Does it Pay Not to Pay? An Empirical Model of Subprime

Mortgage Default from 2000 to 2007�

Patrick Bajari, University of Minnesota and NBER

Sean Chu, Federal Reserve Board of Governors

Minjung Park, University of Minnesota

July 3, 2008

Abstract

To understand the relative importance of various incentives for subprime borrowers to

default on their mortgages, we build an econometric model that nests various potential

drivers of borrower behavior. We allow borrowers to default on their mortgages either

because doing so increases their lifetime utility or because of the borrowers� inability to

pay, treating the decision as the outcome of a bivariate probit speci�cation with partial

observability. We estimate our model using detailed loan-level data from LoanPerformance

and the Case-Shiller home price index, and �nd that liquidity constraints are as empirically

important an explanation as declining house prices for the increase in subprime defaults over

recent years. Expectations about future home price movements and changes in the interest

rate environment also contributed to the recent rise in defaults, but their actual e¤ects are

not large.

�We thank Narayana Kocherlakota, Andreas Lehnert, Monika Piazzesi, Tom Sargent, and Dick Todd for helpful

conversations. Bajari would like to thank the National Science Foundation for generous research support. The

views expressed are those of the authors and do not necessarily re�ect the o¢ cial positions of the Federal Reserve

System. Correspondence: bajari@umn.edu; Sean.Chu@frb.gov; mpark@umn.edu.

1

1 Introduction

Subprime mortgages are made to borrowers with low credit quality or who have a higher prob-

ability of default due to risk factors associated with the loan itself, such as having a low down-

payment. The subprime market experienced dramatic growth starting from the mid- to late

1990s, up until its recent implosion. Fewer than 5% of mortgages originated in 1994 were

subprime; by 2005 that �gure had risen to 20%, according to Moody�s Economy.com. Much of

this growth was made possible by an expansion in the market for private-issue mortgage-backed

securities (MBS). Securitization through MBS and related credit derivatives allowed for loans

that did not conform to the underwriting standards of Fannie Mae and Freddie Mac, the two

government-sponsored securitizers. Beginning in late 2006, the US subprime mortgage market

experienced a sharp increase in the number of delinquencies and foreclosures. In the third quar-

ter of 2005, 10.76% of all subprime mortgages were delinquent and 3.31% were in the formal

process of foreclosure. By contrast, in the fourth quarter of 2007, the corresponding �gures had

risen to 17.31% and 8.65%.

The turmoil in mortgage and housing markets has generated broader �nancial instability.

Subprime lenders such as New Century Financial have been forced to declare bankruptcy. Banks

and investment banks experienced substantial losses from write-downs on the value of MBS and

collateralized debt obligations. Policymakers have initiated a number of responses or proposed

responses to the conditions in the mortgage and housing markets. The Federal Reserve has

lowered the discount rate, and Federal Reserve Chairman Bernanke has advocated reducing

loan principal amounts in order to reduce the incentives of homeowners to default. There have

also been collaborative e¤orts by government and industry to freeze mortgage payments for

certain borrowers with adjustable-rate mortgages. Understanding the determinants of mortgage

defaults is clearly necessary for formulating appropriate policy in mortgage, housing and credit

markets. Also, understanding the determinants of default is an interesting positive economic

question in its own right.

2

In this paper, we explore four alternative explanations for the increase in mortgage defaults,

using a unique data set from LoanPerformance. An observation in the data set is a subprime

or Alt-A mortgage securitized between 1992 and 2007. We observe information from the in-

dividual�s loan application, including the mortgage term, the initial interest rate, interest rate

adjustments, the level of documentation, the appraised value of the property, the loan-to-value

ratio, and the borrower�s FICO score at the time of origination. We also have panel data on

the stream of payments made by the borrower and whether the mortgage goes into default.

We merge the LoanPerformance data with the Case-Shiller home price index for 20 major U.S.

cities. This allows us to track the current value of the home by appropriately in�ating the

original appraisal using this disaggregated price index.

A �rst possible explanation for the rise in defaults is falling home prices. Consider a

frictionless world in which there are no transaction costs from selling a home and no penalties

for defaulting on a mortgage. The buyer should compare the market value of the home to the

outstanding principal balance. If the current home value is less than the outstanding mortgage

balance, it is optimal to default. In the literature, this is referred to as the put option component

of the mortgage (see Crawford and Rosenblatt, 1995; Deng, Quigley, and van Order, 2000; Foster

and van Order, 1985; vandell, 1993).

Second, increased defaults could result from borrowers� inability to pay due to a lack of

income or access to credit. Subprime borrowers are likely to be liquidity-constrained. When

interest rates reset for adjustable-rate mortgages, monthly mortgage payments can rise by a

large amount. Buyers with low credit quality may simply lack the income or access to credit

necessary to make their mortgage payments.

A third explanation is changes in expectations about home prices. In a fully dynamic

model, the put option component of a mortgage is in�uenced by expectations about future

home price appreciation. If home prices are expected to appreciate rapidly, the incentive to

default decreases. This is because default would entail foregone capital gains from the increased

equity in the home. We use two measures of home price expectations. The �rst is a backward-

3

looking measure based on past trends. The second is a forward-looking measure based on the

ratio of rental to purchase prices for homes, following the approach proposed by Himmelberg,

Mayer, and Sinai (2005).

Fourth, increased defaults could be due to an increase in contract interest rates relative to

market rates, particularly for adjustable-rate mortgages. When the contract interest rate is less

than the current market interest rate, a borrower�s incentive to default is lower ceteris paribus.

This is because the borrower would have to pay a higher interest rate than his current mortgage

rate. Conversely, when the interest rates on adjustable-rate mortgages increase, the incentives

for default increase.

We build an econometric model that nests these four possibilities and therefore permits

us to quantify the relative importance of each factor. The dependent variable in the model

is the decision to default. Households act as utility maximizers and default if the expected

utility from continuing to make mortgage payments is less than the utility from defaulting on

the mortgage. We also include a second equation that re�ects a borrower�s ability to continue

paying the mortgage. If the buyer lacks adequate income or access to credit, this may also result

in default. We demonstrate that our structural equations can be represented as a bivariate

probit with partial observability, a type of model �rst studied by Poirier (1980). We check the

robustness of our results by estimating a competing hazards model with unobserved borrower

heterogeneity similar to the speci�cation in Deng, Quigley, and van Order (2000).

We �nd evidence for each of the hypothesized factors in explaining default by subprime

mortgage borrowers. In particular, our results suggest that declining house prices and borrower

and loan characteristics that a¤ect the borrowers�ability to pay are the two most important

factors in predicting default. The �nding that liquidity constraints are as empirically important

an explanation as declining house prices suggests that the increase in subprime defaults over

recent years is partly linked to changes over time in the composition of mortgage recipients.

Higher numbers of borrowers with little or low documentation and low FICO scores, or who

only make small downpayments, contributed to the increase in foreclosures in the subprime

4

mortgage market. The increasing prevalence of adjustable-rate mortgages also contributed to

rising foreclosures. The monthly payments for adjustable-rate mortgages come with periodic�

and sometimes very large� adjustments, forcing liquidity-constrained borrowers to default.

There is a wealth of literature examining various aspects of mortgage borrowers�decision to

default. Existing research has typically focused on the put-option nature of default by studying

how net equity or home prices a¤ect default rates (Deng, Quigley, and van Order, 2000; Gerardi,

Shapiro, and Willen, 2008). Other studies have looked at the importance of borrowers�liquidity

constraints (Archer, Ling, and McGill, 1996; Carranza and Estrada, 2007), borrowers�overall

ability to pay, as measured by their credit quality (Demyanyk and van Hemert, 2008), and the

role of rate resets for adjustable-rate mortgages (Pennington-Cross and Ho, 2006).

We build on these earlier works by considering each of the factors proposed by other re-

searchers. However, our analysis di¤ers from the previous literature in at least four respects.

First, our econometric model nests the various potential incentives for default inside a uni�ed

framework, rather than studying these incentives individually. In particular, we depart from

the previous literature by specifying two latent causes of default� �nancial incentives to raise

lifetime utility by defaulting and the violation of the borrower�s liquidity constraint� and using

the likelihood function that takes into account the fact that we do not observe which of the two

underlying causes was the trigger for default. Second, our data set includes recent observations

from a nationally representative sample of subprime mortgages, allowing us to focus on the

drivers behind the recent wave of mortgage defaults. In contrast, a closely related paper by

Deng, Quigley, and van Order (2000) examines prime mortgage borrowers, for whom default

is much less common. Third, since our data contain detailed information on loan terms and

borrower risk factors, we can control for these observables in our analysis, which some previous

work could not adequately address. Moreover, our paper systematically examines the e¤ects of

several variables that economic theory suggests ought to a¤ect borrower default, including ex-

pectations about home prices, the volatility of home prices, the amount of time remaining until

the next rate reset for ARMs, and the payment-to-income ratio. By using a more comprehensive

5

list of potential drivers of default, we are better able to assess the relative importance of various

factors, compared to previous literature. Fourth, in contrast to more descriptive pieces such

as Demyanyk and van Hemert (2008), our model builds from the assumption that consumers

maximize their utility and face liquidity constraints, from which we then derive the equations

that we estimate.

The rest of this paper proceeds as follows. In Section 2, we present a model of default by

mortgage borrowers. In Section 3 we describe the data. Section 4 presents model estimates

and other empirical �ndings. Section 5 concludes.

2 Model

Our model of housing default builds on Deng, Quigley, and van Order (2000), Archer, Ling,

and McGill (1996), and Crawford and Rosenblatt (1995). We build on the stylized model of

optimal default described in this earlier research. In the model, borrowers maximize expected

discounted utility. At each period in time, a borrower receives utility from housing services

and from consumption of a composite commodity. Consumption of the composite commodity

is equal to income less savings and the costs of housing services. In this environment, it is

optimal for a homeowner to default if and only if defaulting increases the homeowner�s wealth.

