### Economy Lab

Delving into the forces that shape our living standards
for Globe Unlimited subscribers

Economy Lab

# A housing bubble? Even Carney won't go there Add to ...

Bank of Canada Governor Mark Carney's recent speech entitled ' Housing in Canada' does not contain the word 'bubble'. Indeed, his talk was very careful not to venture an opinion on the question of whether or not the Canadian housing market -- and in particular, the Vancouver housing market -- is experiencing a bubble. Nor should he have: asset bubbles are almost impossible to identify in real time; price increases aren't always due to irrational behaviour. And when interest rates are very low, those increases can be very sharp indeed.

Asset prices reflect the present value of future payoffs, and so they depend on both expectations of those payoffs as well as the interest rate used to discount them. Everything else being equal, higher expected future payoffs produce higher asset prices, and higher interest rates generate lower prices.

A simple example is a perpetuity, which offers a constant stream of payoffs over an infinite time horizon. In this case, the formula simplifies to the ratio of the payoff divided by the (constant) interest rate. Even though interest rates aren't constant and houses don't last forever, they do offer a roughly constant stream of housing services for a very long time. So for the purposes of the next two paragraphs, I'm going to assume that modeling houses as perpetuities is a useful approximation that keeps the math simple.

Suppose that a house offers a stream of housing services that is valued at \$10,000 per year -- that is, people would pay \$10,000 a year to rent the house. And suppose also that the interest rate used to discount that stream of housing services is 10 per cent. The resulting valuation is \$10,000/0.10 = \$100,000. If interest rates fall to 9 per cent, the price increases to \$111,111. A one percentage point reduction in interest rates would increase prices by roughly 11 per cent.

Now suppose that interest rates are 5 per cent (price is \$100,000/0.05 = \$200,000), and the interest rate is reduced to 4 per cent, so that the price rises to \$250,000. The effect of a one percentage point decrease would have gone from 11 per cent to 25 per cent. A reduction to 3 per cent will increase prices by 33 per cent, and another percentage point reduction will increase prices by 50 per cent.

The reason I'm going through all this arithmetic is to make the point that as interest rates fall, their effect on asset prices increases. So we shouldn't necessarily be surprised at seeing sharp rises in housing prices as interest rates reached levels not seen in generations.

Mr. Carney noted that housing prices are "13 per cent above their pre-crisis peak". That sounds like a lot, but the five-year conventional mortgage rate has fallen from about 7 per cent in mid-2008 to 5.5 per cent now. A few minutes of playing around with the CMHC Mortgage Payment Calculator, suggests that with this decrease in mortgage rates, you could buy a house that was 15 per cent more expensive without increasing your monthly payments.

Another narrative might hold that pre-crisis prices were produced by a bubble, but such a story would also have to explain why the sharp fall in prices during the crisis wasn't enough to burst the bubble. As Nick Rowe once put it, bubbles pop when they're pricked; they don't reflate.

This isn't to say that Canadian housing markets are bubble-free; the point is that it's very difficult to make such a determination in real time looking at available price data. Even in the U.S., the most convincing contemporary evidence of a housing bubble was the degradation of mortgage underwriting standards.

Probably the biggest reason why Mr. Carney did not mention the possibility of a bubble is that its presence isn't a necessary condition for warning Canadians about the importance of preparing themselves for a significant decline in housing prices in the medium term. If small decreases in interest rates can produce large increases, then small increases in interest rates -- and such increases are inevitable -- can also generate large reductions in house prices.

Stephen Gordon is a professor of economics at Laval University in Quebec City and a fellow of the Centre interuniversitaire sur le risque, les politiques économiques et l'emploi (CIRPÉE). He also maintains the economics blog Worthwhile Canadian Initiative.

Report Typo/Error