Consistent estimation of the urban land value function

Abstract

Previous studies have found that the urban land value function became flatter during the 19th century, apparently due to declining transportation costs and increasing income. Estimates from these studies imply that housing demand became less elastic over the same period (from elastic to unit elastic). This paper demonstrates that the latter conclusion is rejected when the area of the city is defined correctly and consistent estimation procedures are used. By combining urban and non-urban data, previous studies underestimated the degree to which the slope of the land value function declined over time. When only urban data are used, the decline is even greater, and the price elasticity of demand for housing is uniformly unit elastic. In addition, the commonly used Box-Cox transformation is found to be an imprecise method of generalizing functional form and subject to substantial small-sample bias which, if ignored, leads to an underestimate of standard errors.