We begin by considering the case of a frictionless environment in which default is optimal if and

only if the value of the home exceeds the expected discounted mortgage payments. We then

sequentially incorporate additional factors� expectations about home prices, interest rates and,

�nally, credit constraints. We demonstrate that an agent�s optimal decision rules take the form

of a system of inequalities. This system of inequalities is naturally modeled using a discrete

choice framework. We demonstrate that our system of inequalities can be modeled using a

bivariate probit with partial observability, �rst studied by Poirier (1980).

6

2.1 Optimal Default without Liquidity Constraints

Let i index borrowers and t index time periods. Denote by Vit the value of borrower i�s home

at time period t, and denote by Lit the outstanding principal on i�s mortgage. Normalize the

time period in which i purchases her home to t = 0. Let git denote the rate of in�ation in home

price between time period t� 1 and t. Then

Vit = Vi0tQ

t0=1(1 + git0) (1)

That is, the current home value is the initial home value times the gross rate of in�ation in

housing. In our empirical analysis, we shall let git correspond to the Case-Shiller price index for

the city where i resides. Equation (1) tracks the evolution in the value of i�s home. Empirically,

we expect it generally to be the case that Vit > Vi0 for buyers who have held their homes for

many years. However, for more recent buyers it may be the case that Vit < Vi0 because of

declining home prices over a shorter horizon.

The evolution of the outstanding principal, Lit, is somewhat more complicated than the

evolution of Vit. In order to economize on notation, we will not write down an explicit formula

for the outstanding principal, since di¤erent households have di¤erent mortgage contracts. Lit

is a function of the original loan amount, previous mortgage payments by the borrower, the

mortgage term, and contract interest rates. Fortunately, in our empirical work, we have access

to the current principal and a complete speci�cation of the contract terms that determine how

Lit evolves.

We begin by considering an environment without any frictions. In particular, we abstract

from penalties from default and transaction costs, and assume that markets are complete and

that there are no binding credit constraints. In this extremely stylized model, i will choose to

default if

Vit � Lit < 0 (2)

The reason is that if the above inequality holds, the borrower is able to strictly increase her

lifetime utility by defaulting. She could default and then repurchase the same home, and thus

7

keep the same �ow of housing services while increasing her wealth by Lit � Vit. On the other

hand, if Vit � Lit > 0 then default is suboptimal. For example, the borrower would be able to

sell her home at a price that strictly exceeds the outstanding principal. This would leave her

with net wealth Vit � Lit.

The decision to default may be triggered by a fall in home prices git. For recent borrowers

who have made small downpayments, just a few su¢ ciently negative realizations of git may be

su¢ cient for (2) to hold. For borrowers who have made large downpayments or who have held

their homes for many periods in which git > 0, (2) is less likely to hold.

2.1.1 Expectations about Home Prices

In this subsection, we allow our default decision to become slightly more complicated and depend

on expectations about future home prices. This dependence would exist if, for example, there

is a lag between the decision to sell a home and the time period in which the sale actually takes

place. This assumption is quite realistic given that sale times for homes are typically three to

six months during normal housing markets, and may exceed a year during housing downturns.

As a result, there may be a gap between prices at the time during which the decision to sell was

made and the price that the seller was ultimately able to receive in the market.

Let Egit represent borrower i�s expectation in period t, given her current information, about

the future growth rate in home price. If the buyer is risk-neutral, the default decision depends

on the following condition:

Vit(1 + �1Egit)� Lit < 0 (3)

We use the parameter �1 to scale the units of Egit: We shall describe our approach to measuring

Egit in the next subsection.

In a richer model, we would also expect the variance of home prices to in�uence the default

decision. Buyers may be risk-averse and therefore demand a risk premium when home prices

8

�uctuate. Moreover, option pricing theory suggests that the variance in home prices should

in�uence the optimal default decision. For example, homeowners may be willing to take on a

mortgage even when the expected change in Vit is negative, so long as the variance is su¢ ciently

large. The reason is that the borrower would still gain in the event that the house price does

appreciate, while at the same time the option to default mitigates the downside risk if the home

value instead falls.

In practice, measuring expectations about the variance, V git, is even more di¢ cult than

measuring the expected growth rate. Also, modeling the impact of variance on consumer utility

in a structural way is beyond the scope of this paper. As a compromise, we add to (3) a term

that captures the reduced-form impact of the variance of git:

Vit(1 + �1Egit + �2V git)� Lit < 0 (4)

Measuring Expectations about Home Prices We consider two di¤erent measures of Egit:

one based on user costs, and another measure based on price trends in the recent past. For

the former, we follow Himmelberg, Mayer, and Sinai (2005) and exploit a no-arbitrage condition

between renting and purchasing a house. In a given housing market, the annual user cost of

ownership must equal the annual rent:

Cost of ownership at time t =

Vitrrfit + Vit!it � Vit� it(rcit + !it) + Vit�it � VitEgit + Vit it = Rit

(5)

In this equation, Vit is the house price and Rit the annual rent. The term rrfit is the interest

rate the homeowner i would have obtained in an alternative, risk-free investment. Therefore,

Vitrrfit captures the opportunity cost of the house relative to other potential investments. The

term !it is the property tax rate, � it the e¤ective tax rate on income, and rcit the contractual

interest rate on the mortgage. The term Vit� it(rcit + !it) therefore represents savings to the

homeowner due to the tax-deductibility of mortgage payments and property taxes. The term

�it represents the depreciation rate of the house, Egit the expected capital gain, and it the risk

9

premium. Using observed values of Vit, Rit, rrfit , !it, � it, r

cit, �it, and it, obtained from data,

we can deduce the expected capital gain Egit that satis�es (5).

Himmelberg, Mayer, and Sinai (2005) recover Egit from (5) and decompose it into two

components. The �rst is the expected growth due to �fundamentals,�Egfit, which they proxy

using the average annual home price growth rate between 1950 and 2000. The remainder, Egbit,

captures expected growth unexplained by their measure of �fundamentals,�and might be due

to speculative bubbles. For each MSA and quarter, they report the ratio of Vitrrfit + Vit!it �

Vit� it(rcit+!it)+Vit�it�VitEg

fit+Vit it (the �imputed rent�) to the actual rent Rit. Comparing

this expression to (5) shows that the ratio is greater than one if the market expects faster house

price appreciation than warranted by fundamentals (Egbit > 0), with a higher ratio indicating

a larger bubble. Conversely, a ratio less than one indicates that the market expects slower

growth than implied by fundamentals. We include this ratio of imputed rent to actual rent

as one measure of borrowers� expectations about home prices. This measure is denoted by

Exp_HMS in our empirical section.

In addition to looking at the e¤ects of speculative home price appreciation, we also use

backward-looking measures to form expectations about home prices. Speci�cally, we allow the

default decision to depend on home price appreciation in the previous period, based on the idea

that borrowers may be extrapolating from the recent past in forecasting future growth. This

measure is denoted by Exp_Bwd in our empirical section. The econometric model that we

estimate will allow us to separately identify the impacts of these two alternative measures of

expectations.

2.1.2 Interest Rates

Finally, we allow the optimal default decision to depend on interest rates. Theory predicts that

when market interest rates are high relative to the contractual rate, the incentive to default

is lower. Below-market-rate contractual rates imply that borrowers will lose the future value

10

of the discount if they default. To operationalize this idea, we follow Deng, Quigley, and van

Order (2000) and compute the normalized di¤erence between the present value of the payment

stream discounted at the mortgage note rate and the present value discounted at the current

market interest rate. For borrower i in period t,

IRit =

TMitPt=1

Pi(1+rmit =1200)

t �TMitPt=1

Pi(1+rcit=1200)

t

TMitPt=1

Pi(1+rmit =1200)

t

=

TMitPt=1

1(1+rmit =1200)

t �TMitPt=1

1(1+rcit=1200)

t

TMitPt=1

1(1+rmit =1200)

t

(6)

Pi is the monthly payment for the mortgage, TMit is the number of remaining months until

maturity, rmit is the market rate borrower i would get if he obtained a new loan in period t,

and rcit is the contractual interest rate of the mortgage. For adjustable-rate mortgages, Pi and

rcit may vary over the course of the loan, but for simplicity, we assume that Pi and rcit remain

constant at the levels of the current month t.

In practice, the available market rate of interest rmit varies across households because of dif-

ferences in credit histories and other risk factors. Some of these risk factors are unobservable to

us as econometricians. Therefore, in order to determine the market rate of interest available to

a household i at time t, we �rst compute the predicted rates based on observable borrower and

loan characteristics (FICO, loan-to-value, etc.), where the prediction parameters are estimated

using actual originations of all subprime mortgages observed in the data. Since the LoanPer-

formance data cover the universe of subprime mortgage originations, we can get a very precise

estimate of the impact of the risk factors on contract rates. Our estimate of rmit also controls

for unobserved household-level heterogeneity. Details behind the procedure for imputing rmit

are described in Appendix A.

Just as we measure expectations about future house prices, we would also ideally like to

control for household expectations about future interest rates. We have not yet done so, and

leave this extension to future work. Although we currently abstract away from expectations

about market rates, we do incorporate one prominent source of interest rate changes: rate resets

for adjustable-rate mortgages. Borrowers with ARMs presumably are able to anticipate�

at least to a limited degree� future interest rate resets, which a¤ect the option value of not

11

defaulting. If a borrower expects that her contractual interest rates will reset to a higher level

in the near future, the borrower will have a stronger incentive to default at any given level of

net equity. In the data, we observe the number of months until the next rate reset of each

ARM, and we can use this measure to investigate how expectations of future rate changes a¤ect

default decisions. Letting MRit represent the number of months before the next rate reset for

borrower i in period t (for �xed-rate mortgages, we set MRit = 0 and then include a separate

dummy for �xed-rate mortgages), the default decision of the borrower depends on the following

condition:

Vit(1 + �1Egit + �2V git)� Lit(1 + �3IRit + �4MRit) < 0 (7)

Similar to �1 and �2, the terms �3 and �4 are necessary to properly scale the units. Dividing

both sides of the equation by Lit then yields:

VitLit(1 + �1Egit + �2V git)� (1 + �3IRit + �4MRit) < 0 (8)

2.2 Liquidity Constraints

So far, we have considered the optimal default decision of borrowers in a frictionless world

without any liquidity constraints or penalties from default. In such a world, a borrower would

default on her mortgage whenever equation (8) is satis�ed. This type of default rule is sometimes

referred to as �ruthless�default in the mortgage literature (vandell, 1995), which has found that

although the ruthless default rule does explain borrowers�default behavior to some extent, a

signi�cant portion of default behavior remains unexplained. Researchers have conjectured and

also empirically investigated the additional role played by liquidity constraints, reputational

costs, and trigger events such as divorce in explaining default (Deng, Quigley, and van Order,

2000; Kau, Keenan, and Kim, 1993). In particular, for subprime mortgage borrowers, who

tend to have poor credit quality and limited credit lines, liquidity constraints are likely to be a

signi�cant factor for their default decisions.

