Monday, July 06, 2009

Guest Post: Vancouver Housing Price Correlation Model

A recent discussion on the impact of low interest rates on local housing prices had me whipped up a quick, but significant correlation model between Vancouver housing prices and a few key factors.

The regression model is based on quarterly data, dating back to 1990. The independent variables for the regression are: Vancouver's unemployment rate, average 5-year residential mortgage rate, inter-provincial migration into BC, and international migration into BC. The result is as follows:

Adjusted R-Sq Value = 0.85

Volatility:
1) 1% increase in Unemployment rate translates to roughly a 10% housing price decline
2) 1% increase in 5-year mortage rate translates to a 8% housing price decline
3) every 1000 interprovincial migrants into BC increases housing prices by 1.8%, and
4) every 1000 international migrants increase housing prices by 1.7%

Significance Levels (P-Values):
Unemployment = 2.78E-19
Average 5-Year Mortgage Rate = 5.89E-13
Inter-provincial Migration = 8.02E-07
International Migration = 0.0163

Other factors like Canadian/US exchange rate & foreign investment flows are either non-factors or they are already embedded into one or a combination of the above factors. What's also interesting is that international migration has a low correlation and the least significant.

The graph below is a plot of the logarithm of the average housing prices (Source: UBC Centre for Urban Economics and Real Estate) and the regression model. The plot also tries to convey how each of the independent variables (components) are added together to yield the model price. Note that these components are arbitrary shifted so that it can be seen on the same axis. The rising yellow line since Q42008 represents a decline in the 5-year mortgage rate, and the falling dotted unemployment component since Q42008 reflects the rising unemployment rate.






Obviously, the caveats to this type of model are that correlations change over time, the causality of the variables is complex and unknown (i.e. we don't know what causes the other or which is really the independent variable), and there may be non-linear elements, such as a rise in RE price may fuel further decline in unemployment or vice-versa.

With this in mind, I took the liberty of forecasting some numbers through 2011, based on these 3 scenarios:
1) Unemployment gradually rising to 9% (1990s' levels) and the average 5-year mortgage rate constant at 2009Q1 levels of 5% (based scenario)
2) Unemployment rising to 9% and the average 5-year mortgage rate declining further to 2.5% (record low mortgage spreads)
3) Unemployment rising to 9% and the average 5-year mortgage rate rising to 8% ('00 levels)

All 3 scenarios use 2008 numbers for inter-provincial and international migration numbers. Note that the scale on the Y-axis is normal.






In 2007Q2, Vancouver housing prices appear to lose correlation held since 1990. What does this mean? Is there a factor in 2007 that we need to include? or are we just seeing irrational exuberance?


UPDATE 2009-07-07 :
The model was optimized by delaying the effects of the unemployment rate, mortgage rate and international migration by one quarter. New adjusted R-value is slightly better (0.851)

I also added another scenario (unemployment at 7% and 5-Y rate at 5%, unchanged from 2009Q2 through 2011)


19 comments:

barbor62 said...

Great work!!!

It will probably take me two days to analyze it.

A point of clarification: I assume that the variables of unemployment and such are the predictor variables, i.e. independent. And,that price is he response variable- dependent. Or, have I misunderstood the direction of your regression analysis?

Nevertheless, there does appear to be a strong and significant relationship between the variable you have presented.

mike said...

thanks for the correction. They are indeed independent variables.... housing price is the dependent variable.

david said...

Though quite interesting, this is pretty far over my head.

Also, we can run graphs predicting everything we want, but it still wont make it happen.

The huge spring bounce now running on into summer has shown me that the average buyer will jump right into a mortgage they cant afford because the real estate agent and mortgage broker say that it will be no big deal.

The georgia straight article I am sure everyone has already read ( http://www.straight.com/article-237609/firsttimers-rates ) shows that people are willing to assume huge risk just to own a home. Until people start learning the consequences either through first had experience or seeing it happen to others, they will keep buying houses at ridiculously inflated prices because the realtor said it would be fine.

JimTan said...

The key assumption is the 9% unemployment rate. Currently, the national rate is @8% with Ontario manufacturing leading the decline in jobs. BC province is @7.5% and regional is @6.7%.

A new Merrill Lynch forecast calls for Canadian growth in the 2nd half 2009 and modest growth (2.7%) in 2010.

What does the model say if local unemployment peaks this year (or early 2010) at 7.5%? Let's turn it around. What does the model say about the unemployment rate if RE bottomed in spring?

Finally, the 2007/08 anomaly may be due to the commodities boom. For example, oil peaked in June 2008 at $170 per barrel. The main beneficiary was our neighbour Alberta.

jesse said...

Mike, thanks for spending the time to do this. It doesn't pay that well! I would include either housing starts/completions or inventory levels or months of inventory as well; both would intuitively have some effect on price fluctuations. Also interest rates changes have a nonlinear effect on affordability -- a shift from 4% to 5% is more significant than from 7% to 8% from the debtor's perspective.

