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The intercept of the binary response model is not regularly identified (i.e.,
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
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
-consistency of its estimator. We then propose an estimator that achieves the
rate. Last, we extend our tail restrictions to a full-blown model with endogenous regressors.
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