In the 1990s, the empirical relation between money demand and interest rates began to fall apart. We analyze to what extent improved access to money markets can explain this break-down. For this purpose, we construct a microfounded monetary model with a money market, which 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 improved access to money markets can explain the behavior of money demand very well. Furthermore, we show that, by allocating money more efficiently, better access to money markets decrease the welfare cost of inflation substantially.