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Testing Subsets of Structural Parameters in the Instrumental Variables

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  • Frank Kleibergen

    (Brown University and University of Amsterdam)

Abstract

We develop Lagrange multiplier and likelihood ratio statistics to test hypotheses on subsets of the structural parameters in an instrumental variables regression model. The asymptotic distributions of these statistics are robust to instrument quality. A key assumption is, however, that the instruments are valid for the remaining endogenous variables. We show that the statistics lead to 95% confidence sets for the return on education in data from Card (1995) that are considerably different from the confidence sets that result from the 2SLS Wald statistic, which is the common statistic used in the literature. 2004 President and Fellows of Harvard College and the Massachusetts Institute of Technology.

Suggested Citation

  • Frank Kleibergen, 2004. "Testing Subsets of Structural Parameters in the Instrumental Variables," The Review of Economics and Statistics, MIT Press, vol. 86(1), pages 418-423, February.
    • Handle: RePEc:tpr:restat:v:86:y:2004:i:1:p:418-423
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    Citations

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    Cited by:

    1. Donald W. K. Andrews & Patrik Guggenberger, 2015. "Identification- and Singularity-Robust Inference for Moment Condition," Cowles Foundation Discussion Papers 1978, Cowles Foundation for Research in Economics, Yale University.
    2. Mikusheva, Anna, 2013. "Survey on statistical inferences in weakly-identified instrumental variable models," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 29(1), pages 117-131.
    3. Chaudhuri, Saraswata & Zivot, Eric, 2011. "A new method of projection-based inference in GMM with weakly identified nuisance parameters," Journal of Econometrics, Elsevier, vol. 164(2), pages 239-251, October.
    4. Guggenberger, Patrik & Smith, Richard J., 2008. "Generalized empirical likelihood tests in time series models with potential identification failure," Journal of Econometrics, Elsevier, vol. 142(1), pages 134-161, January.
    5. Michael P. Murray, 2006. "Avoiding Invalid Instruments and Coping with Weak Instruments," Journal of Economic Perspectives, American Economic Association, vol. 20(4), pages 111-132, Fall.
    6. Murray Michael P., 2017. "Linear Model IV Estimation When Instruments Are Many or Weak," Journal of Econometric Methods, De Gruyter, vol. 6(1), pages 1-22, January.
    7. Kleibergen, Frank, 2021. "Efficient size correct subset inference in homoskedastic linear instrumental variables regression," Journal of Econometrics, Elsevier, vol. 221(1), pages 78-96.
    8. Flückiger, Matthias & Ludwig, Markus, 2015. "Economic shocks in the fisheries sector and maritime piracy," Journal of Development Economics, Elsevier, vol. 114(C), pages 107-125.
    9. Bekker, Paul A. & Lawford, Steve, 2008. "Symmetry-based inference in an instrumental variable setting," Journal of Econometrics, Elsevier, vol. 142(1), pages 28-49, January.
    10. Noud P.A. van Giersbergen, 2011. "Bootstrapping Subset Test Statistics in IV Regression," UvA-Econometrics Working Papers 11-08, Universiteit van Amsterdam, Dept. of Econometrics.
    11. Angelica Gonzalez, 2007. "Angelica Gonzalez," Edinburgh School of Economics Discussion Paper Series 168, Edinburgh School of Economics, University of Edinburgh.
    12. Martin F. Grace & David L. Sjoquist & Laura Wheeler, 2014. "The Effect of Insurance Premium Taxes on Interstate Differences in the Size of the Property-Casualty Insurance Industry," National Tax Journal, National Tax Association;National Tax Journal, vol. 67(1), pages 151-182, March.
    13. Kumbhakar, Subal C. & Tsionas, Mike G., 2021. "Dissections of input and output efficiency: A generalized stochastic frontier model," International Journal of Production Economics, Elsevier, vol. 232(C).

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