Partial Identification of the Average Treatment Effect Using Instrumental Variables: Review of Methods for Binary Instruments, Treatments, and Outcomes
Open accessAbstract
Several methods have been proposed for partially or point identifying the average treatment effect (ATE) using instrumental variable (IV) type assumptions. The descriptions of these methods are widespread across the statistical, economic, epidemiologic, and computer science literature, and the connections between the methods have not been readily apparent. In the setting of a binary instrument, treatment, and outcome, we review proposed methods for partial and point identification of the ATE under IV assumptions, express the identification results in a common notation and terminology, and propose a taxonomy that is based on sets of identifying assumptions. We further demonstrate and provide software for the application of these methods to estimate bounds. Supplementary materials for this article are available online.
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
The three IV conditions are not sufficient to derive a point estimate of the size of the effect of the exposure on the outcome.
“However, they are not sufficient to derive a point estimate of the size of the effect of the exposure on the outcome.28,29”
From Mendelian randomization (2022) · cites this paper as [28]
Deriving a point estimate requires an additional condition known as a point-estimate identifying condition or fourth IV condition.
“This requires an additional condition 28 known as a point-estimate identifying condition or fourth IV condition.”
From Mendelian randomization (2022) · cites this paper as [28]
Instrumental variable estimation to obtain effect estimates imposes a fourth assumption, typically effect homogeneity or monotonicity.
“When instrumental variable estimation is used to obtain effect estimates, a fourth assumption should then be stated: typically, an assumption of effect homogeneity53 or monotonicity.54”
From Strengthening the Reporting of Observational Studies in Epidemiology using Mendelian Randomisation (STROBE-MR): explanation and elaboration. (2021) · cites this paper as [53]
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Cites
(2013) · American Economic Review · doi:10.1257/aer.103.5.i · Cited by 15,501 · see citing works
Causation, Prediction, and Search
Spirtes, P., Glymour, C., & Scheines, R. (1993) · Lecture Notes in Statistics · doi:10.1007/978-1-4612-2748-9 · Cited by 4,617 · see citing works
Identification of Causal Effects Using Instrumental Variables
Angrist, J. D., Imbens, G. W., & Rubin, D. B. (1996) · Journal of the American Statistical Association · doi:10.1080/01621459.1996.10476902 · Cited by 4,230 · see citing works
Identification and estimation of local average treatment effects
Imbens, G. W., & Angrist, J. D. (1994) · Econometrica · doi:10.2307/2951620 · Cited by 4,101 · see citing works
Causal Diagrams for Epidemiologic Research
Greenland, S., Pearl, J., & Robins, J. M. (1999) · Epidemiology · doi:10.1097/00001648-199901000-00008 · Cited by 3,728 · see citing works
Self-citationAir Pollution and Hospital Admissions for Heart Disease in Eight U.S. Counties
Schwartz, J. D. (1999) · Epidemiology · doi:10.1097/00001648-199901000-00005 · Cited by 3,044 · see citing works
Identification and Estimation of Local Average Treatment Effects
Angrist, J. D., & Imbens, G. W. (1995) · National Bureau of Economic Research · doi:10.3386/t0118 · Cited by 2,898 · see citing works
Robins, J. (1986) · Mathematical Modelling · doi:10.1016/0270-0255(86)90088-6 · Cited by 2,451 · see citing works
Self-citationMaternal Pesticide Exposure from Multiple Sources and Selected Congenital Anomalies
Shaw, G. M., Wasserman, C. R., O’Malley, C. D., Nelson, V. E., & Jackson, R. J. (1999) · Epidemiology · doi:10.1097/00001648-199901000-00011 · Cited by 1,783 · see citing works
The Review of Economics and Statistics
Dorfman, R. (1997) · Edward Elgar Publishing eBooks · doi:10.4337/9781035334919.00011 · Cited by 1,560 · see citing works
Causality: Models, Reasoning, and Inference
Shanmugam, R. (2001) · Neurocomputing · doi:10.1016/s0925-2312(01)00330-7 · Cited by 1,377 · see citing works
An IV Model of Quantile Treatment Effects
Chernozhukov, V., & Hansen, C. (2004) · Econometrica · doi:10.1111/j.1468-0262.2005.00570.x · Cited by 999 · see citing works
Instruments for Causal Inference: An Epidemiologist's Dream?
