The low velocity of circulation of money implies that households hold more money than they normally spend. This behavior is explained if households face uncertain expenditure needs, so that they have a precautionary motive for holding money. We investigate this motive in a search model where households are subject to preference shocks. The model predicts that velocity is not only low but also interest elastic. The model closely fits U.S. data on velocity and interest rates (1892–2004). The empirical analysis reveals a dramatic reduction in precautionary balances toward the end of our sample, which is important for policy issues.