Robust Inference in Panel Data Models. Evidence from the American Economic Review

普通最小二乘(OLS)和两阶段最小二乘(2SLS)是两种广泛使用的线性回归方法。它们的最优性依赖于三个主要假设：严格外生性、不存在完美共线性和同方差。当违反同方差假设时，这两个线性估计仍然是无偏的、一致的和渐近正态分布的，但它们不再有效。因此，研究者不能依赖于用渐近标准误差得出的推断。纠正异方差的一种常见做法是在实证研究中采用稳健的和集群稳健的标准误差(Eicker，1967；Huber，1967；White，1980)。具体地说，在2011年至2015年发表在《美国经济评论》(AER)上的348篇样本文章中，大约70%的文章在横截面和面板数据分析中都使用了稳健的标准误差。然而，在存在影响点的情况下，Eicker-Huber-White估计变得持续向下偏向，特别是在有限样本下。因此，基于过于乐观的标准误差的推断也是无效的。对零假设的过度否定对实证研究产生了巨大的影响，因为它导致了经济学应用著作中的错误结论。也就是说，在传统的1%、5%和10%显著水平下，估计系数可能不再与零有显著差异。根据Efron(1982)的观点，删除一折刀本身应该作为异方差的补救措施，因为它消除了有影响的观测对构造推断的影响。因此，本研究的核心思想是通过比较现有研究中的稳健和折刀标准误差来证明横截面Eicker-Huber-White估计扩展到面板数据的弱点。在这项研究中，我试图回答的主要问题如下：在面板数据模型中，什么条件使稳健推理无效？在存在高杠杆点的情况下，抽样方差的刀切估计器是抽样方差的更好估计器吗？在经验上，我将继续使用荟萃分析方法，以质疑已发表在《美国经济评论》上的论文中所报道的推论的有效性。这个项目的主要目的是证明当数据集包含高杠杆点时，Arellano对横截面Eicker-Huber-White估计的扩展的弱点。然后，我将提出克服异方差对推理的影响的补救措施，并确定一些基本规则，以供实证研究人员进行分析时使用。最后，我将指出那些发表在最负盛名的《经济学评论》(Economics Review)上的论文，这些论文报告的结果带有不正确的推论，可能会破坏研究的最终结论。我将采用的研究方法是荟萃分析方法，我将利用现有的数据集，而不是模拟。本研究主要分为两个阶段，一旦确定了本研究的理论框架，我的工作时间表将准确地遵循研究方法论中解释的两个阶段的程序，本研究试图在其中做出贡献。然后，我将创建一个独特的数据集，其中包含2008-2018年间发表在AER上的所有论文的详细信息；之后，我将开始编写STATA代码，以编程能够检测面板数据模型中的高杠杆点的诊断指标。最后，我将用折刀标准误差代替稳健标准误差来复制符合条件的论文，并对两种结果进行比较。

Ordinary Least Squares (OLS) and Two-Stage Least Squares (2SLS) are two widely used linear regression techniques. Their optimality properties rely on three main assumptions: strict exogeneity, absence of perfect collinearity, and homoskedasticity. When the homoskedastic assumption is violated these two linear estimators remain unbiased, consistent, and asymptotically normally distributed but they are no longer efficient. Consequently, the researcher cannot rely on inference obtained with asymptotic standard errors.A common practice to correct for heteroskedasticity is to adopt robust and cluster-robust standard errors in empirical studies (Eicker, 1967; Huber, 1967; White,1980). Specifically, approximately 70% of articles published in the American Economic Review (AER) between 2011-2015 over a sample of 348 make use of robust standard errors in both cross-sectional and panel data analyses. However, in the presence of influential points the Eicker-Huber-White estimator becomes persistently downward biased, especially in finite samples. Hence, inference based on overly-optimistic standard errors turns out to be invalid as well. The over-rejection of the null hypothesis has a dramatic impact on empirical studies as it leads to incorrect conclusions in applied works in Economics. That is, the estimated coefficients may not be significantly different from zero at the conventional 1%, 5%, and 10% significant levels anymore.According to Efron (1982), the delete-one jackknife itself should be used as a remedy to heteroskedasticity, because it eliminates the effect of the influential observation on inference by construction.Therefore, the core idea of my investigation is to demonstrate the weaknesses of the extension of the cross-sectional Eicker-Huber-White estimator to panel data by comparing inference with robust and jackknife standard errors in already available studies. The main questions I attempt to answer in this study are as follows: What are the conditions that make robust inference invalid in panel data models? Is the jackknife estimator of the sampling variance a better estimator of the sampling variance in the presence of high leverage points? Empirically, I will proceed with a meta-analysis approach in order to question the validity of inference reported in already published papers in the American Economic Review.The primary aim of this project is to demonstrate the weaknesses of the Arellano's extension of the cross-sectional Eicker-Huber-White estimator when the dataset contains high-leverage points. Then, I will propose a remedy to overcome the effects of heteroskedasticity on inference, and identify some basic rules to apply when empirical researchers conduct their analyses. Finally, I will identify those papers, published in one of the most prestigious Economics Review, which report results with incorrect inference that may undermine the final conclusions of the study.The research method I will adopt is a meta-analysis approach, where I will make use of already available datasets instead of simulations. This research is mainly structured in two stages.The schedule of my work will accurately follow the two-stage procedure explained in the research methodology once the theoretical framework, in which this study attempts to give its contribution, has been defined. Then, I will create a unique dataset with the details referring to all papers published in the AER between 2008-2018; after that, I will start working on the Stata codes to program a diagnostic measure able to detect high leverage points in panel data models. Finally, I will replicate eligible papers by using the jackknife standard errors in place of robust standard errors, and compare the two results.