Conditionally parametric quantile regression for spatial data: An analysis of land values in early nineteenth century Chicago

• Conditionally parametric estimation of a quantile regression model
• Land value estimates for Chicago in 1913
• Use of kernel density functions to summarize the results of large nonparametric models

This paper demonstrates that a conditionally parametric version of a quantile regression estimator is well suited to analyzing spatial data. The conditionally parametric quantile model accounts for local spatial effects by allowing coefficients to vary smoothly over space. The approach is illustrated using a new data set with land values for over 30,000 blocks in Chicago for 1913. Kernel density functions summarize the effects of discrete changes in the explanatory variables. The CPAR quantile results suggest that the distribution of land values shifts markedly to the right for locations near the CBD, close to Lake Michigan, near elevated train lines, and along major streets. The variance of the land value distribution is higher in locations farther from the CBD and farther from the train lines.