Signal to noise

 GDP data, which are designed to measure the whole economy as accurately as possible, have a couple of flaws, inherent in their coverage and calculation.  Because they cover so many sectors, they are subject to revision, sometimes going back several years.  It is true that "Flash" estimates are often available shortly after the quarter's end, but these are subject to even bigger revisions as fuller data become available.

Business and consumer surveys are usually available within a few days of the month's end, and only the most recent month is revised.   The most prominent of the monthly surveys are the PMIs (Purchasing Managers' Indices), such as S&P Global's PMI surveys, the ISM (Institute of Supply Management) surveys in the USA, business confidence surveys (such as the ZEW surveys in Germany/Euro Area) and so on.  Now, PMI surveys for most economies only go back for 12 or so years.  But one can make very good estimates of what the PMIs would have been if the surveys had been done before that, using business confidence time series.

But then you encounter other problems.  Quite often, business confidence surveys are very "spiky", i.e., they fluctuate a lot from month to month.  In technical terms, their signal-to-noise ratio is low.  Actually, this also applies to PMI time series, but to a lesser extent.  What I do is use an algorithm created years ago by the US Bureau of the Census, which reduces spikes up or down.  If this isn't enough, I fit a moving average, using my own judgement about whether it should be 3,5 or 7 months long.

Look at the example of the Ivey business confidence surveys in Canada, in the succession of charts below:

Well, frankly, as it stands, this chart is more or less useless.  The month-to-month fluctuations make the trend hard to discern.  What about this one, where I've fitted a 7-month centred linear moving average?

That's a lot better.  You can see the 2001 and 2009 recessions and the covid crash, for example. 

How does this smoothed version of the Ivey business confidence data compare with the headline PMI data?  (I have extreme-adjusted the PMI series to reduce the covid crash spike)  Mostly they move broadly in sync, but sometimes, they move in different directions.

[Chart updated 9/6/2024 to remove incorrect data in 2011]

Since we have no way of knowing which is the better guide to the economy until after all the official data have been released in several months' time, we should prolly use an average of the two series.  Which is what the chart below shows, comparing it with GDP, expressed as a percentage of trend.  I've also fitted an additional layer of smoothing to the PMI/IVEY composite, a 3x15 centred moving average.

What can we read from this chart?  First, the PMI/IVEY composite isn't a bad guide to GDP, provided we smooth the Ivey series first.  And, in my experience, the same is broadly true of PMIs and business confidence indicators in other countries, though smoothing is not always necessary.  Because of the covid spike, extreme-adjustment is almost always essential, as the spike makes scaling charts tricky.  Second, this composite leads the overall economy, by several months at the peaks, less at the troughs.  Third, it is still falling, though more slowly, suggesting that the Canadian economy will continue to slow. (You can see that already, relative to trend, Canadian GDP is decelerating)

Extracting a "signal" from the "noise" of randomly fluctuating time series is a problem in economics, and indeed in many disciplines.  Think of how people struggle to understand that even if global temperatures fall for 5 years, because of, say, La Niña, the underlying trend is still upwards.   Or, if you lose half a kilo this week, you have to look at it in the perspective of the gain of 5 kilos you made over the last year!