We focus on the interaction of frictions both at the firm level and in the banking sector in order to examine the transmission mechanism of the shocks and to reflect on the response of the monetary policy to increases in interest rate spreads, using DSGE models with financial frictions. However, VAR models are linear and the solutions of DSGEs are often linear approximations; hence they do not consider time variation in parameters that could account for inherent nonlinearities and capture the adaptive underlying structure of the economy, especially in crisis periods. A novel method for time-varying VAR models is introduced. As an extension to the standard homoskedastic TVP-VAR, we employ a Markov-switching heteroskedastic error structure. Overall, we conduct a comparative empirical analysis of the out-of-sample performance of simple and hybrid DSGE models against standard VARs, BVARs, FAVARs, and TVP-VARs, using data sets from the U.S. economy. We apply advanced Bayesian and quasi-optimal filtering techniques in estimating and forecasting the models.