Hernán, M. A., & Robins, J. M. (2006) · Epidemiology · doi:10.1097/01.ede.0000222409.00878.37 · Cited by 961 · see citing works
Self-citationProceedings of the 26th Conference on Uncertainty in Artificial Intelligence (UAI 2010)
Adams, R. P., Dahl, G. E., & Murray, I. (2010) · Cited by 943 · see citing works
Mendelian randomization as an instrumental variable approach to causal inference
Didelez, V., & Sheehan, N. (2007) · Statistical Methods in Medical Research · doi:10.1177/0962280206077743 · Cited by 923 · see citing works
NONPARAMETRIC BOUNDS ON TREATMENT EFFECTS
Manski, C. F. (1989) · American Economic Review · Cited by 801 · see citing works
Partial Identification of Probability Distributions
(2003) · Springer Series in Statistics · doi:10.1007/b97478 · Cited by 698 · see citing works
Instrumental variable methods for causal inference
Baiocchi, M., Cheng, J., & Small, D. S. (2014) · Statistics in Medicine · doi:10.1002/sim.6128 · Cited by 687 · see citing works
Medicaid Increases Emergency-Department Use: Evidence from Oregon's Health Insurance Experiment
Taubman, S. L., ALLEN, H. L., Wright, B. J., D, K. B. A., & Finkelstein, A. N. (2014) · Science · doi:10.1126/science.1246183 · Cited by 578 · see citing works
Bounds on Treatment Effects from Studies with Imperfect Compliance
Balke, A., & Pearl, J. (1997) · Journal of the American Statistical Association · doi:10.1080/01621459.1997.10474074 · Cited by 564 · see citing works
Methodological Challenges in Mendelian Randomization
VanderWeele, T. J., Tchetgen Tchetgen, E. J., Cornelis, M., & Kraft, P. (2014) · Epidemiology · doi:10.1097/ede.0000000000000081 · Cited by 555 · see citing works
Correcting for non-compliance in randomized trials using structural nested mean models
Robins, J. M. (1994) · Communication in Statistics- Theory and Methods · doi:10.1080/03610929408831393 · Cited by 534 · see citing works
Self-citationMonotone Instrumental Variables with an Application to the Returns to Schooling
Manski, C. F., & Pepper, J. (1998) · National Bureau of Economic Research · doi:10.3386/t0224 · Cited by 450 · see citing works
Proceedings of the Seventeenth Conference on Uncertainty in Artificial Intelligence (2001)Preprint
Breese, J. S., & Koller, D. (2013) · arXiv (Cornell University) · doi:10.48550/arxiv.1301.4607 · Cited by 435 · see citing works
Monotone Instrumental Variables: With an Application to the Returns to Schooling
Manski, C. F., & Pepper, J. V. (2000) · Econometrica · doi:10.1111/1468-0262.00144 · Cited by 432 · see citing works
Manski, C. F. (1997) · Econometrica · doi:10.2307/2171738 · Cited by 381 · see citing works
Zhang, J. L., & Rubin, D. B. (2003) · Journal of Educational and Behavioral Statistics · doi:10.3102/10769986028004353 · Cited by 308 · see citing works
Cardiovascular features of homozygous familial hypercholesterolemia: Analysis of 16 patients
Sprecher, D. L., Schaefer, E. J., Kent, K. M., Gregg, R. E., Zech, L. A., Hoeg, J. M., McManus, B. M., Roberts, W. C., & Brewer, H. B. (1984) · The American Journal of Cardiology · doi:10.1016/0002-9149(84)90298-4 · Cited by 231 · see citing works
Assumptions of IV Methods for Observational Epidemiology.
