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Identification of causal effects in linear models: beyond instrumental variables

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  • Elena Stanghellini
  • Eduwin Pakpahan

Abstract

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. By exploiting the notion of Markov equivalence, the derivations can also be applied to regression graphs, thereby enlarging the class of models to which the results are of use. Copyright Sociedad de Estadística e Investigación Operativa 2015

Suggested Citation

  • Elena Stanghellini & Eduwin Pakpahan, 2015. "Identification of causal effects in linear models: beyond instrumental variables," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 24(3), pages 489-509, September.
    • Handle: RePEc:spr:testjl:v:24:y:2015:i:3:p:489-509
    DOI: 10.1007/s11749-014-0421-3
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    References listed on IDEAS

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    1. Nanny Wermuth & D. R. Cox, 2008. "Distortion of effects caused by indirect confounding," Biometrika, Biometrika Trust, vol. 95(1), pages 17-33.
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    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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    Cited by:

    1. Manabu Kuroki & Hisayoshi Nanmo, 2020. "Variance formulas for estimated mean response and predicted response with external intervention based on the back-door criterion in linear structural equation models," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 104(4), pages 667-685, December.
    2. Ryusei Shingaki & Hiroshi Kanda & Manabu Kuroki, 2021. "Selection and integration of generalized instrumental variables for estimating total effects," Statistical Papers, Springer, vol. 62(5), pages 2355-2381, October.
    3. Nanmo, Hisayoshi & Kuroki, Manabu, 2021. "Exact variance formula for the estimated mean outcome with external intervention based on the front-door criterion in Gaussian linear structural equation models," Journal of Multivariate Analysis, Elsevier, vol. 185(C).
    4. Breuer, Anita & Asiedu, Edward, 2017. "Can Gender-Targeted Employment Interventions Help Enhance Community Participation? Evidence from Urban Togo," World Development, Elsevier, vol. 96(C), pages 390-407.

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    More about this item

    Keywords

    Causal effect; Confounder; Directed acyclic graph ; Identification; Latent variable; Regression graph; Structural equation model; Primary 62H99; Secondary 62H20;
    All these keywords.

    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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