GDP, GDI, terms of trade and why Canada is in a recession: It's all about the beer and pizza

The Parliamentary Budget Office has released a report (pdf - h/t to Kady O'Malley) that makes note of the distinction between Gross Domestic Product (GDP) and Gross Domestic Income (GDI), and shows that by the latter measure, the fourth quarter of 2008 was even more dreadful than the GDP numbers that made all the headlines.

As a public service, I'm going to explain what the difference is between GDP and GDI and how it relates to the current recession. It starts below the fold, and yes, there will be beer and pizza.

We know that Canada - along with other commodity-exporting countries - has benefited from the rise in commodity prices since 2002. But it's hard to talk about the effect of changes in the relative prices between two goods in the context of a standard single-good macroeconomic framework. So you need a two-good model. And whenever economists are forced to consider a world with two goods, their thoughts turn to beer and pizza. At least mine do.

Suppose that Canada produces 100 beers, but we have to have a pizza with each beer. We don't produce pizza, but other countries do, and we can trade beer for pizza with them at the rate of one beer for one pizza. So we can export 50 beers, import 50 pizzas, and we happily consume our 50 beer-and-pizza combos.

There are two ways that we can see our lot improved. One way would be if we simply produced more beer. If we were somehow able to improve our productivity by 50%, then we could produce 50 extra beers, trade 25 of them for pizzas, and we'd now have 75 beer-and-pizza combos.

Since Canada produces only beer, the increase in GDP is the same thing as the increase in beer production. But what we really care about isn't beer production, it's the consumption of beer-and-pizza combos - and this is what GDI measures. So long as the rate at which beer and pizza are traded on the international markets stays at 1:1, it doesn't matter which measure you use. GDP has gone from 100 to 150 (50% increase), and GDI has gone from 50 to 75 (also a 50% increase).

But there's another way that our situation can be improved. Suppose that beer production is 100, but for some reason - less beer on international markets, more pizza or some combination of the two - the relative demand for beer increases, and beer producers are now able to obtain three pizzas for one beer. This 200% increase in Canada's terms of trade - the ratio of the price of the good it exports to the price of the good it imports - means that Canada can trade 25 beers for 75 pizzas. Even though beer production hasn't changed, we can now consume 75 beer-and-pizza combos.

It is here that the distinction between GDP and GDI becomes important. Since beer production hasn't changed, Statistics Canada would record no increase in GDP. But since we're now able to consume 75 beer-and-pizza combos, measured GDI would increase by 50%.

This story is useful in interpreting what's been going on in Canada since 2002. Although commodities are not the only thing - or even the main thing - that Canada exports, its prices are so volatile that they have been the main driver of movements in the terms of trade:

The commodity price series is from the Bank of Canada; note the differences in the scale of the vertical axes. The run-up that started in 2002Q1 went fairly smoothly until 2007, at which point it accelerated, culminating with the crash in 2008Q4.

So how did Canada respond to the increase in the terms of trade? Pretty much as you'd expect from the beer and pizza model - we imported more:

Look at what happened in 2008Q4. Real exports fell, but real imports fell even more: the effect of net exports on real GDP growth was a positive contribution of one percentage point. If all you were looking at was the effect of the global meltdown of world trade on Canada's net exports, you'd have a very hard time explaining just how Canada went into recession last quarter.

Statscan publishes data that decomposes the contributions of GDI growth by component. In the beer and pizza model, there are only two components (GDP and the terms of trade), but since StatsCan is obliged to work in the real world, it takes other factors into account as well. But it turns out that those other things have only a marginal effect: 

The decline in real GDI in 2008Q4 is pretty dramatic - and most of it comes from the decline in the terms of trade. Over the past weeks and months, there have been any number of articles about how and why Canada fell into recession. But the real story has little to do with declines in housing prices or consumer debt loads. It's all about the terms of trade.

But here's the thing: that decline looks very much like a one-time episode. The Bank's weekly commodity price index has been holding more or less steady so far this quarter. The terms of trade may not be contributing to GDI growth for awhile, but at least it's stopped contributing to its decline.

