patrick.net

I'm not entirely satisfied with the usual patrick.net simplification of "low interest rate=high price, high interest rate=lower price". That's not enough data to make a valid assessment. Can anyone get a graph of Case-Schiller alongside historic average mortgage rate for the past 30 years? That would be a better tool, IMO.

Here is part of it.

http://www.housingbubblebust.com/OFHEO/Major/NorCal.htm

Well, it's definitely true all day every day in the bond market.

Patrick, and that would imply... What? That you think durable goods are like bonds, or that bond markets predict housing prices? ;o

Brand, here you go:

Patrick, I don't see a correlation between the case-shiller composite-10 and 30 yr fixed mortgages...

Actually, Patrick might be on to something, I calculated the Pearson correlation coefficient and it's -0.7163761, which means there is a negative strong correlation between the 30 yr fixed mortgage interest rates and the case-shiller composite 10 index... hmm...

Not sure what a Pearson correlation is, but if you just think about it, it seems obvious to me that higher interest rates mean the same price must cost less with the same monthly payment.

So many people cried "supply and demand" when prices were going up, and they were utterly wrong. It was mostly lower interest rates that caused the bubble.

From a theoretical perspective house prices should not be negatively correlated with interest rates, that is housing prices should not go up when interest rates fall.

From a practical perspective house prices have not been negatively correlated with interest rates in the past.

Here is an example why the correlation does not exist
Scenario 1.
Imagine inflation is 0% per year and a buyer spends 35% of his income on housing. As inflation is zero his income will not rise and he would have spent 35% of his income over 30 years to buy the house assuming a fixed rate mortgage.

Scenario 2
Now imagine inflation jumps to 10% per year. In this scenario mortgage rates would rise dramatically and a naive viewpoint is that house prices would fall so that the buyer spends 35% of his first year's income on housing. But this view misses the fact that with 10% inflation, the buyers income will increase 10% per year such that the second year he only spends 32% of his higher income and falling percentages in subsequent years. In this scenario he would only spend 6.4% of his income over 30 years to buy the house assuming a fixed rate mortgage.

The only way to keep the lifetime income spent on housing the same is to spend smaller fractions of first year's income in the low inflation world and higher fractions of first year's income in the high inflation world.

If you do the math you will find that this makes house prices independent of mortgage rates.

Well, I did the math and that's the correlation I got. Don't forget that correlation does not imply causation.

I basically got the numbers for 30 yr rates from Freddie Mac and the case-shiller index from S&P's website. You're welcome to do the math yourself.

Also note that the whole bubble is in the middle, so that might explain the correlation.

6f6231: I looked at the correlation between change in house prices in the Bay Area before 2004 compared with changes in mortgage rates and I did not get a strong correlation

I don't have the numbers at hand but here are three examples that disprove the correlation

In the late 1970s as mortgage rates rose, house prices rose in the Bay Area. SF house prices grew at a double digit annual pace from 1977 to 1980 while mortgage rates rose from 9% to 15%. Only in 1981 & 1982 when mortgage rates went even higher while there was a severe recession did prices fall

In the early 1990s as mortgage rates fell, house prices also fell. Prices fell from the middle of 1990 to the middle of 1995 while mortgage rates fell from about 10% to 7.5%

Currently mortgage rates have been falling for about a year from about 6.5% to 5% while house prices are falling.

The changes in house prices are for the SF metropolitan area from the FHFA. I haven't looked at the Case-Shiller composite 10 numbers.

gavinln: I suspect you are right and the correlation you get depends on the time period. It'd be interesting to rerun the numbers with the bubble excluded (up to 1998? 99?) and from the peak of the bubble until now.

Unfortunately, the case-shiller composite 10 index only goes back to 1987.

I'll rerun the numbers and post here with a new graph when I have time.

BTW, I also have the Case-Shiller indices for SF (they include all counties from SF down to San Mateo in the SF index). If anyone is interested, I can easily run the numbers using that index too.

Ok, I redid the graphs for two periods:

1987 - 1997 (roughly before the bubble) and got this graph:

the correlation coefficient is -0.1525083
which is pretty low, less than say -0.1 is completely due to chance.

1998 - 2008 (full bubble):
and the correlation coefficient is -0.6276506 which is a pretty strong
negative correlation.

Jan 1999 - May 2006 (bubble):
correlation coefficient is -0.7264818 again, pretty strong negative
correlation.

Jun 2006 - Feb 2009 (bubble pops):
with a correlation coefficient of 0.6946998, which is a strong positive correlation.

I think what it means is that in "normal" times, interest rates and home prices are pretty much independent. However, as the bubble built up, it was inflated by falling interest rates and now that it has popped we're seeing drop even more as a result of government intervention.

gavinln - prices and inflation became disconnected in late 90s.
Overtime there correlation between inflation and RE prices.

http://www.housingbubblebust.com/OFHEO/Major/NorCal.html

6f6231: Actually, that's kind of what I expected. Game theory tends not to track simple models like supply vs. demand. I would expect other factors to correlate much higher-- the DTI ratio of median income vs. Median payment ( interest rate, median house price) should correlate highly to increased home sales. Expected downpayment should also correlate with sales volume, as up front cash limits the pool of candidate buyers.

In other words, I do expect that house prices can roughly track supply and demand. I just doubt that demand is driven purely by interest rates. I think it is driven primarily by accessibility and anticipation of return (downpayment, DTI, lending standards, available loan products, expectation of future return, economic conditions).

also, I think there are multiple factors influencing house prices over time. As Gavin points out, inflation plays a factor, as houses are a durable good. So I guess we'd have to correct incomes and prices for inflation in my thinking above.

This would make a really interesting research paper! ;o

Hm, none of my images made it through (thanks Patrick for letting me know). Here are they again;

1987 - 1997: Correlation -0.1525083

1998-2009: Correlation -0.6276506

Jan 1999 - May 2006: Correlation -0.7264818

Jun 2006 - Feb 2009: Correlation 0.6946998

Brand, if you can give me pointers to where the data is, I can play with it. I've been wanting to plot case-shiller indices vs income for quite a long time, but so far have been unable to find income data anywhere.

Here are the images 6f6231 wanted to post:

And by the way, now everyone should be able to edit their own comments. But not, of course, those of others.