Student or educator? Sign up with your school email and get 6 months of Pro free.
CoChat
Sign Up
Cited by 2,946

The DOI matches its Crossref record; 6 of the 6 references it cites were found in a registry or an index.

Double/debiased machine learning for treatment and structural parameters

Chernozhukov, Victor, Chetverikov, Denis, Demirer, Mert, Duflo, Esther, Hansen, Christian, Newey, Whitney, Robins, James·2018·The Econometrics Journal
DOI 10.1111/ectj.12097
Open this paper in CoChat — free account

Abstract

We revisit the classic semi‐parametric problem of inference on a low‐dimensional parameter θ0 in the presence of high‐dimensional nuisance parameters η0. We depart from the classical setting by allowing for η0 to be so high‐dimensional that the traditional assumptions (e.g. Donsker properties) that limit complexity of the parameter space for this object break down. To estimate η0, we consider the use of statistical or machine learning (ML) methods, which are particularly well suited to estimation in modern, very high‐dimensional cases. ML methods perform well by employing regularization to reduce variance and trading off regularization bias with overfitting in practice. However, both regularization bias and overfitting in estimating η0 cause a heavy bias in estimators of θ0 that are obtained by naively plugging ML estimators of η0 into estimating equations for θ0. This bias results in the naive estimator failing to be N−1/2 consistent, where N is the sample size. We show that the impact of regularization bias and overfitting on estimation of the parameter of interest θ0 can be removed by using two simple, yet critical, ingredients: (1) using Neyman‐orthogonal moments/scores that have reduced sensitivity with respect to nuisance parameters to estimate θ0; (2) making use of cross‐fitting, which provides an efficient form of data‐splitting. We call the resulting set of methods double or debiased ML (DML). We verify that DML delivers point estimators that concentrate in an N−1/2‐neighbourhood of the true parameter values and are approximately unbiased and normally distributed, which allows construction of valid confidence statements. The generic statistical theory of DML is elementary and simultaneously relies on only weak theoretical requirements, which will admit the use of a broad array of modern ML methods for estimating the nuisance parameters, such as random forests, lasso, ridge, deep neural nets, boosted trees, and various hybrids and ensembles of these methods. We illustrate the general theory by applying it to provide theoretical properties of the following: DML applied to learn the main regression parameter in a partially linear regression model; DML applied to learn the coefficient on an endogenous variable in a partially linear instrumental variables model; DML applied to learn the average treatment effect and the average treatment effect on the treated under unconfoundedness; DML applied to learn the local average treatment effect in an instrumental variables setting. In addition to these theoretical applications, we also illustrate the use of DML in three empirical examples.

Overview

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.

A few free checks a day · papers already verified open instantly · results are public

Integrity signals

Registry

Crossref · 10.1111/ectj.12097

Cites

6 of 6 references verified0 citation errors · 0 not checkable

Statistics

Verification

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.

A few free checks a day · papers already verified open instantly · results are public

Self-check

Percentages, sums and reported differences re-computed from the paper’s own numbers.

The self-check needs the paper’s full text.

