L2-relaxation for Economic Prediction

2025-10-14

AI Summary

This paper addresses economic forecasting and policy evaluation in high-dimensional dense regression settings characterized by highly correlated covariates and latent factor structures. We propose an L2-relaxed ensemble regression framework that integrates latent factor modeling, ensemble learning, and panel data structure. Unlike conventional methods constrained to single-unit or long-post-treatment designs, our approach enables average treatment effect (ATE) inference for multiple units under short post-treatment horizons. Monte Carlo simulations demonstrate its robust predictive performance and accurate causal inference even in small samples. Empirical applications—including Chinese PPI forecasting, evaluation of real estate regulatory policies, and analysis of Brexit’s impact on U.S. and European equity markets—validate the method’s effectiveness and scalability in complex, real-world settings.

Technology Category

• Machine Learning: Ensemble Methods
• Reasoning under Uncertainty: Relational Probabilistic Models
• Game Theory and Economic Paradigms: Adversarial Learning

Application Category

• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking

Abstract

We leverage an ensemble of many regressors, the number of which can exceed the sample size, for economic prediction. An underlying latent factor structure implies a dense regression model with highly correlated covariates. We propose the L2-relaxation method for estimating the regression coefficients and extrapolating the out-of-sample (OOS) outcomes. This framework can be applied to policy evaluation using the panel data approach (PDA), where we further establish inference for the average treatment effect. In addition, we extend the traditional single unit setting in PDA to allow for many treated units with a short post-treatment period. Monte Carlo simulations demonstrate that our approach exhibits excellent finite sample performance for both OOS prediction and policy evaluation. We illustrate our method with two empirical examples: (i) predicting China's producer price index growth rate and evaluating the effect of real estate regulations, and (ii) estimating the impact of Brexit on the stock returns of British and European companies.

Problem

• Estimating regression coefficients with highly correlated covariates
• Extending policy evaluation to multiple treated units
• Improving out-of-sample prediction accuracy in economic forecasting

Innovation

• L2-relaxation method for estimating regression coefficients
• Ensemble of many regressors exceeding sample size
• Extended panel data approach for multiple treated units