I think a great take away for those not highly versed in statistics is that improved affordability through low interest rates seems to be tightly linked to price changes.

jesse said...

You can try employment or median incomes instead of unemployment. The strong link between unemployment and price changes is also quite interesting. I don't know if you're cross-correlating but you can try to see if there is a time offset for best fit.

mike said...

The key assumption is the 9% unemployment rate. ... regional is @6.7%.
June's unemployment rate for vancouver region is 7%, and I expect this to go up as the Olympics wrap up and global economy takes its toll on the region. Going back to 1990's level (or worst) is reasonable as this recession should be much worst.

What does the model say about the unemployment rate if RE bottomed in spring?
I suspect the bounce is due to low interest rates, and possibly hot money coming from china, where speculation on commodities is rampant. (Yes, the recent boom is not driven by demand; it is by financial speculation, and we know how that usually ends)

...nonlinear effect on affordability -- a shift from 4% to 5% is more significant than from 7% to 8% from the debtor's perspective.
By taking the logarithm of the price we take this effect out. What I'm concerned about is a 2nd order effect....

JimTan said...

"I suspect the bounce is due to low interest rates, and possibly hot money coming from china, where speculation on commodities is rampant."

Doesn't look like hot money to me. Looks like long term investors/residents.

mike said...

you can try to see if there is a time offset for best fit.

Not a surprise, but an optimized model is to delay the effects of unemployment, mortgage rate and international migration by a quarter. Provincial migration is still best fit with no delay. So, the effects of higher unemployment and lower mortgage rates should be seen in the coming quarter.

Model 2.0 has a slightly better adjusted Rsq value. See the following link.

http://docs.google.com/Presentation?id=dghbwhpz_95hrmr77g2

I'll also update the blog posting...

Deliverator said...

I would include either housing starts/completions or inventory levels or months of inventory as well; both would intuitively have some effect on price fluctuations.

Housing starts would be a lagging indicator, one would think, since builders tend to follow the market - note how many units are still in the pipeline with the market having already topped.

However, completions should definitely have an effect as they directly affect supply.

Dave said...

How can a housing price model not account for income? The two biggest factors should be income and interest rates.

I have trouble believing that every 1,000 migrants would cause a housing price increase of 1.7% to 1.8%. There is probably more correlation here than there is causation. To put it in perspective... there are roughly 2 million households in BC valued at an average of about $400k each. If you take the total value of BC real estate, increase it by 1.7% and attribute that increase to each new migrant, you end up with a value of $14 million per head. Obviously, each new migrant doesn’t cause that level of price increase.

I suggest another iteration of your model start with income, interest rates, unemployment and net migration.

mike said...

How can a housing price model not account for income? The two biggest factors should be income and interest rates.

agreed. This model is not causal; it is a correlation model. I would venture to say that most of the income component probably came in via the unemployment rate and provincial migration.

Declan said...

It's tricky to do, but the model might benefit from incorporating an interest rate element that looks at percentage changes rather than absolute changes.

e.g. A rise from 2% to 4% is treated as 'interest rates double' vs. 'interest rates go up by 2%'

Over time, as people get used to lower rates they take on more debt which in turn makes their finances (and house prices in turn) more sensitive to interest rate changes than they used to be.

In my experience, a composite interest rate metric that is half absolute change and half percentage change vs. say the average over the last 5 years, often gives the best results - but you're getting into tedious and time consuming fine tuning for relatively small gains in explanatory power.

Still, if you look at the current recession, it was preceded by an interest rate increase of only 2.5% (prime from 2.25% in 2004 to 4.75% in 2007), but this was nonetheless a 111% percentage increase - larger than the interest rate increase that trigerred the recession of the early '90s.

buff_butler said...

"Doesn't look like hot money to me. Looks like long term investors/residents."

If its happening to every city in canada all at once then that doesnt make sense...

M- said...

Mike, that's great work! I'm quite impressed!

Dave said...

Mike, I am sure you already know this, but if your model doesn't have any expectation of causation, then I would be suspicious of it's predictive ability.

The immigration correlation makes little sense for the reasons I have shown. Why not add global warming into the model and see what happens? ;)

mike said...

"The immigration correlation makes little sense for the reasons I have shown. Why not add global warming into the model and see what happens?"

if global warming is correlated to economic activity, then it might not be a bad factor use. what should i use? the average annual temperature? but wait, i have to remove the effect of sun spots.....

Kidding aside, doesn't immigration cause more demand for houses? Maybe its effect is not all direct. Perhaps, it's the reason he/she is coming for. Migration may be due to increase local economic activity like a new factory or startup/company.

Correlation change in time, but at this very instant (2009Q1), you have these 4 factors that explain 85% of the price action.

Dave said...

Correlation change in time, but at this very instant (2009Q1), you have these 4 factors that explain 85% of the price action.

No, it doesn't explain anything because causation hasn't been demonstrated.

jesse said...

"it doesn't explain anything because causation hasn't been demonstrated."

Out of curiosity, how would you go about demonstrating causation?