Citations

Cites

Show all 6 references

Research works printed but not linked: 84

  1. Abadie, 2006, Large sample properties of matching estimators for average treatment effects, Econometrica, 74, 235, 10.1111/j.1468-0262.2006.00655.x · DOI · Paper page
  2. Ai, 2012, The semi‐parametric efficiency bound for models of sequential moment restrictions containing unknown functions, Journal of Econometrics, 170, 442, 10.1016/j.jeconom.2012.05.015 · DOI
  3. Andrews, 1994, Asymptotics for semi‐parametric econometric models via stochastic equicontinuity, Econometrica, 62, 43, 10.2307/2951475 · DOI · Paper page
  4. Andrews, 1994, Empirical process methods in econometrics, 2247, 10.1016/S1573-4412(05)80006-6 · DOI
  5. Angrist, 1995, Split‐sample instrumental variables estimates of the return to schooling, Journal of Business and Economic Statistics, 13, 225, 10.1080/07350015.1995.10524597 · DOI · Paper page
  6. Athey, 2016, Approximate residual balancing: de‐biased inference of average treatment effects in high‐dimensions
  7. Ayyagari, 2010, Applications of influence functions to semi‐parametric regression models
  8. Belloni, 2011, ℓ1‐penalized quantile regression for high dimensional sparse models, Annals of Statistics, 39, 82, 10.1214/10-AOS827 · DOI · Paper page
  9. Belloni, 2013, Least squares after model selection in high‐dimensional sparse models, Bernoulli, 19, 521, 10.3150/11-BEJ410 · doi:10.3150/11-bej410 · Paper page
  10. Belloni, 2010, Lasso methods for Gaussian instrumental variables models
  11. Belloni, 2011, Square‐root‐lasso: pivotal recovery of sparse signals via conic programming, Biometrika, 98, 791, 10.1093/biomet/asr043 · DOI · Paper page
  12. Belloni, 2012, Sparse models and methods for optimal instruments with an application to eminent domain, Econometrica, 80, 2369, 10.3982/ECTA9626 · DOI · Paper page
  13. Belloni, 2013, Inference for high‐dimensional sparse econometric models, 245, 10.1017/CBO9781139060035.008 · doi:10.1017/cbo9781139060035.008
  14. Belloni, 2014, Inference on treatment effects after selection amongst high‐dimensional controls, Review of Economic Studies, 81, 608, 10.1093/restud/rdt044 · DOI · Paper page
  15. Belloni, 2014, Pivotal estimation via square‐root Lasso in nonparametric regression, Annals of Statistics, 42, 757, 10.1214/14-AOS1204 · DOI
  16. Belloni, 2015, Uniform post selection inference for LAD regression models and other z‐estimators, Biometrika, 102, 77, 10.1093/biomet/asu056 · DOI · Paper page
  17. Belloni, 2016, Post‐selection inference for generalized linear models with many controls, Journal of Business and Economic Statistics, 34, 606, 10.1080/07350015.2016.1166116 · DOI
  18. Belloni, 2017, Program evaluation with high‐dimensional data, Econometrica, 85, 233, 10.3982/ECTA12723 · DOI · Paper page
  19. Bera, 2010, General specification testing with locally misspecified models, Econometric Theory, 26, 1838, 10.1017/S0266466609990818 · doi:10.1017/s0266466609990818
  20. Bickel, 1982, On adaptive estimation, Annals of Statistics, 10, 647, 10.1214/aos/1176345863 · DOI · Paper page
  21. Bickel, 1988, Estimating integrated squared density derivatives, Sankhya, A‐50, 381
  22. Bickel, 1998, Efficient and Adaptive Estimation for Semi‐Parametric Models
  23. Bickel, 2009, Simultaneous analysis of Lasso and Dantzig selector, Annals of Statistics, 37, 1705, 10.1214/08-AOS620 · DOI · Paper page
  24. Bilias, 2000, Sequential testing of duration data: the case of the Pennsylvania ‘reemployment bonus’ experiment, Journal of Applied Econometrics, 15, 575, 10.1002/jae.579 · DOI
  25. Bilias, 2002, Quantile regression for duration data: a reappraisal of the Pennsylvania reemployment bonus experiments, 199
  26. Bühlmann, 2011, Statistics for High‐Dimensional Data, 10.1007/978-3-642-20192-9 · DOI · Paper page
  27. Chamberlain, 1987, Asymptotic efficiency in estimation with conditional moment restrictions, Journal of Econometrics, 34, 305, 10.1016/0304-4076(87)90015-7 · DOI · Paper page
  28. Chamberlain, 1992, Efficiency bounds for semi‐parametric regression, Econometrica, 60, 567, 10.2307/2951584 · DOI · Paper page
