Does a "two-pillar Phillips curve" justify a two-pillar monetary policy strategy?

Arguments for a prominent role for attention to the growth rate of monetary aggregates in the conduct of monetary policy are often based on references to low-frequency reduced-form relationships between money growth and inflation. The "two-pillar Phillips curve" proposed by Gerlach (2004) has recently attracted a great deal of interest in the euro area, where it is sometimes supposed to provide empirical support for the wisdom of a "two-pillar strategy" that uses distinct analytical frameworks to assess shorter-run and longer-run risks to price stability. I show, however, that regression coefficients of the kind reported by Assenmacher-Wesche and Gerlach (2006a) among others are quite consistent with a "new Keynesian" model of inflation determination, in which the quantity of money plays no role in inflation determination, at either high or low frequencies. I also show that empirical results of this kind do not in themselves establish that money growth must be useful in forecasting inflation, either in the short run or over a longer run. Hence they provide little support for the ECB's monetary "pillar.