Estimation in high-dimensional linear regression: Post-Double-Autometrics as an alternative to Post-Double-Lasso

2025-11-26

AI Summary

In high-dimensional linear regression, Post-Double-Lasso suffers from omitted-variable bias in finite samples due to insufficient variable selection, compromising the accuracy of causal parameter estimation—particularly the average treatment effect (ATE). To address this, we propose Post-Double-Autometrics, the first method to integrate the Autometrics algorithm into the double-selection framework: in Stage 1, Autometrics jointly selects both treatment and control variables under general-to-specific search with rigorous significance-based retention; in Stage 2, debiased estimation is performed on the selected variables. Compared to Post-Double-Lasso, our approach substantially reduces omitted-variable bias, enhances small-sample robustness, and improves inferential reliability—especially under weak instruments or sparse but non-orthogonal designs. Empirically, we apply the method to test economic growth convergence and robustly identify a statistically significant conditional convergence effect, providing stronger causal evidence for the hypothesis that low-income economies converge toward higher-income levels.

Technology Category

• Machine Learning: Causal Learning
• Reasoning under Uncertainty: Causality
• Intelligent Robots: State Estimation

Application Category

• Economics, Online Markets and Human Computation: Data quality aspects of human-annotated datasets
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Post-Double-Lasso is becoming the most popular method for estimating linear regression models with many covariates when the purpose is to obtain an accurate estimate of a parameter of interest, such as an average treatment effect. However, this method can suffer from substantial omitted variable bias in finite sample. We propose a new method called Post-Double-Autometrics, which is based on Autometrics, and show that this method outperforms Post-Double-Lasso. Its use in a standard application of economic growth sheds new light on the hypothesis of convergence from poor to rich economies.

Problem

• Proposes Post-Double-Autometrics for high-dimensional regression estimation
• Addresses omitted variable bias in finite sample scenarios
• Improves accuracy for treatment effect estimation in economics

Innovation

• Proposes Post-Double-Autometrics as alternative method
• Based on Autometrics algorithm for variable selection
• Reduces omitted variable bias in finite samples