M-Estimators of U-Processes With a Change-Point Due to a Covariate Threshold

Lili Tan and Yichong Zhang

Journal of Business & Economic Statistics, 2019, vol. 37, issue 2, 248-259

Abstract: Economic theory often predicts a “tipping point” effect due to multiple equilibria. Linear threshold regressions estimate the “tipping point” by assuming at the same time that the response variable is linear in an index of covariates. However, economic theory rarely imposes a specific functional form, but rather predicts a monotonic relationship between the response variable and the index. We propose new, rank-based, estimators for both the “tipping point” and other regression coefficients, exploiting only the monotonicity condition. We derive the asymptotic properties of these estimators by establishing a more general result for M-estimators of U-processes with a change-point due to a covariate threshold. We finally apply our method to provide new estimates of the “tipping point” of social segregation in four major cities in the United States. Supplementary materials for this article are available online.

Date: 2019
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DOI: 10.1080/07350015.2017.1319373

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