1 The Question

Every empirical paper that estimates a causal effect must choose which covariates to include as controls. This choice is consequential. Omitting a confounding variable biases the treatment effect estimate. Including a bad control—a mediator or a collider—also biases it, sometimes catastrophically [Cinelli et al., 2022]. Including irrelevant covariates reduces precision.

For decades, the standard approach was theory-guided: researchers drew on economic models, institutional knowledge, and domain expertise to identify the set of confounders that must be controlled. A study of minimum wage effects controls for industry, region, and business cycle; not because a LASSO selected these variables, but because economic theory says they drive both wages and employment.

The emergence of high-dimensional machine learning methods has challenged this tradition. Post-double-selection LASSO (PDS-LASSO) [Belloni et al., 2014] and double machine learning (DML) [Chernozhukov et al., 2018] offer a data-driven alternative: let the regularisation algorithm identify which controls matter for prediction of the outcome and treatment, and then use those selected controls for causal estimation.

Which approach is right? This is not a settled debate, and the answer depends on the setting.

2 The Case for Theory-Guided Selection

2.1 Theory Identifies Confounders, Not Predictors

The goal of covariate selection in causal inference is to identify confounders—variables that jointly affect the treatment and the outcome. A predictor of the outcome that does not affect treatment assignment is not a confounder and need not be included to remove bias (though it can be included to reduce variance).

ML algorithms select variables that predict the outcome or the treatment, not necessarily variables that are confounders. A variable that predicts wages—say, industry tenure—may do so because it is a consequence of prior wages (mediator) rather than a cause. Including it as a control may create mediator bias. Pearl [2009] showed using directed acyclic graphs (DAGs) that the correct conditioning set for causal identification is not the full set of predictors but the set that satisfies the backdoor criterion: blocking all backdoor paths from treatment to outcome without opening new paths through colliders. This is a structural criterion that requires knowing the causal graph, not the predictive relationship.

2.2 Bad Controls Cannot Be Identified by Prediction Alone

The bad controls problem—identified by Cinelli et al. [2022] and earlier by Pearl [2009]—is invisible to ML covariate selection. A variable that is both a strong predictor of the outcome and a post-treatment variable (mediator) will be selected by LASSO or DML because it improves prediction, yet including it as a control blocks part of the treatment effect and biases the estimate.

In a study of the effect of education on wages, the occupation in which a worker is employed is a strong predictor of wages. But occupation is partly determined by education—it is a mediator. Including occupation as a control in a regression of wages on education attenuates the estimated return to education. No ML algorithm can detect this problem without knowing that occupation is post-treatment.

2.3 Researcher Degrees of Freedom Are Not Eliminated

A common motivation for ML covariate selection is that it reduces researcher degrees of freedom: if the algorithm chooses the controls, the researcher cannot cherry-pick a specification that supports a favoured conclusion. But this argument is weaker than it appears. The researcher still chooses the outcome model class, the LASSO penalty (λ), the normalisation of variables, the definition of the treatment, and the set of candidate variables to include in the LASSO. These choices affect the selected covariates significantly. ML selection is not an objective procedure; it is a researcher-guided procedure at a higher level of abstraction.

3 The Case for ML-Guided Selection

3.1 Theory Is Often Incomplete

In many applied settings, the researcher does not have a complete causal model. A study of the effect of a new drug on patient outcomes must control for all confounders—but the full set of relevant confounders in a complex biological system is unknown. Similarly, studies of the effect of trade exposure on local economies must control for all pre-existing factors that predict both trade exposure and subsequent outcomes, and the relevant factors may be numerous and their functional forms unknown.

In such settings, a theory-guided approach may omit variables that are genuinely confounding simply because the researcher did not know they mattered. PDS-LASSO and DML offer a way to select from a large candidate set of potential confounders without the researcher needing to know in advance which ones are relevant. If the candidate set is rich enough to include all confounders, ML selection will (approximately) find them.

3.2 PDS-LASSO Reduces Omitted Variable Bias in High Dimensions

The specific advantage of PDS-LASSO [Belloni et al., 2014] over both unaided theory and standard LASSO is that it imposes double-selection: it selects variables that predict the outcome and variables that predict the treatment, and includes the union as controls. This double selection property ensures that the estimator is not biased by the omission of variables that are relevant for predicting the treatment (potential confounders) even if they are irrelevant for predicting the outcome conditional on treatment.

