In its recent release of income data from the 2015 census, Statistics Canada helpfully provided data tables for median incomes in 2005 and 2015 for various regions in Canada. The headline number was the 12.7% increase in median Canadian incomes, and there's been some commentary about how the gains during the last decade were not uniformly shared. But there but there was something missing in those discussions of regional gains, namely, the initial level. When you start thinking about both starting points and the changes, it's not clear why you would expect - or want - the gains to be evenly distributed.
One of the main predictions of the standard Solow-Swan or Ramsey-Cass-Koopmans neoclassical growth models is that economies will eventually converge to the same steady state or the same balanced growth path. Economies with lower incomes will also have higher marginal products of capital: the marginal product of capital is decreasing, and low-income economies have less capital. Higher marginal products of capital mean higher rates of return on investment, so low-income economies will accumulate capital more rapidly, and eventually catch up to higher-income economies.
This prediction of convergence rules out both the possibility that a higher-income economy will see faster growth and pull away from the rest, or that a lower-income economy will see lower growth and fall even farther back. Of course, there are any number of counter-examples, so the strong prediction of 'unconditional convergence' has been abandoned in favour of the hypothesis of 'conditional convergence'. The idea here is that certain characteristics of the economy - legal institutions and so forth - affect economic growth, so we should only expect convergence to occur among economies with similar characteristics.
This brings us back to Canada. Canada's regions share more-or-less the same institutions, so we should expect unconditional convergence to hold: lower-income regions should grow more quickly than high-income regions.
Let's start with the provinces and territories. Here is a scatter plot of the growth rates of real median incomes against the level of real median incomes in 2005. I've drawn axes through the Canadian medians as a point of reference. The convergence story says that we should see observations in the upper-left quadrant (lower-income regions growing faster) and the lower-right quadrant (higher-income regions growing slower). Observations in the upper-right quadrant have both higher initial incomes and higher growth rates are so are pulling away, while those in the lower-left quadrant have both higher initial incomes and higher growth rates are so are pulling away.
Most of the provinces saw growth consistent with convergence. All the traditional 'have-not' provinces had lower median incomes in 2005 and saw higher growth rates, while Ontario combined high initial incomes with low growth. BC is in the lower-left quadrant, but so close to the Canadian median that it's hard to say that it fell back. (You could same thing about Quebec, come to that.) Setting aside the territories, the only clear deviation from the convergence hypothesis is Alberta, which started with higher incomes, and which had higher growth.
Let's move on to the cities, in the form of the Census Metropolitan Areas (CMAs):
Again, most of the cities - 23 of the 37 plotted here (I broke out the Ontario and Quebec parts of the Ottawa CMA) - are in the upper-left or lower-right quadrants, consistent with convergence. If you fit a linear, population-weighted regression to these data, you get a negative relationship between growth rates and initial income levels. A $1000 (2015 dollars) reduction in 2005 median incomes would be associated with an increase of 1.4 percentage points in the growth rate.
What's striking about this chart is all that green in the bottom-right quadrant: almost all of the Ontario CMAs combined high initial incomes with low growth rates. Most of the cities with high growth rates were, unsurprisingly enough, in resource regions. Not all of them were in the west, and not all of them were high-income cities to begin with. St John's, in particular, did very well. (It's probably not a coincidence that the Ontario CMAs with the highest growth were Sudbury and Thunder Bay, both relatively more attached to resources than other Ontario cities.)
Finally, census subdivisions (municipalities) with populations of 5000 or more:
(I will pause for a moment here, so that you might have a chance to thank me for taking the trouble to keep the same colour scheme for all three charts. You're welcome.)
It should be noted here that the scale of the axes has changed: the dispersion of initial incomes and growth rates for census subdivisions (CSDs) is much greater than for CMAs. That said, the convergence pattern is still discernible, if not economically important. A $1000 (2015 dollars) reduction in 2005 median incomes would be associated with an increase of only 0.4 percentage points in the growth rate.
Once again, the lower-right corner consists almost entirely of CSDs in Quebec and Ontario. The lower-left corner - the areas falling behind - starts to come into sharper focus here. The regions where incomes started low and grew more slowly are in Ontario, Quebec and BC. (There are many Atlantic CSDs with low incomes in 2005, but they generally had high growth rates.) I haven't checked them all, but it looks to me as though these regions are generally situated in rural areas, well away from a major city. I leave it as an exercise to the reader to explain why these CSDs fell behind, while apparently similar CSDs in places like New Brunswick and Nova Scotia caught up.
So it's important to think about initial starting points when you break down income growth by region: not all differences in growth rates exacerbate regional disparities. Uneven growth consistent with a story in which low-income regions are catching up to high-income regions is probably not a problem that need solving.