In this paper we discriminate between competing U.S. narrow money demand functions by the use of non-nested test. Some previous studies on this topic used the three-month treasury-bill rate as the fixed interest rate proxy, and found that the consumption-based scale proxies are more suitable than the income-based scale proxies for interpreting the money demand. Unlike these studies, we consider the choices of scale and interest rate proxies at the same time. Our full-sample analysis shows evidence in contrast to their empirical findings and hence generates different policy implications. The sub-sample analysis demonstrates that the appropriate choices of scale proxies and interest rates are not invariant to different sample periods. We characterize such an instability in accordance with the sub-sample non-nested test results, and discuss some related issues.