Optimization Strategy for the Modeling and Estimation of Interactive Effects

Modeling policy effects in the context of high-dimensional data requires a balanced consideration of omitted interaction bias and overfitting problems. This paper investigates the role of machine learning algorithms in stabilizing estimates and demonstrates the possible regularization bias caused by common LASSO methods. To overcome the three problems simultaneously, post-double selection is used to screen for the interaction terms that need to be included in the model, and the variance estimates are expanded to measure the uncertainty of the interaction effects and marginal effects. Monte Carlo simulations analyze the main factors affecting conditional and non-linear relationships: covariance and sample size. The results of empirical examples show that different model settings and estimation methods can lead to observable differences in the conclusion of treatment effect heterogeneity, and in general, post-double selection has better performance than other estimation methods.