Doubly robust instrumental variable regression

Statistica Sinica

Volumn 22, Issue 1, 2012, Pages 173-205

  Okui, Ryo ^a   Small, Dylan S ^b   Tan, Zhiqiang ^c   Robins, James M ^d  

^a KYOTO UNIVERSITY   (Japan)

^b UNIVERSITY OF PENNSYLVANIA   (United States)

^c RUTGERS UNIVERSITY   (United States)

^d HARVARD UNIVERSITY   (United States)

Author keywords

Double robustness; Instrumental variable estimation; Local efficiency; Partial linear model

Indexed keywords

EID: 84858388722     PISSN: 10170405     EISSN: None     Source Type: Journal    
DOI: 10.5705/ss.2009.265     Document Type: Article

References (49)

1. Ai, C. and Chen, X (2003). Efficient estimation of models with conditional moment restrictions containing unknown functions. Econometrica 71, 1795-1843.
2. Angrist, J. D., Imbens, G. W. and Rubin, D. R. (1996). Identification of causal effects using instrumental variables. J. Amer. Statist. Assoc. 91, 444-472.
3. Angrist, J. D. and Krueger, A. B. (2001). Instrumental variables and the search for identification: From supply and demand to natural experiments. J. Economic Perspectives 15, 69-85. (Pubitemid 33594775)
4. Bhattacharya, J., Goldman, D., and McCaffrey, D. (2006). Estimating probit models with selfselected treatments. Statist. Medicine 25, 389-413. (Pubitemid 43174538)
5. Blundell, R. and Powell, J. (2003). Endogeneity in nonparametric and semiparametric regression models. In Advances in Economics and Econometrics (Edited by L. Hansen, Dewatripont, M. and S. Turnovsky), 312-357, Cambridge University Press, Cambridge.
6. Carroll, R. J., Ruppert, D., Stefanski, L. A., and Crainiceanu, C. M. (2006). Measurement Error in Nonlinear Models: A Modern Perspective. 2nd edition. Chapman & Hall, New York.
7. Card, D. (1995). Using geographic variation in college proximity to estimate the return to schooling. In Aspects of Labor Market Behavior: Essays in Honour of John Vanderkamp (Edited by L. Christofides, E. Grant and R. Swidinsky), 201-222, University of Toronto Press, Toronto.
8. Card, D. (2001), Estimating the return to schooling: Progress on some persistent econometric problems. Econometrica, 69, 1127-1160. (Pubitemid 33723035)
9. Chamberlain, G. (1987). Asymptotic efficiency in estimation with conditional moment restrictions. J. Econometrics 34, 305-334.
10. Chamberlain, G. (1992). Efficiency bounds for semiparametric regression. Econometrica 60, 567-596.
11. Cochran, W. G. (1965). The planning of observational studies of human populations (with discussion). J. Roy. Statist. Soc. Ser. A 128, 134-155.
12. Doornik, J. A. (2007). Ox 5 - An Object-oriented Matrix Language. Timberlake Consultant Ltd.
13. Florens, J.-P., Johannes, J. and van Bellegem, S. (2005). Instrumental regression in partially linear models. Unpublished manuscript.
14. Frölich, M. (2007). Nonparametric IV estimation of local average treatment effects with covariates. J. Econometrics 139, 35-75. (Pubitemid 46778785)
15. Griliches, Z. (1977). Estimating the returns to schooling: Some econometric problems. Econometrica 45, 1-22.
16. Hansen, L. P. (1982). Large sample properties of generalized method of moments estimators. Econometrica 50, 1029-1054.
17. Hayfield, T. and Racine, J. S. (2007). np: Nonparametric kernel smoothing methods for mixed datatypes. R package version 0.13-1.
18. Hitomi, K., Nishiyama, Y., and Okui, R. (2008). A puzzling phenomenon in semiparametric estimation problems with infinite-dimensional nuisance parameters. Econometric Theory 24, 1717-1728.
19. Holland, P. W. (1988). Causal Inference, Path Analysis and Recursive Structural Equation Models. Sociological Methodology 18, 449-484.
20. Horowitz, J. L. (2001). The Bootstrap. In Handbook of Econometrics, Volume 5 (Edited by J. J. Heckman and E. Leamer), 3159-3228, Elsevier.
21. Ichimura, H. and Taber, C. (2001). Propensity-score matching with instrumental variables. Amer. Economic Rev. 91, 119-123.
22. Kang, J. D. Y., Joseph L. and Schafer, J. L. (2007), Demystifying double robustness: A comparison of alternative strategies for estimating a population mean from incomplete data, Statist. Sci., 22, 523-539.
