Collaborative Research: Research on Distibutional and Quantile Methods in Econometrics

该项目有两个相互关联的目的：首先，分析正则化技术，在函数的估计和数值逼近中施加形状限制。更具体地说，项目的这一部分研究了对回归、分布和分位数曲线施加单调性和其他形状限制的技术。该项目的第二个目的包括使用正则化条件分位数回归方法进行政策分析。特别是，这一部分发展推理方法来分析反事实政策的影响，或者将变化对利益结果的分布的影响分解为决定该结果的因素的差异（构成效应）和这些因素的影响差异（结构效应）。例如，如果黑人母亲与白人母亲具有相同的经济和健康特征，婴儿出生体重的分布会是怎样的？诸如怀孕期间和产前吸烟数量等因素的贡献是什么？白人母亲和黑人母亲在婴儿出生体重上的差异。该项目主要集中在以下五个部分：(1)分布和分位数估计器的正则化技术；(2)回归估计正则化技术的性质；(3)统计学应用：Edgeworth和Cornish Fisher展开式的正则化；(4)正则化估计的经济应用：收益率曲线、生产和需求函数以及分配效应的工具变量推断；(5)正则化反事实分布的推理。更广泛的影响：建议的正则化技术易于实现，并且期望被从业者常规使用。因此，例如，基于项目第一部分的单调化分位数回归估计的例程已经在免费软件R的分位数回归包中可用（它是免费公开可用的）。反事实分析的推理方法也有望产生广泛的影响，因为这种类型的分析通常用于劳动经济学和其他领域。该项目的最终目的是在R中生成实现所开发的所有方法的公共软件。该项目还将通过两名研究生的帮助产生直接的教育影响。其中一名研究生已成为该项目的第(1)、(2)和(3)部分的合著者；另一名研究生（如果获得批准，将由本项目资助）将成为第(4)部分的共同作者。

The project has two interrelated purposes: First, to analyze regularization techniques to impose shape restrictions in the estimation and numeric approximation of functions. More specifically, this part of the project studies techniques to impose monotonicity and other shape restrictions to regression, distribution, and quantile curves. The second purpose of the project consists of using regularized conditional quantile regression methods for policy analysis. In particular, this part develops inference methods to analyze the effect of counterfactual policies, or to decompose the effect of changes on the distribution of an outcome of interest across time or across subpopulations in differences of factors determining this outcome (composition effect) and differences on the effect of these factors (structure effect). For example, what would have been the distribution of infant birth weights for black mothers had they had the same economic and health characteristics as white mothers, what is the contribution of factors such as number of cigarettes smoked during pregnancy and pre?]natal care to the difference in infant birth weights between white and black mothers.The project is focused on the following five parts:(1) Regularization techniques for distribution and quantile estimators;(2) Properties of regularization techniques for regression estimates;(3) Statistical applications: regularization of Edgeworth and Cornish Fisher expansions;(4) Economic applications of regularized estimates: yield curves, production anddemand functions, and instrumental variables inference for distributional effects;(5) Inference on regularized counterfactual distributions.Broader Impacts: The regularization techniques proposed are simple to implement and expected to be routinely used for practitioners. Thus, for example, a routine to monotonize quantile regression estimates based on the first part of the project is already available in the quantile regression package of freeware software R (which is publicly available at no cost). The inference methods for counterfactual analysis are also expected to have a broad impact since this type of analysis is commonly used in labor economics and other fields. A final purpose of the project is to produce public software in R that implements all the methods developed. The project will also have direct educational impact by involving help of two graduate students. One of the graduate students is already working as co-author of the parts (1), (2), and (3) of the project; and the other graduate student (to be funded by this project, if approved) will be coauthor for parts (4).