To capture the idea that a mortgage borrower may default simply because she cannot meet

12

the monthly payments, and not for the purpose of increasing lifetime wealth, we introduce a

second equation that captures frictions associated with household illiquidity and inability to

pay. Key determinants of whether a household has su¢ cient liquidity to meet its contractual

obligations are its monthly principal and interest payments relative to income, PitYit ,1 and the

household�s overall credit quality, Zit. The latter matters because it has an e¤ect on whether the

household has the ability to borrow from other sources in order to meet its mortgage payments.

We start by making an assumption that subprime borrowers cannot save and that no addi-

tional borrowing is available to the mortgage holders because they cannot tap into the capital

market to borrow against future income. As a result, borrowers must meet their period-by-

period budget constraints in every single period. The period-by-period budget constraint of

household i can be written as follows.

Pit + Cit � Yit (9)

Cit denotes the consumption of the household i in period t. We further assume that the

household must have a minimum level of consumption in each period. The household�s budget

constraint then takes the following form.

Budget Constraint Binds , 1� PitYit

� cit < 0 (10)

where cit is the minimum required consumption as a proportion of the household�s income.

When a household�s monthly payment Pit increases relative to its income, the budget constraint

is more likely to bind, forcing the household to default.

The budget constraint (10) is appropriate only for those who have no access to any form of

credit. Most borrowers, however, have at least limited access to certain forms of credit, with the

level of access varying by their credit quality. For households that are able to borrow from the

capital market in order to meet their monthly payments, the relationship between PitYitand default

is less stark. Only for those with low credit quality and limited borrowing ability do we expect

1Since the imputed income for each household remains constant over time, the variation in the payment-to-

income ratio comes from across households as well as rate resets for a given household.

13

such a rigid relationship between the payment-to-income ratio and default. Under the extreme

assumption of complete capital markets, the relevant budget constraint for a household would be

its lifetime budget constraint, which pools the household�s period-by-period budget constraints

over all time periods. To capture the notion that the relevance of the period-by-period budget

constraint is weaker for borrowers with high credit quality, we interact PitYit

with measures of

borrowers�credit quality. We categorize each borrower into one of three credit quality groups�

low credit, medium credit, and high credit� and allow the impact of the payment-to-income

ratio on default to vary across these groups. We also allow for the possibility that the measures

of credit quality, Zit, may a¤ect the budget constraint independently of their e¤ects through

interactions with the payment-to-income ratio. After making appropriate normalizations, these

considerations yield the following condition.

Budget Constraint Binds, �1Zit + �2Zit(�PitYit)� cit + 1 < 0 (11)

2.3 Bivariate Probit with Partial Observability

The structural equations (8) and (11), derived from our model, represent two drivers of default:

borrowers are utility maximizers and will exercise an option to default either because doing

so increases their wealth or because credit constraints prevent them from continuing to make

payments. Thus, at a given point in time, the household can be in one of four possible situations:

(a) default increases the household�s wealth and the household�s budget constraint is binding, (b)

default increases the household�s wealth and the household�s budget constraint does not bind,

(c) default decreases the household�s wealth and the household�s budget constraint is binding,

and (d) default decreases the household�s wealth and the household�s budget constraint does

not bind. (a), (b), and (c) lead to default, while (d) leads to no default. As econometricians,

all that we observe in the data is whether a given household defaults or not in a given period t.

When we observe no default, we know that (d) holds. However when we observe default, we

cannot distinguish whether it is due to (a), (b), or (c).

If the agents�latent utilities have a bivariate-normally distributed error, the data generating

14

process for the observed outcome corresponds to a bivariate probit model with partial observ-

ability, which was �rst studied by Poirier (1980). By modeling default as the outcome of two

separate (but potentially correlated) underlying propensities, our approach contrasts with the

existing literature, in which researchers have typically included in a single equation both the

determinants of �nancial incentives as well as measures of liquidity (Archer, Ling, and McGill,

1996; Demyanyk and van Hemert, 2008). A single-equation model leads to misspeci�cation be-

cause it fails to account for the fact that the �nancial incentives are relevant for default decisions

only if the liquidity constraint does not bind, and vice versa. Such a fallacy may lead to bias

in the estimated empirical signi�cance of one or the other type of incentive.

Our econometric model is formulated by simply adding stochastic errors to the structural

equations (8) and (11). For household i at time t:

U1;it = �0i +VitLit(1 + �1Egit + �2V git)� (1 + �3IRit + �4MRit) + "1;it

U2;it = �0i + �1Zit + �2Zit(�PitYit) + "2;it

(12)

U1;it represents the latent utility associated with not defaulting, and is equal to the nor-

malized di¤erence between the market value of the house and the option-adjusted value of the

mortgage. The option value stems from either anticipated changes in home prices or interest

rates, or from deviations of the contractual interest rate from the market rate. The term "1;it

is an iid shock, and represents idiosyncratic di¤erences across borrowers in their utility from

not defaulting. The term U2;it represents the budget constraint of household i, and "2;it is

an idiosyncratic shock to the tightness of the household budget constraint. The terms U1;it

and U2;it are correlated with each other through the observable covariates Vit, Lit, Egit, V git,

IRit, MRit, PitYit , and Zit, as well as through the distribution of the unobservables "1;it and "2;it,

which we assume are jointly normal with a variance of 1 and a covariance of �. The terms

�0i and �0i capture the unobserved borrower heterogeneity in U1;it and U2;it.2 Our data are

2We assume that cit, the minimum required consumption as a proportion of the household�s income, remains

constant over time for a given individual. Hence, the term is now subsumed in �0i.

15

in the form of a panel and we will treat �0i and �0i as random e¤ects. In principle, we could

potentially estimate �0i and �0i using �xed e¤ects techniques for discrete choice models in panel

data settings. However, the computational burden of these techniques is prohibitive because of

the large size of our sample.

Among the covariates Zit entering the liquidity equation, we include the most obvious mea-

sures of borrowers�credit quality, such as FICO scores. We also include observable loan charac-

teristics and the monthly unemployment rate at the county level. Among loan characteristics,

we focus on the age of the loan, the level of documentation, and the loan-to-value ratio at orig-

ination. For reasons other than actual �nancial incentives, holders of older loans are less likely

to be liquidity-constrained simply because mortgages held by liquid borrowers are more likely

to survive. Borrowers with low documentation on income or wealth are also more likely to have

low credit and liquidity problems. Finally, after controlling for the current loan-to-value ratio,

loans with higher loan-to-value ratios at origination are more likely to attract illiquid borrowers,

many of whom probably cannot obtain mortgages under tighter terms.

We de�ne the random variable NDit = 1 if household i does NOT default in period t and

as 0 otherwise. The condition for default is as follows:

NDit = U1;it � U2;it = 0 (default) , U1;it < 0 or U2;it < 0 (13)

where the outside options for both U1;it and U2;it are normalized to zero. Given the available

data, when a default occurs we cannot observe whether it is because U1;it < 0, because U2;it < 0,

or for both reasons.

Two points are worth mentioning. First, in principle we could specify the borrower�s de-

cision as a choice among three options, instead of a binary choice, by distinguishing between

prepayment and continued payment according to schedule. In the above baseline speci�cation,

the choice of no default includes both prepayment as well as the decision to continue making

only scheduled payments. However, we do not believe that such an extension would signi�cantly

change our key �ndings with regard to the drivers behind default.3 Nevertheless, as robustness3Ceteris paribus, declining house prices increase the incentive to default and decrease the incentive to prepay.

16

checks, we estimate an alternative model in which prepayment and default are dependent com-

peting hazards, and as a separate exercise also try dropping from the estimation sample all loans

ending in prepayment (leaving only loans that end in default, censoring, or scheduled payment

to maturity).

Second, note that the above speci�cation is basically a static discrete choice model. A

natural alternative would be to incorporate future-looking behavior using a dynamic discrete

choice framework, in the spirit of Rust (1987). However, these types of models require a full

speci�cation of an agent�s optimization problem and constraints. We believe that our current

results are useful for determining our modeling strategy in such a framework. For example,

our results will be informative about whether we should include credit constraints in this model

and how we should model price expectations. We hope to pursue a fully speci�ed model in

upcoming work.

3 Data

Our estimation exploits data from LoanPerformance on subprime and Alt-A mortgages that

were originated between 1992 and 2007 and securitized in the private-label market. The Loan-

Performance data set covers more than 85% of all securitized subprime and Alt-A mortgages.

According to the Mortgage Market Statistical Annual, 55%-75% of all subprime mortgages were

securitized in the early- to mid- 2000s. Because sample selection is based on securitization, the

loans covered by LoanPerformance may di¤er from the subprime mortgage market as a whole.

For each loan, we observe the terms and borrower characteristics reported at the time of loan

origination, including the identity of the originator, the type of mortgage (�xed rate, adjustable

rate, interest-only, etc.), the frequency of rate resets (in the case of ARMs), the initial contract

Therefore, the e¤ects on the choice between �default� and �no default� are unambiguous. On the other hand,

declining interest rates increase the value of the mortgage and therefore increase the propensity both to prepay

as well as to default (See Foster and van Order, 1984 and Quigley and van Order, 1995).

