I had always known that a given debt/GDP ratio would be more worrying for a country with declining population than for a country with a growing population. There will be fewer future people to carry the same future burden. But I had never sat down to do the arithmetic, until just now. What surprised me was just how big this effect was. So if you have never done the arithmetic yourself, or seen anyone else do it, read on.
Suppose the real interest rate is r, the growth rate of per capita GDP is y, and the growth rate of population is g. Define the "debt burden" as the percentage of GDP needed to service the debt to prevent the debt/GDP ratio rising over time.
Then: debt burden = (r-y-g)debt/GDP
In a stationary economy (y=0, g=0) the government needs to set taxes higher than program expenditure so that the resulting "primary surplus" is just big enough to pay the interest on the debt, and prevent the debt rising over time. (Both the interest rate, and the debt, are measured in "real" terms, i.e. adjusted for inflation.)
To my mind, the "primary surplus" needed to prevent the debt/GDP ratio rising over time is a good measure of the burden of the debt. It represents taxes we pay that cannot be spent on the things we want to spend it on.
In a growing economy (y+g>0) the debt burden is smaller (for given real interest rate and debt/GDP ratio). That's because the debt can be allowed to grow at rate y+g while keeping the debt/GDP ratio constant.
Let's plug in some numbers. Suppose r-y=2%. That seems roughly plausible for advanced countries, with real interest rates on government debt around 3%, and real income per person growing around 1%. Now compare two countries: the first has 1% population growth; and the second 0%.
The country that has a growing population has half the debt burden of the country with constant population, if both have the same debt/GDP ratio. And the country with a growing population can handle twice the debt/GDP ratio with the same debt burden.
It's that second way of thinking about the arithmetic that surprised me.
Presumably there is some maximum level of debt burden that a population is willing to accept, because they are paying taxes, but getting nothing in return. (Well, they did get something in return, but that was yesterday's deficits, paying for yesterday's generation's benefits). Past a certain point, if the debt burden gets too high the population may refuse to pay, or may emigrate to avoid the burden, which just raises the burden on those who remain.
Maximum debt/GDP = maximum debt burden/(r-y-g)
All other things equal, if we just looked at projections for population growth rates, my guess is that Canada can handle nearly double the maximum debt/GDP ratio that (say) Greece can handle, since our population will grow at nearly 1 percentage point higher.
Of course, other things matter too, but population growth matters a lot. I hadn't realised the effects of population growth were so big.