Didelez, V., Meng, S., & Sheehan, N. A. (2010) · Statistical Science · doi:10.1214/09-sts316 · Cited by 214 · see citing works
A Test for Instrument Validity
Kitagawa, T. (2015) · Econometrica · doi:10.3982/ecta11974 · Cited by 175 · see citing works
Manski, C. F., & Pepper, J. V. (2018) · Review of Economics and Statistics · doi:10.1162/rest_a_00689 · Cited by 158 · see citing works
Causality and Psychopathology: Finding the Determinants of Disorders and their Cures
Shrout, P. E., Keyes, K. M., & Ornstein, K. A. (2010) · Cited by 147 · see citing works
Issues in the Reporting and Conduct of Instrumental Variable Studies
Davies, N. M., Smith, G. D., Windmeijer, F. A. G., & Martin, R. M. (2013) · Epidemiology · doi:10.1097/ede.0b013e31828abafb · Cited by 146 · see citing works
Heuristics, Probability and Causality. A Tribute to Judea Pearl
Dechter, R., Geffner, H., & Halpern, J. Y. (2010) · Cited by 135 · see citing works
Wang, L., & Tchetgen, E. T. (2017) · Journal of the Royal Statistical Society Series B (Statistical Methodology) · doi:10.1111/rssb.12262 · Cited by 135 · see citing works
The paired availability design: A proposal for evaluating epidural analgesia during labor
Baker, S. G., & Lindeman, K. S. (1994) · Statistics in Medicine · doi:10.1002/sim.4780132108 · Cited by 133 · see citing works
Testing Instrument Validity for LATE Identification Based on Inequality Moment Constraints
Huber, M., & Mellace, G. (2014) · The Review of Economics and Statistics · doi:10.1162/rest_a_00450 · Cited by 116 · see citing works
Testing Local Average Treatment Effect Assumptions
Mourifié, I., & Wan, Y. (2016) · The Review of Economics and Statistics · doi:10.1162/rest_a_00622 · Cited by 108 · see citing works
Instrumental variables, selection models, and tight bounds on the average treatment effect
Heckman, J. J., & Vytlacil, E. (2001) · ZEW economic studies · doi:10.1007/978-3-642-57615-7_1 · Cited by 98 · see citing works
Bounds on Direct Effects in the Presence of Confounded Intermediate Variables
Cai, Z., Kuroki, M., Pearl, J., & Tian, J. W. (2007) · Biometrics · doi:10.1111/j.1541-0420.2007.00949.x · Cited by 96 · see citing works
Sharp bounds on the causal effects in randomized experiments with “truncation-by-death”
Imai, K. (2007) · Statistics & Probability Letters · doi:10.1016/j.spl.2007.05.015 · Cited by 91 · see citing works
On the Testability of Causal Models with Latent and Instrumental VariablesPreprint
Pearl, J. (2013) · arXiv (Cornell University) · doi:10.48550/arxiv.1302.4976 · Cited by 89 · see citing works
Using Secondary Outcomes to Sharpen Inference in Randomized Experiments With Noncompliance
Mealli, F., & Pacini, B. (2013) · Journal of the American Statistical Association · doi:10.1080/01621459.2013.802238 · Cited by 84 · see citing works
Instrumental Variable Models for Discrete Outcomes
Chesher, A. (2010) · Econometrica · doi:10.3982/ecta7315 · Cited by 81 · see citing works
Alternative Graphical Causal Models and the Identification of Direct E!ects
Robins, J. M., & Richardson, T. S. (2010) · Cited by 78 · see citing works
Self-citationPartial identification using random set theory
Beresteanu, A., Molchanov, I. S., & Molinari, F. (2011) · Journal of Econometrics · doi:10.1016/j.jeconom.2011.06.003 · Cited by 74 · see citing works
On the analysis of viral load endpoints in HIV vaccine trials
Hudgens, M. G., Hoering, A., & Self, S. G. (2003) · Statistics in Medicine · doi:10.1002/sim.1394 · Cited by 70 · see citing works
Instrumental variable models for discrete outcomes
Chesher, A. (2008) · doi:10.1920/wp.cem.2008.3008 · Cited by 70 · see citing works
Treatment Effect Bounds under Monotonicity Assumptions: An Application to Swan-Ganz Catheterization
Bhattacharya, J., Shaikh, A. M., & Vytlacil, E. (2008) · American Economic Review · doi:10.1257/aer.98.2.351 · Cited by 69 · see citing works
