The exchange rate and net exports "contribution" to growth

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.

Update: be sure to read Brent Moulton's comment below.

Comments

[Majromax]

I think a problem is that this model conflates changes in the terms of trade with changes in the price level.

By setting the price level in terms of the produced good rather than the consumed good, you've almost set a price level in terms of labour-hours (depending on the apple production function). The resulting confusion is then straightforward from a supply and demand viewpoint without the mess of national accounting: if my salary changes and my working hours change, then my overall consumption can go up or down.

I think you'd have more intuitive results if the model included a non-traded domestic sector, giving us for example apples for export, bananas for import, and haircuts, and then the price level were set in terms of haircuts.

Even still, this reduced-form model does give one classical result: employment, here represented by apple-growers that don't have their apples rot on the ground, goes up when the real exchange rate depreciates.

[Nick Rowe]

Majro: "Even still, this reduced-form model does give one classical result: employment, here represented by apple-growers that don't have their apples rot on the ground, goes up when the real exchange rate depreciates."

Yep, and regardless of whether the exchange rate depreciation caused net exports to rise. The only thing needed is that depreciation causes export demand to rise.

If I relaxed the extreme assumption that the Brits never eat apples, we would also get an effect of depreciation causing Brits to substitute away from consuming bananas to consuming apples, which would strengthen the first effect, and means the depreciation causes a bigger increase in GDP. But the effect on net exports could still be zero (or ambiguous) because it all depends on how much their consumption rises when GDP rises, which depends (in part) on whether they see this as a permanent or temporary increase in GDP (or on whether they are Hand-To-Mouth agents, like in my "model", who always consume their whole income). Again, the Marshall-Lerner conditions (export + import elasticities must sum to greater than one) are irrelevant to whether depreciation increases real GDP (as opposed to real income measured in consumption goods). What matters is that the sum is strictly positive. We need to look at income elasticities too to tell us what happens to net exports.

[marcus nunes]

Nick, I remember, many years ago, a discussion in The Economist. It went more or less like this: "If it weren´t for the large increase in imports, RGDP growth would have been even higher". I bet that if you asked them why imports were so strong, the answer would have been "because RGDP growth was robust"!

The title of one of Scott Sumner´s first posts (Feb 2009) was GDP=C+I+G+(X-M)=Gross Deceptive Partitioning

[Jacques René Giguère]

Nick: "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)."
Because by construction of your model, you assume that balance of payments (equivalent to current account by construction) is balanced. The model collapse to barter. So C must be identical (not equal) to M and identical to X.

[Nick Rowe]

marcus: spot on!

[Nick Rowe]

Jacques Rene: It's not necessarily a barter model. We could imagine the Brits selling apples for money, and using that money to buy foreign money, and using that foreign money to buy bananas. And the fact that quantity of apples sold is identically equal to quantity of apples bought, does not mean that quantity of apples supplied is identically equal to quantity of apples demanded.

Off-topic: had an absolutely lovely road trip and holiday along your neck of the woods last week -- Cote Nord along 138 to Natashquan and back. God it's beautiful. Quebec's little secret. 3,000km round trip from Ottawa.

[Jacques René Giguère]

Nick: your model exclude savings. In the model money is an accounting trick or a veil. Its role as mediating transactions through time is not effective. The model is barter.
Off topic: should have called. Would have shown you where to eat capayous (Casse-Croûte Capayou), the best shrimp pizza (Chez Julie) and lobster ravioli (La Cache d'Amélie). Book your next trip...

[Brent Moulton]

"...but net exports remain at zero and so net exports' "contribution" to GDP growth is zero."

Although net exports remain at zero in current prices, national accountants typically report contributions to changes in GDP in volume terms. In your example, the change in volume of consumption (or its contribution in volume terms) is identical to the change in volume of imports, and the change in GDP volume is identical to the change in volume of exports. The "contribution" of net exports would be the difference of the export and import volume contributions, which depends on the elasticity of demand for exported apples (and perhaps also on which index formula is being used), but it isn't necessarily equal to zero.

