Great moderation or ‘‘Will o’ the Wisp’’? A time–frequency decomposition of GDP for the US and UK

JEL classification: E0 E32 E60 C63 Keywords: Business cycles Growth cycles Economic growth Time–frequency domain Discrete wavelet analysis Volatility a b s t r a c t In this paper the relationship between the growth of real GDP components at different cycle lengths is explored in the frequency domain using discrete wavelet analysis. This analysis is done for both the US and the UK using quarterly data, and the results reveal interesting differences between the two countries. One of the key findings is that the ''great moderation'' shows up only at certain frequencies, and not in all components of real GDP. A second result is that the great moderation appears to have shifted cyclical power from shorter and business cycles to long cycles, which has important implications for both policy formulation and the probability of less frequent but more severe economic crises. We use these results to explain why the incidence of the great moderation has been so ephemeral across GDP components, countries and time periods. This also explains why it has been so hard to detect periods of moderation (or otherwise) reliably in the aggregate data. The frequency domain offers economists a different perspective for analysis of economic data from time series approaches. The number of contributions in economics that use frequency domain analysis is small, and yet a number of important advances have been made in frequency domain methods which have not yet filtered fully into the economics literature. For example, there are now methods available which permit simultaneous analysis of economic time series in both the frequency and time domains. These techniques are typically referred to as ''time–frequency analysis''. While time–frequency techniques are not yet part of the standard toolbox for analysis of time series in economics, these techniques are standard in other disciplines such as engineering, acoustics, neurological sciences, physics, geology and environmental sciences. Our aim in this paper is to study the cyclical behaviour of the expenditure components of output, to evaluate how interactions between the components has changed over time. The rationale for looking at cyclical interactions between the major components of output is twofold: