Instrumental Variable Estimators for Binary Outcomes
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.
|Date of creation:||Jan 2009|
|Date of revision:|
|Contact details of provider:|| Postal: |
Phone: 0117 33 10799
Fax: 0117 33 10705
Web page: http://www.bris.ac.uk/cmpo/
More information through EDIRC
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- 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.
- 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.
- Joshua D. Angrist, 2000. "Estimation of Limited-Dependent Variable Models with Dummy Endogenous Regressors: Simple Strategies for Empirical Practice," NBER Technical Working Papers 0248, National Bureau of Economic Research, Inc.
- Joshua Angrist, 1999. "Estimation of Limited-Dependent Variable Models with Dummy Endogenous Regressors: Simple Strategies for Empirical Practice," Working papers 99-31, Massachusetts Institute of Technology (MIT), Department of Economics.
- Richard Blundell & James Powell, 2001.
"Endogeneity in semiparametric binary response models,"
CeMMAP working papers
CWP05/01, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
- Richard W. Blundell & James L. Powell, 2004. "Endogeneity in Semiparametric Binary Response Models," Review of Economic Studies, Oxford University Press, vol. 71(3), pages 655-679.
- Richard W. Blundell & James L. Powell, 2004. "Endogeneity in Semiparametric Binary Response Models," Review of Economic Studies, Wiley Blackwell, vol. 71, pages 655-679, 07.
- 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.
- Imbens, Guido W & Angrist, Joshua D, 1994. "Identification and Estimation of Local Average Treatment Effects," Econometrica, Econometric Society, vol. 62(2), pages 467-75, March.
- Victor Chernozhukov & Christian Hansen, 2005. "An IV Model of Quantile Treatment Effects," Econometrica, Econometric Society, vol. 73(1), pages 245-261, 01.
- 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.
- 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.
- 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.
- Abadie, Alberto, 2003. "Semiparametric instrumental variable estimation of treatment response models," Journal of Econometrics, Elsevier, vol. 113(2), pages 231-263, April.
- Goldberger, Arthur S, 1972. "Structural Equation Methods in the Social Sciences," Econometrica, Econometric Society, vol. 40(6), pages 979-1001, November.
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.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: ()
If references are entirely missing, you can add them using this form.