The Law of Proportionate Effect: The Growth of the UK Credit Union Movement at National and Regional Level

Abstract: This study examines credit union size‐growth relationships within the context of Gibrat's law of proportionate effect. This relates to the hypothesis that the growth of each firm in each period is random. The analysis covers the period 1994 to 2000 and is undertaken separately for the United Kingdom (UK) and its regions, Northern Ireland, England & Wales and Scotland. Sample attrition is a characteristic of the data and to avoid the problem of survivorship bias the inverse of the Mill's ratio, obtained from a probit regression for surviving credit unions, is introduced into the estimating relationship. In terms of the empirical results, little evidence emerged to support the law of proportionate effect as a theoretical paradigm. Although not universal, three broad findings emerged. First, small credit unions on average grow faster than their larger counterparts, although there was also some evidence of non‐linearity in this relationship. Secondly, growth persistence pertained with credit unions which experienced above average growth (below average growth) in one period, experiencing above average growth (below average growth) in the next. Thirdly, variability of growth was not independent of size with the cross‐sectional variance of the error term inversely related to size suggesting that small credit unions have greater growth variability than larger ones.