Working Paper

Abstract

This paper develops a threshold regression model where an unknown relationship between two variables nonparametrically determines the threshold. The authors allow the observations to be crosssectionally dependent so that the model can be applied to determine an unknown spatial border for sample splitting over a random field. They derive the uniform rate of convergence and the nonstandard limiting distribution of the nonparametric threshold estimator. They also obtain the root-n consistency and the asymptotic normality of the regression coefficient estimator.

The authors' model has broad empirical relevance as illustrated by estimating the tipping point in social segregation problems as a function of demographic characteristics; and determining metropolitan area boundaries using nighttime light intensity collected from satellite imagery. They find that the new empirical results are substantially different from the existing studies.