The Long-Run Phillips Curve: A Structural VAR Investigation

I use structural VARs identified based on either long-run restrictions, or a combination of long-run and sign restrictions, to investigate the long-run tradeoff between inflation and the unemployment rate in the U.S., the Euro area, the U.K., Canada and Australia over the post-WWII period. Results based on VARs featuring a single permanent inflation shock do not allow to reject the null hypothesis of a vertical long-run Phillips curve for either country. Results based on VARs allowing for four permanent inflation shocks, which are sorted out from one another by means of DSGE-based robust sign restrictions, produce a very similar picture. The overall extent of uncertainty is however substantial, thus suggesting that the data are compatible with a comparatively wide range of possible slopes of the long-run trade-off. For all countries, Johansen's cointegration tests point towards the presence of cointegration between either inflation and unemployment, or inflation, unemployment, and a short-term interest rate, with the long-run Phillips trade-off implied by the estimated cointegrating vectors being negative and sizeable. I argue however that this evidence should be discounted, as, conditional on the estimated structural VARs--which, by construction, do not feature cointegration between any variable--Johansen's procedure tends to spuriously detect cointegration a non-negligible, and sometimes large, fraction of the times.