A mathematical formulation of residential housing prices in the United States

In the United States, house prices and corporate credit spreads are accurate predictors of GDP growth, outperforming both liquidity creation and residential investment. House prices also predict macroeconomic indicators such as inflation and unemployment. Therefore, this paper undertakes an examination of the determinants of house prices given that they indirectly affect GDP growth. Residential housing prices are modeled at the levels of affordable middle-class housing and luxury homes. Investor sentiments are modeled as risk-averse, moderate risk-taking, and risk-taking behavior of gradual increase in housing prices. Risk-aversion is presented as the Arrow-Pratt coefficient of risk-aversion. Moderating risk-taking is formulated as a Bessel function. Risk-taking behavior is indicated by an exponential distribution. These investor sentiment functions intersect with a rising Erlang pricing distribution to yield optimal home prices. The luxury home market consists of homes priced at >$1 million. For luxury homes, the same investor sentiments were employed, with housing prices being modeled by a downward-sloping gamma distribution. The mathematical formulations were empirically validated using federal housing data. Theoretical and practical implications are articulated.