A random matrix theory approach to test for agricultural productivity convergence

Originating from multivariate statistics, random matrix theory (RMT) is used in order to test whether the elements of an empirical correlation coefficient matrix are noise dominated or contain true information. In this article, an attempt is made to apply the properties of RMT in macroeconomic time series data, by investigating the degree of convergence in agricultural labour productivity growth among a set of 32 European and Middle East and North Africa countries. Once the distribution of the eigenvalues of the empirical correlation matrix is found to differ from that of a pure random matrix, data are further analysed by means of hierarchical clustering techniques which allow for the creation of data clusters with common properties. This two-step procedure is an alternate means for club convergence tests, while some sensitivity analysis tests indicate an acceptable level of robustness of the proposed methodology even in small sample sizes.