[go: up one dir, main page]
IDEAS home Printed from https://ideas.repec.org/p/bri/cmpowp/09-209.html
   My bibliography  Save this paper

Instrumental Variable Estimators for Binary Outcomes

Author

Listed:
  • Paul Clarke
  • Frank Windmeijer
Abstract
The estimation of exposure effects on study outcomes is almost always complicated by non-random exposure selection - even randomised controlled trials can be affected by participant non-compliance. If the selection mechanism is non-ignorable then inferences based on estimators that fail to adjust for its effects will be misleading. Potentially consistent estimators of the exposure effect can be obtained if the data are expanded to include one or more instrumental variables (IVs). An IV must satisfy core conditions constraining it to be associated with the exposure, and indirectly (but not directly) associated with the outcome through this association. Here we consider IV estimators for studies in which the outcome is represented by a binary variable. While work on this problem has been carried out in statistics and econometrics, the estimators and their associated identifying assumptions have existed in the separate domains of structural models and potential outcomes with almost no overlap. In this paper, we review and integrate the work in these areas and reassess the issues of parameter identification and estimator consistency. Identification of maximum likelihood estimators comes from strong parametric modelling assumptions, with consistency depending on these assumptions being correct. Our main focus is on three semi-parametric estimators based on the generalised method of moments, marginal structural models and structural mean models (SMM). By inspecting the identifying assumptions for each method, we show that these estimators are inconsistent even if the true model generating the data is simple, and argue that this implies that consistency is obtained only under implausible conditions. Identification for SMMs can also be obtained under strong exposure-restricting design constraints that are often appropriate for randomised controlled trials, but not for observational studies. Finally, while estimation of local causal parameters is possible if the selection mechanism is monotonic, not all SMMs identify a local parameter.

Suggested Citation

  • Paul Clarke & Frank Windmeijer, 2009. "Instrumental Variable Estimators for Binary Outcomes," The Centre for Market and Public Organisation 09/209, The Centre for Market and Public Organisation, University of Bristol, UK.
    • Handle: RePEc:bri:cmpowp:09/209
    as

