The Treasury's report on Brexit comes to some pretty stark conclusions.
GDP will be down by 3.6% in the short run and 6.2% in the long run, relative to remaining in the EU. There will be an immediate (though shallow) recession, with unemployment up by 1.6 percentage points, and the prices of stocks, houses and the pound will all fall through the floor.
Of course, the Treasury's analysis is a deeply political document. So what should we make of all these numbers? How sceptical should we be about their weirdly precise estimates? Here I'm going to try to ballpark their estimates, and (spoiler alert!) they're actually quite compatible with reality.
I don't think the task of trying to forecast the impact of Brexit is a totally futile one. In a world with true uncertainty, it would be impossible to judge the likelihood of Brexit causing Mervyn King to mutate into a giant velociraptor and destroying London, but the best evidence in the literature suggests that this is quite unlikely. An estimate is better than no estimate – at least we've got a model that makes some assumptions, and we can evaluate the reasonableness of those assumptions. That's quite a bit better than no model.
One thing that's interesting about the Treasury's model is it's quite ad-hoc. For the long-run model they do a few things:
- Assume trade benefits productivity.
- look at the trade literature to get a number for how much a given change in trade affects productivity.
- Come up with an estimate how much leaving the EU will impact trade.
- Therefore, work out the long-run impact on productivity of leaving the EU.
There's a similar process for the short-run model.
- Assume that in the long run the economy will converge to your long-run forecast.
- Plug data for 1989-2011 into a regression to try and estimate the effect of increased uncertainty on various different variables.
- Assume leaving the EU causes uncertainty to increase by 1 standard deviation.
- Plug that 1 SD increase into the model, and see how that affects convergence to the long-run steady-state predicted by the first model.
This sort of ad-hoc modelling is sort of inevitable. It's hard to build a model that takes into account the full complexity of the situation. But the shortcomings of this kind of approach are somewhat obvious. It's not clear that all fluctuations in trade should have the same impact on productivity, for instance – it depends on the size of the gap in relative prices and the degree to which particular industries experience economies of scale. Similarly, 'uncertainty' is quite a nebulous concept, and it's a bit of a stretch to say that the kind of uncertainty caused by bank failures around the world, as in 2008, has the same economic impacts as the kind of uncertainty caused by firms having less information about what the tariff regime they face will look like over the next decade.
One of the things these sorts of models sacrifice is internal consistency. If your model can't fully encapsulate the relationships between different variables, if you're reliant on inputting parameters for things that should really be endogenous, you run the risk that the stories your model is telling about what's happening to GDP, productivity, asset prices and so on don't quite add up.
So how well does the Treasury's model do by this score?
The Promised Recession
Let's break out the outputs of the short-run model a bit more.
- Real GDP goes down by 3.6%
- Of this, 2.7% is a fall in potential GDP.
- That means the remaining 0.9% of the decline is due to a demand-side recession. In other words, the negative output gap increases by 0.9ppts.
This fall in output is supposed to lead to a 1.6pp increase in the unemployment rate. That seems like quite a big swing in unemployment compared to, for instance, the Great Recession. How much spare capacity there was in the economy before and after the financial crisis is hotly debated, but this OBR working paper estimates a 6pp swing, from 2% above potential to 4% below. And that swing resulted in a trough-to-peak rise in the unemployment rate of about 3%. That was surprisingly low, and no-one is quite sure why, but it seems like a 0.9% rise in the output gap would be unlikely to lead to a proportionally larger rise in the unemployment rate.
The Stock Market Crash
Another weird discrepancy is the huge wedge between GDP and asset prices in the short term model. Stock prices are, after all, the discounted stream of corporate future profits. Assuming that there is not a significant shift in corporate profits as a % of GDP and the risk premium remains the same, we might expect stock prices to move by the same amount as GDP in the long run. But the Treasury model's central scenario predicts a fall in GDP
It makes sense for increased uncertainty to increase the risk premium on stocks. The costs of Brexit are probably not evenly distributed across all possible Brexit-worlds. Most of the time, the status quo is likely to be approximately maintained through the EEA, and it's the unlikely event of a much larger reduction in the UK's openness to trade that is really worrying. But the sheer size of the discrepancy suggests that the rise in the risk premium predicted by the Treasury is unrealistically large.
I'm now going to do a bit of back-of-the-envelope discontinuity analysis to see how realistic the 20% drop in equities is. Shortly before 4pm on Tuesday 31st May, two Guardian/ICM polls dropped suggesting that the nation was perhaps a bit more Brexit-leaning than markets had previously been assuming. On betting markets, the subjective probability of Brexit dropped by around 3-5%.
If you squint, you might be able to make out the impact of the poll on the FTSE 100:
So let's conservatively estimate a .5% drop in the stock market caused by a 5 percentage point increase in the probability of Brexit. That suggests that a 100 percentage-point swing (ie the difference between Brexit and no Brexit) would be about 10%. Quite a bit short of the treasury's esitimate, in other words, but in the same ballpark.
There are some other interesting implications of this sort of estimate. The market capitalisation of HSBC, the second-largest firm traded on the FTSE, is about £88bn. Let's assume that HSBC is about as exposed to Brexit risk as the average FTSE 100 company (this is the reason that I didn't pick Shell, the largest company on the FTSE by market cap). A 1% swing in the probability of Brexit would then cost HSBC's shareholders about 0.1% of its value. Therefore, if spending £88m could shift the probability of Brexit by 1%, it would be a smart thing to do on the part of HSBC's management.
This is a very interesting illustration of the Tullock Paradox and makes the £5m budget of the official Remain campaign look quite low.
This has been quite a long post but here are the two main takeaways:
- We should be very careful to check the calibration of our models, especially ad-hoc ones. Reality, surprisingly, actually has some quite interesting theoretical implications.
- The Treasury analysis perhaps exaggerates the short-term costs of Brexit, but it isn't wildly implausible.