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Viewpoint: An extended class of instrumental variables for the estimation of causal effects

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  • Karim Chalak
  • Halbert White

Abstract

We examine how structural systems can yield observed variables instrumental in identifying and estimating causal effects. We provide an exhaustive characterization of potentially identifying conditional exogeneity relationships and demonstrate how structural relations determine exogeneity and exclusion restrictions that yield moment conditions supporting identification. This provides a comprehensive framework for constructing instruments and covariates. We introduce notions of conditioning and conditional extended instrumental variables (XIVs). These permit identification but need not be traditional instruments, as they may be endogenous. We distinguish between observed XIVs and proxies for unobserved XIVs. A main message is the importance of sufficiently specifying causal relations governing the unobservables.

Suggested Citation

  • Karim Chalak & Halbert White, 2011. "Viewpoint: An extended class of instrumental variables for the estimation of causal effects," Canadian Journal of Economics, Canadian Economics Association, vol. 44(1), pages 1-51, February.
    • Handle: RePEc:cje:issued:v:44:y:2011:i:1:p:1-51
    DOI: 10.1111/j.1540-5982.2010.01622.x
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    Cited by:

    1. Lu, Xun & White, Halbert, 2014. "Robustness checks and robustness tests in applied economics," Journal of Econometrics, Elsevier, vol. 178(P1), pages 194-206.
    2. Schennach, Susanne & White, Halbert & Chalak, Karim, 2012. "Local indirect least squares and average marginal effects in nonseparable structural systems," Journal of Econometrics, Elsevier, vol. 166(2), pages 282-302.
    3. Montes-Rojas, Gabriel & Galvao, Antonio F., 2014. "Bayesian endogeneity bias modeling," Economics Letters, Elsevier, vol. 122(1), pages 36-39.
    4. Joeri Smits & Jeffrey S. Racine, 2013. "Testing Exclusion Restrictions in Nonseparable Triangular Models," Department of Economics Working Papers 2013-02, McMaster University.
    5. Hoderlein, Stefan & Su, Liangjun & White, Halbert & Yang, Thomas Tao, 2016. "Testing for monotonicity in unobservables under unconfoundedness," Journal of Econometrics, Elsevier, vol. 193(1), pages 183-202.
    6. Miranda-Agrippino, Silvia & Ricco, Giovanni, 2023. "Identification with External Instruments in Structural VARs," Journal of Monetary Economics, Elsevier, vol. 135(C), pages 1-19.
    7. Galvao, Antonio F. & Montes-Rojas, Gabriel & Song, Suyong, 2017. "Endogeneity bias modeling using observables," Economics Letters, Elsevier, vol. 152(C), pages 41-45.
    8. Eva Deuchert & Martin Huber, 2017. "A Cautionary Tale About Control Variables in IV Estimation," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 79(3), pages 411-425, June.
    9. Leonardo Marinho, 2022. "Causal Impulse Responses for Time Series," Working Papers Series 570, Central Bank of Brazil, Research Department.
    10. Muhammad Qasim, 2024. "A weighted average limited information maximum likelihood estimator," Statistical Papers, Springer, vol. 65(5), pages 2641-2666, July.
    11. Marc F. Bellemare & Jeffrey R. Bloem & Noah Wexler, 2024. "The Paper of How: Estimating Treatment Effects Using the Front‐Door Criterion," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 86(4), pages 951-993, August.
    12. Huber Martin & Wüthrich Kaspar, 2019. "Local Average and Quantile Treatment Effects Under Endogeneity: A Review," Journal of Econometric Methods, De Gruyter, vol. 8(1), pages 1-27, January.
    13. Graevenitz, Georg von & Weber, Richard, 2011. "How to Educate Entrepreneurs?," Discussion Papers in Business Administration 12280, University of Munich, Munich School of Management.
    14. Cameron McIntosh, 2014. "The presence of an error term does not preclude causal inference in regression: a comment on Krause (2012)," Quality & Quantity: International Journal of Methodology, Springer, vol. 48(1), pages 243-250, January.
    15. Huber, Martin & Wüthrich, Kaspar, 2017. "Evaluating local average and quantile treatment effects under endogeneity based on instruments: a review," FSES Working Papers 479, Faculty of Economics and Social Sciences, University of Freiburg/Fribourg Switzerland.
    16. Lu, Xun & White, Halbert, 2014. "Testing for separability in structural equations," Journal of Econometrics, Elsevier, vol. 182(1), pages 14-26.
    17. Guggenberger, Patrik, 2012. "A note on the (in)consistency of the test of overidentifying restrictions and the concepts of true and pseudo-true parameters," Economics Letters, Elsevier, vol. 117(3), pages 901-904.
    18. Halbert White & Karim Chalak, 2013. "Identification and Identification Failure for Treatment Effects Using Structural Systems," Econometric Reviews, Taylor & Francis Journals, vol. 32(3), pages 273-317, November.
    19. Suyong Song & Stephen S. Baek, 2019. "Shape Matters: Evidence from Machine Learning on Body Shape-Income Relationship," Papers 1906.06747, arXiv.org.
    20. Paulo Parente & Richard Smith, 2012. "Exogeneity in semiparametric moment condition models," CeMMAP working papers CWP30/12, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    21. Diagne, Aliou & Alia, Didier Y. & Wopereis, Marco C.S. & Saito, Kazuki, 2012. "Impact of Rice Research on Income and Poverty in Africa: An Ex-ante Analysis," 2012 Conference, August 18-24, 2012, Foz do Iguacu, Brazil 126874, International Association of Agricultural Economists.

    More about this item

    JEL classification:

    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models
    • C31 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models; Quantile Regressions; Social Interaction Models
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation

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