"Semiparametric Estimation and Inference in Partially Identified Econometric Models"

计量经济学文献已经在经济模型的估计和推断方法方面取得了实质性的进展，在该方法中，感兴趣的参数被识别为一个集合。然而，当这种部分识别的模型同时包含有限和无限维参数时，人们对它们的性质知之甚少。半参数模型在各种实证研究中被广泛用于预测和进行政策评估。它们结合了对经济模型关键特征的易于处理的参数规范和对其余特征的灵活的非参数限制。本项目的主要目标是将半参数推断的范围扩大到主要类别的部分确定的计量经济模型。我们将特别关注半参数效率理论。最近，Kaido和Santos(2011)提出了部分辨识模型的一个重要子集的渐近有效性概念：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的半参数部分辨识模型来扩展这一框架的范围。具体地说，我们考虑了两个主题。第一个主题是带区间截尾变量的半参数回归模型。在微观层面的数据中，区间删失现象频繁发生。我们的目标是估计一个参数，该参数捕捉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。虽然在存在区间截尾的情况下，该参数不是点识别的，但这种方法可以表征其识别的集合。研究人员计划研究这一集合的渐近有效估计。所提出的高效集值估计量将有助于利用调查数据进行实证研究，例如健康与退休研究(HRS)。第二个主题研究由干扰参数指示的参数的有效估计。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结构参数，当均衡选择规则已知时，这些结构参数可以完全恢复。通过改变选择规则，所识别的集合可以被等效地视为它的函数。本项目旨在推广在Kaido and Santos(2011)中提出的效率概念，以研究这类识别集合的有效估计。成功开发这类模型的推理方法将有助于有效地进行政策评估，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.