Selection Without Exclusion
研究了在误差独立于解释变量但分布未知的样本选择模型中，如何通过完整结构约束缩小参数识别集，并给出了锐利边界和更易计算的非锐利边界。
It is well understood that classical sample selection models are not semiparametrically identified without exclusion restrictions. Lee (2009) developed bounds for the parameters in a model that nests the semiparametric sample selection model. These bounds can be wide. In this paper, we investigate bounds that impose the full structure of a sample selection model with errors that are independent of the explanatory variables but have unknown distribution. The additional structure can significantly reduce the identified set for the parameters of interest. Specifically, we construct the identified set for the parameter vector of interest. It is a one‐dimensional line segment in the parameter space, and we demonstrate that this line segment can be short in practice. We show that the identified set is sharp when the model is correct and empty when there exist no parameter values that make the sample selection model consistent with the data. We also provide non‐sharp bounds under the assumption that the model is correct. These are easier to compute and associated with lower statistical uncertainty than the sharp bounds. Throughout the paper, we illustrate our approach by estimating a standard sample selection model for wages.