Homer Simpson once said, “Oh, people can come up with statistics to prove anything, Kent. Forty per cent of all people know that.”
While a quote like that might make some economists cringe, it does serve as a segue to an explanation of the statistical phenomenon known as Simpson’s paradox (different Simpson). It relates to how individual groups can have similar trends, but when the groups are combined, the trend gets flipped upside down.
Simpson’s paradox is something we see whenever the percentage change in average price for a number of individual markets moves in the opposite direction compared to the combination of them.
Consider the following hypothetical example. Let’s say Canada is made up of just three local housing markets (A-town, B-town, and C-town) and that average price in each of them is up by 10 per cent compared to the same month last year:
|
# sales this month last year |
# sales this month |
Year-over-year % change: sales |
Average price this month last year |
Average price this month |
Year-over-year % change: average price |
|
|
A-town |
100 |
40 |
-60 |
$600,000 |
$660,000 |
10 |
|
B-town |
100 |
100 |
0 |
$400,000 |
$440,000 |
10 |
|
C-town |
100 |
160 |
60 |
$300,000 |
$330,000 |
10 |
|
Canada |
300 |
300 |
0 |
$433,333 |
$410,667 |
-5.2 |
While combined sales are unchanged and the average price in each housing market has climbed by 10 per cent, the average price for combined sales is down by 5.2 per cent. Intuitively, one might think that that average price for combined sales should be up because price rose in each of the three markets. Simpson’s paradox suggests that applying intuition to statistics can result in mistaken conclusions.
Our favourite analogy to explain Simpson’s Paradox involves calculating the average height for a classroom of kids: first, calculate the average height. Now excuse the five tallest kids and recalculate average height. While the average has shrunk, the kids haven’t.
The example serves to illustrate how changes in the mix of sales (or kids) can result in changes in average price (or average height).
The MLS® Home Price Index overcomes the shortcomings of average price measurement, because it is not affected by changes in the mix of sales the way that the average (or median) price is. That’s because the HPI involves “apples-to-apples” comparisons of typical homes at the neighbourhood (i.e. subarea) level.
For example, when I look at the description for a Benchmark two-storey single family home in my neighbourhood, it’s basically an exact description of my house — and I can track the evolution of prices for these properties over time in an area no larger than where I walk my dog every night.
The bottom line is that Simpson’s Paradox suggests that understanding average price changes requires understanding of how it is being affected by changes in the mix of sales, whether at the subarea level or for larger areas. That’s because changes in the mix of sales can result in average price changes that contradict your intuition. I think Homer Simpson says it best: ‘d’oh!’
As a home owner and a small portfolio investor, I realize that watching what is happening with trends in real estate is is a lot like watching paint dry. Monitoring it, does not change the outcome. It will go up and it will go down. The only outcome of significance is what becomes the market value of a piece of real estate on the day it changes ownership. If the vendor gets what s/he can walk away with with (with minimal seller’s remorse -those that bought at the peak of ‘Co-Vid Craziness’ in the market, that end up forced to move before they’re able to pay down principal enough to allow them to be equity positive) and the purchaser, is looking forward to living in a home that they feel was worth the price they negotiated, then That is the only market outcome of significance. Each day, we all need to put a roof over our heads and most adults have to pay for that compulsory priority, either as rent or home ownership costs. In between moving days, we can all keep our paint brushes up and out of the way, so the drying ‘paint’ of the market becomes either temporality or permanently redundant.