**UPDATE (thanks jmk for the stats tips):**

I am now showing analysis using the Case Shiller Price Index and the UBC CUER Data based on annual price change calculations. The correlation between Vancouver and Los Angeles is 0.40; San Francisco is 0.22; San Diego is 0.29; Composite is 0.20; and Calgary is 0.38. I also did correlation analysis for Portland and Seattle. Portland is 0.22 with Vancouver. Surprisingly Seattle is has a correlation coefficient of only 0.0559 with Vancouver.

I found historical median price data for San Francisco, Los Angeles and San Diego and here is the comparison between Vancouver and those markets. I have adjusted Vancouver's prices for the difference between the US and CDN currencies based on historical exchange rates in the year in question.

## 25 comments:

It is pretty obvious that Blaze's assertion that the U.S. market does not matter because of 0.09 correlation between Vancouver and U.S. aggregate is utter hogwash.

Also, interesting starting point. How much different would it look if you have started one year earlier?

That assertion you are talking about was so ridiculous it wasn't even worth commenting on! I am truly amazed at some of the complete ignorance out there.

Re - pre-1982 - I wish I had the data to start earlier. The only data I could scrounge up for LA, SD, and SF was starting in 1982.

If anyone can dig up more data I'd be happy to put it in the chart - just post the link here or email it to me.

Here is an interesting analysis of median price gains in Santa Clara, adjusted for square footage. Median prices are a lagging indicator; rising inventories and dropping sales lead.

If you think the historical correlation will continue, Vancouver median price drops are a long way off still.

Slow. Moving. Train. Wreck.

Agreed jesse. The slope of the Vancouver line is ridiculous. I think we're at least a year away from flattening prices, nevermind a decline. I had always thought the wheels would come off this train prior to 2010, but now I'm not so sure, it might be after. Which means it might be 2015 before we're in the bottom of the valley.

Also mohican, you should try cross-correlation of the data to take into account any time lags. That said, this will not provide much more useful insight unless you have more data points and/or you include pre-1982 data ;)

Nice comparison!

One nit: correlating two time series with obvious exponential growth doesn't tell you much about the relationship between the two, other than that they are both experiencing exponential growth. i.e. if you'd correlated Vancouver's house prices with a steady 7% growth, you'd get a correlation of near 0.8.

Try removing the exponential trends and then performing the correlations. This is all best done in log space. Take the logarithms of the prices, and fit linear trends, subtract those and correlate the residual. (If you don't do the correlation in log space, you will bias your results to the recent data). I doubt you would get 0.09, but you won't get anywhere near 0.9 either.

Is the dip at 1990 real in the Van price?

What is your data souce?

jmk - sounds like you know more about this stuff than me - thanks for the tips - I'll look into your suggestions.

Price have declined 3 times in Vancouver in the past 30 years - 1981-85, 1990, 1995-99. Data source is UBC Centre for Urban Economics and Real Estate. They use the Royal Lepage data and make it available online.

Hi Mohican

Just realized that the "easy" way to do the same thing is to correlate the percent-change time series after removing the mean. You'll get very close to the same answer as doing what I described.

I know about the UBC site, which is really great. I was curious what US data you were using.

JMK -

The "issue" you are referred to is called "stationarity" - in order to run the correlation between two data series, they data needs to be "first order stationary".

That's why you should always compare the "rate of change (%, log, etc...)" in each period versus comparing the absolute figures.

Both methods you mention work.

From what I can tell, Vancouver real estate tracks Los Angeles pretty closely. There may be a 6 months lag or so but the markets are highly correlatedThey sure weren't correlated in the 90's.

I think the apparent correlation over your end points comes from the global bubble post-2001, and the climb out of the North American recession post-1982.

I'll bet if you moved the end point to 2000 and the starting point to 1980, to exclude the global bubble and include the earlier Vancouver mania, the correlation would be quite low.

