Wednesday, 8 March 2017

Trade, the Exchange Rate and Real Wages in the UK

Simon-Wren Lewis wrote an interesting post recently, which among other things referred to the impact of sterling depreciation on UK real wage levels.

Any increase in domestic demand in the UK will lead to a greater demand for imports and potential pressure on the exchange rate.  A weaker exchange rate means a higher level of demand can be sustained with the same level of trade balance, but this has implications for real wages.

What I thought would be useful was to make a rough estimate of what exchange rate would be needed if UK GDP for 2016 were to be 5% higher, but with a comparable trade deficit and what this would imply for real wage levels.  To do this, I have set up a simple model using estimated parameters.  These are based on a combination of my own estimates and third party estimates.  Exact specification of the model used is given at the end of the post.

It should be stressed that all of the parameters used here are for long-term elasticities.  Most transactions are based on the use of established suppliers.  Volumes and, to some extent, prices do not respond quickly to exchange rate movements.  If an exchange rate movement is subsequently reversed, there may be no noticeable effect at all.  However, companies do choose where to supply from and long-term differences in cost will effect this.

The point here is that this is not indicative of how the economy will respond in the immediate period following a depreciation.  This is an exercise in counterfactuals or comparative statics.

The scenario I wanted to consider here was what variation in the exchange rate would be required to maintain the trade balance at a constant percentage of GDP, were GDP to be 5% higher, based on 2016 figures.  It turns out that this requires an exchange rate that is 13.4% lower.  It also requires domestic expenditure to be 4.5% higher.

The table below shows the percentage difference in each of the variables:


Exchange rate
Export price index
Import price index
Domestic expenditure price index
GDP deflator
Export volume
Import volume
Domestic expenditure volume

Here, the potential increase in import volume arising from the higher expenditure is substantially offset by the fall in the exchange rate.  Export volume grows slightly, as although export prices rise, they do not rise as much as world prices in sterling terms.

A key assumption here is that domestic unit labour costs are unchanged, so that the only thing impacting on these price indices is the change in the sterling equivalent of world prices.  Given the same level of productivity, the 2.5% higher domestic price index implies 2.5% lower real wages.  (Treating the consumer price index as being the same as that for all domestic expenditure - a simplification.)

Sustaining the change in real exchange rate necessary to achieve this result therefore requires that the reduction in real wage is fully absorbed and is not eroded by increased wage inflation.  (Of course the impact could be alternatively absorbed by a change in production taxes or a reduction in profitability).

Model Specification


Real GDP is the sum of domestic expenditure and exports less imports.

(1)          gdp = dx + ex - im

(2)          GDP = dx . pd + ex . px - im . pm

Exports vary based on the relative price with an elasticity of -0.3.

(3)          ex = 545 . ( px / pw )-0.3

Imports are based on relative price and both domestic expenditure and exports.  Exports have a much greater concentration of import content than domestic expenditure, and this is reflected by inclusion of a term for the share of exports in expenditure.  The price elasticity used is -0.33.

(4)          im = 0.3885 . ( dx + ex ) . [ ex / ( dx + ex ) ]0.34 . ( pm / pd )-0.33

The balance of trade is based on export and import volumes and prices.

(5)          BT = ex . px - im . pm

Price indices for imports, exports and domestic expenditure prices are a weighted average of world prices and domestic unit labour costs.  World prices here means some appropriate measure of prices in the UK's main trading partners, translated into sterling.  General price levels in the rest of the world is assumed unchanged so the only change is due to the exchange rate.  Domestic unit labour costs are also assumed unchanged.

(6)          pm = pw0.7 . ulc0.3

(7)          px = pw0.6 . ulc0.4 

(8)          pd = pw0.2 . ulc0.8



Nominal trade balance
Real domestic expenditure
Real exports
Real GDP
Nominal GDP
Real imports
Price of domestic expenditure
Price of imports
World prices (translated into sterling)
Price of exports
UK unit labour costs

Unit labour costs and all prices are indexed at 1 for 2016 and volume is measured in 2016 prices.  dx and pw are set to give the required level of gdp and ratio of BT to GDP.

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