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Likelihood analysis of the binary instrumental variable model

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  • R. R. Ramsahai
  • S. L. Lauritzen

Abstract

Instrumental variables are widely used for the identification of the causal effect of one random variable on another under unobserved confounding. The distribution of the observable variables for a discrete instrumental variable model satisfies certain inequalities but no conditional independence relations. Such models are usually tested by checking whether the relative frequency estimators of the parameters satisfy the constraints. This ignores sampling uncertainty in the data. Using the observable constraints for the instrumental variable model, a likelihood analysis is conducted. A significance test for its validity is developed, and a bootstrap algorithm for computing confidence intervals for the causal effect is proposed. Applications are given to illustrate the advantage of the suggested approach. Copyright 2011, Oxford University Press.

Suggested Citation

  • R. R. Ramsahai & S. L. Lauritzen, 2011. "Likelihood analysis of the binary instrumental variable model," Biometrika, Biometrika Trust, vol. 98(4), pages 987-994.
    • Handle: RePEc:oup:biomet:v:98:y:2011:i:4:p:987-994
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    File URL: http://hdl.handle.net/10.1093/biomet/asr040
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    Cited by:

    1. Ryo Kato & Takahiro Hoshino, 2018. "Semiparametric Bayes Instrumental Variable Estimation with Many Weak Instruments," Discussion Paper Series DP2018-14, Research Institute for Economics & Business Administration, Kobe University.
    2. Roland R. Ramsahai, 2013. "Probabilistic causality and detecting collections of interdependence patterns," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 75(4), pages 705-723, September.

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