"I think the apparent correlation over your end points comes from the global bubble post-2001, and the climb out of the North American recession post-1982. "

I think it is even simpler. These are nominal prices. The cause of the apparent correlation is simply inflation. You would get decent correlation with Big Macs.

This is good for a laugh. Control C, control V from Ben Jones (thehousingbubbleblog.com)

“Q: Since many contractors are much less busy now than they were, has the labor component cost of a new home decreased? The raw materials? How many fewer subcontractor employees does Lennar utilize in this market now as compared to the market peak?”

“A: Lennar in particular has seen a significant decrease in the cost of building a home. It is our strategy to pass along our costs savings to homebuyers.”

Yeah, that is the reason for the falling new home prices. Builders passing along labour and materials savings.

Hi Freako,

I think it is even simpler. These are nominal prices. The cause of the apparent correlation is simply inflation. You would get decent correlation with Big Macs.You could do that, but you'd probably only

increasethe correlation by making the inflation timeseries common to all the housing timeseries. In any case, you would still need to put the real prices into a log space so fluctuations today, when +/-2% = $10k, are as important as fluctuations in 1982 when +/-2% = $2k. And you need to remove any remaining trend. For those four cities, there will definitely be an exponential trend beyond inflation."You could do that, but you'd probably only increase the correlation by making the inflation timeseries common to all the housing timeseries."

Don't follow. Why would removing inflation increase correlation? Wouldn't that suggest that real pries are more correlated than nominal prices?

If I take two arbitrary products whose real prices are truly random, the nominal prices would still show correlation, no?

"fluctuations today, when +/-2% = $10k, are as important as fluctuations in 1982 when +/-2% = $2k"

Your assumption is that there is large long term growth in real prices. Not so sure that this the case. Definitely, we have seen dramatic real growth recently. As was discussed ad nauseum, using logs on recent real prices MASKS the severity of the abnormal price movements.

On long run real prices? We are increase of 144% from during the entire Sauder data set (1975 to 2006). Should we play god and drop the past 6 years, we get a more moderate real increase of 54%. Should that be logged?

So, LA and Calgary are the markets that are most strongly correlated to Vancouver. What does this mean for us regarding decision making about real estate?

"American men in their 30s earn less than their fathers did at the same age, according to Census Bureau data. In 2004, the median income for an American man in his 30s was $35,010 US, 12 per cent less than 30-something men in 1974, adjusted for inflation. Blame outsourcing and the demise of higher-paying manufacturing jobs."

Hmmm...doesn't this suggest less money available to purchase assets? This would mean that we would expect an unwinding in asset values as the boomers retire?

pondering - the demographic effects on asset prices was the point I brought up in this post . Have a gander.

Hi Freako,

If I take two arbitrary products whose real prices are truly random, the nominal prices would still show correlation, no?Yes, if the real prices were truly random,

and had no trend(i.e. are "stationary"). But that is an assumption that should be tested before correlation statistics are used. Quantifying the real trend is very interesting. It's pretty clear that all of these cities have outstripped inflation over time, with or without the current runup.Your assumption is that there is large long term growth in real prices.Not really. Suppose a price rises at inflation plus a random signal. You want the amplitude of that random signal to be a percentage of current prices, not an absolute value.

Imagine modeling the price of butter today, based on fluctuations 100 years ago. Suppose the price of butter 100 years ago varied by +/-10% around inflation. Back then the absolute value of that fluctuation would be 1 cent (let say). That would be far too small an amplitude for the variation in the price of butter today. But +/-10% may still be fine.

On long run real prices? We are increase of 144% from during the entire Sauder data set (1975 to 2006). Should we play god and drop the past 6 years, we get a more moderate real increase of 54%. Should that be logged?There is no benefit in taking logs of percent changes. If you want to compare the current run up to the one from 1985-1994, percent changes are a great way to measure. By eye, Vancouver went from a low in 1985 of $120k to a high of $310k in 1994, for a 158% increase in 9 years. The current run up is ~179% over 6 years. If you'd plot the prices on a log graph, you'd see that the slope of the previous run-up was shallower than the current one, but that the total distance in log space was only slightly smaller, indicating the total percent change was similar.

jmk / freako - what is your take on the new analysis? 0.40 correlation with LA is pretty strong but not definitive.

