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Identification of casual effects in linear models: beyond Instrumental Variables


  • Elena Stanghellini
  • Eduwin Pakpahan


The Instrumental Variable (IV) formula has become widely used to address the issue of identification of a causal effect in linear systems with an unobserved variable that acts as direct confounder. We here propose two alternative formulations to achieve identification when the assumptions underlying the use of IV are violated. Parallel to the IV, the proposed formulas exploit the conditional independence structure of a Directed Acyclic Graph and can be obtained via a series of univariate regressions, a feature that renders the results particularly attractive and easy to implement.

Suggested Citation

  • Elena Stanghellini & Eduwin Pakpahan, 2013. "Identification of casual effects in linear models: beyond Instrumental Variables," Quaderni del Dipartimento di Economia, Finanza e Statistica 117/2013, Università di Perugia, Dipartimento Economia.
  • Handle: RePEc:pia:wpaper:117/2013

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    References listed on IDEAS

    1. Nanny Wermuth & D. R. Cox, 2008. "Distortion of effects caused by indirect confounding," Biometrika, Biometrika Trust, vol. 95(1), pages 17-33.
    2. Bowden, Roger J, 1973. "The Theory of Parametric Identification," Econometrica, Econometric Society, vol. 41(6), pages 1069-1074, November.
    3. Elena Stanghellini & Nanny Wermuth, 2005. "On the identification of path analysis models with one hidden variable," Biometrika, Biometrika Trust, vol. 92(2), pages 337-350, June.
    4. Rothenberg, Thomas J, 1971. "Identification in Parametric Models," Econometrica, Econometric Society, vol. 39(3), pages 577-591, May.
    5. Judea Pearl, 2003. "Statistics and causal inference: A review," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 12(2), pages 281-345, December.
    6. Manabu Kuroki & Judea Pearl, 2014. "Measurement bias and effect restoration in causal inference," Biometrika, Biometrika Trust, vol. 101(2), pages 423-437.
    7. Manabu Kuroki, 2007. "Graphical identifiability criteria for causal effects in studies with an unobserved treatment/response variable," Biometrika, Biometrika Trust, vol. 94(1), pages 37-47.
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    1. repec:eee:wdevel:v:96:y:2017:i:c:p:390-407 is not listed on IDEAS

    More about this item


    Causal Effect; Confounder; Directed Acyclic Graph; Latent Variable; Regression Graph; Structural Equation Model; Identification; Structural Equation Model;

    JEL classification:

    • C18 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Methodolical Issues: General
    • 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
    • C36 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Instrumental Variables (IV) Estimation


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