This post is about national income accounting, and its dangers. Reading Simon Wren-Lewis’ post about Brexit and real wages made me finally decide to try to get my head clear about something I’ve been meaning to get it clear about for some time. I *think* Simon might be wrong about something (I’m not sure though, and will wait for his response).

Take an extreme case, to make it simpler and clearer. The Brits produce only apples, because they can’t produce anything else. But they never eat any apples; they only eat bananas. So each year they export the apples they have produced, swap them for imported bananas, and consume the bananas. Investment and government expenditure are always zero. And Brits’ savings are always zero too (they swap all of their apples for bananas to be eaten immediately, and never swap any apples for IOUs).

**By construction in this “model”, the value of net exports is always zero. Because the value of exported apples is always equal to the value of the bananas they are swapped for.**

Now suppose the price of apples (in terms of bananas) is too high, so the Brits are unable to sell all the apples they produce. The unsold apples rot on the ground, and don’t get counted in GDP. The real exchange rate (the price of apples in terms of bananas) being too high causes real GDP to be too low. Then something causes the real exchange rate to fall, so the Brits are now able to sell all the apples they produce (in exchange for bananas), and so real GDP (measured in apples produced) rises to the “full employment” (of apple trees) level.

**By construction, the depreciation of the real exchange rate is what caused the rise in real GDP, but net exports remain at zero and so net exports’ “contribution” to GDP growth is zero.**

Did the Brits’ consumption of bananas rise or fall? That depends. On the price-elasticity of demand for exported apples. If it’s elastic (greater than one) a 1% cut in the price of apples (in terms of bananas) causes the quantity of apples sold to rise by more than 1%, so the Brits consume more bananas. If it’s inelastic the Brits consume fewer bananas. But real GDP (measured in apples produced and sold) rises in either case (though Brits are made worse off by depreciation if it’s inelastic because their consumption of bananas falls).

In nominal terms (i.e. dollar pound sterling terms) the national accounts look like this:

Y = C + X – M (where Y is GDP, C is consumption, X is exports, and M is imports).

We can re-write this as:

yPa = cPb + xPa – mPb (where y and x are measured in quantities of apples, and c and m are measured in quantities of bananas, Pa is the price of apples and Pb is the price of bananas, both measured in dollars pounds sterling).

Or divide everything through by Pa to get:

y = c(Pb/Pa) + x – m(Pb/Pa) (which, I think, is how the expenditure decomposition of GDP normally gets reported when talking about “contributions” to GDP growth).

In this “model”, since X=M by construction (so x=m(Pb/Pa)), changes in net exports always make zero “contribution” to GDP growth. The only thing that ever makes any “contribution” to GDP growth is consumption. But consumption is 100% spent on imported goods, and so cannot create demand for domestic GDP, and the *only* thing that can create a demand-induced growth in GDP is exports (exports are also limited by supply-side productivity of apple trees).

Obviously, my “model” here is an extreme example. But extreme examples can be used to clarify and illustrate. What my extreme example shows is the danger of relying on National Income Accounting “contributions” to GDP growth as telling us what is causing that growth.

I suppose I should talk about the irrelevance of the Marshall-Lerner condition, but it’s time for the morning trip to Tims.