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

TL;DR

This paper develops a new inference method to compare the forecasting accuracy of pooled versus individual estimators in high-dimensional panel data, accounting for complex dependencies and large cross-sectional dimensions.

Contribution

It introduces a confidence interval for the difference in forecasting errors, valid under complex dependence and high-dimensional settings, extending existing methods.

Findings

The proposed confidence interval is asymptotically valid under broad dependence structures.

Simulation results demonstrate good finite-sample performance.

Method applies even when cross-sectional units vastly outnumber time periods.

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 $N/T^2 \to 0$. The finite-sample properties of the proposed method are examined in an extensive simulation study.