    Download full text from publisher

    File URL: http://www.bristol.ac.uk/cmpo/publications/papers/2009/wp209.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. James Robins & Andrea Rotnitzky, 2004. "Estimation of treatment effects in randomised trials with non-compliance and a dichotomous outcome using structural mean models," Biometrika, Biometrika Trust, vol. 91(4), pages 763-783, December.
    2. Richard W. Blundell & James L. Powell, 2004. "Endogeneity in Semiparametric Binary Response Models," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 71(3), pages 655-679.
    3. Angrist, Joshua D, 2001. "Estimations of Limited Dependent Variable Models with Dummy Endogenous Regressors: Simple Strategies for Empirical Practice," Journal of Business & Economic Statistics, American Statistical Association, vol. 19(1), pages 2-16, January.
    4. 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.
    5. Abadie, Alberto, 2003. "Semiparametric instrumental variable estimation of treatment response models," Journal of Econometrics, Elsevier, vol. 113(2), pages 231-263, April.
    6. Rivers, Douglas & Vuong, Quang H., 1988. "Limited information estimators and exogeneity tests for simultaneous probit models," Journal of Econometrics, Elsevier, vol. 39(3), pages 347-366, November.
    7. Tan, Zhiqiang, 2006. "Regression and Weighting Methods for Causal Inference Using Instrumental Variables," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1607-1618, December.
    8. S. Vansteelandt & E. Goetghebeur, 2003. "Causal inference with generalized structural mean models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(4), pages 817-835, November.
    9. Goldberger, Arthur S, 1972. "Structural Equation Methods in the Social Sciences," Econometrica, Econometric Society, vol. 40(6), pages 979-1001, November.
    10. Victor Chernozhukov & Christian Hansen, 2005. "An IV Model of Quantile Treatment Effects," Econometrica, Econometric Society, vol. 73(1), pages 245-261, January.
    11. John Mullahy, 1997. "Instrumental-Variable Estimation Of Count Data Models: Applications To Models Of Cigarette Smoking Behavior," The Review of Economics and Statistics, MIT Press, vol. 79(4), pages 586-593, November.
    12. Angrist, Joshua D, 2001. "Estimations of Limited Dependent Variable Models with Dummy Endogenous Regressors: Simple Strategies for Empirical Practice: Reply," Journal of Business & Economic Statistics, American Statistical Association, vol. 19(1), pages 27-28, January.
    13. Mark J. Van Der Laan & Alan Hubbard & Nicholas P. Jewell, 2007. "Estimation of treatment effects in randomized trials with non‐compliance and a dichotomous outcome," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 69(3), pages 463-482, June.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Luke Keele & Dylan Small & Richard Grieve, 2017. "Randomization-based instrumental variables methods for binary outcomes with an application to the ‘IMPROVE’ trial," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 180(2), pages 569-586, February.
    2. Marra Giampiero & Radice Rosalba, 2017. "A joint regression modeling framework for analyzing bivariate binary data in R," Dependence Modeling, De Gruyter, vol. 5(1), pages 268-294, December.
    3. Frank Windmeijer & Helmut Farbmacher & Neil Davies & George Davey Smith, 2019. "On the Use of the Lasso for Instrumental Variables Estimation with Some Invalid Instruments," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 114(527), pages 1339-1350, July.
    4. 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.
    5. 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.
    6. Laing, Timothy, 2015. "Rights to the forest, REDD+ and elections: Mining in Guyana," Resources Policy, Elsevier, vol. 46(P2), pages 250-261.
    7. Paul Clarke & Frank Windmeijer, 2009. "Identification of Causal Effects on Binary Outcomes Using Structural Mean Models," The Centre for Market and Public Organisation 09/217, The Centre for Market and Public Organisation, University of Bristol, UK.
    8. Johannes Jarke-Neuert & Grischa Perino & Henrike Schwickert, 2023. "Free riding in climate protests," Nature Climate Change, Nature, vol. 13(11), pages 1197-1202, November.
    9. Katherine Bobroske & Michael Freeman & Lawrence Huan & Anita Cattrell & Stefan Scholtes, 2022. "Curbing the Opioid Epidemic at Its Root: The Effect of Provider Discordance After Opioid Initiation," Management Science, INFORMS, vol. 68(3), pages 2003-2015, March.
    10. Davies, Neil & Dickson, Matt & Smith, George Davey & Windmeijer, Frank & van den Berg, Gerard J., 2019. "The Causal Effects of Education on Adult Health, Mortality and Income: Evidence from Mendelian Randomization and the Raising of the School Leaving Age," IZA Discussion Papers 12192, Institute of Labor Economics (IZA).
    11. Kitagawa, Toru, 2021. "The identification region of the potential outcome distributions under instrument independence," Journal of Econometrics, Elsevier, vol. 225(2), pages 231-253.
    12. Moler-Zapata, S.; & Grieve, R.; & Basu, A.; & O'Neill, S.;, 2022. "How does a local Instrumental Variable Method perform across settings with instruments of differing strengths? A simulation study and an evaluation of emergency surgery," Health, Econometrics and Data Group (HEDG) Working Papers 22/18, HEDG, c/o Department of Economics, University of York.
    13. Chuhui Li & Donald S. Poskitt & Frank Windmeijer & Xueyan Zhao, 2022. "Binary outcomes, OLS, 2SLS and IV probit," Econometric Reviews, Taylor & Francis Journals, vol. 41(8), pages 859-876, September.
    14. Maarten J. Bijlsma & Ben Wilson, 2017. "Modelling the socio-economic determinants of fertility: a mediation analysis using the parametric g-formula," MPIDR Working Papers WP-2017-013, Max Planck Institute for Demographic Research, Rostock, Germany.
    15. Frank Windmeijer & Xiaoran Liang & Fernando P. Hartwig & Jack Bowden, 2021. "The confidence interval method for selecting valid instrumental variables," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 83(4), pages 752-776, September.
    16. Menon, Seetha, 2014. "Unfinished lives: the effect of domestic violence on neonatal & infant mortality," ISER Working Paper Series 2014-27, Institute for Social and Economic Research.
    17. Jarke-Neuert, Johannes & Perino, Grischa & Schwickert, Henrike, 2021. "Free-Riding for Future: Field Experimental Evidence of Strategic Substitutability in Climate Protest," SocArXiv sh6dm, Center for Open Science.
