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October 18, 20250 citationsOpen Access

L2-relaxation for Economic Prediction

ZSZhentao ShiChinese University of Hong Kong YWYishu WangQilu University of Technology

Key Points

The L2-relaxation method significantly improves economic prediction accuracy and model inference.
Monte Carlo simulations indicate strong finite sample performance for out-of-sample predictions and policy assessments.
The approach extends traditional panel data settings, accommodating multiple units within a brief post-treatment period.
Empirical examples demonstrate successful applications in predicting economic indicators and evaluating policy impacts.

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.

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