17

interest rate, the level of documentation (full, low, or nonexistent4), the appraisal value of the

property, the loan-to-value ratio, whether the loan is a �rst-lien loan, the existence of prepayment

penalties, the location of the property (by zip code), the borrower�s FICO score,5 and the

borrower�s debt-to-income ratio. One limitation of the LoanPerformance data is that they do

not report the number of mortgage points purchased by the borrower at the time of origination,

so we are only able to observe the interest rate before any adjustments for points.6

In addition to loan and borrower characteristics at the date of origination, the data also track

each loan over the course of its life, reporting the outstanding balance, delinquency status, and

the current interest rate in each month. For more detailed discussions of the LoanPerformance

data, see Chomsisengphet and Pennington-Cross (2006), Demyanyk and van Hemert (2007), and

Keys, Mukherjee, Seru, and Vig (2007).

The LoanPerformance data contain detailed information on the credit quality of borrowers,

but do not report their demographic characteristics. Therefore, we match the loan-level data

to 2000-Census data on demographic characteristics at the zip-code level (per-capita income,

average household size and education, racial composition, etc.). In addition, as one measure

that could a¤ect a borrower�s liquidity constraints, we use monthly unemployment rates reported

at the county level by the Bureau of Labor and Statistics (BLS). These variables are a proxy

for individual-level demographics. Because our proxies are measured with error, we will not

be able to consistently estimate the e¤ect of individual-level demographics on mortgage default.

4Full documentation indicates that the borrower�s income and assets have been veri�ed. Low documentation

refers to loans for which some information about only assets has been veri�ed. No documentation indicates there

has been no veri�cation of information about either income or assets.5According to Keys, Mukherjee, Seru, and Vig (2007), FICO scores represent the credit quality of a potential

borrower based on the probability that the borrower will experience a negative credit event (default, delinquency,

etc.) in the next two years. FICO scores fall between 300 and 850, with higher scores indicating a lower

probability of a negative event.6Borrowers may purchase �points� at the time of origination, in return for a reduction in interest rates.

(Negative points are also obtainable in exchange for an increase in interest rates.) Because the lumpsum is not

returned if the borrower prepays, buying points is a better deal for borrowers the longer they plan to keep the

mortgage before prepaying.

18

However, since we expect the proxies to be correlated� and in many cases strongly correlated�

with actual demographics, including these variables will provide some evidence about the impact

of demographics on mortgage default.

Another important variable that enters the equation determining the budget constraint is

the payment-to-income ratio. While we do not observe income at the household level, we can

obtain a noisy imputation of household income based on the reported debt-to-income ratio.7

De�nitions and summary statistics for key variables are reported in Tables 1 and 2.

In Table 2, we also report separate summary statistics according to the termination mode

of each loan� that is, whether a loan prepays (a category comprising 67,056 loans), defaults

(20,060 loans), or is either paid to maturity or censored by the data (111,179 loans). In the

last category, virtually all of the loans are censored, while only 4 loans are observed paying

to maturity, so in the following discussion, we shall simply refer to the third category as the

�censored�observations.

The relationships between the termination mode and the measures of borrowers�ability to

pay are generally consistent with our hypotheses. Loans that default tend to be adjustable-

rate mortgages, are associated with higher initial loan-to-value ratios, and tend to be issued to

borrowers with lower credit scores. For instance, �xed-rate mortgages comprise 26.2% of all

loans, 24.6% among loans that prepay, and 32.1% among the censored loans, while comprising

only 15.4% of loans that default. The average FICO score in the sample is 631 and is lower

conditional on default (596), higher conditional on prepayment (627), and higher still among

censored loans (647).

Table 2 also summarizes the time-varying variables, both as an average over the course of

each loan (the second panel) as well as for the last period in which we observe each loan (the

7Speci�cally, we assume that household income stays constant over time, and approximate it by the scheduled

monthly payment divided by the �front-end� debt-to-income ratio, both reported as of the time of origination.

The front-end ratio measures housing-related principal and interest payments, taxes, and insurance as a percentage

of monthly income.

19

third panel). Relative to the overall average, borrowers that default tend to have less equity

at the point in time when they default, as well as higher payment-to-income ratios and higher

contractual interest rates. Conditional on being an ARM, loans also tend to default at times

when fewer periods remain until the next rate reset, though the e¤ect is weak.

To be more precise about the magnitudes of these e¤ects, log(V=L) is on average 0.512

over the course of each loan and 0.515 in the last observed period. The average is higher

conditional on prepayment (0.572 in the last period), much lower for loans that default (0.365),

and intermediate for the remaining loans (0.466). The average monthly payment-to-income

ratio is 0.294 over the course of the loan and 0.307 in the �nal period. This ratio tends to be

highest among loans that default (on average 0.339 in the �nal period), somewhat lower among

loans that prepay (on average 0.312), and lowest among the censored loans (on average 0.290).

The data are also suggestive of ARM holders tending to default when fewer periods remain until

the next reset, but the di¤erence is small, which suggests to some extent that borrowers do not

so much default in anticipation of rate resets as much as they wait until after the resets have

actually occurred, when the higher payments have come due.

Consistent with theory, default tends to occur at points in time when the trend in housing

prices is low, as measured by the change on the previous month or as realized ex post over

the course of the following month. Default is also associated with lower volatility in housing

prices, though of course, our measure of volatility (i.e., the normalized standard error of housing

prices over the previous twelve months) is highly correlated with the trend. Upon default,

the annualized rates of appreciation over the previous and subsequent months are on average

2.0% and 1.3%, respectively, while the recent volatility is on average 1.053. By contrast, upon

prepayment, the average annualized rates of appreciation in the previous and subsequent months

are 8.7% and 8.1%, respectively, while the recent volatility is on average 1.919. Because the data

are censored at October 2007, when housing markets were falling in many areas, the censored

loans tend to end at a point in time when recent housing appreciation has been negative. Finally,

user costs tell largely the same story as the actual house price trends, though the implied rate

20

of appreciation tends to be much higher� at an average annualized rate of 11.7% at the point in

time when loans default, 14.1% at the point of time when loans prepay, and 22.9% at the �nal

observation for all remaining loans.

Furthermore, as we would expect, the data indicate that conditional on default, borrowers

tend to be paying higher interest rates than the market rate. For loans that end in default,

IR has an average value of 0.0347 at the point of default (versus an overall average of 0.0235

for the �nal observation across all loans). Somewhat surprisingly, at the time of prepayment

for loans that prepay, the average IR is actually somewhat lower (at 0.0208) than the overall

average. However, this is consistent with the fact that market interest rates were quite low at

the censoring date of October 2007, which brings down the overall average.

The demographic data indicate that both default and prepayment tend to occur in zip codes

with higher-than-average unemployment (5.10% and 5.16%, respectively, versus 4.73% for all

other loans). Default is also more prevalent in lower-income zip codes (with the zip-code�level

income averaging $20,880 for loans that default, versus an overall average of $22,340 and an

average of $22,610 among loans that prepay).

To track movements in home prices, we use housing price indices at the MSA level, from

Case-Shiller.8 The HPI for each MSA is normalized to 100 for January 2000. The home price

indices are reported at a monthly frequency, and are determined using the transaction prices of

those properties that undergo repeat sales at di¤erent points in time in a given geographic area.

Since the index is designed to measure price changes for homes whose quality remains unchanged

over time, homes are assigned di¤erent weights depending on the length of time between the two

transactions, along with other rules of thumb indicating that the home has undergone major

renovations.9

8Cities covered by Case-Shiller are Atlanta, Boston, Charlotte, Chicago, Cleveland, Dallas, Denver, Detroit,

Las Vegas, Los Angeles, Miami, Minneapolis, New York, Phoenix, Portland, San Diego, San Francisco, Seattle,

Tampa, and Washington D.C.9The index assigns zero weight to houses that have undergone repeat transactions within a span of six months.

Lower weights are also assigned to houses for which the change in transaction price is an outlier within a geographic

21

4 Results

We begin by discussing estimates from our baseline model, i.e., the bivariate probit with partial

observability. In these speci�cations, the dependent variable �no default�includes both contin-

ued payments and prepayments. We consider a wide range of alternative speci�cations in order

to assess the robustness of our results to alternative modeling assumptions.

The �rst set of speci�cations is described in Table 3a. For a particular speci�cation, the

column eq1 includes the covariates and parameter estimates that determine U1;it in equation

(12). The column eq2 includes the parameter estimates and covariates that determine U2;it.

Each cell in this table contains the parameter estimate, the standard error and the marginal

e¤ect of the covariate.10 In Table 5, we display estimates of the impact of a one-standard-

deviation increase in the independent variables on the probability of default. A particular cell

reports the change in the default probability due to the increase in the independent variable

by one standard deviation, divided by the baseline default probability. The baseline default

probability is de�ned by setting all explanatory variables equal to their sample means.

In Speci�cation 1, we start with a parsimonious model in which U1;it is determined by the

ratio of the home value to the outstanding loan balance. The discussion of Section 2.1 suggests

that the incentives to default decrease as the ratio of the value to the loan increases. In our

empirical analysis, we choose to use the natural logarithm of the ratio of the value to the loan

instead of this ratio directly, as discussed in Section 2.1. In the data, as the term of the loan

ends, the denominator of this ratio can become quite small. These observations have a smaller

e¤ect on our estimates when we use the natural log.

area. Finally, houses with a higher initial sales price are assigned a higher weight.10 In the tables, we express all marginal e¤ects in terms of the e¤ect on the probability of �no default�, P (U1 >

0; U2 > 0), with all independent variables set at their sample means. For the sake of brevity, we shall not always

explicitly state this assumption. Furthermore, because P (U1 > 0) and P (U2 > 0) are each individually very close

to one, and because none of the covariates is included in both equations, the marginal e¤ect of any covariate of

Uj on P (U1 > 0; U2 > 0) is virtually equal to its marginal e¤ect on P (Uj > 0) for j = 1, 2. Therefore, we do

not need to discuss both e¤ects.

22

The estimates of Speci�cation 1, and all other speci�cations used in Table 3a, are consistent

with the predictions of Section 2.1. As the theory predicts, borrowers that have a high value-

to-loan ratio are less likely to default. Our estimates of the marginal e¤ects imply that a

one-standard-deviation increase in log(V

L) is associated with a 47.8% reduction in the hazard of

default in a given month.

