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

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.