Analysis of Multiple Long Run Relations in Panel Data Models with Applications to Financial Ratios

Alexander Chudik, Mohammad Pesaran and Ronald Smith

No 2523, Working Papers from Federal Reserve Bank of Dallas

Abstract: This paper provides a new methodology for the analysis of multiple long-run relations in panel data models where the cross-section dimension, n, is large relative to the time-series dimension, T. For panel data models with large n, researchers have focused on panels with a single long-run relationship. The main difficulty has been to eliminate short-run dynamics without generating significant uncertainty for identification of the long run. We overcome this problem by using non-overlapping sub-sample time averages as deviations from their full-sample counterpart and estimating 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) and show that it applies to unbalanced panels generated from general linear processes with interactive stationary time effects and does not require knowing long-run causal linkages. To our knowledge, no other estimation procedure exists for this setting. We show 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 estimates of the long-run coefficients show small bias and RMSE and have good size and power properties. The utility of our approach is illustrated with an application to key financial variables using an unbalanced panel of U.S. firms from a merged CRSP-Compustat dataset covering 2,000-plus firms over the period 1950–2021.

Keywords: multiple long run relations; Pooled Minimum Eigenvalue (PME) estimator; eigenvalue thresholding; panel data; I(1) regressors; interactive time effects; financial ratios (search for similar items in EconPapers)
JEL-codes: C13 C23 C33 G30 (search for similar items in EconPapers)
Pages: 203
Date: 2025-06-05
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Related works:
Working Paper: Analysis of Multiple Long Run Relations in Panel Data Models with Applications to Financial Ratios (2025)
Working Paper: Analysis of Multiple Long Run Relations in Panel Data Models with Applications to Financial Ratios (2025)
Working Paper: Analysis of Multiple Long Run Relations in Panel Data Models with Applications to Financial Ratio (2025)
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DOI: 10.24149/wp2523

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