The sharp decline in home prices played an important role in the recent increase in foreclo-

sures. Consider a hypothetical household in Phoenix that purchases a home in February 2007

with a 30-year �xed-rate mortgage and no downpayments. The household�s log(V

L) is then 0 at

the time of purchase. Further assume that the household makes monthly payments such that

the outstanding balance on the mortgage in February 2008 is 2930 of the original loan amount.

If there is no change in home price between February 2007 and February 2008, the household�s

log(V

L) in February 2008 would be 0.034. During this time period, however, home prices in

Phoenix fell by 21.7%. If this household�s property value experienced the average home price

change in Phoenix, its log(V

L) at the end of this time period would be -0.211. Thus, the decline

in home price makes the household 25.4% more likely to default in February 2008 compared to

the hypothetical case of no change in home price.

In Speci�cation 1, we see that the variables that enter U2 are important drivers of default

as well. A low-documentation loan has a 0.161 percentage point higher chance of default in a

given month, or equivalently, a 53.1% increase in the default hazard computed at the sample

means. The marginal e¤ect of a one-standard-deviation increase in the FICO score� about 71

points� corresponds to a decrease in default probability of 0.223 percentage points, or 73.7%

of the hazard computed at the sample means. Similarly, a one-standard-deviation increase in

the original loan-to-value (0.14) is associated with a 16.5% greater hazard, and a one-standard-

deviation increase in local unemployment rate (1.36%) is associated with a 9.4% greater hazard.

As we would expect from equation (10), an increase in the ratio of monthly mortgage pay-

ments to monthly income also predicts an increase in the probability of default. A one-standard-

deviation increase in this ratio (0.12) generates an 18.6% increase in the hazard of default. For

23

Speci�cations 2�4 of Table 3a, we interact this ratio with the borrower�s credit score, and �nd

that the e¤ect is stronger for borrowers with low or medium credit than for those with high

credit. This is consistent with the idea that liquidity constraints are less severe for high-credit

households because they have greater access to the capital market.

We also include additional terms representing �nancial incentives to default in U1, and report

the estimates in Speci�cations 2 and 3 of Table 3a. Speci�cation 4 is the most comprehensive

speci�cation, with the loan age, local demographics, MSA dummies, and year �xed e¤ects all

included as regressors. The estimates from Speci�cations 2�4 indicate that higher house price

growth in the previous month (�Exp_Bwd�) reduces the �nancial incentive to default, but that

the e¤ect is not large. The estimate from Speci�cation 4, for instance, implies that in markets

where housing prices have been appreciating at an annual rate 10% above the sample average,

the hazard of default (for a borrower with an average value of log(V

L)) is 2.30% lower than for

an otherwise identical borrower in an average housing market.

Besides the expected trend, expectations about price volatility also a¤ect default behavior,

but again the e¤ect is small. When we include the volatility of housing prices over the past

twelve months (Past V olatility) among the independent variables, along with its interaction

with log(V

L), the uninteracted term has almost no e¤ect, while the interaction decreases the

propensity to default. Speci�cally, at the average level of log(V

L), an increase of 1.47 (one

standard deviation) in the volatility measure is associated with a 3.06% lower hazard of default,

according to our results in Speci�cation 4. Therefore, our �ndings suggest that volatile home

price movements raise the option value of holding on to the mortgage, and that this e¤ect is

larger for those borrowers with higher net equity in the property. It is a bit unclear why the

e¤ect is larger for borrowers with higher net equity. One possibility is that households with

higher net equity have lower risk aversion. This would be the case if risk aversion decreases with

wealth, because borrowers with higher net equity have greater housing wealth, by de�nition.

The estimated impact of log(V

L) declines as we add Exp_Bwd and Past V olatility to

our model (Speci�cations 2 and 3), and declines further as we add MSA- and year �xed e¤ects

24

(Speci�cation 4). This is not surprising given the positive correlation among log(V

L), Exp_Bwd,

and Past V olatility. Adding MSA- and year �xed e¤ects also soaks up some of the variation in

home price changes. However, we still �nd that net equity in the property plays an important

role in default decisions. Speci�cation 4 in Table 5 shows that a one-standard-deviation increase

in log(V

L) is associated with a 8.77% lower hazard of default even after we control for expectations

about home price appreciation, expectations about house price volatility, and MSA- and year

�xed e¤ects.

The estimates on the e¤ect of interest rates are somewhat weak but consistent with model

predictions. A one-standard-deviation increase in the value of IR (a measure of how �over-

priced� contractual interest rates are, relative to the market rate) predicts a 0.19% greater

hazard compared to the sample average (Table 3a, Speci�cation 4). The small magnitude of

this e¤ect is likely due to the fact that high contractual interest rates increase both prepayment

and default and that prepayment is classi�ed under the category of no default in our baseline

speci�cations. As expected, borrowers with ARMs are also somewhat riskier. Conditional on

everything else being equal, they have an 8.9% higher hazard of default. Among ARM-holders,

default is also more likely when rate resets are imminent: adding an extra 12 months between

the present period and the next reset results in a lowering of the hazard of default by about

1.4%.

Finally, the parameter estimates for Loan Age and (Loan Age)2 indicate that there is an

initial increase in the probability of default, but that after approximately the �rst three years,

older loans are much less likely to default, conditional on survival. This �hump-shaped�hazard

pro�le is consistent with the �ndings of other researchers (Gerardi, Shapiro, and Willen, 2008;

von Furstenberg, 1969). Part of this e¤ect is due to unobserved heterogeneity: loans that survive

are, by de�nition, more likely to be held by borrowers with a lower unobserved propensity to

default. However, the estimated e¤ect of loan age is only slightly weaker after controlling for

random e¤ects (Table 4), suggesting that the hazard of default for a given individual indeed

varies over the life of the loan.

25

We also re-run Speci�cations 1-4 using Exp_HMS instead of Exp_Bwd. The results,

reported in Table 3b, suggest that the relationship between default and expectations about

future house prices depends on how we measure expectations. In contrast to our earlier �nding

that higher price growth in the previous month (�Exp_Bwd�) reduces the �nancial incentive

to default, the propensity to default is actually higher in markets where the user-cost approach

implies stronger house price appreciation.11 For a hypothetical borrower who is average in all

observable respects other than living in a market where the user-cost-based expectation of house

price appreciation is 10% above the sample average, the hazard of default is 0.91% higher than

would otherwise be the case (Table 3b, Speci�cation 4). It thus appears that borrower behavior

is more consistent with beliefs that are based on extrapolation, but not with beliefs imputed

from the price-to-rent ratio. Alternatively, it could be the case that price to rent ratios are not

particularly good measures of buyers�expectations or that housing and rental prices are related

by a more complicated mechanism than the one proposed by the standard user cost theory (see

equation (5)).

The two expectation measures have a raw correlation of �0:22. We ought to see this

sort of negative correlation if market participants believe that housing price growth is mean-

reverting, in which case above-average growth in the recent past would lead to below-average

expectations that get capitalized into the price-to-rent ratio. But if this is the case, it is

unclear why� assuming that default and rent-or-buy decisions are optimal given expectations�

borrowers base their expectations on past trends, while the housing market as a whole anticipates

mean-reversion.12

Table 4 adds random e¤ects to the model� �0i and �0i in (12)� in order to control for

11Estimated coe¢ cients for other �nancial and credit quality variables are very similar in Tables 3a and 3b.12We also run the same speci�cations using a measure of expectation based on perfect foresight, an extreme form

of rational expectations. Speci�cally, we use the next period�s home price growth rate, Exp_Fwd, as a measure

of borrowers� expectations about future home price, and investigate the relationship between this expectation

measure and default behavior. The results are reported in Table A2. The results are very similar to those from

a speci�cation that use Exp_Bwd (Table 3a), which is not surprising given that there is a very high correlation

between home price growth rates in two adjacent months.

26

unobserved borrower heterogeneity. In principle, we might be able to include �xed e¤ects in

our model. However, given the number of observations in our sample, this does not appear

to be computationally feasible. In our random e¤ects speci�cation, we see that the results

are very similar to those in Table 3, both qualitatively and quantitatively. As before, higher

net equity, higher expectations about future home prices (measured using Exp_Bwd), higher

volatility in home prices, and lower contractual rates all lead to a smaller hazard of default.

Similarly, we still �nd that variables representing higher credit quality and less severe liquidity

constraint predict a lower probability of default. The only noticeable change compared to

Table 3 is that now low-credit borrowers do not appear any more sensitive to high payment-to-

income ratios than high-credit borrowers. The random e¤ects scale parameters in U1;it and U2;it

are signi�cantly di¤erent from zero, suggesting that there is a substantial degree of unobserved

borrower heterogeneity in�uencing the �nancial incentives to default and the tightness of budget

constraint. We �nd it reassuring that most results carry over to the random e¤ects speci�cations

despite the large degree of unobserved borrower heterogeneity.

Table 5, which reports estimates of the impact of a one-standard-deviation increase in the

independent variables on the probability of default, is informative in conveying the relative

signi�cance of each regressor in default decisions. Alternatively, we could ask the following

question to determine the impact of each regressor: We know that 2006 vintage loans have

much worse performance than 2004 vintage loans. The empirical probability of default within

the �rst 12 months is 1.50% and 8.28% for mortgages originated in 2004 and 2006, respectively.

Then, how much of this increase in defaults could be explained by the observed change in

each regressor? Table 6 provides an answer to this question. Table 6 reports the mean

values of each regressor among 2004 vintage loans and 2006 vintage loans (the �rst and second

columns), the change in the mean for each regressor (the third column), and multiplies it by the

marginal e¤ect to obtain the contribution of each regressor to the high default probability of

2006 vintage loans compared to 2004 vintage loans (the fourth column).13 Table 6 con�rms our

13We use the marginal e¤ects from Speci�cation 3 in Table 3a, not Speci�cation 4. Since our objective is to

compare loans of di¤erent vintages, it makes more sense to use a speci�cation that does not include year �xed

e¤ects.

