I did a post back in May about manufacturing in the UK and its role in productivity growth and in foreign trade. My purpose was to stress that, for an economy as open as the UK, industry concentration was more about trade than about productivity growth.
The fact is that simply securing productivity growth can actually be detrimental for a country. The reasons for this are not immediately obvious, so I drew up a little model to illustrate it.
There are two countries: Country A and Country B. Each country produces haircuts and one type of fruit - Country A produces apples and Country B produces bananas. Haircuts are not traded internationally; fruit is. So households in each country consume two types of fruit and domestic haircuts.
Wages are fixed in the currency of each country. All prices are set at the same fixed mark-up to unit labour costs. We'll call Country A's currency the $, and Country B's £.
The elasticity of substitution in demand is the same for each product and in each country. We start by assuming that in both countries, households spend an equal amount on each of the three products they consume and that 1/3rd of the workforce is employed in producing haircuts and 2/3rds in producing fruit.
The £ / $ exchange rate floats to ensure that the value of exports equals the value of imports for each country. The labour supply is fixed and demand is managed to ensure continual full employment.
So far, each country is identical. The difference we want to introduce is to suppose that there is a 3% per period growth in labour productivity in the production of bananas. There is no change in labour productivity in the production of apples or haircuts.
The charts below are based on an elasticity of substitution in demand of 0.75 and are normalised to give opening values of unity.
The first thing to notice is that the banana producing Country B has GDP growth and Country A does not. (GDP is calculated here as a chained volume measure at opening year prices.) This is hardly surprising. The GDP growth rate is less than the rate of growth in banana productivity, because there is no change in productivity in haircuts.
Rising banana productivity means falling unit labour costs and falling banana prices in the domestic currency, £.
At the prevailing exchange rate, a fall in the £ banana price would lead to a drop in the value of exports for Country B, even though the volume of exports rises, given that the demand elasticity is less than 1. The exchange rate therefore has to change leading to a fall in the value of the £ against the $. This means that the $ price of bananas falls by even more than the £ price. It also means that £ price of apples rises, even though the $ price of apples is unchanged.
These further price changes alter trade volumes until the values of trade flows balance. The chart below shows that this involves a big increase in the banana exports of Country B, whilst there is a slight decline in Country A's apple exports. This is consistent with Thirlwall's Law and what is happening here to GDP.
The exchange rate movement also means that consumer prices fall by more in Country A than in Country B. This means that real wages (based on a consumption price index - not the GDP deflator) rise more slowly in Country B than in Country A, notwithstanding that Country B is generating all of the growth in production.
In this model, Country A wages rise faster than those in Country B whenever the elasticity of substitution in demand is less than 1. In fact, if the elasticity is less than about 0.61, then real wages in Country B actually fall, because the £ price of apples rises faster than the £ price of bananas falls. This result is somewhat counter-intuitive.
These elasticity levels are not at all unrealistic for international trade flows.
As a further point it is worth noting that Country B can mitigate the reduction in its own real wages by depressing domestic demand. This reduces employment and GDP in Country B. It raises real wages in Country B, but reduces them in Country A. Imposing tariffs (whether on exports or on imports) will also raise real wages in Country B at the expense of those in Country A, but does not involve reduced employment.
The purpose of this post is simply to highlight two points:
1. GDP growth is not the same as growth in living standards. A country that has a high proportion of activity in industries with strong productivity growth is likely to have high GDP growth. But this, in itself, is not a good reason to concentrate on such industries.
2. Elasticities in traded goods are crucial.
However, it is not the purpose of this post to suggest that it is a bad thing to have industries with high potential productivity growth. In practice growth in productivity is not mainly about producing more of the same for given inputs; it is about producing new and better products. This innovation is itself important in developing and sustaining export demand. We cannot separate developments in trade from what is happening with productivity growth. The important point though is that trade is a critical part of the picture; productivity growth alone tells us very little.
Consumption of each good in each country is based on a consumption index and the price relative to a consumption price index.
1. CAa = CA / 3 . (p$a / pA)-ε
2. CAb = CA / 3 . (p$b / pA)-ε
3. CAh = CA / 3 . (p$h / pA)-ε
4. CBa = CB / 3 . ( p£a / pB)-ε
5. CBb = CB / 3 . (p£b / pB)-ε
6. CBh = CB / 3 . (p£h / pB)-ε
With the price indices calculated as:
7. pA = ( p$a . CAa + p$b . CAb + p$h . CAh) / CA
8. pB = ( p£a . CBa + p£b . CBb + p£h . CBh) / CB
All domestic prices are set at the same mark-up to unit labour costs.
9. p£b = λ . wB / σb
10. p£h = λ . wB / σh
11. p$a = λ . wA / σa
12. p$h = λ . wA / σh
Import prices reflect the exchange rate.
13. p£a = e . p$a
14. p$b = p£b / e
The value of exports equals the value of imports. (This equation is used to find the market clearing exchange rate.)
15. CAb . p$b = CBa . p$a
Employment is based on consumption and productivity. (In the basic scenario described, the levels of the consumption indices CA and CB are set so that all available labour is employed in both countries.)
16. LB = CBh / σh + ( CAb + CBb ) / σb
17. LA = CAh / σh + ( CAa + CBa ) / σa
CXy Consumption of y in country X
CX Consumption index in country X
pzy Price of y denominated in z
pX Price index in country X, denominated in domestic currency
wX Nominal wages in country X, denominated in domestic currency
σy Labour productivity in production of y
LX Employment in country X
e Exchange rate ( £ per $ )
σ is given the same value for each good, in the first period.