How long is the long run in the relationship between money growth and inflation? How important are high inflation episodes for the unit slope finding in the quantity theory of money? To answer these questions, we study the relationship between excess money growth and inflation over time and across frequencies using annual data from 1870 to 2013 for 16 developed countries. Wavelet-based exploratory analysis shows the existence of a close stable relationship between excess money growth and inflation only over long time horizons, i.e. periods greater than 16–24 years, with money growth mostly leading. When we investigate the sensitivity of the unit slope finding to inflation episodes using a “time-frequency-based” panel data approach, we find that low-frequency regression coefficients estimated over variable-length subsamples are largely affected by high inflation episodes occurring in the 1910s, the 1940s, and the 1970s. Taken together, our results suggest that inflationary upsurges affect regression coefficients, but not the closeness of the long-run relationship. This reconciles the validity of the quantity theory of money with the current disinterest of monetary policymaking in money growth.