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Sensitivity Analysis of an OLS Multiple Regression Inference with Respect to Possible Linear Endogeneity in the Explanatory Variables, for Both Modest and for Extremely Large Samples

1
Department of Economics, Virginia Polytechnic Institute and State University, Blacksburg, VA 24060, USA
2
Department of Economics, University of Miami, Coral Gables, FL 33146, USA
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Author to whom correspondence should be addressed.
Econometrics 2020, 8(1), 11; https://doi.org/10.3390/econometrics8010011
Received: 14 January 2020 / Revised: 28 February 2020 / Accepted: 2 March 2020 / Published: 16 March 2020
This work describes a versatile and readily-deployable sensitivity analysis of an ordinary least squares (OLS) inference with respect to possible endogeneity in the explanatory variables of the usual k-variate linear multiple regression model. This sensitivity analysis is based on a derivation of the sampling distribution of the OLS parameter estimator, extended to the setting where some, or all, of the explanatory variables are endogenous. In exchange for restricting attention to possible endogeneity which is solely linear in nature—the most typical case—no additional model assumptions must be made, beyond the usual ones for a model with stochastic regressors. The sensitivity analysis quantifies the sensitivity of hypothesis test rejection p-values and/or estimated confidence intervals to such endogeneity, enabling an informed judgment as to whether any selected inference is “robust” versus “fragile.” The usefulness of this sensitivity analysis—as a “screen” for potential endogeneity issues—is illustrated with an example from the empirical growth literature. This example is extended to an extremely large sample, so as to illustrate how this sensitivity analysis can be applied to parameter confidence intervals in the context of massive datasets, as in “big data”. View Full-Text
Keywords: robustness; exogeneity; multiple regression; inference; instrumental variables; large samples; big data robustness; exogeneity; multiple regression; inference; instrumental variables; large samples; big data
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A. Ashley, R.; F. Parmeter, C. Sensitivity Analysis of an OLS Multiple Regression Inference with Respect to Possible Linear Endogeneity in the Explanatory Variables, for Both Modest and for Extremely Large Samples. Econometrics 2020, 8, 11.

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