Nevertheless, I strongly agree that contributions of net exports (or of imports) to GDP growth is not useful and can be misleading. I prefer an approach taken by Statistics Netherlands in this memo, in which the imports are absorbed into the contributions of the expenditure categories to which they are applied. In your example, the contribution of consumption would be fully offset by the contribution of imports, leaving exports as the only contributor to GDP growth, which aligns with the economics of your story. In practice, the Statistics Netherlands method is calculated from coefficients of an input-output matrix, which makes the calculations a bit opaque and led to reluctance by BEA management to consider it. But conceptually I think that's the better way to do the contributions calculation.

[Nick Rowe]

Brent: Aha! Good! The expert weighs in!

But help me understand what UK's ONS are doing in Figure 4 in Simon's post, when they report "Expenditure components percentage contributions to GDP growth" for "Net trade" "chained volume measure". In my example, if the real exchange rate depreciates by (say) 1%, and the elasticity is (say) 2, then the volume of exports rises by 2%, and the volume of imports rises by approx 1%, so the volume of net exports rises by approx 2%-1%=1%? And if the elasticity were 1, the "contribution" would be the same 1%-0%=1%? Is that right? If so, that's a big problem, because we know in my "model" the bigger the elasticity the bigger the effect of a 1% depreciation on GDP growth.

[Nick Rowe]

And your description of the Dutch way of doing it makes a lot of sense to me. So it reads: Total expenditure on Dutch-produced goods = expenditure by the Dutch on Dutch-produced goods + expenditure by foreigners on Dutch-produced goods. "Net exports" is not a category. But I can see it gets tricky if you have imported components in domestically-produced goods.

[Scott Sumner]

Don't get me going on this topic . . . .

[JKH]

Rewrite the equation in the context of your example:

Y = (C – M) + I + G + X

Or generalizing:

Y = ((C + I + G) – M) + X

I don’t see the problem as one of the basic national income accounting equation

The problem seems to stem from a rigid algebraic grouping within that equation, which may lead to poor economic reasoning

I don’t believe that the relevant national income accounting equation mandates that (X – M) is a sacrosanct, untouchable component that must not be rearranged

But you may instruct me that “net exports” as in (X – M) is a sacrosanct concept in economics – untouchable in effect

If so, I think that’s the problem

But I wouldn’t blame that on national income accounting

(It's possible we're saying something similar; not sure)

[Nick Edmonds]

Re your reply to Brent Moulton, I think the difference is that, in the case of elasticity = 2, you would also be recording a contribution of 1% to GDP from consumption.

[Nick Rowe]

JKH: Writing it "Y=C+I+G+(X-M)" isn't (or shouldn't be) sacrosanct, but it is very conventional. As Brent says above the Dutch don't follow that convention, and do it your way (except they split M into 3 components Mc, Mi, and Mg, so write it as Y=(C-Mc)+(I-Mi)+(G-Mg)+X.

I think my point is that NIA is always conventional, and that any given convention can mislead us. Yes, in this particular example, re-writing it the Dutch way solves the problem. But it may not work in other examples; we always need to be careful.

Nick E: I think that's right. And the bigger the elasticity, the bigger the "contribution" from consumption?

[C Trombley]

Bloomberg's Noah Smith also advocated moving to a Y=(C-Mc)+(I-Mi)+(G-Mg)+X conceptual framework a while back:

https://www.bloomberg.com/view/articles/2016-12-28/trump-s-trade-chief-peter-navarro-makes-a-rookie-mistake

[Yoshinori Shiozawa]

I came to know this site by a blog post by Lars Syll in Real World Economics Review blog: The history of 'New Keynesianism' September 6, 2017.

Your "extreme" model is interesting in two points. First, it represents long tradition of international trade theory since John Stuart Mill: each of two countries is producing one kind of commodity that each exports to another. (In Mill 1844 On Some Unsettled Questions, England produces broad cloth and Germany produces linen. The only difference is that both countries consume what they produce.). Second, the terms of trade (or real exchange rate) are determined purely by the demand side.

I am thinking that this long tradition is completely wrong (if you like, please read my paper An Origin of the Neoclassical Revolution: Mill's "Reversion" and its Consequences), but your extreme model is still interesting. It reveals that trade balance has little relevance in the determination of the real exchange rate. (Or more precisely the trade balance is not the unique factor that determines the exchange ratio.) Many (or most of) theories on exchange rates are based on the assumption that the trade balance is the main factor which drives the exchange rate. Your "extreme" model shows persuasively that it may not be the case. In my not very humble opinion, this change of view is extremely important.