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Forecasting with panel data: Estimation uncertainty versus parameter heterogeneity

M. Hashem Pesaran, Andreas Pick, Allan Timmermann

TL;DR

This paper analyzes forecasting with panel data across individual, pooled, fixed effects, and empirical Bayes (EB) estimators, and develops forecast combination schemes to mitigate estimation uncertainty and parameter heterogeneity. It derives MSFE decompositions showing the trade-offs between pooling advantages and heterogeneity costs, and demonstrates that EB and forecast combinations often outperform unit-specific forecasts, especially when heterogeneity is substantial or correlated with regressors. Monte Carlo experiments confirm these patterns under varying $N$, $T$, and heterogeneity, and two empirical applications (U.S. house prices and CPI sub-indices) show EB and combination forecasts delivering substantial accuracy gains while maintaining low downside risk. The results suggest a practical forecasting strategy: lean on forecast combinations and EB to hedge against model misspecification and the presence of heterogeneous parameters, rather than relying on a single unit-specific or pooled approach. Overall, EB and forecast combinations provide a robust, risk-aware toolkit for panel forecasting in economics and finance.

Abstract

We provide a comprehensive examination of the predictive performance of panel forecasting methods based on individual, pooling, fixed effects, and empirical Bayes estimation, and propose optimal weights for forecast combination schemes. We consider linear panel data models, allowing for weakly exogenous regressors and correlated heterogeneity. We quantify the gains from exploiting panel data and demonstrate how forecasting performance depends on the degree of parameter heterogeneity, whether such heterogeneity is correlated with the regressors, the goodness of fit of the model, and the dimensions of the data. Monte Carlo simulations and empirical applications to house prices and CPI inflation show that empirical Bayes and forecast combination methods perform best overall and rarely produce the least accurate forecasts for individual series.

Forecasting with panel data: Estimation uncertainty versus parameter heterogeneity

TL;DR

This paper analyzes forecasting with panel data across individual, pooled, fixed effects, and empirical Bayes (EB) estimators, and develops forecast combination schemes to mitigate estimation uncertainty and parameter heterogeneity. It derives MSFE decompositions showing the trade-offs between pooling advantages and heterogeneity costs, and demonstrates that EB and forecast combinations often outperform unit-specific forecasts, especially when heterogeneity is substantial or correlated with regressors. Monte Carlo experiments confirm these patterns under varying , , and heterogeneity, and two empirical applications (U.S. house prices and CPI sub-indices) show EB and combination forecasts delivering substantial accuracy gains while maintaining low downside risk. The results suggest a practical forecasting strategy: lean on forecast combinations and EB to hedge against model misspecification and the presence of heterogeneous parameters, rather than relying on a single unit-specific or pooled approach. Overall, EB and forecast combinations provide a robust, risk-aware toolkit for panel forecasting in economics and finance.

Abstract

We provide a comprehensive examination of the predictive performance of panel forecasting methods based on individual, pooling, fixed effects, and empirical Bayes estimation, and propose optimal weights for forecast combination schemes. We consider linear panel data models, allowing for weakly exogenous regressors and correlated heterogeneity. We quantify the gains from exploiting panel data and demonstrate how forecasting performance depends on the degree of parameter heterogeneity, whether such heterogeneity is correlated with the regressors, the goodness of fit of the model, and the dimensions of the data. Monte Carlo simulations and empirical applications to house prices and CPI inflation show that empirical Bayes and forecast combination methods perform best overall and rarely produce the least accurate forecasts for individual series.
Paper Structure (33 sections, 6 theorems, 189 equations, 1 figure, 5 tables)

This paper contains 33 sections, 6 theorems, 189 equations, 1 figure, 5 tables.

Table of Contents

  1. Introduction
  2. Setup and assumptions
  3. Panel regression model
  4. Assumptions
  5. Theoretical results on forecasting performance
  6. Forecasts based on individual and pooled estimation
  7. Forecasts based on fixed effects estimation
  8. Forecast combinations
  9. Combinations of individual and pooled forecasts
  10. Combining individual and fixed effect forecasts
  11. Estimation of combination weights
  12. Empirical Bayes forecasts
  13. Monte Carlo experiments
  14. Data generating process
  15. Simulation results
  16. ...and 18 more sections

Key Result

Proposition 1

Figures (1)

  • Figure 1: Distributions of ratios of MSFEs

Theorems & Definitions (8)

  • Proposition 1
  • Proposition 2
  • Proposition 3
  • Proposition 4
  • Lemma 1
  • proof
  • Lemma 2
  • proof