Random Matrix Theory and the Evolution of Business Cycle Synchronisation, 1886-2006 - Paul Ormerod (Kiel Institute for the World Economy (IfW), 2008)
Bordo and Helbing (2003) examine the business cycle in Western economies over the 1881-2001 period. They examine four distinct periods in economic history and conclude that there is a secular trend towards greater synchronisation for much of the 20th century, and that it takes place across these different regimes. Most of the analytical techniques used in the business cycle convergence literature rely upon the estimation of an empirical correlation matrix of time series data of macroeconomic aggregates in the various countries. However due to the finite size of both the number of economies and the number of observations, a reliable determination of the correlation matrix may prove to be problematic. The structure of the correlation matrix may be dominated by noise rather than by true information. Random matrix theory was developed in physics to overcome this problem, and to enable true information in a matrix to be distinguished from noise. It has been successfully applied in the analysis of financial data. Using a very similar data set to Bordo and Helbing, I use random matrix theory, and the associated technique of agglomerative hierarchical clustering, to examine the evolution of convergence of the business cycle between the capitalist economies. The results confirm that there is a very clear degree of synchronisation of the business cycle across countries during the 1973-2006 period. In contrast, during the pre-First World War period it is not possible to speak of an international business cycle in any meaningful sense. The crosscountry correlations of annual real GDP growth are indistinguishable from those which could be generated by a purely random matrix. Contrary to the findings of Bordo and Helbing, it does not seem possible to speak of a ?secular trend? towards greater synchronisation over the 1886-2006 period as a whole. The periods 1920-1938 and 1948-1972 do show a certain degree of synchronisation – very similar in both periods in fact – but it is weak. In particular, the cycles of the major economies cannot be said to be synchronised during these periods. Such synchronisation as exists in the overall data set is due to meaningful comovements in sub-groups. So the degree of synchronisation has evolved fitfully, and it is only in the most recent period, 1973-2006, that we can speak of a strong level of synchronisation of business cycles between countries. More detailed analysis of the evolution of synchronisation of the 6 major economies since 1948 suggests it can vary considerably over relatively short periods of time. During the 1990s, for example, the degree of synchronisation of the cycle was similar to that of the 1950s, and lower than it was in the 1970s and 1980s following the oil shocks.
Keywords: E32; C69; N10; 330; International business cycle; synchronisation; random matrix theory; Konjunkturzusammenhang; Entwicklungskonvergenz; Korrelation; Statistischer Fehler; Welt