A response to Kevin Milligan's pension post: A math issue

Kevin Milligan is an associate professor of economics at the University of British Columbia. I’m a journalist who bailed on his undergraduate minor in economics when I ran into too much math in ECON 2310 and 2410. So I approach this response to some math issues in Milligan’s excellent post on the state of our public retirement income system with a bit of trepidation.

But I’ll plunge in away.

Milligan writes:

By 2031 — at the peak of the baby-boom retirement wave — the share of GDP spent on Old Age Security will rise to 3.14 per cent, for an increase of 0.73 per cent over today’s level [of 2.41 per cent of GDP]. Now, an increase of 0.73 per cent of GDP cannot be ignored, but neither is it disastrous. To provide some scale, David Dodge and Richard Dion project that spending on health will grow from 12 per cent to 18.7 per cent of GDP by 2031, for an increase of 6.7 percentage points.

We have, in this paragraph, some issues that journalists have long wrestled with. How do you express the change in two numbers and do so in a meaningful way using non-specialist language that accurately sums up the change? I’ve been to journo conferences where entire morning workshops are given to arguing about this issue.

To begin with, when Milligan speaks of Old Security spending rising to 3.14 per cent of GDP, Milligan is using a common ratio: Expressing something as a percentage of something else. In this case, Milligan is saying that in 2031, the government will spend $3.14 for every $100 of the country’s gross domestic product (the sum of all economic activity in a country). The other ratio we’re interested in is current spending. Milligan says right now Ottawa is spending $2.41 for every $100 of GDP.

Now here’s the tricky part: How do you compare two ratios?

I think Milligan accurately compares these two ratios when he speaks about healthcare spending at the back of the paragragh. Noting that healthcare spending as a percentage of GDP will rise from 12 per cent now to 18.7 per cent in 2031, Milligan says that is an increase of 6.7 percentage points. That’s quite true: If we spend the equivalent right now of 12 percentage points (or units) of GDP now and we will spend 18.7 percentage points in the future, we will be spending 6.7 percentage points (or units) more in the future.

But Milligan uses a slightly different way of comparing the two ratios of OAS-to-GDP now and in the future. He says that ratio will experience “an increase of 0.73 per cent over today’s level.” That is not the same as saying it will increase 0.73 percentage points.

If we are spending $2.41 for every $100 of GDP and plan to spend $3.14 for every $100 of GDP, then we’ve increased spending 73 cents. How much bigger is our starting figure $2.41 when we add 73 cents to it as a percentage of our starting figure? The answer to that is 30 per cent. If you have 400 apples now and you had 300 apples a year ago, you now have about 30 per cent more apples. That’s because the difference in the number of apples — 100 apples — is one-third or about 30 per cent larger than the number you started with — 300 apples. So last year you would have said, to borrow Milligan’s phrasing, that you expected  “an increase of 30 per cent over today’s level.”

Now that may not be, if you’ll pardon the pun, an apple-to-apple comparison. For in my apple example, I’m comparing two integers — two actual numbers-of-things. Milligan is comparing two ratios and trying to use an other ratio to do that. That opens the door to some confusion. I think the appropriate way to do that is to stick to the phrase he used the second time around and say Old Age Security costs, as percentage of GDP, will rise by just 0.73 percentage points.

Still, I’d be interested to hear from folks more expert than me on this issue so jump in in the comments section below.

As to Milligan’s overall point, that “our public pension commitments are not a substantial threat to our public finances” , I am 100 per cent in agreement!

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