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In the 1990s, the empirical relationship between money demand and interest rates began to fall apart. We analyze to what extent financial innovations can explain this breakdown. For this purpose, we construct a microfounded monetary model with a money market that provides insurance against liquidity shocks by offering short‐term loans and by paying interest on money market deposits. We calibrate the model to U.S. data and find that the introduction of the sweep technology at the beginning of the 1990s, which improved access to money markets, can explain the behavior of money demand very well. Furthermore, by allowing a more efficient allocation of money, the welfare cost of inflation decreased substantially.