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Estimation and Testing Using Jackknife IV in Heteroskedastic Regressions With Many Weak Instruments


  • John Chao

    () (University of Maryland)

  • Norman Swanson

    () (Rutgers University)


This paper develops Wald type tests for general possibly nonlinear restrictions, in the context of heteroskedastic IV regression with many weak instruments. In particular, it is ¯rst shown that consistency and asymptotically normality can be obtained when estimating structural parameters using JIVE, even when errors exhibit heteroskedasticity of unkown form. This is not the case, however, with other well known IV estimators, such as LIML, Fuller's modi¯ed LIML, 2SLS, and B2SLS, which are shown to be inconsistent. Second, new covariance matrix estimators (and corresponding Wald test statistics) are proposed for JIVE, which are consistent even when instrument weakness is such that the rate of growth of the concentration parameter, rn is slower than the rate of growth of the the number of instruments, Kn and possibly much slower than the sample size, n, provided that (Kn)^.5 /rn, rn goes to 0 as n goes to infinity. The primary advantage of our tests, relative to those proposed previously in the literature, is that one can test general nonlinear hypotheses, as opposed to simple null hypotheses of the form H0: Beta=Beta star, where beta star is the value of beta under the null. We feel that this feature, taken together with the fact that the tests are robust to unconditional heteroskedasticity, is important from the perspective of empirical application, given that general linear and nonlinear hypotheses are often of interest to empirical researchers, and given that heteroskedasticity is prevalent, particularly in microeconomic datasets.

Suggested Citation

  • John Chao & Norman Swanson, 2004. "Estimation and Testing Using Jackknife IV in Heteroskedastic Regressions With Many Weak Instruments," Departmental Working Papers 200420, Rutgers University, Department of Economics.
  • Handle: RePEc:rut:rutres:200420

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    References listed on IDEAS

    1. Whitney K. Newey & Richard J. Smith, 2004. "Higher Order Properties of Gmm and Generalized Empirical Likelihood Estimators," Econometrica, Econometric Society, vol. 72(1), pages 219-255, January.
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    3. Blomquist, Soren & Dahlberg, Matz, 1999. "Small Sample Properties of LIML and Jackknife IV Estimators: Experiments with Weak Instruments," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 14(1), pages 69-88, Jan.-Feb..
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    6. Smith, Richard J, 1997. "Alternative Semi-parametric Likelihood Approaches to Generalised Method of Moments Estimation," Economic Journal, Royal Economic Society, vol. 107(441), pages 503-519, March.
    7. Angrist, Joshua D & Krueger, Alan B, 1995. "Split-Sample Instrumental Variables Estimates of the Return to Schooling," Journal of Business & Economic Statistics, American Statistical Association, vol. 13(2), pages 225-235, April.
    8. Marcelo J. Moreira, 2003. "A Conditional Likelihood Ratio Test for Structural Models," Econometrica, Econometric Society, vol. 71(4), pages 1027-1048, July.
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    17. John C. Chao & Norman R. Swanson, 2003. "Asymptotic Normality of Single-Equation Estimators for the Case with a Large Number of Weak Instruments," Departmental Working Papers 200312, Rutgers University, Department of Economics.
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    Cited by:

    1. Paul J. Devereux & Daniel A. Ackerberg, 2006. "Comment on 'The case against JIVE'," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(6), pages 835-838.
    2. Hansen, Christian & Hausman, Jerry & Newey, Whitney, 2008. "Estimation With Many Instrumental Variables," Journal of Business & Economic Statistics, American Statistical Association, vol. 26, pages 398-422.
    3. Whitney K. Newey & Frank Windmeijer, 2005. "GMM with many weak moment conditions," CeMMAP working papers CWP18/05, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    4. Daniel A. Ackerberg & Paul J. Devereux, 2009. "Improved JIVE Estimators for Overidentified Linear Models with and without Heteroskedasticity," The Review of Economics and Statistics, MIT Press, vol. 91(2), pages 351-362, May.
    5. Jaeger, David A. & Parys, Juliane, 2009. "On the Sensitivity of Return to Schooling Estimates to Estimation Methods, Model Specification, and Influential Outliers If Identification Is Weak," IZA Discussion Papers 3961, Institute for the Study of Labor (IZA).

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    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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