The Trouble with DTI as an Underwriting Variable--and as an Overlay

Access to mortgage credit continues to be a problem.  Laurie Goodman at the Urban Institute shows that, under normal circumstances (say those of the pre-2002 period), we would expect to see 1 million more mortgage originations per year in the market than we are seeing. I suspect an important reason for this is the primacy of Debt-to-Income (DTI) as an underwriting variable.

There are two issues here.  First, while DTI is a predictor of mortgage default, it is a fairly weak predictor.  The reason is that it tends to be measured badly, for a variety of reasons.  For instance, suppose someone applying for a loan has salary income and non-salary income.  If the salary income is sufficient to obtain a mortgage, both the borrower and the lender have incentives not to report the more difficult to document non-salary income.  The borrower's income will thus be understated, the DTI will be overstated, and the variable's measurement contaminated.  There are a number of other examples that also apply.

Let's get more specific.  Below are results from a linear default probability regression model based on the performance of all fixed rate mortgages purchased by Freddie Mac in the first quarter of 2004. This is a good year to pick, because it is rich in high DTI loans, and because its loans went through a (ahem) difficult period.  The coefficients are predicting probability of not defaulting.

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                              COEF          SE             T-STAT

FICO >= 620    .1324914   .0039244    33.76   

FICO >= 680    .1259424   .0021756    57.89   

FICO >= 740    .0600775   .0020249    29.67   

FICO >= 790   -.0030439   .0036585    -0.83   

CLTV >=  60    -.0336153   .0025297   -13.29  

CLTV >=  80    -.0375928   .0021508   -17.48   

CLTV >=  90     -.0155193   .0029713    -5.22   

CLTV >=  95     -.0261145   .0035061    -7.45   

DTI                    -.0013991    .000069   -20.26   

Broker              -.0439482   .0308106    -1.43   

Corresp.           -.0128272   .0277559    -0.46   

Other                -.0295511   .0277441    -1.07   

Cash-out           -.0520243   .0023775   -21.88   

Refi no cash      -.0364152   .0021331   -17.07  

The definition of default is ever-90 days late.  I tried adding a quadratic term for DTI, but it was not different from zero.  This is an estimation sample with 166,585 randomly chosen observations; I did not include 114,583 observations so I could do out-of-sample prediction (which will come later).  The default rate for the estimation sample is 14.34 percent; for the hold out sample is 14.31 percent, so Stata's random number generator did its job properly.  For those that care, the R^2 is .12.

Note that while DTI is significant, it is not particularly important as a predictor of default.  To place this in context, note that a cash-out refinance is 5.2 percentage points more likely to default than a purchase money loan, while a 10 percentage point change in DTI will produce a 1.3 percent increase the probability of default.  One can look at the other coefficients to see the point more broadly.

But while this is an issue, it is not a big issue.  It is certainly reasonable to include DTI within the confines of a scoring model based on its contribution to a regression.  The problem arises when we look at overlays.

The Consumer Financial Protection Board has deemed mortgages with DTIs above 43 percent to not be "qualified."  This means lenders making these loans do not have a safe-harbor for proving that the loans meet an ability to repay standard.  Fannie and Freddie are for now exempt from this rule, but they have generally not been willing to originate loans with DTIs in excess of 45 percent.  This basically means that no matter the loan-applicant's score arising from a regression model predicting default, if her DTI is above 45 percent, she will not get a loan.

This is not only analytically incoherent, it means that high quality borrowers are failing to get loans, and that the mix of loans being originated is worse in quality than it otherwise would be.  That's because a well-specified regression will do a better job sorting borrowers more likely to default than a heuristic such as a DTI limit.

To make the point, I run the following comparison using my holdout sample: the default rate observed if we use the DTI cut-off rule vs a rule that ranks borrowers based on default likelihood.  If we used the DTI rule, we would have made loans to 91185 borrowers within the holdout sample, and observed a default rate of 14.0 percent.  If we use the regression based rule, and make loans to slightly more borrowers (91194--I am having trouble nailing the 91185 number), we get an observed default rate of 10.0 percent.  One could obviously loosen up on the regression rule, give more borrowers access to credit, and still have better loan performance.  

