It’s been 3 years since I last reviewed the UK GDP data with some analysis (GDP1, GDP2, GDP 3) and notes (GDP4). At that point GDP had been in a considerable dip for a number of quarters and showed a little indication of changing direction as an absolute measure or but not relative to the long term mean model, strongly correlating to an exponential growth pattern.

Not long after that the ONS changed their website and, it seemed, had eliminated the type of time series data I’d been using. I decided to leave further analysis on the back burner. Now 3 years on, I’ve looked again at the ONS site and found the updated file I was looking for – GDP back to 1948 (1955 for quarterly data).

This post is an initial look at the data with some re-analysis, so let’s start by looking at a graph…

Figure 1: Graph of Quarterly Gross Domestic Product from Q1 1955 (chained volume measures, seasonally adjusted £m), with exponential model applied to whole time series.

### Observations

- The peak GDP before the last dip was in Q1 2008.
- The model derived from all the data has a strong exponential profile, with an R² of 0.9905.
- It is equivalent to an average annual growth of 2.73% over the whole period.
- Previous peaks and troughs are evident.
- Troughs typically have an asymmetric profile, taking longer to return to mean behaviour than they did to ‘snap’ away.
- Even though UK GDP has returned to it’s pre-recession absolute level (in £m) it is still far away from the mean model, i.e. arguably where it should have been at this time had the recession had not been so deep.
- I have raised the possibility in previous posts, that some fundamental components in the GDP system have changed, an ‘elastic band’ has broken and that GDP will not be able to return to the longer term historical profile (prior to 2008). This remains to be seen and will be discussed in further posts.
- An exponential model derived from the data up to the peak at Q1 2008 (see Fig 2) is slightly above the revised model, but still shows that in the years prior to the ‘crash’ GDP was stretching away from the long term mean. If we think of actual GDP on a piece of elastic attached to the mean model, one might argue that a ‘snap’ back to the mean, and indeed carrying it’s momentum beyond the mean is at some point inevitable.
- It is also possible (indeed probable) that the long term model is not purely exponential and may conform to a different form, perhaps the S-curve signature of a damped differential equation – 2nd order-like in it’s simplest form.

Fig 2: GDP Exponential Model at the 2008 peak (dotted) compared to 2014 (solid)

### Deviation from the Mean Model

As in previous posts, I have also calculated and plotted the deviation of GDP from the current long-term model, as a percentage of GDP, to illustrate typical patterns.

Fig 3: Relative Deviation from the long-term mean model (as a proportion of GDP).

- Using this relative scale we can see something of the nature of each of the troughs.
- Most notably, those in the early 1980s and early 1990s have an asymmetric profile, characterised by a steep drop to the trough then slower rise.
- The 2008 trough appears that it may have bottomed out at around 9% of GDP recently and it is starting to move back to the mean model. It may not, however.
- When I last looked at this in 2011, GDP was still accelerating away from the mean model, perhaps suggesting that something fundamental had changed (snapped-elastic)
- For reference, it’s interesting that most other G7 economies have recovered earlier

Let’s assume that UK GDP is the bottom of the trough. We can make a crude projection by looking at the profile of previous troughs and applying (graphically) the same shape to this most recent data. Fig 4. illustrates this approach.

Fig 4. Applying graphical approximations to deviation data.

- Providing we are at the bottom of this deviation trough and it takes a typical ‘tick’ profile, we might hazard a guess that GDP will return to the longer term mean at or around 2023 (assuming no other shocks come along – quite possible !)

Using this crude projection of deviation and back-calculating I then derived a projection of actual GDP in Fig 5.

Fig. 5: Projection of GDP based on crude graphical projection (x-axis in quarters)

- Looking at this projection and how long it takes to get back, my gut feeling is that GDP will not return to the current long-term model, and will find a new mean profile somewhat below but possibly parallel to the mean line.
- Over this length of time I would expect there to be another dip, again taking GDP away from it’s current long-term mean

That’s it for the moment. I may update this post, as ideas come to mind and in the next post I will discuss a growth model and growth as a property of GDP itself.

Reblogged this on Dr. JAH and commented:

Now wonder if this data includes elements of the ‘Black Economy’