The welfare costs of expected and unexpected inflation

The monetary search model by Lagos and Wright (2005) is extended with imperfect information about nominal shocks as in Lucas (1972). An analytical solution exists with logarithmic preferences. In general, individuals hold precautionary balances. Calibrated to United States postwar data, the welfare cost of the monetary cycle is calculated to be small (below 0.0003% of GDP) compared to the welfare cost of the inflation tax (around 0.25% of GDP). The main reason for the minute welfare cost of the monetary cycle is its low amplitude in 1947-2007. But, monetary crashes, such as those experienced during the Great Depression, can generate important welfare costs.