上海财经大学经济学院：推断点和部分鉴定半非参数条件矩模型

　　上海财经大学经济学院邀请Jing Tao老师作了一场题为“Inference for Point and Partially Identified Semi-Nonparametric Conditional Moment Models(推断点和部分鉴定半非参数条件矩模型)”的讲座，上海财经大学目前拥有会计学、财政学、经济思想史3个国家级重点学科，金融学为国家重点(培育)学科;拥有4个财政部重点学科、6个上海市重点学科；设有国家经济学基础人才培养基地、国家大学生文化素质教育基地、教育部人文社会科学重点研究基地--会计与财务研究院3个国家级基地；并拥有理论经济学、应用经济学、工商管理、管理科学与工程4个一级学科博士学位授权点，44个二级学科博士学位授权点，哲学、理论经济学、应用经济学、工商管理4个博士后流动站。讲座的主要内容是：

　　这项工作考虑半非参数条件矩模型，其中感兴趣的参数包括有限维参数和未知的功能。我们主要专注于在这个框架的两个推理问题。首先，我们提供了参数和参数的函两finite-和无限维成分的估计一致推断的新方法。基于这些结果，我们可以，例如，建立对未知函数和未知函数的偏导数均匀置信带。最近，各种车型统一的信心乐队如条件均值和分位数都使用强近似方法(贝罗尼，Chernozhukov和费尔南德斯 - 瓦尔，2011年，和相关工作)相继推出。我们延长了强烈的近似方法提供统一的推论在条件矩限制型号的内生性。其次，对于大班的条件矩限制车型，我们提供了新的推理结果时的参数只有部分确定。在部分鉴定，我们将展示如何通过转换，它也点标识下使用准似然比(QLR)统计，构建逐点置信区间。我们提供用于获得对应于所述QLR临界值一致的乘数自举过程。此外，我们概括从点确定情况下，统一置信带统一的信心通过反转SUP-QLR统计设置了未知功能的域。新方法应用于构造逐点置信区间和均匀的置信带为形状不变恩格尔曲线。

　　原文：This work considers semi-nonparametric conditional moment models where the parameters of interest include both finite-dimensional parameters and unknown functions. We mainly focus on two inferential problems in this framework. First, we provide new methods of uniform inference for the estimates of both finite- and infinite-dimensional components of the parameters and functionals of the parameters. Based on these results, we can, for instance, construct uniform confidence bands for the unknown functions and the partial derivatives of the unknown functions. Recently, uniform confidence bands for a variety of models such as conditional mean and quantiles have been introduced using strong approximation methods (Belloni, Chernozhukov and Fernández-Val, 2011, and related work). We extend the strong approximation approach to provide uniform inference in conditional moment restriction models with endogeneity. Second, for a large class of conditional moment restrictions models, we provide new results for inference when parameters are only partially identified. Under partial identification, we show how to construct pointwise confidence regions by inverting a quasi-likelihood ratio (QLR) statistic that is also employed under point identification. We provide a consistent multiplier bootstrap procedure for obtaining critical values corresponding to the QLR. Furthermore, we generalize the uniform confidence bands from point identified case to uniform confidence sets over the domain of the unknown functions by inverting a sup-QLR statistic. The new methods are applied to construct pointwise confidence intervals and uniform confidence bands for shape-invariant Engel curves.