Numerical Bootstrap and Constrained Estimation

数值引导和约束估计

• 批准号: 1658950
• 负责人: Han Hong
• 金额: $ 17.43万
• 依托单位: Stanford University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2017
• 资助国家: 美国
• 起止时间: 2017-07-01 至 2022-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1658950&HistoricalAwards=false
• 关键词: Numerical; Bootstrap; Constrained; Estimation; Numerical; Bootstrap; Constrained; Estimation

Many economic models used for policy evaluation are highly nonlinear, and are typically subject to nonlinear constraints on the parameters. The computational challenge in estimating these models has posed a significant obstacle for utilizing these models in effective policy making. This project assists in economic policy making by developing a new method of statistical inference that can be used to provide valid evaluation of the statistical uncertainty associated with policy-related functions of estimated parameters of economic models. This new method combines one-sided numerical differentiation with bootstrap resampling techniques to allow for non-differentiability in the policy function, and is both computationally simple and easy to implement. It can be applied to analyze oligopolistic competition in industrial organization, the effect of education policy such as the impact of smaller class sizes, and many other areas of applied economic analysis. These tools contribute to the welfare of the society by enabling models to evaluate the effectiveness of economic policies. This project studies a numerical Delta method for inference on a directionally differentiable function of regular parameters. This method is computationally efficient, does not require analytic knowledge of the structure of the function of interest, and provides uniformly valid inference for testing a one-sided hypothesis of a convex function of the parameters. In situations where the first order Delta method limiting distribution is degenerate, the second (or higher) order Delta method may provide the necessary nondegenerate large sample approximation. The investigator further generalizes the numerical Delta method to a new resampling technique called the numerical bootstrap that can consistently estimate the limit distribution in many cases -- where the conventional bootstrap is not valid and subsampling has been the most commonly used inference approach, and where the parameters are not known to be directionally differentiable. Applications include constrained and unconstrained M-estimators converging at both regular and nonstandard rates such as the maximum score model, partially identified models, misspecified simulated GMM models, and many sample size dependent statistics.

用于政策评估的许多经济模型都是高度非线性的，通常受到参数的非线性限制。估计这些模型的计算挑战为利用这些模型进行有效政策制定带来了重要的障碍。该项目通过开发一种新的统计推断方法来帮助制定经济政策，该方法可用于对与经济模型的估计参数的策略相关功能相关的统计不确定性进行有效评估。这种新方法将单方面的数值差异与引导程序重新采样技术相结合，以允许在策略函数中差异性，并且在计算上都是简单且易于实现的。它可以应用于分析工业组织中的寡头竞争，教育政策的效果，例如较小的阶级规模的影响以及许多其他应用经济分析领域。这些工具通过使模型能够评估经济政策的有效性来促进社会的福利。该项目研究了一种用于推断常规参数的定向可区分函数的数值增量方法。该方法在计算上是有效的，不需要对感兴趣函数的结构进行分析知识，并且为测试参数的凸功能的单方面假设提供了统一的有效推断。在第一阶数字限制分布分布的情况下，第二（或更高）阶的Delta方法可能会提供必要的非排定大型样品近似值。研究人员进一步将数值增量方法推广到一种称为数值引导程序的新的重采样技术，该技术可以始终如一地估计限制分布，而在许多情况下，传统的引导程序无效，并且亚次采样是最常用的推论方法，而在参数中不知道该参数是方向差异的。应用程序包括以常规和非标准速率收敛的受约束和无约束的M估计器，例如最大分数模型，部分鉴定的模型，误指定的模拟GMM模型以及许多依赖样本量的统计量。