Technological Progress in a Model of the Housing – Land Cycle

Abstract

A stationary-state perfect foresight model is developed in which housing and land are treated as investment assets convertible to each other at some cost. Investors hold either land or housing and are heterogeneous in the i.i.d. idiosyncratic shocks to their conversion costs in every time period. Hence, there are endogenously determined probabilities that a unit of land will be converted to housing ("construction probability") and that a unit of housing will be converted to land ("demolition probability") in any given time period. This model is used to analyze the effects of a decrease in construction cost on the asset prices of land and housing, on housing rent and on the stationary stocks of land and housing. A decrease in construction cost always raises land values, may either raise or lower housing values, and increases both the construction and demolition probabilities. The housing stock increases (decreases) if the construction probability increases proportionally more (less) than the demolition probability. Since housing rent is inversely related to the stock of housing, the fall in construction costs may cause rents to rise. Thus, paradoxically, technological progress may hurt renters. The moral of the model is important: in contrast to models of the housing market without land or to models in which land price is exogenous, the long-run supply price of housing is not fully determined by construction cost, but depends as well on demolition cost and on the endogenous value of land.