Let's do one more exercise, and impose the DTI rule on top of the regression rule I used above.  The number of borrowers getting loans drops to 73133 (or about 20 percent), while the default rate drops by .7 percent relative to the model alone.  That means an awful lot of borrowers are rejected in exchange for a modest improvement in default.  If one used the model alone to reduce the number of approved loans by 20 percent, one would improve default performance by 1.4 percent relative to the 10 percent baseline.  In short, whether the goal is access to credit, or loan performance (or, ideally, both), regression based underwriting just works far better than DTI overlays.  

(I am happy to send code and results to anyone interested).

Update: if you want output files, please write directly to me at richarkg@usc.edu.  To obtain the dataset, which is freely available, you need to register with Freddie Mac at link referenced above.

  
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Changing Character

I live in a very pleasant suburb of Los Angeles called Pasadena.  Many of you will know it from the Rose Parade and Bowl.  But it also has a number of people who object to any sort of dense housing, saying "it will change the character of Pasadena."

So I can't help but think what they would say about:

Wren: "It's terrible!  What he wants will change the character of the city!"

Haussmann: "It's terrible!  What he wants will change the character of the city!"

Burnham and Root: "It's terrible!  What they want will change the character of the city!"

Sullivan: "It's terrible!  What he wants will change the character of the city!"

Le Corbusier:  "It's terrible!"  OK, in that case it is.

Aesthetics and Cost

I grew up in La Crosse, Wisconsin, which sits at a particularly beautiful spot on the Mississippi River.  It is in the middle of an area called the driftless region, because unlike most of the upper Midwest, glacial "drift" did not sheer off topographical features.   The Mississippi thus has dramatic bluffs on both sides of it at La Crosse.

A 50-year old interstate highway bridges crossed the river just north of La Crosse; to say its aesthetics didn't match the surrounding area would be understatement.

 
Photo credit: https://upload.wikimedia.org/wikipedia/commons/5/5f/Mississippi_River_Lock_and_Dam_number_7.jpg.

Because the bridge had reached the end of its useful life, the Minnesota Department of Transportation, perhaps not wanting another bridge to fall into the Mississippi, decided to replace it. But the replacement is hardly better.

Photo credit: http://www.bridgeweb.com/Dresbach-Bridge-reaches-project-milestone/3983

When I read that the bridge was going to be replaced, I was hoping for something along the lines of the Stan Musial Bridge just north of St. Louis.

Photo credit: https://upload.wikimedia.org/wikipedia/commons/9/96/Stan_Musial_Veterans_Memorial_Bridge_Aerial.jpg

Here's the problem.  The bridge between Minnesota and Wisconsin cost around $190 million to build.  The Musial Bridge cost slightly under $700 million.  The bridge at La Crosse has traffic about about 26,000 vehicles per day; the bridge at St. Louis has 40,000 per day.  Is it worth more than doubling the price of a project per user to make it pretty instead of pedestrian?  I actually don't know.

Capital and New Construction

Bankers like to complain about Basel III capital rules. Among other things, they argue that the rules make construction lending more expensive.  A nice summary of those rules notes:

As part of the standardized approach, the final rule requires banking organizations to assign a higher risk weight of 150% to any high-volatility commercial real estate (HVCRE) exposure, defined as “a credit facility that finances or has financed the acquisition, development, or construction (ADC) of real property.” 

This means that lenders must put more capital behind construction loans than other types of loans. Bankers argue that because capital (in the form of paid-in equity and retained earnings) gets paid after debt, it requires higher returns than debt, and therefore higher capital requirements lead to higher lending costs.

In a pure Modigliani-Miller (MM) world, where capital structure is irrelevant to corporate valuation, this argument doesn't make sense.  While debt is cheaper than equity, firms with less leverage are less risky than firms with more leverage, and so as the amount of debt used falls, the return on equity investors require also falls.

