This paper develops a threshold regression model where an unknown relationship between two variables nonparametrically determines the threshold. We 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. 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 the existing studies

Document Type

Working Paper




Sample Splitting, Threshold, Nonparametric, Random Field, Tipping Point, Metropolitan Area Boundary




Working Papers Series


We thank Bo Honoré, Sokbae Lee, Yuan Liao, Myung Seo, Ping Yu, and participants at numerous seminar/conference presentations for very helpful comments. Financial supports from the ApplebyMosher grant and the CUSE grant are highly appreciated.


Economic Policy | Economics | Public Affairs, Public Policy and Public Administration



Additional Information

Working paper no. 222


Local input

Creative Commons License

Creative Commons Attribution 4.0 International License
This work is licensed under a Creative Commons Attribution 4.0 International License.



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