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Random matrix theory and the evolution of business cycle synchronisation 1886-2006


  • Paul Ormerod


The major study by Bordo and Helbing (2003) analyses the business cycle in Western economies 1881-2001. 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. Their analysis, in common with the standard economic literature on business cycle synchronisation, relies upon the estimation of an empirical correlation matrix of time series data of macroeconomic aggregates. However because of the small number of observations and economies, the empirical correlation matrix may contain considerable noise. Random matrix theory was developed to overcome this problem. I use random matrix theory, and the associated technique of agglomerative hierarchical clustering, to examine the evolution of business cycle synchronisation between the capitalist economies in the long-run. Contrary to the findings of Bordo and Helbing, it is not possible to speak of a 'secular trend' towards greater synchronisation over the period as a whole. During the pre-First World War period, the cross-country correlations of annual real GDP growth are indistinguishable from those which could be generated by a purely random matrix. The periods 1920-38 and 1948-72 do show a certain degree of synchronisation, but it is very weak. In particular, the cycles of the major economies cannot be said to be synchronised. Such synchronisation as exists in the overall data is due to meaningful co-movements in sub-groups. So the degree of synchronisation has evolved fitfully. It is only in the most recent 1973-2006 period that we can speak meaningfully of anything resembling an international business cycle.

Suggested Citation

  • Paul Ormerod, 2008. "Random matrix theory and the evolution of business cycle synchronisation 1886-2006," Papers 0807.1771,
  • Handle: RePEc:arx:papers:0807.1771

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    Cited by:

    1. Leonidas Sandoval Junior & Italo De Paula Franca, 2011. "Correlation of financial markets in times of crisis," Papers 1102.1339,, revised Mar 2011.
    2. Iyetomi, Hiroshi & Nakayama, Yasuhiro & Yoshikawa, Hiroshi & Aoyama, Hideaki & Fujiwara, Yoshi & Ikeda, Yuichi & Souma, Wataru, 2011. "What causes business cycles? Analysis of the Japanese industrial production data," Journal of the Japanese and International Economies, Elsevier, vol. 25(3), pages 246-272, September.
    3. Sandoval, Leonidas & Franca, Italo De Paula, 2012. "Correlation of financial markets in times of crisis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(1), pages 187-208.

    More about this item

    JEL classification:

    • E32 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Business Fluctuations; Cycles
    • C69 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Other
    • N10 - Economic History - - Macroeconomics and Monetary Economics; Industrial Structure; Growth; Fluctuations - - - General, International, or Comparative


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