Over the last two centuries, the cross-spectral coherence between either narrow or broad money growth and inflation at the frequency ω=0 has exhibited little variation–being, most of the time, close to one–in the U.S., the U.K., and several other countries, thus implying that the fraction of inflation’s long-run variation explained by long-run money growth has been very high and relatively stable. The cross-spectral gain at ω=0, on the other hand, has exhibited significant changes, being for long periods of time smaller than one. The unitary gain associated with the quantity theory of money appeared in correspondence with the inflationary outbursts associated with World War I and the Great Inflation–but not World War II–whereas following the disinflation of the early 1980s the gain dropped below one for all the countries and all the monetary aggregates I consider, with one single exception. I propose an interpretation for this pattern of variation based on the combination of systematic velocity shocks and infrequent inflationary outbursts. Based on estimated DSGE models, I show that velocity shocks cause, ceteris paribus, comparatively much larger decreases in the gain between money growth and inflation at ω=0 than in the coherence, thus implying that monetary regimes characterised by low and stable inflation exhibit a low gain, but a still comparatively high coherence. Infrequent inflationary outbursts, on the other hand, boost both the gain and coherence towards one, thus temporarily revealing the one-for-one correlation between money growth and inflation associated with the quantity theory of money, which would otherwise remain hidden in the data.
band-pass filtering Bayesian estimation cross-spectral analysis DSGE Models frequency domain inflation Quantity theory of money trend inflation