Threshold Regression With Nonparametric Sample Splitting

Yoonseok Lee, Yulong Wang

Journal of Econometrics, June 2023

Yoonseok Lee

Yulong Wang

Economics Department

Center for Policy Research

Research Methods

Journal of Econometrics

Yoonseok Lee

Yulong Wang

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. We illustrate empirical relevance of this new model 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.