M-estimators of U-processes with a change-point due to a covariate threshold - TAN, Lili (Institutional Knowledge at Singapore Management University, 2019)
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.