Collaborative Research: Inference Methods for Machine Learning and High-Dimensional Data in Policy Evaluation and Structural Economic Models

经验经济学的大部分重点是估计经济政策的因果效应或弹性等基础经济模型的特征，并得出可信的推论。研究人员用来帮助完成这项任务的数据类型日益丰富和复杂。虽然这些增加的数据资源带来了许多新的机会，但它们也带来了额外的挑战，因为研究人员必须使用数据简化技术--例如，来自“大数据”分析的技术--以使分析复杂的数据和模型变得可行和信息丰富，而天真地应用这些技术可能会使关于经济影响的结论无效。这一研究项目将建立一个一般的、正式的框架，为估计和推理工具的构建提供指导，并适当使用来自“大数据”或数据挖掘的工具，以提供关于感兴趣的经济对象的可靠结论。拟议的研究将提供方法和相应的理论保证，以涵盖在经济学和社会科学的实证研究中遇到的各种情况，提供实证应用，并在社会科学中流行的统计软件包中提供可用的软件。因此，理论和实证工作将有助于弥合社会科学实践与“大数据”之间的差距，并将提供提高所得出科学结论可信度的方法。拟议的研究将在高维统计建模和应用社会科学研究之间架起桥梁。将高维方法与经济上相关的建模框架和目标相结合，对于为研究人员提供工具非常重要，这些工具可以用于分析现代、复杂的数据，并提供关于感兴趣对象的可靠推理陈述。所提出的研究将推动正则化推理理论的发展，正则化推理是现代大数据集推理的关键要素。该研究项目的主要目的是通过提供一个包罗万象的框架，包括有趣的非线性模型和估计过程，如最大似然法和广义矩方法，来推广关于感兴趣的低维目标参数的推断的现有结果。我们还将提供一个扩展，以涵盖感兴趣的目标是函数值的情况，例如当感兴趣的是一组分位数处理范围内的分位数处理效果时。这一进展将扩大高维方法在目标是对模型参数集进行推断的应用中的应用的前沿。这种扩展即使在低维模型中也是有用的，而且随着大型、复杂的数据集变得更容易获得，这种扩展可能会变得至关重要。除了提供理论结果外，本研究还旨在为这些方法的应用提供R和STATA的说明性实证实例和软件。

Much of empirical economics focuses on estimating and drawing credible inferences about the causal effects of economic policies or about features of underlying economic models such as elasticities. The type of data that researchers have at their disposal to aid in this task is increasingly rich and complex. While these increased data resources open up many new opportunities, they also pose additional challenges as researchers must employ data-reduction techniques - for example, techniques from the analysis of "big data" - to make analyzing complex data and models feasible and informative, and naïve application of such techniques may render conclusions drawn about economic effects invalid. This research project will establish a general, formal framework to provide guidance about construction of estimation and inference devices coupled with appropriate use of tools from "big data" or data-mining that will deliver reliable conclusions about economic objects of interest. The proposed research will present the methods and corresponding theoretic guarantees to cover a variety of situations encountered in empirical research in economics and the social sciences, offer empirical applications, and provide usable software in statistical packages popular within the social sciences. The theoretical and empirical work will thus help bridge the gap between social science practice and "big data", and will provide methods that will enhance the credibility of the drawn scientific conclusions. The proposed research will provide bridges between high-dimensional statistical modeling and applied social science research. Integrating high-dimensional methods with economically relevant modeling frameworks and targets is important in providing researchers tools which can be used to analyze modern, complex data and provide reliable inferential statements about the objects of interest. The proposed research will advance the theory of inference following regularization which is a key element to inference in modern, large data sets. The main goal of this research project is to generalize available results about inference for a low-dimensional target parameter of interest by providing an encompassing framework that will include interesting nonlinear models and estimation procedures such as maximum likelihood and generalized method of moments. We will also provide an extension to cover cases where the target of interest is function valued, such as when interest is in a set quantile treatment effects across a range of quantile indices. This advancement will expand the frontier for applications of high-dimensional methods in applications where inference about sets of model parameters is the goal. This expansion is useful even in low-dimensional models and is likely to become crucial as large, complicated data sets become more readily available. In addition to providing theoretical results, the research aims to provide illustrative empirical examples and software in both R and Stata for application of these methods.