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.
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