Identification of Structural Vector Autoregressions by Stochastic Volatility

In Structural Vector Autoregressive (SVAR) models, heteroskedasticity can be exploited to identify structural parameters statistically. In this paper, we propose to capture time variation in the second moment of structural shocks by a stochastic volatility (SV) model, assuming that their log variances follow latent AR(1) processes. Estimation is performed by Gaussian Maximum Likelihood and an efficient Expectation Maximization algorithm is developed for that purpose. Since the smoothing distributions required in the algorithm are intractable, we propose to approximate them either by Gaussian distributions or with the help of Markov Chain Monte Carlo (MCMC) methods. We provide simulation evidence that the SV-SVAR model works well in estimating the structural parameters also under model misspecification. We use the proposed model to study the interdependence between monetary policy and the stock market. Based on monthly US data, we find that the SV specification provides the best fit and is favored by conventional information criteria if compared to other models of heteroskedasticity, including GARCH, Markov Switching, and Smooth Transition models. Since the structural shocks identified by heteroskedasticity have no economic interpretation, we test conventional exclusion restrictions as well as Proxy SVAR restrictions which are overidentifying in the heteroskedastic model.