Brexit boom or bust?

Nick Rowe has an interesting piece on the possibility of a Brexit Boom. It’s nifty analysis because it applies a simple IS-LM framework to Brexit.  This simple framework allows you to think through the problem slowly (but not too slowly) in a logical fashion rather than relying on intuitive reasoning and fast thinking. Using the model, Nick thinks that Brexit will cause a temporary boom. Torrens has a different view he thinks that here might be a permanent loss of income from Brexit and finds that, if so, there are two possible outcomes a recession in which the exchange rate depreciates and overshoots its long-run value and a temporary boom in which the exchange rate undershoots its long-run value. In Torrens’ view, the former seems to fit with recent developments better than the latter.  

To work through the issue, start like Nick by first imagining the long-run equilibrium that arises due to a permanent fall in exports because the UK loses access to the EU.  The loss in export market results in two things happening: 1) the UK permanently loses access to its main export market implying a loss of export revenue, 2) it also suffers a permanent loss of income.  The second aspect is additional to Nick’s; it is not necessary but adds some extra realism.

The reason for the loss in income is that although gross domestic product (i.e. the quantity of goods and services produced in the UK itself) might not change, but its gross domestic income — the purchasing power of its GDP — is reduced because the same amount of exports can no longer buy the same value of imports as before).  For a small open economy, this is what counts and it is what should be measured on the horizontal axis of the IS-LM chart. Nick has lamented about the lack of a foreign price in the model. In his post, Nick includes the first, but not the second.  Torrens reckons this is just as important as the first.

In terms of the IS-LM model above, we start at point A, before Brexit. The interest rate is i_w, the world rate,  and income (not GDP) is at full employment, Y1*. The IS curve shifts left because both exports fall (1) and consumption falls (Brits are paying higher prices for imported goods and can afford to consume less) (2).  Because consumption falls, and some consumption is on imported goods, so do imports. This means that the real depreciation that is required to restore the balance of payments equilibrium is less than if the  permanent level of income stayed the same. The increase in exports (3) arising from the depreciation does not fully offset the initial fall in export earnings  — i.e. the  leftward movement in the IS curve (1) is larger than the rightward movement (3).

Compared to Nick’s analysis, the effect of lowering permanent income after Brexit means the IS curve does not move back to its original position but gets stuck to the left of it.  The new equilibrium is at point C, where the new IS curve intersects with the BP curve (and though I haven’t shown it, the LM is to the left, intersecting the IS curve at Y2*, reflecting the fact that less money is required when output is lower). Output is lower,  the interest rate is equal to the world rate and the exchange rate is lower.  

Now, following Nick’s two-step procedure, put  the  above example aside for one moment and think about what happens today, when the Brexit announcement comes that the UK will lose favourable export access to the EU market in 2019. The factors that shift the IS curve are just as in the long run (above), except the cut to exports does not occur right now. That is, in the short run, people realise that their expected permanent income is lower, so spending falls (the leftward shift (2) in the above diagram); and they also realise that the exchange rate must weaken in the future, so arbitrage in the forex market causes the exchange rate to depreciate today by the amount that is expected to bring about a long run post-Brexit equilibrium (ignoring discounting of the future). This boosts exports and shifts the IS to the right (shift (3) above).
For the moment, do nothing else and pause here.  And think what the temporary equilibrium looks like. We started at A the IS moved left as expected income falls and then right as the exchange rate depreciated to its long-run equilibrium. The position of the IS curve could be to the left or right of its original position. The exchange rate, for the moment, is at its long-run equilibrium level (the one that was reached in the long-run analysis above), so, for the moment, the is no further expected alleviation or depreciation; the BP curve is horizontal at the world rate of interest.

Let’s suppose that the IS curve ends up to the left of A in our temporary equilibrium at a point like point B on the diagram below. With output below full employment and the interest rate below the world rate.  In this case, because the domestic interest rate is below the world rate, the exchange rate must have to depreciate even further below its long-run value. For this to happen, the market must he expecting that the exchange rate will appreciate in the future to get back to the long run equilibrium value. That is, the exchange rate has temporarily overshot its equilibrium value.  The extra depreciation moves the IS curve a little further to the right, but not all the way to restore full employment in equilibrium, just enough so that in equilibrium the  rate of interest in the UK plus the expected appreciation of pound just equals the world rate of interest. Such an equilibrium is shown in the diagram below.  

So there we have the short run equilibrium with  a recession, not a boom.  We still get Nick’s extra depreciation, but it is not enough to achieve full employment let alone a boom.  The Bank of England could stimulate the economy further to try and get the economy back to full employment by shifting  the LM curve to the right, but that would mean lower rates today and inflation (by keeping the economy at full employment, it is likely that the BoE would avoid any fall in prices of non-traded goods, but import prices will rise because of the depreciation,  meaning there will be inflation).


Alternatively, the IS  curve could end up to the right of the original IS curve if the impact of the loss of expected income  (step 2 in the first diagram) is smaller than the effect of the expected long-run depreciation on exports (as in Nick’s post).  That would result in an equilibrium to the north-east of point A on the diagram.  This would indeed involve a temporary boom.  But with the  interest rate above the world rate, the pound would have to appreciate relative to its long-run value — meaning that, in the short-run, it would not depreciate fully, and that a further depreciation would be expected (i.e. there would be some undershooting). In this case, the BoE may want to tighten policy.


Which version of the story is correct is an empirical matter.  Torrens reckons that facts fit the first version.  Since the announcement, the pound has fallen to its lowest level since the mid-1980s, bond yields have fallen (the 5 year gilt now yields about 0.4% compared to 0.8% before the Brexit vote), the Bank of England announced significant stimulus, and inflation expectations have risen.


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