"Semiparametric Estimation and Inference in Partially Identified Econometric Models"

计量经济学文献在经济模型的估计和推理方法方面取得了实质性进展，其中感兴趣的参数被确定为一个集合。然而，当这些部分确定的模型包含有限和无限维参数时，对它们的性质知之甚少。半参数模型已广泛应用于各种实证研究中进行预测和进行政策评估。他们结合了对经济模型关键特征的可处理的参数规范和对其余部分的灵活的非参数限制。该项目的主要目标是将半参数推理的范围扩展到部分识别的计量经济模型的主要类别。特别的重点将放在半参数效率的理论。最近，Kaido和Santos（2011）为部分识别模型的一个重要子集提出了一个渐近效率概念：由凸矩不等式定义的模型类。提出的研究旨在通过研究其他主要类别的半参数部分识别模型来扩展该框架的范围。具体考虑两个主题。第一个主题是关于区间截尾变量的半参数回归模型。区间滤波在微观数据中经常发生。目标是估计一个参数，该参数捕获协变量对区间值结果变量的边际影响，而不假设回归函数的任何特定函数形式。回归函数的加权平均导数就是这样的参数之一。虽然该参数在存在区间审查时不是点识别，但该方法可以表征其识别集。研究人员计划研究该集合的渐近有效估计。提出的有效集值估计器将有助于利用健康与退休研究（HRS）等调查数据进行实证研究。第二个主题研究了由干扰参数索引的参数的有效估计。许多计量经济学模型都包含这样的参数。例如，用于研究各种行业的进入博弈模型，包含了当均衡选择规则已知时可以完全恢复的结构参数。通过改变选择规则，可以等效地将识别集视为它的函数。本项目旨在扩展在Kaido和Santos（2011）中开发的效率概念，以研究这类识别集的有效估计。这类模型的推理方法的成功开发将有助于有效地进行策略评估，同时允许部分识别和灵活的半参数规范。

The econometrics literature has made substantial progress on estimation and inference methods for economic models, in which the parameter of interest is identified as a set. Yet, little is known about their properties when such partially identified models contain both finite and infinite dimensional parameters. Semiparametric models have been used widely in various empirical studies to make predictions and to conduct policy evaluations. They combine tractable parametric specification on key features of an economic model with flexible nonparametric restrictions on the rest. The main objective of this project is to expand the scope of semiparametric inference to major classes of partially identified econometric models. A particular focus will be placed on the theory of semiparametric efficiency. Recently, Kaido and Santos (2011) proposed an asymptotic efficiency concept for an important subset of partially identified models: the class of models defined by convex moment inequalities. The proposed research aims to expand the scope of this framework by studying other major classes of semiparametric partially identified models. Specifically two topics are considered.The first topic is on semiparametric regression models with an interval-censored variable. Interval censoring occurs frequently in micro-level data. The goal is to estimate a parameter that captures the marginal impacts of covariates on an interval-valued outcome variable without assuming any specific functional form of the regression function. The weighted average derivative of the regression function is one of such parameters. Although this parameter is not point identified in the presence of interval censoring, this approach may characterize its identified set. The researchers plan to study asymptotically efficient estimation of this set. The proposed efficient set-valued estimator will be useful for conducting empirical studies with survey data such as the Health and Retirement Study (HRS).The second topic studies efficient estimation of parameters indexed by a nuisance parameter. Many econometric models contain such parameters. Entry game models, for example, that are used to study various industries, contain structural parameters that could be fully recovered when the equilibrium selection rule were known. By varying the selection rule, the identified set can be equivalently viewed as a function of it. This project aims to to extend the efficiency concept developed in Kaido and Santos (2011) to study efficient estimation of this type of identified sets. Successful developments of inference methods for this class of models will be useful for conducting policy evaluations efficiently while allowing partial identification and flexible semiparametric specification.