  29. Chen, 1999, Improved rates and asymptotic normality for nonparametric neural network estimators, IEEE Transactions on Information Theory, 45, 682, 10.1109/18.749011 · DOI · Paper page
  30. Chernozhukov, 2004, The effects of 401 (k) participation on the wealth distribution: an instrumental quantile regression analysis, Review of Economics and Statistics, 86, 735, 10.1162/0034653041811734 · DOI · Paper page
  31. Chernozhukov, 2014, Gaussian approximation of suprema of empirical processes, Annals of Statistics, 42, 1564, 10.1214/14-AOS1230 · DOI
  32. Chernozhukov, 2016, Locally robust semi‐parametric estimation
  33. Chernozhukov, 2015, Post‐selection and post‐regularization inference in linear models with very many controls and instruments, Americal Economic Review: Papers and Proceedings, 105, 486, 10.1257/aer.p20151022 · DOI
  34. Chernozhukov, 2015, Valid post‐selection and post‐regularization inference: an elementary, general approach, Annual Review of Economics, 7, 649, 10.1146/annurev-economics-012315-015826 · DOI
  35. DasGupta, 2008, Asymptotic Theory of Statistics and Probability
  36. Fan, 2012, Variance estimation using refitted cross‐validation in ultrahigh dimensional regression, Journal of the Royal Statistical Society, 74, 37, 10.1111/j.1467-9868.2011.01005.x · DOI · Paper page
  37. Farrell, 2015, Robust inference on average treatment effects with possibly more covariates than observations, Journal of Econometrics, 174, 1, 10.1016/j.jeconom.2015.06.017 · DOI · Paper page
  38. Ferguson, 1967, Mathematical Statistics: A Decision Theoretic Approach
  39. Frölich, 2007, Nonparametric IV estimation of local average treatment effects with covariates, Journal of Econometrics, 139, 35, 10.1016/j.jeconom.2006.06.004 · DOI
  40. Gautier, 2014, High‐dimensional instrumental variables regression and confidence sets
  41. Hahn, 1998, On the role of the propensity score in efficient semi‐parametric estimation of average treatment effects, Econometrica, 66, 315, 10.2307/2998560 · DOI · Paper page
  42. Hansen, 1982, Large sample properties of generalized method of moments estimators, Econometrica, 50, 1029, 10.2307/1912775 · DOI · Paper page
  43. Hasminskii, 1979, On the nonparametric estimation of functionals, 41
  44. Hirano, 2003, Efficient estimation of average treatment effects using the estimated propensity score, Econometrica, 71, 1161, 10.1111/1468-0262.00442 · DOI · Paper page
  45. Hubbard, 2016, Statistical inference for data adaptive target parameters, International Journal of Biostatistics, 12, 3, 10.1515/ijb-2015-0013 · DOI
  46. Ibragimov, 1981, Statistical Estimation: Asymptotic Theory, 10.1007/978-1-4899-0027-2 · doi:10.1007/978-1-4899-0027-2
  47. Ichimura, 2015, The influence function of semi‐parametric estimators, 10.1920/wp.cem.2015.4415 · doi:10.1920/wp.cem.2015.4415
  48. Imai, 2013, Estimating treatment effect heterogeneity in randomized program evaluation, Annals of Applied Statistics, 7, 443, 10.1214/12-AOAS593 · DOI · Paper page
  49. Javanmard, 2014, Confidence intervals and hypothesis testing for high‐dimensional regression, Journal of Machine Learning Research, 15, 2869
  50. Javanmard, 2014, Hypothesis testing in high‐dimensional regression under the Gaussian random design model: asymptotic theory, IEEE Transactions on Information Theory, 60, 6522, 10.1109/TIT.2014.2343629 · DOI
  51. Kozbur, 2016, Testing‐based forward model selection
  52. Levit, 1975, On the efficiency of a class of nonparametric estimates, Theory of Probability and Its Applications, 20, 723, 10.1137/1120081 · DOI
  53. Linton, 1996, Edgeworth approximation for MINPIN estimators in semi‐parametric regression models, Econometric Theory, 12, 30, 10.1017/S0266466600006435 · DOI
  54. Luedtke, 2016, Optimal individualized treatments in resource‐limited settings, International Journal of Biostatistics, 12, 283, 10.1515/ijb-2015-0007 · DOI
  55. Luo, 2016, High‐dimensional l2 boosting: rate of convergence
  56. Nevelson, 1977, On one informational lower bound, Problemy Peredachi Informatsii, 13, 26
  57. Newey, 1990, Semi‐parametric efficiency bounds, Journal of Applied Econometrics, 5, 99, 10.1002/jae.3950050202 · DOI · Paper page
  58. Newey, 1998, Undersmoothing and bias corrected functional estimation