But while MM is helpful for thinking about capital structure, it makes some unrealistic assumptions. The most important MM assumption for thinking about capital and banks involves the cost of financial distress.  MM in its purest form assumes the problem away--that debt will always be repaid, and so costs arising from potential default are irrelevant.  One of the current presidential candidates shows that this assumption is problematic.  When lenders (in this case, those who lend money to banks, such as depositors) think there is a chance they will not be repaid, they add a default premium to the cost of debt, and hence discourage leverage beyond some critical point.  Thus the market disciplines the issuance of debt.

Yet for banks who rely entirely on deposits for funding, the MM assumption about the absence of default costs is realistic, because deposits are nearly all guaranteed by FDIC (the exception is corporations who briefly deposit money beyond the FDIC maximum for the purpose of paying workers). Banks (except for those that have bond financing as well as deposits) face less market discipline, and so get debt more cheaply than other businesses.  Let me pause here to note that to me the benefits of deposit insurance have demonstrably outweighed the costs.

To return to the major point, however: for banks that rely on deposits for funding, higher capital requirements do indeed raise costs, because they limit the amount of subsidized debt they are permitted to use.  For those of us worried about an absence of new construction in housing, this is a problem, because while Basel III does raise cost, it is doing so by attempting to prevent banks from avoiding market discipline.  In other words, we are now probably closer to a world in which banks pay a more efficient price for funding construction loans than we were before.  And compared to what we are used to, that price is expensive.  

I would very much welcome other thoughts about this.

Use up-zoning, but don’t give it away

Los Angeles has three interrelated issues: for a city of its size, it is not, by world standards, very dense (see Figure 1.  The pictures of London and Los Angeles taken from the same height—the two metros have similar populations, but settlement in LA takes up far more land); its housing is expensive relative to its incomes; and its infrastructure (transport and water) should be better.  The absence of density has created a land shortage, which in turn has driven up land (and therefore house) prices, but density is not politically popular, in part because of the perception that Los Angeles hasn’t the infrastructure necessary to support more density. 

Yet cites far denser than Los Angeles—such as London, Singapore and Hong Kong—manage to remain quite pleasant and at the same time provide large numbers of people housing subsidies.  Los Angeles can learn from Hong Kong how to fund infrastructure and housing, and from both Singapore and Hong Kong about the provisions of subsidized housing.

The government of Hong Kong uses its greatest asset—land—to fund its operations, and particularly infrastructure.  When the Special Autonomous Region grows, the government puts undeveloped land up for bid, and the highest bidder at auction wins the land.  The reservation price of the land is sufficient to finance the infrastructure needed to support the new development.  Because Hong Kong uses well designed auctions to sell properties, it extracts substantially more revenue than it would if it went through an RFP process.  The revenue allows the government to subsidize housing for more than half the residents of the SAR.

While the city of Los Angeles does not own a lot of land (relative to its size), it does effectively own a lot of development rights, in the form of air rights.  Some cities, such as New York, have given developers air rights in exchange for the production of deed restricted affordable housing (within the deeds, rents or prices are restricted to being affordable).  While the goals of the New York policy are laudable, there is some evidence that the newly created affordable housing crowds out older affordable housing (the same is true of inclusionary zoning policies).  A policy that extracted the maximum amount of revenue from developers in exchange for air rights would be more effective.  It would allow the city to fund the infrastructure necessary to support denser development, and/or acquire property for a housing trust fund that would allow for affordable purchase housing (this is essentially Singapore’s model), or provide subsidies to tenants.

We know auctions are an effective mechanism for the government to raise money; the federal government has generated far more revenues from the sale of the broadcast spectrum and drilling rights since it starting using auctions as its sales mechanism. 

One final note—while Los Angeles needs far more housing, housing supply will not alone solve our affordability problem.  Large, attractive cities around the world all have high house prices.  Building a lot will mitigate the affordability problem, but not solve it.  To accommodate those workers that all cities need, LA will need to provide subsidies, which means it needs to generate revenue.  In a Proposition 13 world, where pure ad valorem property taxes are not available, using auctions for air rights might produce just that revenue.

LA from 40 miles above.
Note: LA cannot be contained within photo.

London from 40 miles above.