Inference in Econometric Models with Asymptotic Discontinuities

本文研究基于统计量的推理问题，其渐近分布是产生观测值的真分布的不连续函数。计量经济学和其他统计领域的许多问题都表现出这一特征。该建议涉及(i)开发新的和改进的基于具有渐近不连续的统计推断的一般方法，以及（ii）对出现渐近不连续的特定模型的进一步分析。开发了不基于子抽样或m out of n自举的一般方法。这样做的动机是有理由相信，在具有渐近不连续的模型中，子抽样和m / n的基于自举的测试不能提供尽可能高的功率。此外，众所周知，后一种方法在渐近大小上表现出相对较大的误差。相当多的精力将投入到力矩不平等模型。对于这样的模型，本项目研究了一类新的广义矩选择程序和递归尺寸校正程序。该项目介绍了条件矩不等式模型的新程序。在非线性回归、ARMA（1,1）、阈值AR和随机优势模型中，它分析了现有的并开发了新的置信集和检验，所有这些模型都表现出渐近不连续。最后，本课题研究了渐近不连续情况下不确定性估计量和测度的渐近风险。在另一个主题上，本项目结合Ibragimov and m<e:1>(2006)和Andrews（2004）的思想，研究了一种新的异方差和自相关（HAC）推断方法。最后，该项目继续安德鲁斯、莫雷拉和斯托克（2006）发起的关于弱仪器最优推理的研究。本研究的重点是在异方差存在下的推理。拟议研究的更广泛影响包括以下方面。(i)拟议的研究将通过改进经验方法使社会受益，从而导致更准确的经验研究，从而使政策分析更有根据。这项研究将通过利用研究生作为研究助理和合作研究人员以及通过编制与赞助研究有关的讲稿来促进教学和训练。研究将涉及在经济学和计量经济学方面代表性不足的群体，特别是妇女。PI将与之合作的四名研究生，即徐成，段亚欣，朴善英和施晓霞，是女性。这项研究将通过提供新的计算机软件供专业人员使用来加强基础设施。研究结果将通过在国际会议上发表的方式广泛传播

This proposal deals with the problem of inference based on statistics whose asymptotic distributions are discontinuous functions of the true distribution that generates the observations. Numerous problems in econometrics and other areas of statistics exhibit this feature. The proposal involves a combination of (i) the development of new and improved general methods for inference based on statistics with asymptotic discontinuities and (ii) further analysis of particular models where asymptotic discontinuities arise. General methods that are not based on subsampling or the m out of n bootstrap are developed. The motivation for this is that there are reasons to believe that subsampling and m out of n bootstrap-based tests do not provide as high power as is possible in models with asymptotic discontinuities. In addition, the latter methods are well known to exhibit relatively large errors in asymptotic size.Considerable effort will be devoted to moment inequality models. For such models, this project investigates a new class of generalized moment selection procedures and recursive size-correction procedures. The project introduces new procedures for conditional moment inequality models. It analyzes existing and develops new confidence sets and tests in nonlinear regression, ARMA(1, 1), threshold AR, and stochastic dominance models, all of which exhibit asymptotic discontinuities. Finally, this project undertakes research on the asymptotic risk of estimators and measures of uncertainly in the context of asymptotic discontinuities.On a different topic, this project studies a new method of heteroskedasticity and autocorrelation (HAC) inference based on combining ideas in Ibragimov and Müller (2006) and Andrews (2004). Finally, the project continues research initiated in Andrews, Moreira, and Stock (2006) on optimal inference with weak instruments. This research focuses on inference in the presence of heteroskedasticity.The broader impact of the proposed research includes the following. (i) The proposed research will benefit society through improved empirical methods that lead to more accurate empirical research and, consequently, better informed policy analysis.(ii) The research will promote teaching and training through the use of graduate students as research assistants and collaborative researchers and through the development of lecture notes related to the sponsored research. (iii) The research will involve groups that are under-represented in economics and econometrics, in particular women. Four of the graduate students that the PI will work with, viz., Xu Cheng, Yaxin Duan, Sun-Young Park, and Xiaoxia Shi, are women. (iv) The research will enhance infrastructure by making new computer software available for use by the profession. (v) The results of the research will be disseminated broadly via presentation at international conferences