 Including the Instruments in the Regression is the Hausman TestMark Stater and Christopher Hoag Annals of Economics and Statistics, 2023, issue 152, 43-64 Abstract: The Hausman test evaluates the potential endogeneity of a regressor by examining an artificial regression that includes the residuals from a first-stage regression of the endogenous variable on the available instruments. We highlight a conceptually simpler way to compute the Hausman test statistic: include the instruments in the original regression. When the model with potentially endogenous variables is exactly identified, a test of statistical significance on the coefficients of the residuals in the artificial regression algebraically equals the test of statistical significance on the coefficients of the instruments included in the original regression. The test statistic equality holds across multiple classical tests, including robust or cluster-robust versions of the Wald test, the robust score test, and the likelihood ratio test. We then modify the original Hausman test to extend the result to the overidentified case. Adding the instruments to the original regression provides a simple method of computing the Hausman test. Keywords: Hausman Test; Instrumental Variables (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:adr:anecst:y:2023:i:152:p:43-64 DOI: 10.2307/48754784 Access Statistics for this article Annals of Economics and Statistics is currently edited by Laurent Linnemer More articles in Annals of Economics and Statistics from GENES Contact information at EDIRC. |
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