The money demand literature presents much conflicting evidence on this question. For example, Lucas (1988) reports unrestricted money demand regressions which seem to imply that long-run money demand elasticities are highly unstable across subsamples. At the same time, he also presents evidence from money demand regressions with the income elasticity restricted to unity which seem to suggest stability. We conduct a formal analysis which weighs these apparently conflicting facts to determine which hypothesis is more plausible; the hypothesis that money demand is stable, or the hypothesis that money demand is unstable. We find that the stability hypothesis is the more plausible one. Thus, according to our data set, the answer to the question in the title is "yes".