Robust inference in structural VARs with long-run restrictions

Résumé

Long-run restrictions (Blanchard and Quah, 1989) are a very popular method for identifying structural vector autoregressions (SVARs). A prominent exam- ple is the debate on the effect of technology shocks on employment, which has been used to test real business cycle theory (Gali, 1999, Christiano Eichenbaum and Vigfusson, 2003). The long-run identifying restriction is that non-technology shocks have no permanent effect on productivity. This can be used to identify the technology shock and the impulse responses to it. It is well-known that long-run restrictions can be expressed as exclusion restrictions in the SVAR and that they may suffer from weak identification when the degree of persistence of the instru- ments is high (Pagan and Robertson, 1998). This introduces additional nuisance parameters and entails nonstandard distributions, so standard weak-instrument- robust methods of inference are inapplicable. We develop a method of inference that is robust to this problem. The method is based on a combination of the Anderson and Rubin (1949) test with instruments derived by filtering potentially non-stationary variable to make them near stationary (Magdalinos and Phillips, 2009, Phillips, 2014, Kostakis Magdalinos and Stamatogiannis, 2015). In the case of Blanchard and Quah (1989), we find that long-run restrictions yield very weak identification. On the hours debate, we find that the difference specification of Gali (1999) is very well identified, while the level specification of Christiano et. al. (2003) is weakly identified.