Root-n consistency of intercept estimators in a binary response model under tail restrictions

• Main Authors: TAN, Lili, ZHANG, Yichong
• Format: text
• Language: English
• Published: Institutional Knowledge at Singapore Management University 2018
• Subjects: Extremal quantile; Tail index; Econometrics
• Online Access: https://ink.library.smu.edu.sg/soe_research/2028; https://ink.library.smu.edu.sg/context/soe_research/article/3027/viewcontent/main_rnc_v4.pdf
• Institution: Singapore Management University

The intercept of the binary response model is irregularly identified when the supports of both the special regressor V and the error term ε are the whole real line. This leads to the estimator of the intercept having potentially a slower than √n convergence rate, which can result in a large estimation error in practice. This paper imposes addition tail restrictions which guarantee the regular identification of the intercept and thus the √n-consistency of its estimator. We then propose an estimator that achieves the √n rate. Finally, we extend our tail restrictions to a full-blown model with endogenous regressors.