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:

Variable	Variation
Exchange rate	-13.4%
Export price index	+7.8%
Import price index	+9.2%
Domestic expenditure price index	+2.5%
GDP deflator	+2.1%
Export volume	+1.5%
Import volume	+0.1%
Domestic expenditure volume	+4.5%
GDP	+5.0%

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

Equations

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 = pw^0.7 . ulc^0.3

(7)          px = pw^0.6 . ulc^0.4 

(8)          pd = pw^0.2 . ulc^0.8

Variables

Name	Description
BT	Nominal trade balance
dx	Real domestic expenditure
ex	Real exports
gdp	Real GDP
GDP	Nominal GDP
im	Real imports
pd	Price of domestic expenditure
pm	Price of imports
pw	World prices (translated into sterling)
px	Price of exports
ulc	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.

Role of the Exchange Rate in Portfolio Preference Weightings

Brian Romanchuk has a post on portfolio allocation, including its representation in SFC models.  One area he discusses compares different ways of weighting portfolios.

In Monetary Economics, Godley & Lavoie use portfolio allocation functions that assign fixed weights to different asset classes (subject to changes in relative expected returns).  In the context of international allocations this means, for example, that investors in Country A allocate x% of investment to domestic assets and (100 - x)% to Country B assets.

If we ask ourselves what kind of value x might be, it should seem that it depends to some extent on the relative size of the economies of Country A and Country B.  If the economy of Country B is only 10% the size of that of Country A, it is unlikely that Country A investors are going to be investing 50% of their assets there, or even 25%.

We should expect investors to show some home preference, but beyond that we should expect the amount that investors wish to invest in a particular country to be influenced by the relative size of its economy.

How do we compare the size of different economies?  We have to translate GDP's into a common currency using suitable exchange rates.  Therefore, if we wanted to have portfolio allocation functions that reflected the different sizes of economies, we would need to include exchange rates in these functions.  This is not the route that Godley & Lavoie take. 

This may seem like a relatively unimportant point but, as I have stressed before, portfolio preference actually has a big impact.  How international weightings are determined can make a big difference to the response to changes in trade propensities, including whether that response is primarily an exchange rate response or a trade balance response.

Unfortunately, it's very difficult to identify portfolio allocation behaviour from the data, so it's hard to form a view on this.  My guess is that weightings are based on relative sizes of economies, but only in the longer run.  That is, weightings do not adjust to short-term movements in the exchange rate, but over time they come back into line.  This would seem to fit with a rule-of thumb approach to dealing with Brian's observation that it is best to adjust weightings for trend movements, but not for fluctuations.