Robust inference in structural vector autoregressions with long-run restrictions

Abstract

Long-run restrictions (Blanchard and Quah, AER 1989) are a very popular method for identifying structural vector autoregressions (SVARs). A prominent example is the unsettled debate on the effect of technology shocks on employment, which has been used to test real business cycle theory (Gali, AER 1999, Christiano et al, JEEA 2006). 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 instruments is high (Pagan and Robertson, RES 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 (AMS 1949) test with so-called IVX instruments (Magdalinos and Phillips, 2009, Phillips, ECMA 2014). Our proposed method has good size and power properties and can be used to produce robust confidence bands on the impulse response function to the identified structural shock(s). No paper