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« Mortgage Availability and Personal Consumption: Some Dubious Evidence from Doug Kass | Main | Payroll Employment and Weekly Jobless Claims »

March 07, 2007



Regarding CXO, here's an example of how they use Pearson correlations and lags to demonstrate that ECRI WLI is a coincident indicator at best for the stock market.


Hi RB,

I am generally a fan of the CXO work. Some of their topics are on my agenda. I'm not show how they use a Pearson coefficient to gain insight into causality. It may be a superior correlation measure. When looking at time series data we often try for relationships with lags of different lengths.

In this series, the chart makes it seem that no lag is helpful. In fact, using Year-over-year data for PCE and quarterly changes for mortgages makes it seem that, if there is causality (unlikely), it might run the other way.


Using Pearson correlation with two time series is a serious methodological error. One could get a high (spurious) correlation for many pairs of series. Economic statistics move together for a reason, and this reason is seldom a matter of simple causation.


Calculated Risk --
Thanks for stopping by and for commenting. I have had your site on my RSS reader for quite some time. I have visited, although I have never commented.

We are all interested in the relationship between housing and the economy, and we all agree there is some effect. I just do not think that the Fed survey tells us much.
I'm sure that many of my readers share your interpretation of the charts, and that is fine.

We should, however, get exactly the same correlation. I suggest an email spreadsheet exchange! We'll get it sorted out.

Thanks again --


Jeff, I've always been hesitant to put any statistics in my posts - for precisely the reason you noted - some readers might not understand what I'm writing. This is only the second time I've mentioned degrees of freedom and correlation coeffiecients, and some people definitely get confused!

Also I didn't discuss causation vs. correlation - I was being brief and I hope most of my readers understand my arguments for less growth in consumption going forward.

I have a few points of disagreement with your first post. First, I don't think the "fit" / "no-fit" graph with circles tells us much. I think we are looking for more macro moves than micro moves. So I think some of those "no fit" areas are actually pretty good fits. One of the key areas you circle as "no fit" (that I agree with and noted) might be a strong argument for the wealth effect from the stock market - something I mentioned in my original post.

Another issue is your "Looking at the Data" segment. You wrote: we "know little about whether the current standards are high, medium, or low by historic norms." I think the absolute level of tightness is immaterial, I believe it is the change that matters for the economy.

Of course we agree completely that the limited amount of data is a drawback. So I wouldn't make Kass' argument:

" ... the clear relationship of mortgage availability to personal consumption expenditures ... occurs in every cycle (up and down). You simply can't deny this relationship."

That is way too strong for me!

And finally, I calculate a correlation of .66, not .43. If your number is correct, then the confidence level of a positive correlation is lower than 99%.

Best Wishes and thanks for your analysis. I wish I had seen it before I posted.


Just a question -- the CXO people use some sort of Pearson coefficient and see where it peaks to see if one is a leading indicator for the other. I suppose to see if mortgage tightening is a leading or coincident indicator, we could apply something similar here to see where the Pearson coefficient peaks?


Thanks for the explanation. I've been to plenty of grad school but I really need to learn some statistics now.

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