🔍 The Problem and Aim

Estimating treatment-effect variation often relies on including a multiplicative interaction between treatment and a proposed effect modifier in a regression. This simple approach can produce biased inferences when the modifier interacts with other covariates that are not modeled, while adding many interaction terms can cause unstable estimates from overfitting. The paper investigates these trade-offs and asks how adaptive, machine-learning methods can be used to stabilize interaction estimates without introducing new biases.

🧪 How the Methods Were Evaluated

• Illustrates how off-the-shelf adaptive methods introduce two distinct forms of regularization bias:
• direct regularization bias (coefficients are shrunk toward zero by penalization), and
• indirect regularization bias (variable selection or shrinkage omits or downweights covariates that interact with the modifier, biasing the interaction estimate).
• Proposes a post-double selection strategy that uses several lasso estimators to choose which interactions to include in the final model, then estimates interaction and marginal effects with uncertainty quantification.
• Compares performance through simulation experiments and two empirical applications to demonstrate practical consequences.

📈 Key Findings

• The post-double selection approach yields more reliable interaction and marginal effect estimates than competing methods in simulations, including settings with many covariates.
• Machine-learning methods used without careful selection can produce misleading results because of both direct and indirect regularization bias.
• In two empirical examples, the choice of estimation method substantially altered conclusions about effect heterogeneity, showing real-world importance.

💡 Why It Matters

These results show that routine interaction tests can be fragile in observational and high-dimensional settings. The proposed lasso-based post-double selection framework reduces model misspecification and bias while allowing valid uncertainty assessment for interaction and marginal effects, helping researchers draw more credible inferences about treatment-effect heterogeneity.