Inference for Forecasting Accuracy: Pooled versus Individual Estimators in High-dimensional Panel Data

2025/12/17 by Kutta, Tim, Schumann, Martin, Dette, Holger
#Econometrics (econ.EM) #FOS: Computer and information sciences #FOS: Economics and business #FOS: Mathematics #Methodology (stat.ME) #Statistics Theory (math.ST)

paper · doi:10.48550/arxiv.2512.15592

Abstract

Panels with large time (T) and cross-sectional (N) dimensions are a key data structure in social sciences and other fields. A central question in panel data analysis is whether to pool data across individuals or to estimate separate models. Pooled estimators typically have lower variance but may suffer from bias, creating a fundamental trade-off for optimal estimation. We develop a new inference method to compare the forecasting performance of pooled and individual estimators. Specifically, we propose a confidence interval for the difference between their forecasting errors and establish its asymptotic validity. Our theory allows for complex temporal and cross-sectional dependence in the model errors and covers scenarios where N can be much larger than T-including the independent case under the classical condition N/T² → 0. The finite-sample properties of the proposed method are examined in an extensive simulation study.

Citations

• Forecasting with panel data: Estimation uncertainty versus parameter heterogeneity
• Validating Approximate Slope Homogeneity in Large Panels
• Efficient Inference in a Random Coefficient Regression Model
• Testing slope homogeneity in large panels

Related

• Forecasting with panel data: Estimation uncertainty versus parameter heterogeneity
• To Pool or Not to Pool: Revisited
• Inference in High-Dimensional Panel Models: Two-Way Dependence and Unobserved Heterogeneity
• Estimation and inference for linear panel data models under misspecification when both n and T are large
• Forecasting with Dynamic Panel Data Models