This article investigates the issues of the stability and predictability and interest-sensitivity of money demand over 1870–1997. Two different estimation methodologies are used - random coefficient (RC) modeling and vector error correction (VEC) modeling. The former procedure allows the profiles of the coefficients to be traced over time and relaxes several restrictions routinely imposed in applied work. The results indicate that different estimation methodologies using different data periods and frequencies yield estimates of some of the coefficients of the long-run demand for money that fall within a fairly narrow range. The results also suggest that specification errors have had an important influence on the time profile of the interest elasticity of money demand and that there is a tendency for the interest elasticity to decline in absolute value as interest rates decline.