Partial Identification of Local Average Treatment Effects With an Invalid Instrument
Flores, C. A., & Flores‐Lagunes, A. (2013) · Journal of Business and Economic Statistics · doi:10.1080/07350015.2013.822760 · Cited by 63 · see citing works
Instrumentality Tests RevisitedPreprint
Bonet, B. (2013) · arXiv (Cornell University) · doi:10.48550/arxiv.1301.2258 · Cited by 46 · see citing works
Implementing Intersection Bounds in Stata
Chernozhukov, V., Kim, W., Lee, S., & Rosen, A. (2015) · The Stata Journal Promoting communications on statistics and Stata · doi:10.1177/1536867x1501500103 · Cited by 45 · see citing works
Bounds on Average and Quantile Treatment Effects of Job Corps Training on Wages
Blanco, G., Flores, C. A., & Flores‐Lagunes, A. (2013) · The Journal of Human Resources · doi:10.1353/jhr.2013.0017 · Cited by 42 · see citing works
Kaufman, S., Kaufman, J. S., & MacLehose, R. F. (2009) · Journal of Statistical Planning and Inference · doi:10.1016/j.jspi.2009.03.024 · Cited by 40 · see citing works
Huber, M., Lafférs, L., & Mellace, G. (2015) · Journal of Applied Econometrics · doi:10.1002/jae.2473 · Cited by 39 · see citing works
Causal inference using influence diagrams: the problem of partial compliance
Dawid, A. P. (2003) · doi:10.1093/oso/9780198510550.003.0005 · Cited by 38 · see citing works
Partially Identifying Treatment Effects with an Application to Covering the Uninsured
Kreider, B., & Hill, S. C. (2009) · The Journal of Human Resources · doi:10.3368/jhr.44.2.409 · Cited by 37 · see citing works
Transparent Parametrizations of Models for Potential Outcomes
Richardson, T. S., Evans, R. J., & Robins, J. M. (2011) · Oxford University Press eBooks · doi:10.1093/acprof:oso/9780199694587.003.0019 · Cited by 33 · see citing works
Self-citationPartially Identifying Treatment Effects with an Application to Covering the Uninsured
Kreider, B., & Hill, S. C. (2009) · The Journal of Human Resources · doi:10.1353/jhr.2009.0012 · Cited by 32 · see citing works
Identification region of the potential outcome distributions under instrument independence
Kitagawa, T. (2009) · doi:10.1920/wp.cem.2009.3009 · Cited by 31 · see citing works
McCarthy, I., Millimet, D. L., & Roy, M. (2015) · The Stata Journal Promoting communications on statistics and Stata · doi:10.1177/1536867x1501500205 · Cited by 29 · see citing works
Partially Identified Treatment Effects Under Imperfect Compliance: The Case of Domestic Violence
Siddique, Z. (2013) · Journal of the American Statistical Association · doi:10.1080/01621459.2013.779836 · Cited by 27 · see citing works
Bounding the per-protocol effect in randomized trials: an application to colorectal cancer screening
Swanson, S. A., Holme, Ø., Løberg, M., Kalager, M., Bretthauer, M., Hoff, G. S., Aas, E., & Hernán, M. Á. (2015) · Trials · doi:10.1186/s13063-015-1056-8 · Cited by 27 · see citing works
Self-citationNonparametric Bounds for the Causal Effect in a Binary Instrumental-Variable Model
Palmer, T., Ramsahai, R. R., Didelez, V., & Sheehan, N. A. (2011) · The Stata Journal Promoting communications on statistics and Stata · doi:10.1177/1536867x1101100302 · Cited by 23 · see citing works
Implementing intersection bounds in Stata
Chernozhukov, V., Kim, W., Rosen, A., & Lee, S. (2013) · doi:10.1920/wp.cem.2013.3813 · Cited by 20 · see citing works
Causal bounds and observable constraints for non-deterministic models
Ramsahai, R. R. (2012) · Cited by 16 · see citing works
ACE Bounds; SEMs with Equilibrium Conditions
Richardson, T. S., & Robins, J. M. (2014) · Statistical Science · doi:10.1214/14-sts485 · Cited by 15 · see citing works
Self-citationACE Bounds; SEMs with Equilibrium ConditionsPreprint
Richardson, T. S., & Robins, J. M. (2016) · Cited by 15 · see citing works
Self-citationSensitivity checks for the local average treatment effect
