A Time-Frequency Analysis of the Coherences of the US Business Cycle and the European Business Cycle

The search for and dating of a possible european business cycle, has been inconclusive. At this stage, there is no consensus on the existence of such a cycle, or of its periodicity and amplitude, or of the relationship of individual member countries to that cycle. Yet cyclical convergence is the key consideration for countries which have to decide whether they wish to be members of a currency union such as the euro. The confusion over whether and to what degree the UK is converging on the cycles of its European partners, or whether its cycle is more in line with the US, is a classic example of the difficulties caused by this lack of consensus. We argue that different countries will vary in the components and characteristics that make up their output cycles, as well as vary in the state of their cycle at any point of time. We show how to decompose a business cycle in a time-frequency framework. This then allows us to decompose movements in output, both at the European level and in member countries, into their component cycles and allows those component cycles to vary in importance and cyclical characteristics over time. It also allows us to determine if the nonconclusive results so far have appeared because member countries have some cycles in common, but diverge (i.e. have nothing in common) at other frequencies.