Research in Econometric Methods

计量经济学方法研究

• 批准号: 0001706
• 负责人: Donald Andrews
• 金额: $ 20.05万
• 依托单位: Yale University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2001
• 资助国家: 美国
• 起止时间: 2001-03-15 至 2004-09-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0001706&HistoricalAwards=false
• 关键词: Research; Econometric; Methods

This proposal describes research on several new topics and continued research in several areas. First, the PI will consider bias-reduced semiparametric estimation of the long memory parameter 'd'. The most common estimator of this parameter, the Geweke and Porter-Hudak (GPH) estimator, has been found to have substantial finite sample bias. The PI and P. Guggenberger, a graduate student at Yale, will develop an alternative GPH estimator whose bias is reduced by an order of magnitude, whose variance is increased only by a multiplicative constant, and whose rate of convergence is faster than that of the GPH estimator. We plan to establish the optimal rate of convergence of estimators of 'd' when the normalized spectral density is smooth of order s at zero and show that the bias-reduced GPH estimator attains this rate, but, for s 2, the GPH estimator does not. Working with Yixiao Sun, a graduate student at Yale, the PI will develop a local polynomial Whittle estimator that behaves like other local Whittle estimators, but has reduced bias and a faster rate of convergence.The second area of proposed research is on the bootstrap for nonlinear estimators. This research continues work already reported by the PI.. We aim to obtain higher-order improvements for bootstrapping minimum distance and indirect inference estimators, stronger higher-order improvement results for the iid nonparametric bootstrap than those currently available, and new results for residual-based and BCa bootstraps and Lagrange multiplier (LM) and likelihood ratio (LR) tests.The third area of research is to develop some new asymptotic optimality properties of the classical LM, LR, and Wald tests. The idea is to generalize the finding that the LM test for serial correlation against AR(1) errors is the same as that against MA(1) errors. This finding implies that the LM, LR, and Wald tests have Wald-type asymptotic optimality properties for testing against both AR(1) and MA(1) errors. Results of this type hold more generally, both in this model and in many other models. The object of the proposed research is to obtain some general results that determine different classes of alternative models for which a given LM, LR, or Wald test has asymptotic optimality properties.The fourth area of proposed research continues the PI's research on testing problems when a parameter is on the boundary of the maintained hypothesis and a parameter appears under the alternative but not under the null hypothesis. Numerous examples of such problems already exist, and we believe that problems of this sort will become increasingly prevalent as researchers rely more and more on nonlinear models. We aim to show that the LR, LM, and Wald tests are asymptotically admissible, develop new tests that maximize weighted average power for certain weight functions, construct a complete class of tests, and establish the asymptotic null distribution of the LR, LM, and Wald tests in the Markov regime switching model. Finally, we plan to show that the LR, LM, and Wald tests for testing for conditional heteroskedasticity of GARCH(1, 1) form are consistent against any form of serial correlation in the squared errors.

该提案描述了几个新主题的研究以及多个领域的持续研究。 首先，PI 将考虑长记忆参数“d”的偏差减少半参数估计。该参数最常见的估计量 Geweke 和 Porter-Hudak (GPH) 估计量已被发现具有显着的有限样本偏差。 PI 和耶鲁大学研究生 P. Guggenberger 将开发一种替代的 GPH 估计器，其偏差减少了一个数量级，其方差仅增加乘法常数，并且其收敛速度比GPH 估计器。我们计划建立当归一化谱密度在 0 级平滑时 'd' 估计器的最佳收敛速率，并表明偏差减少的 GPH 估计器达到此速率，但是，对于 s 2，GPH 估计器确实不是。 PI 将与耶鲁大学研究生 Yixiao Sun 合作，开发一种局部多项式 Whittle 估计器，其行为与其他局部 Whittle 估计器类似，但减少了偏差并提高了收敛速度。拟议研究的第二个领域是引导非线性估计器。这项研究继续 PI 已经报告的工作。我们的目标是获得引导最小距离和间接推理估计器的高阶改进，独立同分布非参数引导的比当前可用的更强的高阶改进结果，以及残差的新结果。基于 BCa 引导以及拉格朗日乘子 (LM) 和似然比 (LR) 检验。第三个研究领域是开发经典 LM、LR 和 Wald 的一些新的渐近最优性属性测试。这个想法是概括这一发现：针对 AR(1) 错误的序列相关性的 LM 测试与针对 MA(1) 错误的序列相关性的 LM 测试相同。这一发现意味着 LM、LR 和 Wald 检验具有 Wald 型渐近最优性，可用于测试 AR(1) 和 MA(1) 误差。这种类型的结果在该模型和许多其他模型中都更普遍。拟议研究的目的是获得一些一般结果，以确定给定 LM、LR 或 Wald 检验具有渐近最优性属性的不同类别的替代模型。拟议研究的第四个领域继续 PI 在以下情况下对测试问题的研究：参数位于维持假设的边界上，并且参数出现在备择假设下，但不在原假设下。 此类问题的例子已经存在，而且我们相信，随着研究人员越来越依赖非线性模型，此类问题将变得越来越普遍。我们的目标是证明 LR、LM 和 Wald 检验是渐近可接受的，开发新的检验来最大化某些权重函数的加权平均功效，构建一类完整的检验，并建立 LR、LM 和 Wald 的渐近零分布Wald 在马尔可夫政权切换模型中进行测试。 最后，我们计划证明用于测试 GARCH(1, 1) 形式的条件异方差性的 LR、LM 和 Wald 检验对于平方误差中任何形式的序列相关性都是一致的。