Is the Uk really doing as well as eveyone is spinning after today’s announcement of the 0.5% increase in GDP cancelling out the 0.5% fall in Decembers release?

For those of a mathematical bent the answer would appear to be no we are not (and this is more of an annoyed rant at sloppy maths than the economy in general).

What defines a recession in generally accepted terms :

In a 1975

New York Timesarticle, economic statistician Julius Shiskin suggested several rules of thumb for defining a recession, one of which was “two down quarters of GDP”

Today’s statistics release has reports like the following from The Telegraph :

GDP growth in the first three months of the year was 0.5pc, the

Office for National Statistics(ONS) revealed,but the figure merely offsets the 0.5pc contraction in the final quarter of 2010.

And, more of the same from our political masters as reported at The BBC :

The prime minister told MPs that the 0.5% increase in GDP in the first quarter of this year was “good news” and accused Labour of “talking the economy down”.

But the Labour leader accused him of “extraordinary complacency” and said the economy had “flatlined”.

The 0.5% increase cancels out the 0.5% contraction at the end of 2010.

Even the ONS has the same take in it’s press release :

Gross Domestic Product (GDP) increased by 0.5 per cent in the first quarter of 2011, following a decrease of 0.5 per cent in the fourth quarter of 2010. The effect of the abnormal weather conditions in December 2010 is estimated to have subtracted 0.5 per cent from growth in the fourth quarter.

GDP is estimated now to have returned to the level in the third quarter of 2010.

Mathematically speaking though we have had a contraction over two quarters which could technically be described as a recession although I am sure the purists would say that both quarters should show a contraction individually rather than both combined.

A little demonstration of the maths using nice round numbers :

GDP is 1000 units and contracts by 0.5% leaving GDP at 995.

GDP, now at 995 increases by 0.5% giving the new measure as 999.975.

Whilst rounding up does give us the original 1000 GDP measure it is still short of the original figure despite the claims of 0.5% growth cancelling out a 0.5% contraction.

You may argue that small decimal point figures are of no significance but you need to take into account the size of the GDP figure we are playing with. A very small difference between very large numbers still amounts to a sizeable amount.

As a reminder (and I just got into a tangle myself on the calculator) :

one million = 1,000,000

one billion = 1,000,000,000

one trillion – 1,000,000,000,000

UK nominal GDP is somewhere around £1.440 trillion :

Just how large is the UK’s Gross Domestic Product and how quickly is it growing? Well, the latest Quarterly National Accounts from the Office for National Statistics show that the value of our economy’s output in Q3 2010 was £365.9 million. When measured across the latest four quarters, i.e. from the start of Q4 2009 to the end of Q3 2010, the total value of our economy’s output was £1.440 trillion.

If we apply the same calculations to the £1.440 trillion figure the results are not small change at all :

£1.440 trillion at the end of Q3 2010 contracting by 0.5% gives GDP of £1.4328 trillion.

Increasing £1.4328 trillion by 0.5% gives £1.439964 trillion.

Bugger all difference?

Well we are talking over a trillion pounds or in full – £1,439,640,000,000 and remember that we started with $1,440,000,000,000.

The small round error there turns into a full £360,000,000 or £360 million pounds which is rather a lot of lottery rollovers combined. If it can be marked down as a rounding error then send it my way and I will keep quite, promise!

A technical recession?

Well over 6 months the economy is worth £360 million less than it was at the end on October 2010. Then again, when debt figures are bandied about willy nilly in the billions and trillions what is a few million between friends?

**Update**

As FD points out in the comments**, **I have buggered up the maths as well – the difference between the figures being £36 million rather than £360 million.

I agree with your point completely (and these days, where everyone is off by at least a factor of 1000, even the details of your calculation can be argued to be substantially correct).

I just fear that the overall uncertainty in those numbers may be far bigger – if you settle with the £36 million “rounding error”, may I ask for a slice of the difference between the government’s figures and the actual GDP?

And I’m not even being greedy here – I just realize we better had a lot of money if all those bailouts will have to be paid for by our taxes…

FD – indeed – the £36 million rounding error probably doesn’t even come close to the size of the unmeasured black economy which only grows as taxes and regulation rise.

Sorry to say this, but your desire to rub it into the government’s face got the better of you.

The reported increase of 0.5 percent should not be taken to be exactly 0.500000 percent – and all it would take to return to previous levels would be a 0.5025 percent increase.

Also, assuming we had had both a contraction of exactly 0.5 percent and an expansion of the exact same percentage, with a 1.4 trillion GDP the rounding error would be a mere 35 million – you’re off by a factor of ten!

Sloppy mathematics indeed!

But more to the point, I would like to put those numbers into question – determining GDP down to the pound is clearly doomed to fail – and if that’s inflation-adjusted, by far the biggest source of uncertainty will be the inflation figure, which is affected by politics and concepts like hedonistic regression, which allows you to basically adjust your model until you come out with the desired inflation figure.

FD – mea culpa!

I was trying to make the point that a half percent down and back up again doesn’t leave you with the same amount as the linked articles and ONS press release were suggesting. Rounding and eveything else will obviously get in the way even if you agree with the actual measures in the first place.

Having said that, I would still settle for £36 million if it was ignored as a rounding error in these days or billions and trillions bandied about with no though of how big those numbers actually are.