Perhaps you may remember a recently published paper by Michael Woodford on the inclusion of monetary aggregates and his treatment on the empirical-motivated two-pillar Phillips curve of Assenmacher-Wesche/Gerlach. The latter observed a cointegration of money and inflation at low frequencies and proposed a modified price equation with cyclical components (such as output) and trend componentes (such as trend money growth). Woodford showed that in a simple forward-looking model with a money demand equation trend money and trend inflation are cointegrated, too, without modeling inflation dynamics as a function of trend money.I replicated his findings by simulating his model with Matlab. I used the HP-Filter instead of a Bandpass filter. What is surprising that you can even see that trend money leads trend inflation although money does not appear in the inflation-determining equation. I will have to think about this issue and keep you updated for a possible explanation.