27

prior �ndings: The biggest contributors to the high probability of default among 2006 vintage

loans are declining home prices and deteriorations in the credit quality and liquidity conditions

of mortgage borrowers. Our results indicate that declining home equity led to a 5.26% higher

hazard of default for 2006 vintage loans compared to 2004 ones. A decrease in house price

volatility, which could largely re�ect the slowdown in home price appreciation, made the holders

of 2006 vintage loans 5.65% more likely to default than otherwise identical holders of 2004

vintage loans. Lower credit quality, as measured by FICO scores, is responsible for an almost

50% larger hazard of default among 2006 vintage mortgage holders. Finally, low downpayments

and high payment-to-income ratios among low- to medium-credit borrowers are also signi�cant

contributors to the high incidence of defaults among 2006 vintage loans.

Our �ndings can be summarized as follows:

(1) The estimation results provide evidence for each of the hypothesized factors discussed in

Section 2 in explaining default by subprime mortgage borrowers.

(2) Declining home prices are an important driver of subprime mortgage default. For

a borrower who purchased a home a year earlier with a 30-year �xed-rate mortgage and no

downpayment, a 20% decline in home price makes the borrower 23.2% more likely to default

than an otherwise identical borrower whose home price remained stable.14

(3) Borrower and loan characteristics a¤ecting borrowers�ability to pay are as empirically

important in predicting default as declining house prices, as evidenced by the magnitudes of the

marginal e¤ects in Table 5.15 Our results suggest that the increase in defaults in recent years is

partly linked to changes over time in the composition of mortgage recipients. Higher numbers of

14Based on Speci�cation 1 in Table 3a. If we use the marginal e¤ects from Speci�cation 4, a 20% decline in

home price would make the borrower 4.26% more likely to default, which is much smaller than 23.2%, but still

economically signi�cant.15We will also compare loglikelihoods from two speci�cations: a univariate probit model with �nancial covariates

only and a univariate probit model with measures of credit quality and liquidity constraints only (corresponding to

Speci�cations 1 and 2 of Table 7). The comparison, which we will discuss in the next section, provides additional

support for this claim that liquidity constraints are as important as declining home prices in explaining default.

28

borrowers with little or no documentation and low FICO scores, or who only make small down-

payments, contributed to the increase in foreclosures in the subprime mortgage market. The

increasing prevalence of adjustable-rate mortgages also contributed to rising foreclosures, be-

cause the monthly payments for adjustable-rate mortgages come with periodic� and sometimes

very large� adjustments, forcing liquidity-constrained borrowers to default.

(4) Other option-value-based indicators of whether it makes �nancial sense to default�

expected housing price appreciation, home price volatility, the gap between the market rate and

contract interest rate, and an expectation of future rate resets for ARMs� have e¤ects that are

consistent with economic theory. However, they do not appear to be quantitatively important

factors in default decisions. These results therefore suggest, albeit not strongly, that subprime

mortgage borrowers are not very forward-looking in making their default decisions. The main

drivers behind subprime mortgage holders�default decisions are realized home price movements

up to the time of decision-making and whether the budget constraint is binding in this period,

while the option value of waiting� due to expectations about future home price movements or

interest rate changes� does not seem to matter as much.

4.1 Univariate Probit Results

As a check for robustness, we also estimate a univariate probit model. Similar to the baseline

speci�cation, the outcome is default or no default in a given month. Here, however, we assume

that both the �nancial incentive to default and borrowers� liquidity constraints enter into an

equation determining a single latent utility. Table 7 reports the estimates.

Speci�cation 1 uses only the covariates included in the �nancial incentives equation (eq1)

for Speci�cation 3 of the bivariate probit (reported under Table 3a). Similarly, Speci�cation 2

includes only the covariates related to the liquidity equation (eq2) of the bivariate probit model

(except for loan age). Each of these speci�cations is equivalent to the bivariate probit model with

the constant term for one or the other equation constrained to equal in�nity and the covariance

29

of the errors constrained to equal zero. The model �t (as measured by the loglikelihood or

pseudo-R2) is very similar for Speci�cation 1 and Speci�cation 2, providing additional support

for the notion that illiquidity is an equally important driver behind default as �nancial incentives.

From Speci�cations 3-4, we see that the qualitative results from the univariate probit model

are generally similar to those from the bivariate probit model, with a few exceptions. Similar

to before, default is more likely if the borrower has low net equity in the house. Moreover, the

probability of default also declines with Exp_Bwd, although the e¤ect is less robust. How-

ever, unlike the case with the bivariate probit, the user-cost-based expectations have the same

qualitative e¤ect as the backward-looking measure: higher expectations of future home prices

are associated with less default, whether based on extrapolation or measured from user costs.

The implications are the same as before for the measures related to interest rates. Default is

less likely when the market interest rate is higher than the contract rate, because default entails

losing access to the discounted rate. Likewise, for ARMs, default is more likely as the next rate

reset gets closer in time.

Parameter estimates for the measures that represent the liquidity constraint and the overall

credit quality of the borrowers also con�rm prior results. A high payment-to-income ratio, a

low FICO score, a low documentation level and a high loan-to-value ratio at origination all lead

to increased probability of default. The impact of a high payment-to-income ratio on default

is also larger for borrowers with low-credit quality than for borrowers with high-credit quality.

Speci�cation 5 of Table 7 reports estimation results when we add loan-level random e¤ects

to the model. We see that the results are robust to the inclusion of loan-level random e¤ects, as

was the case with the bivariate probit. Finally, to partially address the concern that continued

payments and prepayments are rather distinct events, we re-run Speci�cation 4 after excluding

prepaid cases from the category of no default. The results are reported under Speci�cation 6

of Table 7, which shows that all of the coe¢ cients are qualitatively stable.

Although the results are qualitatively very similar between the bivariate and univariate probit

30

models, the magnitudes of the coe¢ cients for log(V

L) and log(

V

L) � Exp_Bwd change a great

deal: their magnitudes are almost �ve times larger in the bivariate probit results than in the

univariate probit. On the other hand, the magnitudes of the coe¢ cients for the liquidity and

credit quality measures are similar between the two models. The �nancial incentives become

directly relevant for default only when the liquidity constraint does not bind. Because the

univariate probit model does not take this dependency into account, and because many defaults

are driven by the liquidity constraints of subprime mortgage borrowers, the univariate probit

model underestimates the e¤ects of �nancial incentives on default. Our bivariate probit model

with partial observability does not su¤er from this misspeci�cation, giving us better parameter

estimates for the �nancial incentive variables. This provides justi�cation for our baseline model.

4.2 Competing Hazards Model

As an alternative to the partial observability model, we also estimate a �competing hazards�

model, in which a mortgage can be terminated by either default or prepayment. Similar to

the univariate probit model, this model does not distinguish between covariates that a¤ect the

�nancial incentive to default and covariates that a¤ect household budget constraints: all of the

relevant observable characteristics simply a¤ect outcomes by shifting the hazards of default and

prepayment. The advantages of the hazards model, as compared to the bivariate probit baseline

model, include the fact that it treats prepayment and regularly scheduled payment as separate

outcomes and that we can allow default and prepayment to be correlated due to unobservables.

Moreover, the hazards model may be conceptually more appealing than the period-by-period

probit model, in the following sense. We essentially observe only one outcome for each loan� the

point in time when the loan defaults (if ever)� which the hazards model addresses by treating

the time to default (or prepayment) as the dependent variable. On the other hand, the period-

by-period probit model treats the status of the loan in each month as a separate observation,

arti�cially de�ating the standard errors.16 Of course, the disadvantage of the hazards model,

16The clustered standard errors that we report partially address this problem, but not entirely. To further

investigate how treating each period as a separate observation might a¤ect our standard errors, we re-run var-

31

compared to the bivariate probit model, is the misspeci�cation resulting from treating default

as being determined by only a single equation instead of two equations.

For household i, denote the time of default as Tdi and time of prepayment as Tpi, where Tdi

and Tpi are discrete random variables (Obviously, at least one of these stopping times must be

censored). The probabilities of survival past some time t in the future are:

P [Tdi > t] = exp

��

tPk=1

hd(k)

�P [Tpi > t] = exp

��

tPk=1

hp(k)

� (14)

Suppose the instantaneous hazards of default and prepayment, hd(t) and hp(t), follow a propor-

tional hazards model as follows:

hdi(t) = exp(�d(t) + 0dXit + �di)

hpi(t) = exp(�p(t) + 0pXit + �pi)

(15)

In other words, the hazards depend on a time-dependent �baseline�hazard common across all

borrowers, �d(t) and �p(t); on (potentially) time-varying covariates, Xit; and on unobserved,

borrower-speci�c random e¤ects �di and �pi. Changing the observed covariates Xit results in

a new hazard function that is proportional to the baseline hazard function, hence the name

�proportional hazards.�

As is well known (Lunn and McNeil, 1995), if the unobserved heterogeneity terms �di and �pi

are independent, the two risks are independent conditional on observables, so separate estimation

of the two hazard functions yields consistent estimates. When estimating the hazard of default,

we would simply treat loans that end in prepayment as censored observations, similar to loans

that are censored by the end of the sample period. Similarly, when estimating the hazard of

prepayment, either a default or the end of the sample period would result in censoring. When

ious speci�cations of the univariate probit model using data aggregated by quarter, instead of using monthly

observations (and still clustering our standard errors). The results are reported in Table A1. Using quar-

terly observations increases our standard errors only very slightly, indicating that clustering largely mitigates the

problem of understated standard errors.

32

�di and �pi are not independent, estimation becomes more involved, but we can still estimate the

parameters using maximum likelihood, as in Deng, Quigley, and van Order (2000) and McCall

(1996). The likelihood function and estimation details for the dependent competing hazards

model are provided in Appendix B.

In Speci�cation 1 of Table 8, we report the estimation results for a particular case of inde-

pendent hazards. Speci�cally, we assume that the hazards only depend on observables (i.e.,

�di = �pi = 0), while making no parametric assumptions about the underlying baseline hazards,

�d(t) and �p(t). This speci�cation is simply the standard Cox proportional hazards model (Cox,

1972; Cox and Oakes, 1984), and we can estimate the coe¢ cients d and p by minimizing the

�partial loglikelihood,�while essentially netting out the baseline hazards.