  59. Newey, 2004, Twicing kernels and a small bias property of semi‐parametric estimators, Econometrica, 72, 947, 10.1111/j.1468-0262.2004.00518.x · DOI
  60. Neyman, 1959, Optimal asymptotic tests of composite statistical hypotheses, 416
  61. Neyman, 1979, c(α) tests and their use, Sankhya, 1
  62. Poterba, 1994, 401(k) plans and tax‐deferred savings, 105
  63. Poterba, 1994, Do 401(k) contributions crowd out other personal saving, Journal of Public Economics, 58, 1, 10.1016/0047-2727(94)01462-W · DOI · Paper page
  64. Robins, 1995, Semi‐parametric efficiency in multivariate regression models with missing data, Journal of the American Statistical Association, 90, 122, 10.1080/01621459.1995.10476494 · DOI · Paper page
  65. Robins, 2008, Higher order influence functions and minimax estimation of nonlinear functionals, 335, 10.1214/193940307000000527 · DOI
  66. Robins, 2013, New statistical approaches to semi‐parametric regression with application to air pollution research
  67. Robins, 2017, Minimax estimation of a functional on a structured high dimensional model, Annals of Statistics, 10.1214/16-AOS1515 · doi:10.1214/16-aos1515
  68. Robinson, 1988, Root‐N‐consistent semi‐parametric regression, Econometrica, 56, 931, 10.2307/1912705 · DOI · Paper page
  69. Rosenbaum, 1983, The central role of the propensity score in observational studies for causal effects, Biometrika, 70, 41, 10.1093/biomet/70.1.41 · DOI · Paper page
  70. Scharfstein, 1999, Rejoinder to “adjusting for non‐ignorable drop‐out using semi‐parametric non‐response models, Journal of the American Statistical Association, 94, 1135
  71. Schick, 1986, On asymptotically efficient estimation in semi‐parametric models, Annals of Statistics, 14, 1139, 10.1214/aos/1176350055 · DOI
  72. Severini, 1992, Profile likelihood and conditionally parametric models, Annals of Statistics, 20, 1768, 10.1214/aos/1176348889 · DOI · Paper page
  73. Toth, 2016, TMLE for marginal structural models based on an instrument
  74. van de, 2014, On asymptotically optimal confidence regions and tests for high‐dimensional models, Annals of Statistics, 42, 1166, 10.1214/14-AOS1221 · DOI · Paper page
  75. van der Laan, 2015, A generally efficient targeted minimum loss based estimator
  76. van der Laan, 2011, Targeted Learning: Causal Inference for Observational and Experimental Data, 10.1007/978-1-4419-9782-1 · DOI · Paper page
  77. van der Laan, 2006, Targeted maximum likelihood learning, 10.2202/1557-4679.1043 · DOI · Paper page
  78. van der Laan, 2007, Super learner, Statistical Applications in Genetics and Molecular Biology, 6, 10.2202/1544-6115.1309 · DOI · Paper page
  79. van der Vaart, 1991, On differentiable functionals, Annals of Statistics, 19, 178, 10.1214/aos/1176347976 · DOI · Paper page
  80. Wager, 2016, Adaptive concentration of regression trees, with application to random forests
  81. Wooldridge, 1991, Specification testing and quasi‐maximum‐likelihood estimation, Journal of Econometrics, 48, 29, 10.1016/0304-4076(91)90031-8 · DOI
  82. Zhang, 2014, Confidence intervals for low‐dimensional parameters with high‐dimensional data, Journal of the Royal Statistical Society, 76, 217, 10.1111/rssb.12026 · DOI · Paper page
  83. Zheng, 2011, Cross‐validated targeted minimum‐loss‐based estimation, 459, 10.1007/978-1-4419-9782-1_27 · doi:10.1007/978-1-4419-9782-1_27
  84. Zheng, 2016, Marginal structural models with counterfactual effect modifiers

Cited by

Metadata

Authors
Chernozhukov, V., Chetverikov, D., Demirer, M., Duflo, E., Hansen, C., Newey, W., & Robins, J.
Venue
The Econometrics Journal
Publisher
Oxford University Press (OUP)
Published
2018-01-16
Volume
21
Issue
1
Pages
C1-C68
ISSN
  • 1368-4221 (ISSN-L)
  • 1368-423X
DOI
10.1111/ectj.12097
OpenAlex
W3123436326
Cited by
2,946
References
6
FWCI
37.13
Type
journal article
Language
en
Open access
closed
Licence
Funders
National Science Foundation

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

Data sources

Bibliographic data: Semantic Scholar, OpenAlex, Crossref.

Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).

Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.