What cycles in US consumption look like....

So what do cycles look like in something like US consumption?  Part of my recent research using a technique that originated in signal processing called "wavelet analysis", allows the researcher to separate out the different frequencies embedded in any economic variable.  The plot below is taken from a forthcoming paper with Andrew Hughes Hallett.

Below in the plot I've taken the year on year change in US consumption expenditures (from the US Bureau of Economic Research) and used wavelet analysis ( - for those of you interested MODWT with a Debauchies 8-tap wavelet) to extract the different cycles at different frequencies.  The first line (labelled "d1") are the cycles in the data at 2-4 quarters, the second line (d2) the cycles at 1-2 years, the third (d3) shows cycles at 2-4 years, the fourth (d4) shows cycles at 4-8 years, the fifth (d5) shows 8-16 year cycles and the sixth shows 16-32 year cycles.  The last (s6 - or what is known as the "smooth") shows what is left over when all the other cycles are removed from the series.

So what do we find here?  Well I hope you agree that the results here are quite revealing. 

First, we definitely see cycles at different frequencies, and clearly the strongest of these cycles is in the d3, d4 and d5 lines, although there are other cycles apparent in the data at other frequencies.  So these cycles correspond to 2 to 16 year cycles which is a little surprising as it implies that there are quite strong fluctuations in consumer expenditures at cycles outside what most economists would think of as the conventional "business cycle".

Second, economists have been intrigued about what they have termed "the Great Moderation", when refers to roughly the post-mid-1980s period when growth became much more stable.  Here when looking at these different frequency cycles we can see that this stability is due almost entirely to short cycles becoming less volatile - notably d2 and d3, so 1-4 year cycles, but that the longer cycles do not seem to have changed in their volatility. 

Third, economists have always hypothesized a long cycle of up to 50 years (or even beyond), but if we look at this analysis, it is clear that there's nothing beyond a 30 year cycle (which is clearly in the last line of the plot or s6). 

Lastly, look at the current recession.  It is clear that it has been caused by a coincident downturn in all of the cycles.  This leads to a new way of thinking about how recessions occur.  Instead of thinking of them as being caused by "shocks" hitting a stable growth trajectory, this view of the world thinks of them as being caused by the coincidence of fluctuations in growth occurring at a variety of different frequencies.

More on investment soon...