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Long-run restrictions have been used extensively for identifying structural shocks in vector autoregressive (VAR) analysis. Such restrictions are typically just-identifying but can be checked by utilizing changes in volatility. This paper reviews and contrasts the volatility models that have been used for this purpose. Three main approaches have been used, exogenously generated changes in the unconditional residual covariance matrix, changing volatility modelled by a Markov switching mechanism and multivariate generalized autoregressive conditional heteroskedasticity (GARCH) models. Using changes in volatility for checking long-run identifying restrictions in structural VAR analysis is illustrated by reconsidering models for identifying fundamental components of stock prices.

I describe a new method for imposing zero restrictions (both short and long-run) in combination with conventional sign-restrictions. In particular I extend the Rubio-Ramirez et al. (2010) algorithm for applying short and long-run restrictions for exactly identified models to models that are underidentified. In turn this can be thought of as a unifying framework for short-run, long-run and sign restrictions. I demonstrate my algorithm with two examples. In the first example I estimate a VAR model using the Smets & Wouters (2007) dataset and impose sign and zero restrictions based on the impulse responses from their DSGE model. In the second example I estimate a BVAR model using the Mountford & Uhlig (2009) data set and impose the same sign and zero restrictions they use to identify an anticipated government revenue shock.

I describe a new method for imposing zero restrictions (both short and long-run) in combination with conventional sign-restrictions. In particular I extend the Rubio-Ramirez et al. (2010) algorithm for applying short and long-run restrictions for exactly identified models to models that are underidentified. In turn this can be thought of as a unifying framework for short-run, long-run and sign restrictions. I demonstrate my algorithm with two examples. In the first example I estimate a VAR model using the Smets & Wouters (2007) dataset and impose sign and zero restrictions based on the impulse responses from their DSGE model. In the second example I estimate a BVAR model using the Mountford & Uhlig (2009) data set and impose the same sign and zero restrictions they use to identify an anticipated government revenue shock. ; publishedVersion