Estimation and Inference with Nonparametric and High-Dimensional Econometric Models

这项研究涉及三个一般性问题：(1)非参数工具变量(IV)估计，(2)高维数据集估计，(3)经济理论对需求函数的非参数估计施加形状限制。非参数IV估计是一种很有前途的新计量经济学方法，近年来在计量经济学文献中受到了极大的关注。本研究旨在解决阻碍非参数IV方法在应用计量经济学中实际应用的两个障碍。首先是寻找实现非参数IV估计器所需的调谐参数的方法。第二个主题是扩展估计稀疏高维回归模型的方法，使其在经济学和其他社会科学中更有用。高维数据集在这些领域中广泛可用。统计问题是决定将哪些变量包括在模型中并估计结果模型。许多现有的同时选择和估计模型的方法都是受到基因组学问题的推动。它们的设计目的是从经验上识别零的回归系数，并估计不是零的回归系数。然而，在社会科学应用中，更有可能的是，一些系数“太小而无关紧要”，而另一些系数则“很大”。这项拟议的研究将开发出经验上区分“小”和“大”系数的方法。第三个主题是将经济理论中的斯拉茨基条件强加于需求函数的非参数估计。以往的研究表明，对平均需求的非参数估计施加Slutsky条件可以极大地提高估计的有限样本性能和实用价值。目前的研究将开发将Slutsky条件强加于不可分需求函数估计的方法。它还将开发在Slutsky条件下进行估计的方法，当收入数据被区间删失，因此需求函数不是点识别时，这是经常发生的情况。第一个研究主题之所以重要，是因为它放松了经济研究中经常使用的任意假设，从而使研究人员能够获得更准确和现实的结果。第二个话题很重要，因为经济数据往往包含很多变数。人们很少事先清楚哪些变量与感兴趣的问题相关，而关于使用哪些变量的决定通常是相当武断的。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可靠性更高的结果。第三个主题将提出估计需求函数的改进方法。这对于评估经济政策干预的效果很重要，包括税收和价格的变化。

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.