23. Lee, L. F. (1981). Simultaneous equation models with discrete and censored dependent variables. In Structural Analysis of Discrete Data with Economic Applications, (Edited by C. Manski and D. McFadden), MIT Press, Cambridge.
24. Lee, M.-J. (1996). Methods of Moments and Semiparametric Econometrics for Limited Dependent Variable Models. Springer-Verlag, New York.
25. Lunceford, J. and Davidian, M. (2004). Stratification and weighting via the propensity score in estimation of causal effects: a comparative study. Statist. Medicine 23, 2937-2960. (Pubitemid 39200133)
26. Neugebauer, R. and Van der Laan, M. (2005). Why prefer doubly robust estimates? J. Statist. Plann. Inference 129, 405-426.
27. Newey, W. K. (1990). Semiparametric efficiency bounds. J. Appl. Econometrics 5, 99-135.
28. Newey, W. K. and McFadden, D. (1994). Large sample estimation and hypothesis testing. In Handbook of Econometrics, 4 (Edited by R. F. Engle and D. L. McFadden), 2111-2245. Elsevier.
29. Neyman, J. (1923). On the application of probability theory to agricultural experiments. Trans. D. Dabrowska, Statist. Sci. (1990) 5, 463-480.
30. Rivers, D. and Vuong, Q. H. (1988). Limited information estimators and exogeneity tests for simultaneous probit models. J. Econometrics 39, 347-366.
31. Robins, J. M. (1994). Correcting for non-compliance in randomised trials using structural nested mean models. Comm. Statist. Theory Methods 23, 2379-2412.
32. Robins, J. (2000). Robust estimation in sequentially ignorable missing data and causal inference models. Proc. Amer. Statist. Assoc. Section on Bayesian Statistical Science, 6-10.
33. Robins, J. and Ritov, Y. (1997). Toward a curse of dimensionality appropriate (CODA) asymptotic theory for semi-parametric models. Statist. Medicine 16, 285-319. (Pubitemid 27029303)
34. Robins, J. and Rotnitzky, A. (2001). Comment on the Bickel and Kwon article "On double robustness." Statist. Sinica 11, 920-936.
35. Robins, J. and Rotnitzky, A. (2004). Estimation of treatment effects in randomised trials with non-compliance and a dichotomous outcome using structural mean models. Biometrika 91, 763-783. (Pubitemid 41388918)
36. Robins, J., Rotnitzky, A. and Van der Laan, M. (2000). Comment on the Murphy and Van der Vaart article "On profile likelihood." J. Amer. Statist. Assoc. 90, 106-121.
37. Robinson, P. M. (1988). Root-N-consistent semiparametric regression. Econometrica 56, 931-954.
38. Rosenbaum, P.R. (2002). Observational Studies. 2nd edition. New York.
39. Rubin, D.B. (1974). Estimating causal effects of treatments in randomized and non-randomized Studies. J. Educational Psychology 66, 688-701.
40. Scharfstein, D., Rotnitzky, A., and Robins, J. (1999). Adjusting for nonignorable drop-out using semiparametric nonresponse models. J. Amer. Statist. Assoc. 94, 1096-1120 (with Rejoinder, 1135-1146).
41. Small, D. S. (2007). Sensitivity analysis for instrumental variables regression with overidentifying restrictions. J. Amer. Statist. Assoc. 102, 1049-1058.
42. Tan, Z. (2006a). A distributional approach for causal inference using propensity scores. J. Amer. Statist. Assoc. 101, 1619-1637.
43. Tan, Z. (2006b). Regression and weighting methods for causal inference using instrumental variables. J. Amer. Statist. Assoc. 101, 1607-1618.
44. Tan, Z. (2010a). Nonparametric likelihood and and doubly robust estimating equations for marginal and nested structural models. Canad. J. Statist. 38, 609-632.
45. Tan, Z. (2010b). Marginal and nested structural models using instrumental variables. J. Amer. Statist. Assoc. 105, 157-169.
46. Tsiatis, A. A. (2006). Semiparametric Theory and Missing Data. Springer-Verlag, New York.
47. Van der Laan, M., Hubbard, A. and Jewell, N. (2007). Estimation of treatment effects in randomized trials with non-compliance and a dichotomous outcome. J. Roy. Statist. Soc. Ser. B 69, 463-482.
48. Van der Laan, M. and Robins, J. (2003). Unified Methods for Censored Longitudinal Data and Causality. Springer-Verlag, New York.
49. Vansteelandt, S. and Goetghebeur, E. (2003). Causal inference with generalized structural mean models. J. Roy. Statist. Soc. Ser. B 65, 817-835. (Pubitemid 37434232)