In settings with hundreds of potential covariates and genuine uncertainty about which are the relevant confounders, PDS-LASSO provides theoretical guarantees that a theory-guided approach cannot: under sparsity conditions, the resulting estimator of the treatment effect is √n consistent and asymptotically normal, even in the presence of many irrelevant controls.

3.3 DML Separates Causal and Nuisance Estimation

DML [Chernozhukov et al., 2018] makes a more nuanced claim: use flexible ML for nuisance estimation (the functions 𝔼[Y|X] and 𝔼[D|X]) but maintain the causal model structure (the parameter θ in the partially linear model). This framing—ML for nuisance, theory for structure—reconciles the two approaches. The causal model is theory-specified; only the high-dimensional controls are estimated using ML.

This framing has become influential as a synthesis position [Imbens, 2020]: the research design (the source of identifying variation) is theory-driven, but the estimation of confounding functions is data-driven. A minimum wage study uses the Card-Krueger quasi-experimental design (theory); it uses ML to estimate how observable county characteristics predict employment trends (nuisance).

4 Finding Common Ground

The debate is partly a false dichotomy. Both approaches agree on the fundamental goal: to control for confounders while avoiding bad controls. They disagree on the best way to identify which variables achieve this. The most defensible position, articulated by Imbens [2020] and Belloni et al. [2014], is:

1. Use theory to specify the causal model: Define the treatment, the outcome, and the estimand. Identify the causal assumptions (unconfoundedness, exclusion restriction, parallel trends) that justify the identification strategy. Use DAGs or structural equations to check which variables are confounders, mediators, and colliders.
2. Use ML to estimate within the causal model: Once the set of potential confounders is identified (even if the exact functional form and which subset matter most is unknown), use LASSO, DML, or causal forests to estimate the relevant nuisance functions without imposing incorrect parametric forms.
3. Pre-specify and report: Whether using theory or ML, specify the covariate selection procedure before analysis, report the procedure transparently, and conduct sensitivity analyses that vary the selected control set.

5 A Scenario Where Each Approach Fails

Theory fails: A researcher studying the effect of neighbourhood poverty on child outcomes controls for a theory-motivated set of family characteristics. But they miss that school quality, which is correlated with both neighbourhood poverty and child outcomes, is omitted from their theory because it was not included in the standard model. ML selection, with school quality in the candidate set, would have found the omission.

ML fails: A researcher studying the effect of a job training programme includes as a LASSO candidate the participant's subsequent industry of employment. LASSO selects this variable because it strongly predicts wages. But industry is post-treatment (partly determined by the training programme), and including it blocks the effect of the programme on wages through industry upgrading. ML selection cannot detect the mediator problem without causal knowledge.

6 Conclusion

The choice between ML and theory for covariate selection is not a binary one. Theory is indispensable for specifying the causal model, avoiding bad controls, and interpreting results. ML is valuable for efficiently identifying relevant confounders in high-dimensional settings and for estimating nuisance functions flexibly. The optimal approach combines both: theory-specified causal structure, ML-estimated nuisance components, and transparent pre-specification of the procedure. Neither approach, used alone, is adequate for rigorous causal inference.

References

1. Belloni, A., Chernozhukov, V., and Hansen, C. (2014). Inference on treatment effects after selection among high-dimensional controls. Review of Economic Studies, 81(2):608-650.
2. Brodeur, A., Cook, N., and Heyes, A. (2020). Methods matter: p-hacking and publication bias in causal analysis in economics. American Economic Review, 110(11):3634-3660.
3. Chernozhukov, V., Chetverikov, D., Demirer, M., Duflo, E., Hansen, C., Newey, W., and Robins, J. (2018). Double/debiased machine learning for treatment and structural parameters. Econometrics Journal, 21(1):C1-C68.
4. Cinelli, C., Forney, A., and Pearl, J. (2022). A crash course in good and bad controls. Sociological Methods & Research, 53(3):1071-1104.
5. Imbens, G. W. (2020). Potential outcome and directed acyclic graph approaches to causality: Relevance for empirical practice in economics. Journal of Economic Literature, 58(4):1129-1179.
6. Pearl, J. (2009). Causality: Models, Reasoning, and Inference. Cambridge University Press, 2nd edition.
7. Wager, S. and Athey, S. (2018). Estimation and inference of heterogeneous treatment effects using random forests. Journal of the American Statistical Association, 113(523):1228-1242.