We also estimate a speci�cation that allows for unobserved correlation in the hazards of

default and prepayment, following Deng, Quigley, and van Order (2000). Speci�cally, we

assume that there are two types of borrowers, where

(�di; �pi) =

8<: (�d1; �p1) with probability �

(�d2; �p2) with probability 1� �(16)

Results for the model with correlated unobserved hazards are in Speci�cations 2-4 of Table 8.

All of Speci�cations 1-4 generate implications for default behavior that are similar to what

we see in the bivariate probit and univariate probit models. We �nd that higher net equity

decreases the probability of default, while its impact on the probability of prepayment is unclear.

The greater the contractual rate relative to the market interest rate, the more likely the borrower

is to default and prepay. In Speci�cation 2, the impact of IR on default is stronger than its

e¤ect on prepayment, but as we add more regressors (Speci�cations 3�4), the impact of IR

on prepayment is stronger than its e¤ect on default. Borrowers are less likely to default or

prepay if they are farther away from the next rate reset for adjustable-rate mortgages. Again

not surprisingly, �xed-rate mortgages are less likely to default or prepay than adjustable-rate

mortgages. The estimated hazard ratio indicates that adjustable-rate mortgages are about

three- to four times more likely to default and about three times more likely to prepay than

33

�xed-rate mortgages. The measures of liquidity constraints display similar patterns as before:

borrowers with low documentation, low FICO scores, high loan-to-value ratios at origination,

and high payment-to-income ratios are more likely to default.

Finally, we �nd that there is a high degree of unobserved heterogeneity in both default

and prepayment risk, with the unobserved heterogeneity being greater for default. This result

contrasts with the �ndings of Deng, Quigley, and van Order (2000) who �nd substantial and

statistically signi�cant unobserved heterogeneity in exercising the prepayment option but not

in exercising the default option. The di¤erence between their �nding and ours may be due to

the di¤erent pools of borrowers in our respective data sets: while their sample is con�ned to

prime mortgage borrowers, who have a low probability of default in any case, we study subprime

mortgage borrowers, for whom the default risk is much higher. Thus, it makes intuitive sense

that our sample exhibits a much greater degree of unobserved heterogeneity in default behavior.

5 Conclusion

In this paper, we estimate a model of optimal default by subprime mortgage borrowers. Our

model nests four possible explanations for the recent increase in mortgage defaults: falling

home prices, lower expectations about future home prices, increases in borrowers�contractual

interest rates relative to market rates, and borrowers�inability to pay due to a lack of income

or credit. The �rst three factors a¤ect borrowers��nancial gains from default, while the last

factor represents the possibility that liquidity constraints may force borrowers to default even

when defaulting is against their �nancial best interest. We account for the fact that long-run

�nancial incentives are relevant to default decisions only if the liquidity constraint does not bind,

and vice versa, thereby addressing a key misspeci�cation in previous studies. The structural

equations of this model can be represented as a bivariate probit with partial observability, as

formulated by Poirier (1980).

We estimate our model using unique data from LoanPerformance that track each loan over

34

the course of its life, and �nd evidence for each of the hypothesized factors in explaining default

by subprime mortgage borrowers. In particular, our results suggest that borrower and loan

characteristics that a¤ect borrowers� ability to pay are as important in predicting default as

the fundamental determinants of whether it makes �nancial sense to default. Declining home

prices are indeed an important driver behind the recent surge in defaults, but for the particular

segment of homeowners represented in our data, liquidity constraints are an equally important

factor. This �nding may provide some guidance on appropriate policy responses to the current

housing market turmoil. For example, the empirical importance of liquidity constraints suggests

that taking measures toward relaxing these constraints, such as providing income support to

struggling mortgage borrowers, could signi�cantly decrease the likelihood of default.

The framework of this paper is essentially static: To capture the dynamic nature of borrow-

ers�default decisions, we simply account for the reduced-form e¤ects of various option values

associated with holding a mortgage. In future work, we shall examine how our results change

when we explicitly model borrowers�default decisions as an optimal stopping problem. The

�ndings in this paper will be useful in informing us on whether to include credit constraints and

on how best to model price expectations in the fully dynamic model.

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38

Appendix A

Imputation of counterfactual re�nancing interest rates for individual households

We assume that in each time period t, household i is able to re�nance its mortgage at rate

rmit , the market rate adjusted by a household-speci�c risk premium. To impute this hypothetical

rate from the data, we make the following assumptions about the relationship between rmit and

rci0, the initial contractual rate owed during the �rst month of the household�s actual loan. Let

ti0 denote the time period corresponding to the initial month of the actual loan. j = 1 : : : J

index observable covariates other than time, with the covariates zij denoting the observable

household and loan characteristics upon which actual interest rates are determined, and zmij

denoting the covariates that determine the re�nancing rate. Then,

rci0 = f(ti0) +JXj=1

gj(ti0)zij + �i

rmit = f(t) +

JXj=1

gj(t)zmij + �i

(17)

Crucially, among the covariates zit we include controls for the type of mortgage (ARM, hybrid,

�xed-rate, etc.) held by household i.17 We assume that zmij = zij for all characteristics j except

for dummies related to the mortgage type: to preserve comparability across households, we

assume that all consumers re�nance into �xed-rate mortgages. By restricting the error, �i, to

be equal across equations, we are assuming that the household�s risk premium is constant over

time.

The function f(t) captures the time-varying �baseline�market interest rate, and the func-

tions gj(t) capture the time-varying premia on characteristics j = 1 : : : J . For estimation, we

approximate f(t) and gj(t) by �natural�cubic spline functions. A natural cubic spline function

f(t) consists of piecewise cubic polynomials fn(t); n = 0; : : : ; N � 1 passing through nodes at

t0; t1; : : : ; tN , with the restriction that f(t) be twice-continuously di¤erentiable at each node and

17Thus, we are also assuming that the risk premium does not vary with mortgage type. In principle, we could

allow the error to be nonadditive and to interact with the mortgage type.

39

with the boundary conditions f 00(t0) = f 00(tN ) = 0. The boundary conditions� which impose

local linearity at the furthest endpoints� mitigate the tendency for cubic polynomials to take

on extreme values near the endpoints.

We include the following variables among the covariates zit:

� FICO score

� �Low documentation�and �No documentation�dummies

� Dummy for �rst liens

� Dummies for mortgage type. We categorize mortgages as �xed-rate mortgages, ARMs

that have a �rst reset less than a year after origination (which tend to have much lower

initial contractual rates), and other types of ARMs.

� The total loan-to-value ratio (for all liens) at origination

� The �front-end�debt-to-income ratio: the ratio of monthly housing-related principal and

interest payments, taxes, and insurance to monthly income.

� The �back-end� debt-to-income ratio: similar to the front-end ratio, but also including

in the numerator all payments for non�housing-related debts (e.g., car loans, credit card

debt), as a percentage of monthly income.

Note that by setting zmij = zij for all characteristics j other than the mortgage type, we

abstract from the fact that re�nancing generally alters the debt-to-income ratio. Moreover, the

debt-to-income and loan-to-value ratios are endogenous, because the amount of debt borrowers

are willing to take on is presumably correlated with the interest rates they are able to obtain.

We ignore these issues, because our goal is not to obtain unbiased structural estimates for

the e¤ect of each covariate on interest rates, but merely to obtain adequate estimates for the

residual household risk premium. The operative assumption is that unobservable determinants

of borrowers�interest rates do not change over time.

40

Appendix B

Estimation details for dependent competing risks model

As a robustness check, we estimate a model of dependent competing risks. We assume that

at time t, borrower i is described by (potentially) time-dependent observable characteristics Xit

as well as a pair of unobservable characteristics (�di; �pi), which shift the hazards of default and

prepayment. We follow Han and Hausman (1990), Deng, Quigley, and van Order (2000), and

McCall (1996) in writing the likelihood function of this model.

Denote the time to default as Td and time to prepayment as Tp, both being discrete random

variables. For economy of notation, we omit the subscript for individual i. The joint survival

function, conditional on observable characteristics X and unobservable type, is then as follows:

S(td; tp j X; �d; �p) = exp (�tdPk=1

exp(�d(k) + 0dXk + �d)

�tpPk=1

exp(�p(k) + 0pXk + �p))

(18)

We approximate the baseline hazards �d(t) and �p(t) using a third-order polynomial function

of time (t).

�d(t) = �0d + �1dt+ �2dt2 + �3dt

3

�p(t) = �0p + �1pt+ �2pt2 + �3pt

3(19)

For the system to be identi�ed, we normalize �0d and �0p to 0 (because these parameters are

not separately identi�ed from the population means of �d and �p). As a practical matter, using

a polynomial approximation does not seem to drive the results, in the sense that re-estimating

Speci�cation 1 of Table 8 but using nonparametric baseline hazard functions yields essentially

the same estimates for the remaining parameters.

Default and prepayment are competing risks, so we only observe the duration associated

with the �rst terminating event. De�ne Fd(k j X; �d; �p) as the probability that the mortgage

is terminated by default in period k, Fp(k j X; �d; �p) as the probability of termination by

41

prepayment in period k, and Fc(k j X; �d; �p) as the probability of censoring at period k by the

end of the sample. Following Deng, Quigley, and van Order (2000), and McCall (1996), we can

write the probabilities as follows:

Fd(k j X; �d; �p) = S(k; k j X; �d; �p)� S(k + 1; k j X; �d; �p)� 0:5(S(k; k j X; �d; �p)

+S(k + 1; k + 1 j X; �d; �p)� S(k + 1; k j X; �d; �p)� S(k; k + 1 j X; �d; �p))

Fp(k j X; �d; �p) = S(k; k j X; �d; �p)� S(k; k + 1 j X; �d; �p)� 0:5(S(k; k j X; �d; �p)

+S(k + 1; k + 1 j X; �d; �p)� S(k + 1; k j X; �d; �p)� S(k; k + 1 j X; �d; �p))

Fc(k j X; �d; �p) = S(k; k j X; �d; �p)

(20)

The term 0:5(S(k; k j �d; �p)+S(k+1; k+1 j �d; �p)�S(k+1; k j �d; �p)�S(k; k+1 j �d; �p)) is

an adjustment that is necessary because the durations are discrete random variables. Because

we do not observe �d or �p in the data, we must form the likelihood function using unconditional

probabilities, obtained by mixing over the type distribution:

Fd(k j X) = �Fd(k j X; �d1; �p1) + (1� �)Fd(k j X; �d2; �p2)

Fp(k j X) = �Fp(k j X; �d1; �p1) + (1� �)Fp(k j X; �d2; �p2)

Fc(k j X) = �Fc(k j X; �d1; �p1) + (1� �)Fc(k j X; �d2; �p2)

(21)

The log likelihood function of this model is then given by:

logL =NPi=1[(yi = d) log(Fd(Ki)) + (yi = p) log(Fp(Ki)) + (yi = c) log(Fc(Ki))] (22)

where (yi = j) is equal to one if borrower i�s mortgage ends by termination mode j, and equals

zero otherwise.

