Working Paper Revision

Analysis of Multiple Long-Run Relations in Panel Data Models

Abstract: The literature on panel cointegration is extensive but does not cover data sets where the cross-section dimension, n, is larger than the time-series dimension T. This paper proposes a novel methodology that filters out the short-run dynamics using sub-sample time averages as deviations from their full-sample counterpart, and estimates the number of long-run relations and their coefficients using eigenvalues and eigenvectors of the pooled covariance matrix of these sub-sample deviations. We refer to this procedure as pooled minimum eigenvalue (PME). We show that the PME estimator is consistent and asymptotically normal as n and T → ∞ jointly, such that T ≈ nd, with d > 0 for consistency and d > 1/2 for asymptotic normality. Extensive Monte Carlo studies show that the number of long-run relations can be estimated with high precision, and the PME estimators have good size and power properties. The utility of our approach is illustrated by micro and macro applications using Compustat and Penn World Tables.

JEL Classification: C13; C23; C33; G30;

https://doi.org/10.24149/wp2523r2

Bibliographic Information

Provider: Federal Reserve Bank of Dallas

Part of Series: Working Papers

Publication Date: 2025-09-29

Number: 2523

Note: Previous versions were titled, "Analysis of Multiple Long Run Relations in Panel Data Models with Applications to Financial Ratios."

Related Works

• Working Paper Revision (2025-09-29) : You are here.
• Working Paper Revision (2025-08-20) : Analysis of Multiple Long Run Relations in Panel Data Models with Applications to Financial Ratios
• Working Paper Original (2025-06-05) : Analysis of Multiple Long Run Relations in Panel Data Models with Applications to Financial Ratios