Tristani (2010, 2011), Bekiros and Paccagnini (2013), Hallin (1980, 1983, 1986), Francq and Zako¨ıan (2001), and Franchi et al. (2013, 2015).