    18. Taylor, Amy E. & Davies, Neil M. & Ware, Jennifer J. & VanderWeele, Tyler & Smith, George Davey & Munafò, Marcus R., 2014. "Mendelian randomization in health research: Using appropriate genetic variants and avoiding biased estimates," Economics & Human Biology, Elsevier, vol. 13(C), pages 99-106.
    19. Myoung‐jae Lee, 2021. "Instrument residual estimator for any response variable with endogenous binary treatment," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 83(3), pages 612-635, July.
    20. Berhanu, Wassie, 2011. "Recurrent shocks, poverty traps and the degradation of pastoralists’ social capital in southern Ethiopia," African Journal of Agricultural and Resource Economics, African Association of Agricultural Economists, vol. 6(1), pages 1-15, March.
    21. Ditte Nørbo Sørensen & Torben Martinussen & Eric Tchetgen Tchetgen, 2019. "A causal proportional hazards estimator under homogeneous or heterogeneous selection in an IV setting," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 25(4), pages 639-659, October.
    22. Stephan, Gesine & van den Berg, Gerard & Homrighausen, Pia, 2016. "Randomizing information on a targeted wage support program for older workers: A field experiment," VfS Annual Conference 2016 (Augsburg): Demographic Change 145487, Verein für Socialpolitik / German Economic Association.
    23. Robert Carroll & Chris Metcalfe & Sarah Steeg & Neil M Davies & Jayne Cooper & Nav Kapur & David Gunnell, 2016. "Psychosocial Assessment of Self-Harm Patients and Risk of Repeat Presentation: An Instrumental Variable Analysis Using Time of Hospital Presentation," PLOS ONE, Public Library of Science, vol. 11(2), pages 1-13, February.
    24. Goeun Lee & Myoung-jae Lee, 2023. "Regression Discontinuity for Binary Response and Local Maximum Likelihood Estimator to Extrapolate Treatment," Evaluation Review, , vol. 47(2), pages 182-208, April.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Paul Clarke & Frank Windmeijer, 2009. "Identification of Causal Effects on Binary Outcomes Using Structural Mean Models," The Centre for Market and Public Organisation 09/217, The Centre for Market and Public Organisation, University of Bristol, UK.
    2. Guilhem Bascle, 2008. "Controlling for endogeneity with instrumental variables in strategic management research," Post-Print hal-00576795, HAL.
    3. Paul S. Clarke & Tom M. Palmer & Frank Windmeijer, 2011. "Estimating structural mean models with multiple instrumental variables using the generalised method of moments," CeMMAP working papers CWP28/11, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    4. Guillermo Cruces & Sebastian Galiani, 2003. "Generalizing the Causal Effect of Fertility on Female Labor Supply," Labor and Demography 0310002, University Library of Munich, Germany.
    5. Joshua D. Angrist, 2004. "Treatment effect heterogeneity in theory and practice," Economic Journal, Royal Economic Society, vol. 114(494), pages 52-83, March.
    6. Guido W. Imbens & Jeffrey M. Wooldridge, 2009. "Recent Developments in the Econometrics of Program Evaluation," Journal of Economic Literature, American Economic Association, vol. 47(1), pages 5-86, March.
    7. Daniela Benavente, 2010. "Constraining and supporting effects of the multilateral trading system on U.S. unilateralism," IHEID Working Papers 09-2010, Economics Section, The Graduate Institute of International Studies.
    8. Nguezet, Paul Martin Dontsop & Diagne, Aliou & Okoruwa, Victor Olusegun & Ojehomon, Vivian, 2011. "Impact of Improved Rice Technology (NERICA varieties) on Income and Poverty among Rice Farming Households in Nigeria: A Local Average Treatment Effect (LATE) Approach," Quarterly Journal of International Agriculture, Humboldt-Universitaat zu Berlin, vol. 50(3), pages 1-25.
    9. Andreas Kuhn & Jean-Philippe Wuellrich & Josef Zweim�ller, 2010. "Fatal attraction? Access to early retirement and mortality," IEW - Working Papers 499, Institute for Empirical Research in Economics - University of Zurich.
    10. 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.
    11. 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.
    12. Lokossou, Jourdain & Arouna, Aminou & Diagne, Aliou & Biaou, Gauthier, 2015. "Gender differential Impact of NERICA adoption on Total Factor Productivity: evidence from Benin Republic," 2015 Conference, August 9-14, 2015, Milan, Italy 212056, International Association of Agricultural Economists.
    13. Matthew A Masten & Alexandre Poirier, 2023. "Choosing exogeneity assumptions in potential outcome models," The Econometrics Journal, Royal Economic Society, vol. 26(3), pages 327-349.
    14. Bo Wei & Limin Peng & Mei‐Jie Zhang & Jason P. Fine, 2021. "Estimation of causal quantile effects with a binary instrumental variable and censored data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 83(3), pages 559-578, July.
    15. Tommasi, Denni & Zhang, Lina, 2024. "Bounding program benefits when participation is misreported," Journal of Econometrics, Elsevier, vol. 238(1).
    16. Kern, Holger & Hainmueller, Jens, 2007. "Opium for the Masses: How Foreign Free Media Can Stabilize Authoritarian Regimes," MPRA Paper 2702, University Library of Munich, Germany.
    17. Pedro H. C. Sant'Anna & Xiaojun Song & Qi Xu, 2022. "Covariate distribution balance via propensity scores," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 37(6), pages 1093-1120, September.
    18. Manuel Arellano & Stéphane Bonhomme, 2017. "Quantile Selection Models With an Application to Understanding Changes in Wage Inequality," Econometrica, Econometric Society, vol. 85, pages 1-28, January.
    19. Han, Sukjin, 2021. "Identification in nonparametric models for dynamic treatment effects," Journal of Econometrics, Elsevier, vol. 225(2), pages 132-147.
    20. Steffen Reinhold & Hendrik Jürges, 2010. "Secondary school fees and the causal effect of schooling on health behavior," Health Economics, John Wiley & Sons, Ltd., vol. 19(8), pages 994-1001, August.

    More about this item

    Keywords

    Econometrics; Generalized methods of moments; Parameter identification; Marginal structural models; Structural mean models; Structural models;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:bri:cmpowp:09/209. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: the person in charge (email available below). General contact details of provider: https://edirc.repec.org/data/cmbriuk.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.