Homework in Monetary Economics: Inflation, Home Production, and the Production of Homes

We study models incorporating money, household production, and investment in housing. Inflation, as a tax on market activity, encourages substitution into household production, and thus investment in household capital. Hence, inflation increases the (appropriately deflated) value of the housing stock. This is documented in various data sources. A calibrated model accounts for a fifth to a half of the observed relationships. While this leaves much to be explained, it demonstrates the channel is economically relevant. We also show models with home production imply higher costs of inflation than models without it, especially when home and market goods are close substitutes.