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Unformatted text preview: 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) inuentially 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 dont change much is taken to be evidence 1 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....
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