Selection bias and land development in the monocentric city model

Abstract

The land development process implied by the monocentric city model is extremely simple. The model, as set forth by Muth [13] and Mills [12], contains no error terms and the city lies on a featureless plain. Land is converted to urban use whenever urban land values rise relative to agricutural land values; the assumptions of the model assure that land development in any period takes place in a ring at the edge of the city. In this paper, we relax the assumption that the city is a featureless plain by introducing error terms to the urban and non-urban land value functions. This simple addition-a necessity for empirical work-produces a much richer land development process than is imbedded in the simple Muth-Mills model. The error terms in the land value functions, which represent the effects of missing variables such as the fertility of the soil, influence the selection of land for urban and non-urban use. This selection process, in turn, causes a bias in OLS estimates of land value functions. The form of the selection bias implies three possible land development patterns. First, if traits that produce high urban land values cause low non-urban values, relatively low value non-urban land is developed first and has above average value in urban use. However, if unusually productive agricultural land is also highly valued in urban use then the development process depends on the relative magnitudes of the variances of the two land value distributions. For example, if the variance of the urban distribution is the larger, then relatively high value non-urban land is developed first and has above average land value in urban use: the greater variance in the urban distribution implies that unusually good farmland can earn more in urban use. Thus, the expanded Muth-Mills model incorporates urban expansion at the expense of high-quality agriculture and a more benign land market in which only comparatively low-quality agricultural land is taken by cities. The expanded Muth-Mills model implies the existence of selection bias in land value equations. Selection bias has only recently been recognized