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Robustness Checks

Robustness Checks - Robustness Checks and Robustness Tests...

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Robustness Checks and Robustness Tests in Applied Economics Halbert White Xun Lu Department of Economics University of California, San Diego June 18, 2010 Abstract A common exercise in empirical studies is a "robustness check," where the researcher examines how certain "core" regression coe¢ cient estimates behave when the regression speci°cation is modi°ed by adding or removing regressors. If the coe¢ cients are plausible and robust, this is commonly interpreted as evidence of structural validity. Here, we study when and how one can infer structural validity from coe¢ cient robustness and plausibility. As we show, there are numerous pitfalls, as commonly implemented robustness checks give neither necessary nor su¢ cient evidence for structural validity. Indeed, if not conducted properly, robustness checks can be completely uninformative or entirely misleading. We discuss how critical and non-critical core variables can be properly speci°ed and how non- core variables for the comparison regression can be chosen to ensure that robustness checks are indeed structurally informative. We provide a straightforward new Hausman (1978)- type test of robustness for the critical core coe¢ cients, additional diagnostics that can help explain why robustness test rejection occurs, and a new estimator, the Feasible Optimally combined GLS (FOGLeSs) estimator, that makes relatively e¢ cient use of the robustness check regressions. A new procedure for Matlab, testrob , embodies these methods. 1 Introduction A now common exercise in empirical studies is a "robustness check," where the researcher exam- ines how certain "core" regression coe¢ cient estimates behave when the regression speci°cation is modi°ed in some way, typically by adding or removing regressors. Leamer (1983) in±uentially advocated investigations of this sort, arguing that "fragility" of regression coe¢ cient estimates is indicative of speci°cation error, and that sensitivity analyses (i.e., robustness checks) should be routinely conducted to help diagnose misspeci°cation. Such exercises are now so popular that standard econometric software has modules designed to perform robustness checks automatically; for example, one can use the STATA commands rcheck or checkrob . A °nding that the coe¢ cients don²t change much is taken to be evidence 1
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that these coe¢ cients are "robust." 1 If the signs and magnitudes of the estimated regression coe¢ cients are also plausible, this is commonly taken as evidence that the estimated regression coe¢ cients can be reliably interpreted as the true causal e/ects of the associated regressors, with all that this may imply for policy analysis and economic insight. Examples are pervasive, appearing in almost every area of applied econometrics. For exam- ple, of the 98 papers published in The American Economic Review during 2009, 76 involve some data analysis. Of these, 23 perform a robustness check along the lines just described, using a
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