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A New Matrix Statistic for the Hausman Endogeneity Test under Heteroskedasticity

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  • Alecos Papadopoulos

    (Department of Economics, Athens University of Economics and Business, TK 10434 Athens, Greece)

Abstract

We derive a new matrix statistic for the Hausman test for endogeneity in cross-sectional Instrumental Variables estimation, that incorporates heteroskedasticity in a natural way and does not use a generalized inverse. A Monte Carlo study examines the performance of the statistic for different heteroskedasticity-robust variance estimators and different skedastic situations. We find that the test statistic performs well as regards empirical size in almost all cases; however, as regards empirical power, how one corrects for heteroskedasticity matters. We also compare its performance with that of the Wald statistic from the augmented regression setup that is often used for the endogeneity test, and we find that the choice between them may depend on the desired significance level of the test.

Suggested Citation

  • Alecos Papadopoulos, 2023. "A New Matrix Statistic for the Hausman Endogeneity Test under Heteroskedasticity," Econometrics, MDPI, vol. 11(4), pages 1-11, October.
    • Handle: RePEc:gam:jecnmx:v:11:y:2023:i:4:p:23-:d:1257018
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    References listed on IDEAS

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    1. Wu, De-Min, 1973. "Alternative Tests of Independence Between Stochastic Regressors and Disturbances," Econometrica, Econometric Society, vol. 41(4), pages 733-750, July.
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