Many causal and policy effects of interest are defined by linear functionals of high-dimensional or non-parametric regression functions. Root-n consistent and asymptotically normal estimation of the object of interest requires debiasing to reduce the effects of regularization and/or model selection on the object of interest. Debiasing is
typically achieved by adding a correction term to the plug-in estimator of the functional, which leads to properties such as semi-parametric efficiency, double robustness, and Neyman orthogonality. We implement an automatic debiasing procedure based on automatically learning the Riesz representation of the linear functional using Neural
Nets and Random Forests. Our method only relies on black-box evaluation oracle access to the
linear functional and does not require knowledge of its analytic form. We propose a multitasking Neural Net debiasing method with stochastic gradient descent minimization of a combined Riesz representer and regression loss, while sharing representation layers for the two functions. We also propose a Random Forest method which learns a locally linear representation of the Riesz function. Even though our method applies to arbitrary functionals,
we experimentally find that it performs well compared to the state of art neural net based algorithm of Shi et al. (2019) for the case of the average treatment effect functional. We also evaluate our method on the problem of estimating average marginal effects with continuous treatments, using semi-synthetic data of gasoline price changes on gasoline demand. Code available at github.com/victor5as/RieszLearning.
more »
« less
Automatic Debiased Machine Learning of Causal and Structural Effects
Many causal and structural effects depend on regressions. Examples include policy effects, average derivatives, regression decompositions, average treatment effects, causal mediation, and parameters of economic structural models. The regressions may be high‐dimensional, making machine learning useful. Plugging machine learners into identifying equations can lead to poor inference due to bias from regularization and/or model selection. This paper gives automatic debiasing for linear and nonlinear functions of regressions. The debiasing is automatic in using Lasso and the function of interest without the full form of the bias correction. The debiasing can be applied to any regression learner, including neural nets, random forests, Lasso, boosting, and other high‐dimensional methods. In addition to providing the bias correction, we give standard errors that are robust to misspecification, convergence rates for the bias correction, and primitive conditions for asymptotic inference for estimators of a variety of estimators of structural and causal effects. The automatic debiased machine learning is used to estimate the average treatment effect on the treated for the NSW job training data and to estimate demand elasticities from Nielsen scanner data while allowing preferences to be correlated with prices and income.
more »
« less
- Award ID(s):
- 1757140
- NSF-PAR ID:
- 10469495
- Publisher / Repository:
- Journal of the Econometric Society
- Date Published:
- Journal Name:
- Econometrica
- Volume:
- 90
- Issue:
- 3
- ISSN:
- 0012-9682
- Page Range / eLocation ID:
- 967 to 1027
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
Abstract Standard estimators of the global average treatment effect can be biased in the presence of interference. This paper proposes regression adjustment estimators for removing bias due to interference in Bernoulli randomized experiments. We use a fitted model to predict the counterfactual outcomes of global control and global treatment. Our work differs from standard regression adjustments in that the adjustment variables are constructed from functions of the treatment assignment vector, and that we allow the researcher to use a collection of any functions correlated with the response, turning the problem of detecting interference into a feature engineering problem. We characterize the distribution of the proposed estimator in a linear model setting and connect the results to the standard theory of regression adjustments under SUTVA. We then propose an estimator that allows for flexible machine learning estimators to be used for fitting a nonlinear interference functional form. We propose conducting statistical inference via bootstrap and resampling methods, which allow us to sidestep the complicated dependences implied by interference and instead rely on empirical covariance structures. Such variance estimation relies on an exogeneity assumption akin to the standard unconfoundedness assumption invoked in observational studies. In simulation experiments, our methods are better at debiasing estimates than existing inverse propensity weighted estimators based on neighborhood exposure modeling. We use our method to reanalyze an experiment concerning weather insurance adoption conducted on a collection of villages in rural China.more » « less
-
Randomized A/B tests within online learning platforms represent an exciting direction in learning sciences. With minimal assumptions, they allow causal effect estimation without confounding bias and exact statistical inference even in small samples. However, often experimental samples and/or treatment effects are small, A/B tests are underpowered, and effect estimates are overly imprecise. Recent methodological advances have shown that power and statistical precision can be substantially boosted by coupling design-based causal estimation to machine-learning models of rich log data from historical users who were not in the experiment. Estimates using these techniques remain unbiased and inference remains exact without any additional assumptions. This paper reviews those methods and applies them to a new dataset including over 250 randomized A/B comparisons conducted within ASSISTments, an online learning platform. We compare results across experiments using four novel deep-learning models of auxiliary data and show that incorporating auxiliary data into causal estimates is roughly equivalent to increasing the sample size by 20% on average, or as much as 50-80% in some cases, relative to t-tests, and by about 10% on average, or as much as 30-50%, compared to cutting-edge machine learning unbiased estimates that use only data from the experiments. We show that the gains can be even larger for estimating subgroup effects, hold even when the remnant is unrepresentative of the A/B test sample, and extend to post-stratification population effects estimators.more » « less
-
Randomized A/B tests within online learning platforms represent an exciting direction in learning sciences. With minimal assumptions, they allow causal effect estimation without confounding bias and exact statistical inference even in small samples. However, often experimental samples and/or treatment effects are small, A/B tests are under-powered, and effect estimates are overly imprecise. Recent methodological advances have shown that power and statistical precision can be substantially boosted by coupling design-based causal estimation to machine-learning models of rich log data from historical users who were not in the experiment. Estimates using these techniques remain unbiased and inference remains exact without any additional assumptions. This paper reviews those methods and applies them to a new dataset including over 250 randomized A/B comparisons conducted within ASSISTments, an online learning platform. We compare results across experiments using four novel deep-learning models of auxiliary data, and show that incorporating auxiliary data into causal estimates is roughly equivalent to increasing the sample size by 20% on average, or as much as 50-80% in some cases, relative to t-tests, and by about 10% on average, or as much as 30-50%, compared to cutting-edge machine learning unbiased estimates that use only data from the experiments. We show the gains can be even larger for estimating subgroup effects, that they hold even when the remnant is unrepresentative of the A/B test sample, and extend to post-stratification population effects estimators.more » « less
-
more » « less
Machine learning (ML) methods for causal inference have gained popularity due to their flexibility to predict the outcome model and the propensity score. In this article, we provide a within-group approach for ML-based causal inference methods in order to robustly estimate average treatment effects in multilevel studies when there is cluster-level unmeasured confounding. We focus on one particular ML-based causal inference method based on the targeted maximum likelihood estimation (TMLE) with an ensemble learner called SuperLearner. Through our simulation studies, we observe that training TMLE within groups of similar clusters helps remove bias from cluster-level unmeasured confounders. Also, using within-group propensity scores estimated from fixed effects logistic regression increases the robustness of the proposed within-group TMLE method. Even if the propensity scores are partially misspecified, the within-group TMLE still produces robust ATE estimates due to double robustness with flexible modeling, unlike parametric-based inverse propensity weighting methods. We demonstrate our proposed methods and conduct sensitivity analyses against the number of groups and individual-level unmeasured confounding to evaluate the effect of taking an eighth-grade algebra course on math achievement in the Early Childhood Longitudinal Study.
- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.3982/ECTA18515
