Threshold Regression with Nonparametric Sample Splitting

TL;DR

This paper introduces a novel threshold regression model with a nonparametric threshold that can handle cross-sectional dependence, providing new tools for spatial and demographic analysis with broad empirical applications.

Contribution

It develops a nonparametric threshold regression framework allowing for unknown thresholds and dependence, with theoretical properties and practical applications demonstrated.

Findings

New empirical results differ significantly from existing studies.

The model accurately estimates spatial borders and tipping points.

The estimator achieves root-n consistency and asymptotic normality.

Abstract

This paper develops a threshold regression model where an unknown relationship between two variables nonparametrically determines the threshold. We allow the observations to be cross-sectionally dependent so that the model can be applied to determine an unknown spatial border for sample splitting over a random field. We derive the uniform rate of convergence and the nonstandard limiting distribution of the nonparametric threshold estimator. We also obtain the root-n consistency and the asymptotic normality of the regression coefficient estimator. Our 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. We find that the new empirical results are substantially different from those in the existing studies.