ROOT-N CONSISTENCY OF INTERCEPT ESTIMATORS IN A BINARY RESPONSE MODEL UNDER TAIL RESTRICTIONS

Lili Tan and Yichong Zhang

Econometric Theory, 2018, vol. 34, issue 6, 1180-1206

Abstract: The intercept of the binary response model is not regularly identified (i.e., $\sqrt n$ consistently estimable) when the support of both the special regressor V and the error term ε are the whole real line. The estimator of the intercept potentially has a slower than $\sqrt n$ convergence rate, which can result in a large estimation error in practice. This paper imposes additional tail restrictions which guarantee the regular identification of the intercept and thus the $\sqrt n$-consistency of its estimator. We then propose an estimator that achieves the $\sqrt n$ rate. Last, we extend our tail restrictions to a full-blown model with endogenous regressors.

Date: 2018
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