Comments

[Marc]

Stephen, you had me right up to the point where Canada starts running a trade deficit in mid-2004. Something missing in the explanation?

[Nick Rowe]

It is amazing how closely the terms of trade and commodity prices track each other in your graph.

Commodity prices (the ones you plotted) are measured in C$, right? Are the different commodities weighted by their shares in Canadian production, or shares in Canadian exports, do you know?

It makes me wonder what is happening to the terms of trade of non-commodity exports and imports. Staying constant? Which would be strange.

[Nick Rowe]

Marc: isn't that because the export and import series are deflated by their own price indices, not by some common price index? So they represent the quantity of beer exported, and quantity of pizza imported, not the values. The trade deficit is the value of pizza imported minus the value of beer exported. (I always have difficulty keeping my head straight on this, so it really helps me thinking about beer and pizza.)

[Adam]

But here's the thing of it, and it really goes back to the debate we were all having about QE/inflating our way out. If I may briefly paraprhase the story, we have a situation where the real price of commodities (world market price) went up. Since Canada was selling commodities our real incomes went up. Now the qestion arrises, do we spend the income on imports or domestically produced goods and services? The answer was: imports. Now why was that? Well, we where at full employment, it was not physically possible for us to produce more at home. Higher demand for domestic production would just raise its price. More to the point, the improvement in our terms of trade made foreign tradeables look cheaper relative to domestic production (tradeable or not), thus there was a price signal causing us to substitute away from domestic production and towards imports.

So why does this matter? Because Stephen's story doesn't live up to the title of the post. It explains why Canadians have lost real income but NOT why we have unemployment. The qestion is, as the terms of trade deteriorate, why don't we substitute back to domestic consumption? Why does domestic aggregate demand slump? After all, this sort of price signal is somethng like the story in favour of floating exchange rates, is it not?

You could tell stories of real frictions, our stock of real and human capital was not set up to produce non-tradeables or something like that and so we may have an increase in the natural rate of unemployment for a time. However, a simpler explanation goes back to what we've been arguing about over the last week. Consumption was high, now it is and will for some time be lower, thus people's conumption euler equations say they should all save. The solution then is inflation, in our arguments over the last week Nick and I disagreed about the various transmission mechanisms from monetary policy to the real economy (we also argued over the basic causes of the trap, the last sentance was my version). But we always agreed on the prescription.

The post basically says that the drop in real commodity prices means Canadians have gotten poorer, this nobody can argue with. But that doesn't HAVE to mean a recession.

[Adam]

One more quick point. The unexpected drop in incomes could also cause people to become liquidity constrained, as in Nick's recent model. I was not arguing between mine and Nick's story. I only claim that you need one of our stories, or something else, to explain why we have a recession. It doesn't seem to me that the story in the post does it.

[Stephen Gordon]

Marc: Those are the constant-dollar series (as labeled on the vertical axis). If export prices grow faster than import prices, then the nominal trade balance can stay in surplus even if real imports rise while real exports remain constant.

Adam: Import-substitution on the part of consumers is perhaps not as smooth a transition as all that.

[Adam]

Stephen you say it so lightly!

So your story is of real frictions, that is, our stock of real and human capital was not set up to produce non-tradeables or something like that. But this is a radically different interpretation than Nick's and it begs for the opposite policy response. Your story is fundamentally an RBC interpretation in the time-to-build tradition. If that's the case then expansionary monetary policy is the absolute last thing we should be doing.

The difference matters!

For what it's worth though, seems to me the liquidity trap/demand slump story is a better description of reality, it's not clear why your story would produce disinflation/deflationary pressures.

[calmo]

Kudos to you Stephen for such a delightful and engaging post (I'm notifying AA on your behalf just so's you know how engaged I am) and esp for the last Fig which looks normal until you click on it to see the post 2008 part (the gods are with you or you are beyond smart with these graphic thingies).

But the real story has little to do with declines in housing prices or consumer debt loads. It's all about the terms of trade.

You figure the real story is about housing price declines & consumer debt loads...in the US...soon to arrive in Canada, not just another country in the gobal economy, but almost another state in the US?