标题： 估计非可分选择模型：一种函数收缩方法 显示英文标题

标题： Estimating Nonseparable Selection Models: A Functional Contraction Approach

摘要： 我们提出了一种新的估计非可分选择模型的方法。 我们证明，给定选择规则和观察到的选定结果分布，潜在结果分布可以表征为一个算子的不动点，我们证明该算子是一个函数压缩映射。 我们提出了一种两步半参数最大似然估计量来估计选择模型和潜在结果分布。 估计量的一致性和渐近正态性得到了确立。 我们的方法在蒙特卡洛模拟中表现良好，并适用于各种只有部分结果样本被观察到的实证情境。 例如包括仅观测到交易价格的消费者需求模型、存在不完整出价数据的拍卖模型以及仅观测到接受工资数据的Roy模型。 显示英文摘要

摘要： We propose a novel method for estimating nonseparable selection models. We show that, given the selection rule and the observed selected outcome distribution, the potential outcome distribution can be characterized as the fixed point of an operator, which we prove to be a functional contraction. We propose a two-step semiparametric maximum likelihood estimator to estimate the selection model and the potential outcome distribution. The consistency and asymptotic normality of the estimator are established. Our approach performs well in Monte Carlo simulations and is applicable in a variety of empirical settings where only a selected sample of outcomes is observed. Examples include consumer demand models with only transaction prices, auctions with incomplete bid data, and Roy models with data on accepted wages.