To detect the quantity theory of money, we follow Lucas (1980) by looking at scatter plots of filtered time series of inflation and money growth rates and interest rates and money growth rates. Like Whiteman (1984), we relate those scatter plots to sums of two-sided distributed lag coefficients constructed from fixed-coefficient and time-varying VARs for US data from 19002005. We interpret outcomes in terms of population values of those sums of coefficients implied by two DSGE models. The DSGE models make the sums of coefficients depend on the monetary policy rule via cross-equation restrictions of a type that Lucas (1972) and Sargent (1971) emphasised in the context of testing the natural unemployment rate hypothesis. When the US data are extended beyond Lucas's 195575 period, the scatter plots mutate in ways that we attribute to prevailing monetary policy rules.