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Instrumental Variable Estimators for Binary Outcomes

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  • Paul Clarke
  • Frank Windmeijer

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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.

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Bibliographic Info

Paper provided by Department of Economics, University of Bristol, UK in its series The Centre for Market and Public Organisation with number 09/209.

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Length: 23 pages
Date of creation: Jan 2009
Date of revision:
Handle: RePEc:bri:cmpowp:09/209

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Keywords: Econometrics; Generalized methods of moments; Parameter identification; Marginal structural models; Structural mean models; Structural models;

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References

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  1. 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, American Statistical Association, vol. 19(1), pages 2-16, January.
  2. Abadie, Alberto, 2003. "Semiparametric instrumental variable estimation of treatment response models," Journal of Econometrics, Elsevier, Elsevier, vol. 113(2), pages 231-263, April.
  3. 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.
  4. Joshua D. Angrist & Guido W. Imbens, 1995. "Identification and Estimation of Local Average Treatment Effects," NBER Technical Working Papers 0118, National Bureau of Economic Research, Inc.
  5. Richard Blundell & James Powell, 2001. "Endogeneity in semiparametric binary response models," CeMMAP working papers, Centre for Microdata Methods and Practice, Institute for Fiscal Studies CWP05/01, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  6. Goldberger, Arthur S, 1972. "Structural Equation Methods in the Social Sciences," Econometrica, Econometric Society, Econometric Society, vol. 40(6), pages 979-1001, November.
  7. Rivers, Douglas & Vuong, Quang H., 1988. "Limited information estimators and exogeneity tests for simultaneous probit models," Journal of Econometrics, Elsevier, Elsevier, vol. 39(3), pages 347-366, November.
  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.
  9. Tan, Zhiqiang, 2006. "Regression and Weighting Methods for Causal Inference Using Instrumental Variables," Journal of the American Statistical Association, American Statistical Association, American Statistical Association, vol. 101, pages 1607-1618, December.
  10. Victor Chernozhukov & Christian Hansen, 2005. "An IV Model of Quantile Treatment Effects," Econometrica, Econometric Society, Econometric Society, vol. 73(1), pages 245-261, 01.
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Cited by:
  1. 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, Elsevier, vol. 13(C), pages 99-106.
  2. Paul Clarke & Frank Windmeijer, 2009. "Identification of Causal Effects on Binary Outcomes Using Structural Mean Models," The Centre for Market and Public Organisation, Department of Economics, University of Bristol, UK 09/217, Department of Economics, University of Bristol, UK.
  3. 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, African Association of Agricultural Economists, vol. 6(1), March.

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