Crazy Timmy Geithner impersonates adman Jerry Carroll in Treasury’s gilded Cash Room.
Photo: © 2009 Joshua Roberts/Bloomberg – New York Times, 10 Feb 2009.

The Federal Reserve’s quarterly Flow of Funds Z1 Release underestimated the decline in US home values by roughly $2 to $4 trillion until after the November 2008 elections.

After I detailed the oversight in last week’s Would You Believe $4 Trillion, I received a brief note from a reader in the mortgage risk management business. The note asked:

• Which Home Price Index (HPI) is best?

I e-mailed back an answer:

• Short answer is “there is none” in absolute. It depends upon context, types of assets that you care about or hold, and your risk exposure.

Below is a longer, but still simplified, answer.

METRIC

I will begin by assuming that we care about foreclosures. I believe that the US Government shares this concern, and it inspired the Treasury to unveil the Homeowner Affordability and Stability Plan on 18 Feb 2009.

Assuming that we care about and are trying to understand foreclosures, let’s attempt to answer the following simple question:

• Which Home Price Index (HPI) does the best job of explaining foreclosures?

Note: There are, of course, other metrics or benchmarks that could be used. I am simply picking one to get the ball rolling. You can use any metric that you’d like, as mentioned in my “short answer.”

DATA SOURCES AND CONVENTIONS

For foreclosures, I will use “foreclosures started” figures, as a percent of the total number of loans, from the Mortgage Bankers Association National Delinquency Survey.

For alternative HPI’s, I will use three broad-based national series available on the web:

• FHFA/OFHEO
• S&P/Case Shiller National
• Radar Logic/RPX 25 MSA Composite

Below is a quick summary of each of these home price data sources. Additional details are available from the websites linked above.

Figure 1: High Level Home Price Index Comparison

To make the comparison as consistent as I can, I will average the RPX 25 MSA Composite, which is available on a daily basis with a two-month lag (more about this later), into a quarterly time series, consistent with the offerings from FHFA/OFHEO and S&P Case Shiller.

Finally, I will construct year-over-year percentage changes from all three series, using a common 2000Q1 – 2008Q3 data interval. This produces three series of annual changes for 2001Q1 – 2008Q3, to be used to judge “explanations” foreclosure starts.

LOOK AT YOUR DATA

When I studied statistical regression at MIT, the professor said:

• If you only remember one thing from this class, here it is: LOOK AT YOUR DATA

That IS all that I remembered; so let’s give it a try.

Figure 2: Foreclosures and Annual Change In Home Price Indices

Gee …. That was useful. But if we chart Foreclosures on a separate axis, then we get something a little more compelling.

Figure 3: Foreclosures and Annual Change In HPI, With Left & Right Axis

The additional axis surfaces the negative, or inverse, relationship between foreclosures and the year-over-year percentage changes in the HPI’s (“YoY %”). Let’s take a look at a few scatterplots.  Year-over-year percentage change in HPI is on the vertical axis, and foreclosures are on the horizontal axis.

 
 
 
Figure 4: Three Scatterplots – HPI versus Foreclosures

The above graphs share common vertical and horizontal scales. Each data set slopes down from the top left to the bottom right – demonstrating again that there is a rough negative (or inverse) relation between foreclosures and HPI, as we saw in Figure 3.

LINE DRAWING

How rough is the relation? Let’s draw some lines on the scatterplots and see.

 
 
Figure 4: Three Scatterplots With Regression Lines – HPI vs Foreclosures

As noted in Figure 4, above, I’ve drawn regression lines on each scatterplot, and labeled each with the R2, which is a statistical measure of how well the regression line approximates the data points in each chart. An R2 of 1.0 indicates that the regression line perfectly fits the data. Lower R2’s denote “poorer fits” than higher R2’s.

This simple benchmark suggests that the HPI used by the Federal Reserve in the Z1 Release until 11 Dec 2008 does not do as good of a job in “explaining” foreclosures (in this simple model) than either the S&P Case Shiller National or RPX 25 MSA Composite series.

MODELS, ACTUALS and FITTED

To see the type of error that one might make, IF one had relied upon, or disseminated figures based on the FHFA/OFHEO HPI (as the Fed did until 11 Dec 2008), let’s look at simple models for foreclosures based on each HPI.

 
 
Figure 5: Thee Linear Foreclosure Models, Using HPI

Figure 5, above, contains three simple models of foreclosures, with each is of the form:

• Foreclosures % = a + b * (Year-Over-Year Percentage Change in HPI)

Note: One could, of course, construct more complicated models using other information or techniques. This is, as I noted when we began, just a simplified example.

In each chart, I’ve drawn actual foreclosures with a blue line, and the ‘modelled’ foreclosures with a red line. I’ve also annotated each chart (with a circle) to focus your attention upon the performance of these simple models during the last year for which we have data from all three sources – specifically, from 2007Q3 – 2008Q3.

I hope you can see that the model in the first chart, using FHFA/OFHEO, does the poorest job of “explaining” foreclosures than either of the other two alternatives. In particular, a simple FHFA/OFHEO model has consistently “under-predicted” foreclosures for the last year. This confirms our earlier observations (see Figure 4, above).

The S&P Case Shiller National and the RPX 25 MSA Composite each do a much better job of “explaining” foreclosures than the FHFA/OFHEO HPI used by the Fed in the Z1 until 11 Dec 2008, and the RPX Composite does a slightly better job than S&P Case Shiller.

TIMING IS EVERYTHING

I think we can all agree on two things with respect to monetary policy:

1. Timing is everything; and
2. Monetary policy works with long and variable lags.

If that’s the case, then it’s pretty clear to me that the RPX Composite would be the “best HPI” – if one cares about foreclosures.

That’s because – due to the daily availability of the RPX Composite (see Figure 1) – one does not have to wait until two months after the end of each calendar quarter (as one does with either the FHFA/OFHEO or S&P Case Shiller National HPI’s) to learn what happened in that quarter. I believe the “early warning” provided by this index might have been useful in guiding policy, and perhaps we might have avoided some of the current carnage.

That’s just my guess of course.

The only way to know is to ask the folks at the Fed who make these decisions and are employed (unlike yours truly). And after you ask them that question, you can then ask:

• Why did the Fed wait until 11 Dec 2008 to change from the FHFA/OFHEO HPI in the quarterly Z1 Release?

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I used to work with numbers for a living. I hope that the doors will not remain closed as I continue my search for a new job or at least my next idea. Till next time.