Three Projects in Econometric Theory

计量经济学理论的三个项目

• 批准号: 1627660
• 负责人: Ulrich Mueller
• 金额: $ 19.93万
• 依托单位: Princeton University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2016
• 资助国家: 美国
• 起止时间: 2016-08-01 至 2019-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1627660&HistoricalAwards=false
• 关键词: Three; Projects; Econometric; Theory

Most empirical methods in economics and the social sciences derive their validity from the thought experiment on how they would perform in very large samples. The implicit hope is that ensuring good performance in large samples leads to acceptable performance in moderately small data sets as well. For some inference problems, however, it is known that the standard large sample approximation is too inaccurate to be a reliable guide for the sample sized typically encountered in empirical work. As a constructive remedy, it is sometimes possible to embed the original problem in an alternative large sample approximation that better captures the small sample features. This project aims at developing such alternative large sample approximations in three empirically relevant econometric problems: How to conduct inference with persistent time series; how to account for the presence of a large number of control variates in a linear regression; and how to conduct inference about the probability and properties of extreme events. Recent advances in econometric theory often consider sequences of parameter or tuning parameter values that lead to a different form of large sample approximations. Prominent examples include weak instrument asymptotics, local-to-unity time series asymptotics where the largest autoregressive root takes on values ever closer to one, and heteroskedasticity and autocorrelations robust inference with a bandwidth equal to a fixed fraction of the sample size. This research develops similar alternative asymptotics in three distinct inference problems: The first project generalizes the local-to-unity model by letting p autoregressive roots, as well as p-1 MA roots, converge to unity at the appropriate rate. The second project studies inference about a linear regression coefficient in the presence of a large number of potential controls, where the control coefficients are known to satisfy a particular L_2 bound that can be interpreted as a bound on the R^2 in a regression of the outcome on the controls. The third project concerns the problem of inference about tail properties based on an i.i.d. sample, under the sole assumption that extreme value theory to hold for the largest k observations, for a given and fixed k.

经济学和社会科学方面的大多数经验方法从思想实验中得出了他们在很大的样本中的表现的有效性。隐含的希望是，确保大型样本中的良好性能也会导致中等小的数据集的可接受性能。但是，对于某些推断问题，众所周知，标准的大样本近似值太不准确，无法成为经验工作中通常遇到的样本大小的可靠指南。作为一种建设性的补救措施，有时可以将原始问题嵌入到替代大型样本近似中，以更好地捕获小样本特征。该项目旨在在三个经验相关的计量经济学问题中开发这种替代大型样本近似值：如何使用持续时间序列进行推理；如何考虑线性回归中大量控制变化的存在；以及如何对极端事件的概率和特性进行推断。计量经济学理论的最新进展通常考虑参数或调谐参数值的序列，这些序列导致不同形式的大样本近似值。突出的例子包括较弱的仪器渐近学，局部到统一的时间序列渐近器，其中最大的自回归根均具有越来越接近一个的值，以及异性和自相关性可靠的鲁棒性推断，带宽等于相当于样本尺寸的固定分数。这项研究在三个不同的推论问题中开发了类似的替代渐近学：第一个项目通过让P自回旋根和P-1 MA根来概括局部对不合性模型，以适当的速度融合到统一。第二个项目研究在存在大量潜在控制的情况下对线性回归系数的推断，其中已知控制系数可以满足特定的L_2结合，该结合可以解释为在控件上结果回归中的r^2上的结合。第三个项目涉及基于I.I.D.尾部属性的推断问题。在给定k和固定k的唯一假设中，样本是最大的k观测值的极值理论。