随机矩阵理论与经济周期同步性的演变1886-2006
Random matrix theory and the evolution of business cycle synchronisation 1886-2006
摘要：
Bordo和Helbing（2003）的主要研究分析了1881-2001年西方经济体的商业周期。他们研究了经济史上四个不同的时期，并得出结论，在20世纪的大部分时间里，存在着一种长期的趋势，即经济增长的同步性更强。他们的分析与关于商业周期同步性的标准经济学文献一样，依赖于对宏观经济总量的时间序列数据的经验相关矩阵的估计。然而，由于观测数量少和经济性，经验相关矩阵可能包含相当大的噪声。随机矩阵理论就是为了克服这个问题而发展起来的。我使用随机矩阵理论，以及相关的凝聚层次聚类技术，从长远来看，资本主义经济体之间的商业周期同步性的演变。与Bordo和Helbing的研究结果相反，在整个时期内，不可能说有一个“长期趋势”朝着更大的同步发展。在第一次世界大战前，年度实际GDP增长的跨国相关性与纯随机矩阵产生的相关性无法区分。1920- 1938年和1948- 1972年这两个时期确实显示出某种程度的同步性，但这种同步性非常弱。特别是，主要经济体的周期不能说是同步的。整体数据中存在的这种同步是由于子组中有意义的共同运动。因此，同步的程度一直在断断续续地发展。只有在最近的1973-2006年期间，我们才能有意义地谈论任何类似于国际商业周期的东西。
英文摘要：
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.
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