{"title":"A Practical Method for Testing Many Moment Inequalities","authors":"Yuehao Bai, Andrés Santos, A. Shaikh","doi":"10.2139/ssrn.3454610","DOIUrl":null,"url":null,"abstract":"This paper considers the problem of testing a finite number of moment inequalities. For this problem, Romano et al. (2014) propose a two-step testing procedure. In the first step, the procedure incorporates information about the location of moments using a confidence region. In the second step, the procedure accounts for the use of the confidence region in the first step by adjusting the significance level of the test appropriately. An important feature of the proposed method is that it is “practical” in the sense that it remains computationally feasible even if the number of moments is large. Its justification, however, has so far been limited to settings in which the number of moments is fixed with the sample size. In this paper, we provide weak assumptions under which the same procedure remains valid even in settings in which there are “many” moments in the sense that the number of moments grows rapidly with the sample size. We confirm the practical relevance of our theoretical guarantees in a simulation study. We additionally provide both numerical and theoretical evidence that the procedure compares favorably with the method proposed by Chernozhukov et al. (2019), which has also been shown to be valid in such settings.","PeriodicalId":11465,"journal":{"name":"Econometrics: Econometric & Statistical Methods - General eJournal","volume":"1 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2019-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"13","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Econometrics: Econometric & Statistical Methods - General eJournal","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.2139/ssrn.3454610","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 13
Abstract
This paper considers the problem of testing a finite number of moment inequalities. For this problem, Romano et al. (2014) propose a two-step testing procedure. In the first step, the procedure incorporates information about the location of moments using a confidence region. In the second step, the procedure accounts for the use of the confidence region in the first step by adjusting the significance level of the test appropriately. An important feature of the proposed method is that it is “practical” in the sense that it remains computationally feasible even if the number of moments is large. Its justification, however, has so far been limited to settings in which the number of moments is fixed with the sample size. In this paper, we provide weak assumptions under which the same procedure remains valid even in settings in which there are “many” moments in the sense that the number of moments grows rapidly with the sample size. We confirm the practical relevance of our theoretical guarantees in a simulation study. We additionally provide both numerical and theoretical evidence that the procedure compares favorably with the method proposed by Chernozhukov et al. (2019), which has also been shown to be valid in such settings.
研究了有限个矩不等式的检验问题。针对这个问题,Romano et al.(2014)提出了一个两步测试程序。在第一步中,该程序使用置信区域合并关于矩的位置的信息。在第二步中,该程序通过适当调整测试的显著性水平来解释第一步中置信区域的使用。所提出的方法的一个重要特征是它是“实用的”,即即使矩的数量很大,它仍然在计算上可行。然而,到目前为止,它的理由仅限于矩数与样本量固定的设置。在本文中,我们提供了一些弱假设,在这些假设下,即使在存在“许多”矩的情况下,即矩的数量随着样本量的增加而迅速增长,相同的过程仍然有效。我们在模拟研究中证实了我们的理论保证的实际相关性。此外,我们还提供了数值和理论证据,证明该程序优于Chernozhukov等人(2019)提出的方法,该方法也被证明在这种情况下是有效的。