Panel unit root tests of the size and growth of large US credit unions

This article explores the size‐growth relationship for a panel of large US credit unions, using the panel unit root tests of Im et al. (2003) and Maddala and Wu (1999). The reference point is Gibrat’s Law, or the Law of Proportionate Effect, according to which firm growth rates are independent of firm sizes. The panel unit root tests are applied to the log as sets and log membership series of a sample of 997 surviving credit unions which reported data over the period 1993 to 2002. In each case the panel unit root tests fail to reject the null hypothesis of non‐stationarity in the logarithmic size series for all credit unions. The implication is that credit union sizes follow random walks, producing a tendency for industry concentration to increase in the long term. With many of the largest institutions currently offering portfolios of products and services similar to those of commercial banks and other financial institutions, these implications of the panel unit root test results appear consistent with observed patterns within the sector in recent years.