INTERCEPT ESTIMATION IN NONLINEAR SELECTION MODELS
针对非线性选择模型，提出多种半参数估计方法，分别利用单调指标限制和倾向得分接近1的观测来估计截距，并通过蒙特卡洛模拟和计数数据实例验证其有限样本表现。
We propose various semiparametric estimators for nonlinear selection models, where slope and intercept can be separately identified. When the selection equation satisfies a monotonic index restriction, we suggest a local polynomial estimator, using only observations for which the marginal cumulative distribution function of the instrument index is close to one. Data-driven procedures such as cross-validation may be used to select the bandwidth for this estimator. We then consider the case in which the monotonic index restriction does not hold and/or the set of observations with a propensity score close to one is thin so that convergence occurs at a rate that is arbitrarily close to the cubic rate. We explore the finite sample behavior in a Monte Carlo study and illustrate the use of our estimator using a model for count data with multiplicative unobserved heterogeneity.