Analysis of Multiple Long-Run Relations in Panel Data Models

TL;DR

This paper introduces the pooled minimum eigenvalue (PME) method for estimating long-run relations in panel data models where the cross section exceeds the time dimension, demonstrating its consistency, normality, and practical effectiveness.

Contribution

It proposes a novel PME methodology for panel cointegration with large cross sections, addressing a gap in existing literature and providing consistent, asymptotically normal estimators.

Findings

PME estimator is consistent and asymptotically normal under specified conditions.

High accuracy in estimating the number of long-run relations in simulations.

Demonstrated utility through micro and macroeconomic data applications.

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 PME estimator is consistent and asymptotically normal as $n$ and $T \rightarrow \infty$ jointly, such that $T\approx n^{d}$, 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.