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.

Wage Inflation and Unemployment in the UK

As a further follow up on the NAIRU discussions mentioned in my last two posts, I have looked at the historical relationship between wage inflation and unemployment in the UK. 

The first of the two graphs below shows annual change in average earnings against unemployment from 1973 to 2016.  The second graph shows the change in the change, what we might think of as the acceleration of wage inflation.  I have divided the points into three periods: 

1973 - 1979: the period before the Thatcher government

1980 - 1991: up to inflation targeting

1992 - 2016: the period of inflation targeting

The trend line covers the whole period.

 A few points are worth making here.

Both charts show quite a wide scatter.  Although both show a vague trend across the whole period, the correlation is not particularly strong in either.

Although the correlation is somewhat weak, the charts suggest that both the level of wage inflation and its acceleration are negatively correlated with unemployment.

There appears to be a somewhat better correlation if we look at the periods individually.  Each individual period generally continues to show the same direction of correlation.  However, the steepness declines over time, both in relation to wage inflation and its acceleration. 

For the period of inflation targeting, there appears to be very little correlation between unemployment and the actual level of wage inflation, whilst there is still a slight correlation with its acceleration.  This is probably the opposite of what I would have expected.

I addition to displaying the steepest relationship, the plot for the 70's also shows the greatest scatter.  This probably reflects various external factors such as the oil price shock and the social contract.

The only really clear conclusion here is that the relationship between these variables is a complex one, but it does appear that there is some connection between unemployment and not only, wage inflation, but also its acceleration.

Understanding Household Spending with Stocks and Flows

Household expenditure is the largest component of GDP, so understanding why and how it varies is crucial to understanding recessions.

Mainstream economics tends to look to the real interest rate and a household rate of time preference as the central explanation for such variations.  Stock flow models tend to place greater emphasis on the levels of financial stocks. 

The idea here is that household expenditure is driven by a desire to influence various ratios between financial stocks and the level of income.  Stock-flow models often describe certain target ratios, sometimes called stock-flow norms.   Household expenditure is equal to income[1] less the net acquisition of net financial assets.  If we can explain the acquisition and disposal of financial assets and liabilities in terms of a desire to move towards stock-flow norms, then we can explain why household expenditure might vary.

Looking at the UK, it is useful to divide household net financial assets into the following:

1. Pensions and life insurance

2. Other financial assets

3. Debt (i.e. liabilities of households)

The graph below shows the level of each of these relative to household disposal income.

I'll say something about each of these in turn, dealing first with pensions, then debt, then other financial assets.

Pensions

It seems likely that there should be some kind of target ratio between pension assets and income.  On the whole, people want to achieve a balance between what they can spend during their working years and what they can spend in retirement.  This means they have to save a certain amount whilst working to be run down in later life. This process is naturally going to generate a stable stock-flow ratio.

In fact, we don't need to even postulate that people have a given stock-flow ratio in mind.  Much of the time, the amount of pension contributions will be in a fixed relationship to wage levels, and amounts paid as pensions will be related to the stock level of pension funds.  Institutional arrangements including the tax system influence this.  This process will give rise to a stock-flow norm, even if no-one has such a ratio in mind.

If we look at the graph, however, we can see a clear upward trend in the ratio of pension assets to income.  There are various reasons for this.  The most important is rising life expectancy.  This has reduced the amount of pension income that a given stock of pension assets will buy.  Achieving a similar balance between working and retirement consumption therefore means building a greater stock of pension assets during the working lifetime.

The decline in the yields on government securities has a similar effect.  Pension annuities are priced off fixed income yields, so as these have come down, pension funds need to become larger.

The actual size of pension funds is also impacted by the returns on those funds including stock market gains.  So we should expect to see the actual ratio rising when the stock market is doing well.

Debt

The ratio of debt to income shows less fluctuations than the two asset classes, because it is not subject to the sort of variations in value due to market movements.

With debt levels, it also seems likely that that stock-flow ratios are important.  In particular, credit constraints will tend to limit the amount that can be borrowed relative to income.  The growth in debt levels between around 1999 and 2008 reflect a general relaxation of credit criteria. 

Maximum acceptable debt levels are often assessed by comparing the interest expense to income.  The upper bound to the debt to income ratio is therefore likely to be a function of interest rates to some extent.  At the current low level of rates, interest expense is at its lowest level of this period (see chart below), which partly explains why the debt ratio remains high despite tightening credit conditions.

Credit constraints may impose a cap on this stock-flow ratio, but that is not the same as saying this is a target ratio.  It could be that households prefer a debt ratio below that dictated by credit conditions.  However, it seems likely that credit conditions provide the binding constraint in most cases for new borrowers, and this element is a key driver of the stock-flow ratio.

Other Assets

Whilst there are good reasons for thinking that stock-flow considerations play an important role in determining accumulation of pensions and debt, it is less clear in the case of other assets.  Typical stock-flow consistent models tend to assume that there is a target ratio for holdings of other assets, but I'm not sure this is necessarily the case. 

With pensions and debt, we should be able to predict what sort of target ratios we expect to see from a knowledge of things like life patterns, the tax structures, regulatory issues and so on.  No such considerations determine the holding of other assets, so it's quite possible that any target ratio could develop over time, including in response to changes in the actual.

However, looking at the first graph, the ratio of other assets has actually changed the least over time.  Apart from an apparent slight upward trend, two factors appear to drive the variations.

1. As with pensions assets, the level of other financial assets is subject to variations in asset valuations such as stock market movements.

2. The periods of strong growth in debt levels seems to be associated with an increase in holdings of other financial assets.  There are reasons why we might expect this to be the case.  The largest part of debt is for house purchase, and an increase in debt reflects a greater volume of house purchase and/or higher house prices.  This means that those households receiving property sales proceeds and not repaying debt (otherwise overall debt levels are not increasing) are receiving greater windfalls.  This type of cash receipt, does not get spend all at once, if it gets spend at all, and it therefore adds to the accumulation  of deposits, which makes up the largest part of this catergory of assets.

Once these elements are taken into account, it does appear that there is some reversion-to-norm taking place in this stock-flow ratio.  When the actual ratio is increased or decreased by one of these factors, accumulation reacts to bring it back to a more "normal" level.  It is remains an open question, however, how stable this "normal" level is over time.

Conclusion

 

An analysis of household stock-flow ratios provides a useful insight on what drives changes in household spending.  This is particularly so when we apply a certain level of disaggregation, rather than looking at net finacial assets as a single whole.  Often, we can relate the trends to things that we know are going on.  This approach is likely to be more useful than trying to relate spending to variations in the real interest rate.

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[1] Household disposable income is usually calculated after certain pension contributions and pension income.  To align more closely with the theoretical issues, we need here to think about household income before these items.