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Nonparametric bounds for the causal effect in a binary instrumental-variable model

Author

Listed:
  • Tom M. Palmer

    (University of Bristol, UK)

  • Roland R. Ramsahai

    (University of Cambridge, UK)

  • Vanessa Didelez

    (University of Bristol, UK)

  • Nuala A. Sheehan

    (University of Leicester, UK)

Abstract

Instrumental variables can be used to make inferences about causal effects in the presence of unmeasured confounding. For a model in which the instrument, intermediate/treatment, and outcome variables are all binary, Balke and Pearl (1997, Journal of the American Statistical Association 92: 1172–1176) derived nonparametric bounds for the intervention probabilities and the average causal effect. We have implemented these bounds in two commands: bpbounds and bpboundsi. We have also implemented several extensions to these bounds. One of these extensions applies when the instrument and outcome are measured in one sample and the instrument and intermediate are measured in another sample. We have also implemented the bounds for an instrument with three categories, as is common in Mendelian randomization analyses in epidemiology and for the case where a monotonic effect of the instrument on the intermediate can be assumed. In each case, we calculate the instrumental-variable inequality constraints as a check for gross violations of the instrumental-variable conditions. The use of the commands is illustrated with a re-creation of the original Balke and Pearl analysis and with a Mendelian randomization analysis. We also give a simulated example to demonstrate that the instrumental-variable inequality constraints can both detect and fail to detect violations of the instrumental-variable conditions. Copyright 2011 by StataCorp LP.

Suggested Citation

  • Tom M. Palmer & Roland R. Ramsahai & Vanessa Didelez & Nuala A. Sheehan, 2011. "Nonparametric bounds for the causal effect in a binary instrumental-variable model," Stata Journal, StataCorp LP, vol. 11(3), pages 345-367, September.
    • Handle: RePEc:tsj:stataj:v:11:y:2011:i:3:p:345-367
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    References listed on IDEAS

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    1. Christopher F Baum & Mark E. Schaffer & Steven Stillman, 2003. "Instrumental variables and GMM: Estimation and testing," Stata Journal, StataCorp LP, vol. 3(1), pages 1-31, March.
    2. Imbens, Guido W & Angrist, Joshua D, 1994. "Identification and Estimation of Local Average Treatment Effects," Econometrica, Econometric Society, vol. 62(2), pages 467-475, March.
    3. Andrew Chesher, 2010. "Instrumental Variable Models for Discrete Outcomes," Econometrica, Econometric Society, vol. 78(2), pages 575-601, March.
    4. Paul S. Clarke & Frank Windmeijer, 2012. "Instrumental Variable Estimators for Binary Outcomes," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(500), pages 1638-1652, December.
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    1. Geneletti, Sara & Baio, Gianluca & O'Keeffe, Aidan & Ricciardi, Federico, 2019. "Bayesian modelling for binary outcomes in the regression discontinuity design," LSE Research Online Documents on Economics 100096, London School of Economics and Political Science, LSE Library.

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