Underidentified SVAR models: A framework for combining short and long-run restrictions with sign-restrictions

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.