The latest update of Project Link includes estimates for national accounts income measures: Gross National Income (formerly known as Gross National Product), Net National Income, compensation of employees, and disposable income, all going back to 1947Q1.

I've also added Gross Domestic Income. GDI is a fairly recent arrival in the national accounts, and it takes into account the income effects of changes in the terms of trade. Looking at GDI has been particularly useful in understanding the Canadian economy over the past fifteen years, since it picked up the incomes gains and losses incurred as the prices of Canadian resource exports rose and fell. Since GDP measures activity - and not necessarily the income it generates, GDP was not as useful as it usually is. (See my beer and pizza explainer.)

Movements in GDP and GDI were virtually indistinguishable during the twenty years preceding the resource boom, and I was curious to see what the relationship had been before then. It turns out that they had been tracking each other very closely during 1961-1980 as well:

You can see a bit of daylight between the two series during the surge of oil prices in the 1970s, but otherwise, the two series say pretty much the same thing between 1961 and 2002. So I wondered if the same held true for 1947-1960 as well.

Project Link is about piecing together old fragments of Statistics Canada series, but as I just mentioned, GDI is a relative newcomer to the national accounts, so there aren't old GDI estimates that I could link to the current series. So I decided to look more closely at how they were constructed.

My guide is Section 7.6 of this Statistics Canada explainer, and equations (7.20) and (7.21) in particular:

**Real GDI = Real GDP + Trading Gain**

**Trading Gain = (X-M)/P - (X/P ^{x} - M/P^{m}) **

where *X* and *M* are exports and imports with prices *P ^{x}* and

*P*.

^{m}*P*is some measure of prices for domestic expenditures, and apparently the choice is 'debatable'. I can see why, but I don't want to get into it, so I'm going to go along with Statistics Canada's choice of usin the deflator for Gross Final Domestic Expenditures:

**GFDE = GDP - (X-M)**

This deflator is published as Cansim series v61992662. I constructed my own deflator by dividing nominal GFDE by its real counterpart. This doesn't reproduce the StatsCan estimate (it's not a Fisher index), but it's close enough.

There are a couple of things to note here.

- You can see how the terms of trade affect the trading gain. If
*P*goes up and/or^{x}*P*goes down, then the trading gain increases,^{m}*ceteris paribus*. An increase in Canada's terms of trade increases Canadians' purchasing power on the world markets. - Since we're using price indices normalised to 100 in the reference period (2007, in this case), the trading gain in the reference period is always zero: all the price indices would be the same, so the (X-M) terms cancel out exactly.

This last point explains, I think, one thing that had puzzled me at first: why does Statistics Canada publish its GDI estimates as an index (2007 = 100) instead of in constant dollar terms? The answer seems to be that since the trading gain in the price index reference year must be zero, the trading gain expression above is better interpreted as the difference between the trading gain at a certain point and the trading gain in 2007.

This timing is a bit of a problem. As you may recall, 2007 was the height of the resource boom, so estimates for training gains that set 2007 at zero are going to produce a large number of negative numbers. And that's what you get: of the 285 observations between 1947Q1 and 2018Q1, only 22 show positive trading gains using the 2007 reference year. As you can imagine, the communications challenge would be formidable: the 'trading gain' defined above is not the same thing as the gains from trade as we usually think of them, so the potential for confusion is enormous. "Statistics Canada says Canada loses from trade" is not a headline that they want to see, and there are too many who will pass incuriously over the nuances of price index reference periods.

Even so, the changes in the trading gains still of interest. Here are my estimates for the trading gain from 1947Q1 to 2018Q1:

To repeat, the story of this chart is * not* that Canadians were 'losing' from international trade for 60 years: 2007 was an exceptional year, and the measure defines the trading gain in 2007 to be zero. The story is the changes; in particular the increase of $4000 per person increase over 1998-2008. This is a much, much bigger story than the decline in manufacturing employment during this time.

This chart also offers some potential insight into the years of income stagnation in Canada: real trading gains decreased by $2000 per Canadian over the 1980s and 1990s. It's hard to get ahead when the prices of what you're selling are falling while the prices of what you're buying are going up.

Since it's so easy to do, I've also calculated the trading gains for the United States using the same methodology. But again, the US reference year of 2009 is also problematic: the US was still in the deepest throes of their recession. Even so, it's constructive to compare the variations in the trading gains:

This one is ... striking. The variations in per-capita trading gains over the past 20 years look very, very different. And since the trading gains are driven by changes in the terms of trade, here are they are:

Once again, I don't see how you can shoehorn a US narrative about how trade has affected incomes over the past couple of decades into the Canadian context, but that certainly hasn't stopped people from trying.

## Comments

You can follow this conversation by subscribing to the comment feed for this post.