This paper considers a sticky price model with a cash-in-advance constraint where agents forecast inflation rates with the help of econometric models. Agents use least squares learning to estimate two competing models of which one is consistent with rational expectations once learning is complete. When past performance governs the choice of forecast model, agents may prefer to use the inconsistent forecast model, which generates an equilibrium where forecasts are inefficient. While average output and inflation result the same as under rational expectations, higher moments differ substantially: output and inflation show persistence, inflation responds sluggishly to nominal disturbances, and the dynamic correlations of output and inflation match U.S. data surprisingly well
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