Huber, M. (2014) · Economics Letters · doi:10.1016/j.econlet.2014.02.018 · Cited by 14 · see citing works
Wang, L., & Tchetgen, E. T. (2016) · arXiv (Cornell University) · doi:10.48550/arxiv.1611.09925 · Cited by 8 · see citing works
Robins, J. M., & Greenland, S. (1996) · Journal of the American Statistical Association · doi:10.1080/01621459.1996.10476903 · Cited by 2 · see citing works
Self-citationThe Oregon Health Insurance Experiment
Finkelstein, A. N., Welch, K., Taubman, S. L., et al. (2013) · AEA Randomized Controlled Trials · doi:10.1257/rct.28-1.0 · Cited by 1 · see citing works
Flagged first, then by citations
Research works printed but not linked: 1
- Robins JM, and Greenland S (1996), “ Identification of Causal Effects Using Instrumental Variables: Comment,” Journal of the American Statistical Association, 91, 456– 458. [ 937,943,945]
Cited by
Sorted by citations
Sanderson, E., Glymour, M. M., Holmes, M. V., Kang, H., Morrison, J., Munafò, M. R., Palmer, T., Schooling, C. M., Wallace, C., Zhao, Q., et al. (2022) · Nature Reviews Methods Primers · doi:10.1038/s43586-021-00092-5 · Cited by 2,229 · see citing works
Skrivankova, V. W., Richmond, R. C., Woolf, B. A. R., Davies, N. M., Swanson, S. A., VanderWeele, T. J., Timpson, N. J., Higgins, J. P. T., Dimou, N., Langenberg, C., et al. (2021) · BMJ · doi:10.1136/bmj.n2233 · Cited by 1,648 · see citing works
Self-citationBurgess, S., & Labrecque, J. A. (2018) · European Journal of Epidemiology · doi:10.1007/s10654-018-0424-6 · Cited by 569 · see citing works
Labrecque, J., & Swanson, S. A. (2018) · Current Epidemiology Reports · doi:10.1007/s40471-018-0152-1 · Cited by 190 · see citing works
Self-citationA Practical Guide to Selection Bias in Instrumental Variable Analyses
Swanson, S. A. (2019) · Epidemiology · doi:10.1097/ede.0000000000000973 · Cited by 36 · see citing works
Self-citation
- Authors
- Swanson, S. A., Hernán, M. A., Miller, M., Robins, J. M., & Richardson, T. S.
- Affiliations
- Harvard University (US)
- Department of Epidemiology, Harvard T. H. Chan School of Public Health, Boston, MA
- Northeastern University (US)
- University of Washington (US)
- Corresponding author
- Swanson, Sonja A.
- Venue
- Journal of the American Statistical Association
- Publisher
- Informa UK Limited
- Published
- 2018-04-03
- Volume
- 113
- Issue
- 522
- Pages
- 933-947
- ISSN
- 0162-1459 (ISSN-L)
- 1537-274X
- PMC
- PMC6752717
- OpenAlex
- W2807279683
- Cited by
- 93
- References
- 72
- Citations by year
- 2026: 5 · 2025: 14 · 2024: 15 · 2023: 11 · 2022: 12 · 2021: 13 · 2020: 8 · 2019: 9 · 2018: 6
- FWCI
- 7.47
- Type
- journal article
- Language
- en
- Update notices
- correction (2020-03-02)
- Open access
- bronze
- doi.org
- Locations
- Journal of the American Statistical Association (publishedVersion)
- PubMed (publishedVersion)
- EUR Research Repository (Erasmus University Rotterdam) (publishedVersion, other-oa)
- Europe PMC (PubMed Central) (acceptedVersion, cc-by-nc-nd)
- PubMed Central (acceptedVersion, cc-by-nc-nd)
- EUR Research Repository (Erasmus University Rotterdam) (submittedVersion, other-oa)
- RePub (Erasmus University Rotterdam) (submittedVersion, other-oa)
- RePEc: Research Papers in Economics (submittedVersion)
- Funders
- National Institutes of Health (R01 AI032475,R01 AI102634)
- Nederlandse Organisatie voor Wetenschappelijk Onderzoek (91617066)
- Office of Naval Research (N00014-15-1-2672)
- Topics
- Physical Sciences › Mathematics › Statistics and Probability › Advanced Causal Inference Techniques
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods in Clinical Trials
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Bayesian Inference
- Keywords
- average treatment effect, partial identification, point identification, instrumental variables, binary instrument, binary treatment, binary outcomes, identification assumptions
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
