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Estimation with Valid and Invalid Instruments


  • Jinyong Hahn
  • Jerry Hausman


We demonstrate analytically that for the widely used simultaneous equation model with one jointly endogenous variable and valid instruments, 2SLS has smaller MSE error, up to second order, than OLS unless the R², or the F statistic of the reduced form equation is extremely low. We also consider the relative bias of estimators when the instruments are invalid, i.e. the instruments are correlated with the stochastic disturbance. Here, both 2SLS and OLS are biased in finite samples and inconsistent. We investigate conditions under which the approximate finite sample bias or the MSE of 2SLS is smaller than the corresponding statistics for the OLS estimator. We again find that 2SLS does better than OLS under a wide range of conditions, which we characterize as functions of observable statistics and one unobservable statistic.

Suggested Citation

  • Jinyong Hahn & Jerry Hausman, 2005. "Estimation with Valid and Invalid Instruments," Annals of Economics and Statistics, GENES, issue 79-80, pages 25-57.
  • Handle: RePEc:adr:anecst:y:2005:i:79-80:p:25-57

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    Cited by:

    1. Zi-Yi Guo, 2017. "Health Insurance and the Demand for Medical Care: a Case Study from China," Asian Journal of Economics and Empirical Research, Asian Online Journal Publishing Group, vol. 4(1), pages 8-13.
    2. Lee, Seojeong, 2014. "Asymptotic refinements of a misspecification-robust bootstrap for generalized method of moments estimators," Journal of Econometrics, Elsevier, vol. 178(P3), pages 398-413.
    3. Guo, Zijian & Kang, Hyunseung & Cai, T. Tony & Small, Dylan S., 2018. "Testing endogeneity with high dimensional covariates," Journal of Econometrics, Elsevier, vol. 207(1), pages 175-187.
    4. Qichun He, 2011. "Does FDI Promote Human Capital Accumulation? The Role of Gradual Financial Liberalization," CEMA Working Papers 455, China Economics and Management Academy, Central University of Finance and Economics.
    5. Lukáš Lafférs, 2019. "Identification in Models with Discrete Variables," Computational Economics, Springer;Society for Computational Economics, vol. 53(2), pages 657-696, February.

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