Estimation and Inference with Nonparametric and High-Dimensional Econometric Models

研究涉及三个一般性主题：（1）非参数工具变量（IV）估计，（2）估计与高维数据集，（3）施加形状限制的经济理论的非参数估计的需求函数。 非参数IV估计是近年来受到广泛关注的一种新的计量经济学方法。 本研究旨在解决非参数IV方法在应用计量经济学中实际应用的两个障碍。 首先是寻找方法来选择所需的调整参数，实现非参数IV估计。 另一个是找到一种方法来构造非参数IV估计的函数的置信带。 第二个主题是扩展稀疏高维回归模型的估计方法，使其对经济学和其他社会科学更有用。 高维数据集在这些领域中广泛存在。 统计学问题是决定模型中包含哪些变量，并估计结果模型。 许多现有的方法，同时模型选择和估计的动机在基因组学的问题。 它们被设计为根据经验识别为零的回归系数，并估计不为零的回归系数。 然而，在社会科学的应用中，更有可能的是一些系数“太小而不重要”，而另一些系数则“很大”。“拟议的研究将开发方法，以经验区分“小”和“大”系数。 第三个主题是关于对需求函数的非参数估计施加经济理论的斯卢茨基条件。 以往的研究表明，对平均需求的非参数估计施加斯卢茨基条件，大大提高了估计的有限样本性能和实用性。 目前的研究将开发的方法来施加斯卢茨基条件的不可分离的需求函数的估计。 它也将开发方法进行估计时，经常发生的情况下，Slutsky条件下，收入数据是区间删失，因此，需求函数是不确定的。第一个研究课题很重要，因为它放松了经济研究中经常使用的武断假设，从而使研究人员能够获得更准确和更现实的结果。 第二个主题很重要，因为经济数据往往包括许多变量。 我们很少能先验地清楚哪些变量与我们感兴趣的问题相关，而且关于使用哪些变量的决定往往是相当武断的。 这项研究将提供系统的方法来做出这些决定，使经济学和其他社会科学的研究人员能够获得更可靠的结果。 第三个主题将产生估计需求函数的改进方法。 这对于评估经济政策干预的影响，包括税收和价格的变化，十分重要。

The research addresses three general topics: (1) nonparametric instrumental variables (IV) estimation, (2) estimation with high-dimensional data sets, and (3) imposing shape restrictions given by economic theory on nonparametric estimates of demand functions. Nonparametric IV estimation is a promising new econometric method that has received much recent attention in the econometrics literature. The research aims at solving two barriers that stand in the way of practical application of nonparametric IV methods in applied econometrics. The first is finding ways to choose the tuning parameters required to implement nonparametric IV estimators. The other is finding a way to construct confidence bands for functions estimated by nonparametric IV. The second topic is extending methods for estimating sparse, high-dimensional regression models in ways that make them more useful for economics and other social sciences. High-dimensional data sets are widely available in these fields. The statistical problem is to decide which variables to include in a model and to estimate the resulting model. Many existing methods for simultaneous model selection and estimation were motivated by problems in genomics. They are designed to identify empirically regression coefficients that are zero and estimate the ones that are not. In social science applications, however, it is more likely that some coefficients are "too small to matter," whereas others are "large." The proposed research will develop methods to discriminate empirically between "small" and "large" coefficients. The third topic is concerned with imposing the Slutsky condition of economic theory on nonparametric estimates of demand functions. Previous research has shown that imposing the Slutsky condition on a nonparametric estimate of average demand greatly improves the estimate's finite-sample performance and practical usefulness. The current research will develop ways to impose the Slutsky condition on estimates of non-separable demand functions. It also will develop ways to carry out estimation subject to the Slutsky condition when, as often happens, the income data are interval censored and, consequently, the demand function is not point identified. The first research topic is important because it relaxes arbitrary assumptions that are frequently used in economic research, and thereby enables investigators to achieve results that are more accurate and realistic. The second topic is important because economic data often include many variables. It is rarely clear a priori which ones are relevant to the questions of interest, and decisions about which variables to use are often quite arbitrary. The research will provide systematic ways to make these decisions, enabling investigators in economics and other social sciences to achieve results of improved reliability. The third topic will yield improved methods for estimating demand functions. This is important for assessing the effects of economic policy interventions, including changes in taxes and prices.