Paradoxes in instrumental variable studies with missing data and one-sided noncompliance

Kennedy, Edward H.; Small, Dylan S.

Journal de la société française de statistique, Tome 161 (2020) no. 1, pp. 120-134.

It is common in instrumental variable studies for instrument values to be missing, for example when the instrument is a genetic test in Mendelian randomization studies. In this paper we discuss two apparent paradoxes that arise in so-called single consent designs where there is one-sided noncompliance, i.e., where unencouraged units cannot access treatment. The first paradox is that, even under a missing completely at random assumption, a complete-case analysis is biased when knowledge of one-sided noncompliance is taken into account; this is not the case when such information is disregarded. This occurs because incorporating information about one-sided noncompliance induces a dependence between the missingness and treatment. The second paradox is that, although incorporating such information does not lead to efficiency gains without missing data, the story is different when instrument values are missing: there, incorporating such information changes the efficiency bound, allowing possible efficiency gains. This is because some of the missing values can be filled in, based on the fact that anyone who received treatment must have been encouraged by the instrument (since the unencouraged cannot access treatment).

Classification : 35L05, 35L70
Keywords: users guide, J-SFdS document class
Mots clés : mode d’emploi, classe du J-SFdS

[1] Angrist, Joshua D; Imbens, Guido W; Rubin, Donald B Identification of causal effects using instrumental variables, Journal of the American Statistical Association, Volume 91 (1996) no. 434, pp. 444-455 | DOI | Zbl

[2] Angrist, Joshua D; Rokkanen, Miikka Wanna get away? Regression discontinuity estimation of exam school effects away from the cutoff, Journal of the American Statistical Association, Volume 110 (2015) no. 512, pp. 1331-1344 | DOI | MR

[3] Baiocchi, Michael; Cheng, Jing; Small, Dylan S Instrumental variable methods for causal inference, Statistics in Medicine, Volume 33 (2014) no. 13, pp. 2297-2340 | DOI | MR

[4] Bickel, Peter J; Klaassen, Chris AJ; Ritov, Ya’acov; Wellner, Jon A Efficient and Adaptive Estimation for Semiparametric Models, Johns Hopkins University Press, 1993 | MR

[5] Battistin, Erich; Rettore, Enrico Ineligibles and eligible non-participants as a double comparison group in regression-discontinuity designs, Journal of Econometrics, Volume 142 (2008) no. 2, pp. 715-730 | DOI | MR | Zbl

[6] Burgess, Stephen; Seaman, Shaun; Lawlor, Debbie A; Casas, Juan P; Thompson, Simon G Missing data methods in Mendelian randomization studies with multiple instruments, American Journal of Epidemiology, Volume 174 (2011) no. 9, pp. 1069-1076 | DOI

[7] Chaudhuri, Saraswata; Guilkey, David K GMM with multiple missing variables, Journal of Applied Econometrics, Volume 31 (2016) no. 4, pp. 678-706 | DOI | MR

[8] Frölich, Markus; Melly, Blaise Identification of treatment effects on the treated with one-sided non-compliance, Econometric Reviews, Volume 32 (2013) no. 3, pp. 384-414 | DOI | MR

[9] Hernán, Miguel A; Robins, James M Instruments for causal inference: an epidemiologist’s dream?, Epidemiology, Volume 17 (2006) no. 4, pp. 360-372 | DOI

[10] Hahn, Jinyong; Todd, Petra; Van der Klaauw, Wilbert Identification and estimation of treatment effects with a regression-discontinuity design, Econometrica, Volume 69 (2001) no. 1, pp. 201-209 | DOI

[11] Imbens, Guido W; Angrist, Joshua D Identification and estimation of local average treatment effects, Econometrica, Volume 62 (1994) no. 2, pp. 467-475 | DOI | Zbl

[12] Imbens, Guido W; Lemieux, Thomas Regression discontinuity designs: a guide to practice, Journal of Econometrics, Volume 142 (2008) no. 2, pp. 615-635 | DOI | MR | Zbl

[13] Kennedy, Edward H Efficient nonparametric causal inference with missing exposures, arXiv preprint arXiv:1802.08952 (2018)

[14] Mogstad, Magne; Wiswall, Matthew Instrumental variables estimation with partially missing instruments, Economics Letters, Volume 114 (2012) no. 2, pp. 186-189 | DOI | MR | Zbl

[15] Pitt, Mark M; Khandker, Shahidur R The impact of group-based credit programs on poor households in Bangladesh: Does the gender of participants matter?, Journal of Political Economy, Volume 106 (1998) no. 5, pp. 958-996 | DOI

[16] Robins, James M; Rotnitzky, Andrea Semiparametric efficiency in multivariate regression models with missing data, Journal of the American Statistical Association, Volume 90 (1995) no. 429, pp. 122-129 | DOI | MR | Zbl

[17] Rubin, Donald B Estimating causal effects of treatments in randomized and nonrandomized studies., Journal of Educational Psychology, Volume 66 (1974) no. 5, pp. 688-701 | DOI

[18] Tsiatis, Anastasios A Semiparametric Theory and Missing Data, Springer, 2006 | MR

[19] van der Vaart, Aad W Asymptotic Statistics, Cambridge University Press, 2000 | MR

[20] van der Laan, Mark J; Robins, James M Unified Methods for Censored Longitudinal Data and Causality, Springer, 2003 | DOI | MR

[21] Wright, Sewall Appendix to “Tariff on animal and vegetable oils” by P.G. Wright (1928)

[22] Wright, Sewall The method of path coefficients, The Annals of Mathematical Statistics, Volume 5 (1934) no. 3, pp. 161-215 | DOI | Zbl

[23] Zelen, Marvin A new design for randomized clinical trials, New England Journal of Medicine, Volume 300 (1979) no. 22, pp. 1242-1245 | DOI