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On the equivalence of instrumental variables estimators for linear models

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  • Galvao, Antonio F.
  • Montes-Rojas, Gabriel

Abstract

This note shows the equivalence of different instrumental variables estimators to solve the endogeneity problem in linear models when valid instruments are available. We demonstrate that the exclusion restriction estimator proposed by Chernozhukov and Hansen (2006) is equivalent to the two-stage least squares and the control function estimators for linear models.

Suggested Citation

  • Galvao, Antonio F. & Montes-Rojas, Gabriel, 2015. "On the equivalence of instrumental variables estimators for linear models," Economics Letters, Elsevier, vol. 134(C), pages 13-15.
    • Handle: RePEc:eee:ecolet:v:134:y:2015:i:c:p:13-15
    DOI: 10.1016/j.econlet.2015.06.001
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    1. Amemiya, Takeshi, 1982. "Two Stage Least Absolute Deviations Estimators," Econometrica, Econometric Society, vol. 50(3), pages 689-711, May.
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    3. Alberto Abadie & Joshua Angrist & Guido Imbens, 2002. "Instrumental Variables Estimates of the Effect of Subsidized Training on the Quantiles of Trainee Earnings," Econometrica, Econometric Society, vol. 70(1), pages 91-117, January.
    4. Han Hong & Elie Tamer, 2003. "Inference in Censored Models with Endogenous Regressors," Econometrica, Econometric Society, vol. 71(3), pages 905-932, May.
    5. Xiaohong Chen & Oliver Linton & Ingrid Van Keilegom, 2003. "Estimation of Semiparametric Models when the Criterion Function Is Not Smooth," Econometrica, Econometric Society, vol. 71(5), pages 1591-1608, September.
    6. Galvao Jr., Antonio F., 2011. "Quantile regression for dynamic panel data with fixed effects," Journal of Econometrics, Elsevier, vol. 164(1), pages 142-157, September.
    7. Joshua D. Angrist & Jörn-Steffen Pischke, 2009. "Mostly Harmless Econometrics: An Empiricist's Companion," Economics Books, Princeton University Press, edition 1, number 8769.
    8. Honore, Bo E & Hu, Luojia, 2004. "On the Performance of Some Robust Instrumental Variables Estimators," Journal of Business & Economic Statistics, American Statistical Association, vol. 22(1), pages 30-39, January.
    9. Victor Chernozhukov & Christian Hansen, 2005. "An IV Model of Quantile Treatment Effects," Econometrica, Econometric Society, vol. 73(1), pages 245-261, January.
    10. Jun, Sung Jae, 2008. "Weak identification robust tests in an instrumental quantile model," Journal of Econometrics, Elsevier, vol. 144(1), pages 118-138, May.
    11. Powell, James L, 1983. "The Asymptotic Normality of Two-Stage Least Absolute Deviations Estimators," Econometrica, Econometric Society, vol. 51(5), pages 1569-1575, September.
    12. Lee, Sokbae, 2007. "Endogeneity in quantile regression models: A control function approach," Journal of Econometrics, Elsevier, vol. 141(2), pages 1131-1158, December.
    13. Hausman, Jerry A., 1983. "Specification and estimation of simultaneous equation models," Handbook of Econometrics, in: Z. Griliches† & M. D. Intriligator (ed.), Handbook of Econometrics, edition 1, volume 1, chapter 7, pages 391-448, Elsevier.
    14. Joshua Angrist & Alan Krueger, 2001. "Instrumental Variables and the Search for Identification: From Supply and Demand to Natural Experiments," Working Papers 834, Princeton University, Department of Economics, Industrial Relations Section..
    15. Chernozhukov, Victor & Hansen, Christian, 2008. "Instrumental variable quantile regression: A robust inference approach," Journal of Econometrics, Elsevier, vol. 142(1), pages 379-398, January.
    16. Chernozhukov, Victor & Hansen, Christian, 2006. "Instrumental quantile regression inference for structural and treatment effect models," Journal of Econometrics, Elsevier, vol. 132(2), pages 491-525, June.
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    Citations

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    Cited by:

    1. Javier Alejo & Antonio F Galvao & Gabriel Montes-Rojas, 2023. "A first-stage representation for instrumental variables quantile regression," The Econometrics Journal, Royal Economic Society, vol. 26(3), pages 350-377.
    2. Javier Alejo & Antonio F. Galvao & Gabriel Montes-Rojas, 2020. "A first-stage test for instrumental variables quantile regression," Asociación Argentina de Economía Política: Working Papers 4304, Asociación Argentina de Economía Política.
    3. Rocha, Leonardo Andrade & Silva, Napiê Galvê Araújo & Almeida, Carlo Alano Soares de & Oliveira, Denison Murilo de & Fernandes, Kaio César, 2020. "Growth and heterogeneity of human capital: effects of the expansion of higher education on the income increase in Brazilian municipalities," Revista CEPAL, Naciones Unidas Comisión Económica para América Latina y el Caribe (CEPAL), August.

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    More about this item

    Keywords

    Instrumental variables; Least-squares; Control function; Quantile regression;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C23 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Models with Panel Data; Spatio-temporal Models

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