Abstract
In this paper the relationship between the growth of real GDP components is explored in the frequency domain using both static and dynamic wavelet analysis. This analysis is carried out separately for both the US and the UK using quarterly data, and the results are found to be substantially different in the two countries. One of the key findings in this research is that the “great moderation” shows up only at certain frequencies, and not in all components of real GDP. We use these results to explain why the incidence of the great moderation has been so patchy 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. We argue it cannot be done without breaking the GDP components down into their frequency components across time and these results show why: the predictions of traditional real business cycle theory often appear not to be upheld in the data.
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Notes
- 1.
An analysis of fluctuations in real GNP itself has already been undertaken in Crowley (2010).
- 2.
These are shocks from new investment which contains new technology rather than investment that either replaces depreciated equipment or just adds to the stock of existing capital without upgrading the technology.
- 3.
Note that the vertical axes are scaled differently for each component.
- 4.
In mathematics and, in particular, functional analysis, convolution is a mathematical operation on two functions f and g, producing a third function that is typically viewed as a modified version of one of the original functions. Convolution is similar to cross-correlation. It has applications that include statistics, computer vision, image and signal processing, electrical engineering, and differential equations.
- 5.
But given that we seek the same resolution of cycles at different frequencies, this is still the most efficient way to estimate the crystals.
- 6.
Given the previous footnote, it is obvious that by doing this, it will lead to “redundancy” as the wavelet coefficients have already been combined with most of the same datapoints.
- 7.
One of the issues with spectral time-frequency analysis is the Heisenberg uncertainty principle, which states that the more certainty that is attached to the measurement of one dimension ( - frequency, for example), the less certainty can be attached to the other dimension ( - here the time location).
- 8.
As Percival and Walden (2000) note, the MODWT is also commonly referred to by various other names in the wavelet literature such as non-decimated DWT, time-invariant DWT, undecimated DWT, translation-invariant DWT and stationary DWT. The term “maximal overlap” comes from its relationship with the literature on the Allan variance (the variation of time-keeping by atomic clocks)—see Greenhall (1991).
- 9.
The MODWT was found superior to both the cosine packet transform and the short-time Fourier transform.
- 10.
These can also be accessed online at: http://faculty.tamucc.edu/pcrowley/Research/frequency_domain_economics.html.
- 11.
This also appears in GNP data as shown in Crowley (2010).
- 12.
Separating automatic from discretionary fiscal policies in a cyclical environment is not an easy matter. Bernoth et al. (2013) review different methods, and show how it can be done by combining real time and ex-post data.
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Acknowledgements
This research was completed while Crowley was visiting the School of Public Policy at George Mason University in Fairfax, VA, USA during the fall of 2009. Dean Kingsley Haynes should be thanked for hosting Crowley at George Mason University in 2009 and Texas A&M University - Corpus Christi is acknowledged for providing faculty development leave funding.
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Crowley, P.M., Hallett, A.H. (2014). The Great Moderation Under the Microscope: Decomposition of Macroeconomic Cycles in US and UK Aggregate Demand. In: Gallegati, M., Semmler, W. (eds) Wavelet Applications in Economics and Finance. Dynamic Modeling and Econometrics in Economics and Finance, vol 20. Springer, Cham. https://doi.org/10.1007/978-3-319-07061-2_3
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