Homework in monetary economics: Inflation, home production, and the production of homes

We introduce household production and the production of houses (construction) into a monetary model. Theory predicts inflation, as a tax on market activity, encourages substitution into household production and hence investment in housing. In the model, the stock and appropriately-deflated price of housing increase with inflation or nominal interest rates. We document this in data for the U.S. and other countries. A calibrated model accounts for up to 52% (87%) of the relationship between interest rates and housing wealth deflated by nominal output (by the money supply). It also implies the cost of inflation is higher than in models without home production.