Hi Mohican,

I am now showing analysis using the Case Shiller Price Index and the UBC CUER Data based on annual price change calculations.So those are the percent changes of the real prices from UBC? Very interesting, though it makes it look like Vancouver has done better than 5% over inflation for the last 20 years. Is that correct?

Anyhow those correlations look reasonable. You could try lag correlations, as jesse suggests. My guess is that lag=0 will be the best because all the percent changes track quite closely 87-91, and I bet that is where most of the correlation is.

What does it all mean? I doubt you can say anything about tomorrow's prices in Van based on todays' prices in LA. But it seems to me that on a gross scale they follow the same economic pressures.

" It's pretty clear that all of these cities have outstripped inflation over time, with or without the current runup."

So you are still of the opinion that real RE prices will show a higher degree of correlation than nominal prices?

"Imagine modeling the price of butter today, based on fluctuations 100 years ago. Suppose the price of butter 100 years ago varied by +/-10% around inflation. Back then the absolute value of that fluctuation would be 1 cent (let say). "

Still not sure I follow. If I modeled the real price of butter over time, I would pick a year for baseline and state the rest based on that. I could state 2007 butter in 1907 dollars, or I could state 1907 butter in 2007 dollars. A low absolute value for 1907 butter would also mean a low absolute value for 2007 butter. And vice versa. Am I missing something?

"There is no benefit in taking logs of percent changes. "

That is not what I suggested. I just pointed out that the range of prices isn't enormous. Unlike for example nominal Dow Jones over the last 100 years. In linear terms, even the crash of 1929 looks like molehill. Clearly logs are essential when we have price differentials of 100 orders of magnitude. But is that the case for real RE where we are dealing with a doubling or so? I presume no harm. As suggested, percentage changes would be easiest.

"jmk / freako - what is your take on the new analysis? 0.40 correlation with LA is pretty strong but not definitive. "

Honestly, just looking at the graph tells me what I need to know with regards to historical correlation.

The coefficient doesn't mean that much to me, mostly because I don't believe that all correlation is created equal. Each signficant change in prices occur for a potentially different reason.

If Calgary runs because of oil, I don't expect a huge correlation to other cities. If Vancouver falls because of Hong Kong anti-climax, I don't expect much correlation with non-Westcoast cities. If LA flies because of Hispanic immigration, I don't expect correlation with Vancouver.

Real estate prices move for any number of reasons. Many local, some national, some even global. I am totally convinced that the global increase in RE prices is not a one in a billion chance event where local factors just happen to coincide. Rather, I believe that it has common cause. And that is all I need to know. Past correlation is interesting, but not that relevant to the situation at at hand.

For you stats hounds, here is a related challenge. What is the probability that the recent run up in world prices in multiple markets occurred by chance? For example, how often has RE appreciated double digits in real terms for 3 or more years in a row? How many metro markets have had that type of appreciation at any given time. The number for the present situation must be through the roof. Clearly there is common cause. If there is common cause, what are the chances that Vancouver will avoid the fate of LA, San Diego, LV or Miami?

Anyhow, appreciate the graphs. Sometimes the obvious needs to be compiled and graphed.

Hi Freako

I would pick a year for baseline and state the rest based on that. I could state 2007 butter in 1907 dollars, or I could state 1907 butter in 2007 dollars. A low absolute value for 1907 butter would also mean a low absolute value for 2007 butter. And vice versa. Am I missing something?Nope - I was misunderstanding what was meant by "real" prices. Sorry about that!

Nope - I was misunderstanding what was meant by "real" prices. Sorry about that!No worries. Your sophisticated understanding of statistics is very much appreciated by laymen such as myself.

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