Inference in models with partially identified control functions
针对控制函数部分可识别的情况，提出基于观测对比较的推断方法，利用控制函数边界不重叠的观测对构建函数不等式，并分析其性质。
In multiple contributions to the literature, James L. Powell and coauthors have developed estimators for semiparametric models where sample selectivity and/or endogeneity can be handled through a "control function". Their methods rely on pairwise comparisons of observations which match (asymptotically) the control functions. Conditional on this matching, a moment condition can identify the parameters of the model. However, there exist instances where the control functions are unobserved, but we have bounds for them which depend on observable covariates. These bounds can arise directly from the nature of the data available (e.g, with interval data), or they can be derived from an economic model. The inability to observe the control functions precludes the matching proposed in Powell's methods. In this paper we show that, under certain conditions, testable implications can still be obtained through pairwise comparisons of observations for which the control-function bounds are disjoint. Testable implications now take the form of pairwise functional inequalities. We propose an inferential procedure based on these pairwise inequalities and we analyze its properties.