42

Table 1: Variable Definitions

Variable Definition

NDit= 1 if loan i does not default in period t, = 0 if defaults (in foreclosure orReal Estate Owned)

V/L Market value of the property / Outstanding principal balance

Exp_Bwd Previous month’s home price growth rate, multiplied by 12

Exp_HMS

Expected home price appreciation based on user costs. This is equal toImputed Rent  / Actual Rent  reported  in Himmelberg, Mayer, and Sinai(2005). This measure is normalized to an MSA­specific 24­yr average.See the text for a detailed description

Exp_Fwd Next month’s home price growth rate, multiplied by 12

Past Volatility Standard deviation of home prices for the past 12 months, divided by 10

IRDifference in the present values of the payment stream at the mortgagenote rate and the current interest rate. Described in the text

MR The number of months until the next reset for an ARM

FRM = 1 if the mortgage is a fixed rate mortgage, = 0 otherwise

Low Doc = 1 if the loan was done with no or low documentation, = 0 otherwise

FICOFICO score, a credit score developed by Fair Isaac & Co. Scores rangebetween 300 and 850, with higher scores indicating higher credit quality.

Low FICO = 1 if FICO is less than 600, = 0 otherwise

Medium FICO = 1 if FICO is between 600 and 700, = 0 otherwise

High FICO = 1 if FICO is above 700, = 0 otherwise

Original LTVLoan to value at origination. For second (third, fourth, … ) lien loans, thiswill be the combined 1st and 2nd lien LTV

Unemployment Monthly unemployment rate at the country level from BLS

PI ratio

Monthly  Payments  /  Income. We  assume  that  Income  stays  constantover time, and approximate it by the scheduled monthly payment dividedby  the  “front­end”  debt­to­income  ratio,  both  reported  at  the  time  oforigination.    (The  front­end  ratio  measures  housing­related  principaland  interest payments,  taxes, and  insurance as a percentage of monthlyincome).    Monthly Payments may vary over time

Loan Age The age of the loan in months

Localdemographics

Log  population,  mobility,  per­capita  income,  %  college  educated,  %black, % Hispanic 43

Table 2: Summary Statistics for Estimation Sample

Prepaid Defaulted Censored or All loans

paid to maturity

Loan-level variables

Mean Mean Mean Mean Std dev

FRM .246 .154 .321 .262 .440

Original L=V .780 .806 .782 .783 .135

(FICO score)/100 6.270 5.955 6.474 6.307 .709

Low FICO dummy .372 .532 .244 .345 .475

Med. FICO dummy .458 .407 .530 .477 .500

High FICO dummy .170 .061 .226 .178 .382

Low documentation .400 .385 .439 .412 .492

No. obs. 67,056 20,060 111,179 198,295

Time-dependent loan-level variables over all periods

log(V=L) .519 .361 .537 .512 .460

Mo. payment/income .306 .328 .272 .294 .120

Loan age in months 14.98 15.48 19.66 16.94 12.23

Mo. until next reset� 14.64 13.81 17.06 15.41 13.45

Eg from user cost 1.084 1.081 1.167 1.118 .189

Eg from recent past .103 .046 .0160 .062 .119

Eg from near future .101 .043 .006 .057 .123

Recent volatility of V 1.827 1.046 1.401 1.581 1.474

IR .023 .030 -.0141 .008 .097

No. obs. 1,827,840 337,612 1,497,954 3,663,406

44

Table 2: Summary Statistics for Estimation Sample, continued

Prepaid Defaulted Censored or All loans

paid to maturity

Time-dependent loan-level variables, as last observed for each loan

Mean Mean Mean Mean Std dev

log(V=L) .572 .365 .466 .515 .504

Mo. payment/income .312 .339 .290 .307 .129

Loan age in months 19.02 19.36 25.42 21.22 13.27

Mo. until next reset� 11.71 11.18 11.47 11.57 11.16

Exp_HMS 1.141 1.117 1.23 1.168 .193

Exp_Bwd .087 .020 -.120 .010 .144

Exp_Fwd .081 .013 -.183 -.015 .166

Recent volatility of V 1.919 1.053 1.302 1.623 1.381

IR .021 .035 .025 .024 .107

No. obs. 67,056 20,060 111,179 198,295

Zip-code�level demographics for each loan

Unemployment (%) 5.163 5.102 4.729 5.010 1.359

log(Population) 10.38 10.36 10.33 10.36 .70

Mobility .006 -.259 .067 -.0002 2.312

Per-cap. inc. ($K ) 22.61 20.88 22.34 22.34 9.68

Pct. college grad. .352 .328 .348 .348 .130

Pct. black .178 .270 .190 .191 .265

Pct. Hispanic .224 .173 .210 .214 .227

No. obs. 67,056 20,060 111,179 198,295

� Conditional on being an ARM. �Mobility�is the year in which the average resident moved into her current

house, minus the nationwide average (1994.697, or August 1994).

45

Table 3a: Bivariate Probit with Partial Observability using Exp_Bwd

Specification 1 Specification 2 Specification 3 Specification 4

Eqn 1 Eqn 2 Eqn 1 Eqn 2 Eqn 1 Eqn 2 Eqn 1 Eqn 2

Log(LV

)

1.939

(0.109)

0.003

0.961

(0.123)

0.0004

0.937

(0.075)

0.0004

1.008

(0.102)

0.0001

log(LV

)×

Exp_Bwd

6.796

(0.648)

0.003

5.324

(0.284)

0.002

5.512

(0.511)

0.001

Past Volatility

­0.058

(0.012)

­0.00002

­0.036

(0.014)

­0.00001

­0.065

(0.016)

­0.00001

log(LV

)×

Past Volatility

0.730

(0.059)

0.0003

0.642

(0.069)

0.0003

0.626

(0.087)

0.0001

IR

­0.251

(0.050)

­0.0001

­0.245

(0.069)

­0.00004

MR

0.014

(0.0004)

6.65e­06

0.014

(0.0005)

2.66e­06

FRM

0.757

(0.0311)

0.0002

1.167

(0.156)

0.0002

Low Doc

­0.187

(0.007)

­0.001

­0.182

(0.008)

­0.001

­0.191

(0.008)

­0.001

­0.210

(0.008)

­0.001

FICO/100

0.394

(0.007)

0.003

0.431

(0.017)

0.002

0.431

(0.016)

0.002

0.380

(0.015)

0.002

Original LTV

­0.462

(0.026)

­0.003

­0.440

(0.028)

­0.003

­0.459

(0.031)

­0.002

­0.505

(0.029)

­0.003

46

Table 3a Continued

Specification 1 Specification 2 Specification 3 Specification 4

Eqn 1 Eqn 2 Eqn 1 Eqn 2 Eqn 1 Eqn 2 Eqn 1 Eqn 2

Unemployment

­0.026

(0.002)

­0.0002

­0.028

(0.002)

­0.0001

­0.019

(0.002)

­0.0001

­0.028

(0.004)

­0.0001

PI ratio

­0.589

(0.081)

­0.004

PI ratio×

Low FICO

­0.563

(0.097)

­0.003

­0.536

(0.093)

­0.003

­0.522

(0.087)

­0.003

PI ratio×

Medium FICO

­0.721

(0.076)

­0.004

­0.691

(0.075)

­0.004

­0.678

(0.065)

­0.004

PI ratio×

High FICO

­0.361

(0.106)

­0.002

­0.313

(0.088)

­0.001

­0.359

(0.096)

­0.002

Loan Age

­0.029

(0.001)

­0.0001

­0.029

(0.0009)

­0.0002

Loan Age2/100

0.039

(0.002)

0.0002

0.040

(0.001)

0.0002

Local

DemographicsYes

MSA Dummies Yes

Year Dummies Yes

Corr. b/w

ε1 and ε2

­0.186

(0.032)

­0.162

(0.038)

­0.598

(0.037)

­0.494

(0.031)

No. Obs 3649405 3646195 3444334 3390424

Log Likelihood ­118289.46 ­117308.79 ­106896.56 ­104551

Dependent Variable = No Default. No Default includes both continued payments and prepayments.

No random effects. Contents of each cell: estimated coefficient, standard error, marginal effects.

Standard errors are clustered by loan. 47

Table 3b: Bivariate Probit with Partial Observability using Exp_HMS

Specification 1 Specification 2 Specification 3 Specification 4

Eqn 1 Eqn 2 Eqn 1 Eqn 2 Eqn 1 Eqn 2 Eqn 1 Eqn 2

Log(LV

)

1.939

(0.109)

0.003

2.813

(0.171)

0.001

2.300

(0.152)

0.001

1.775

(0.303)

0.0007

log(LV

)×

Exp_HMS

­1.934

(0.104)

­0.001

­1.386

(0.094)

­0.0009

­0.928

(0.202)

­0.0004

Past Volatility

­0.061

(0.014)

­0.00004

­0.044

(0.015)

­0.00003

­0.053

(0.020)

­0.00002

log(LV

)×

Past Volatility

1.086

(0.073)

0.0007

0.869

(0.072)

0.0006

0.712

(0.105)

0.0003

IR

­0.248

(0.052)

­0.0001

­0.325

(0.075)

­0.0001

MR

0.014

(0.0004)

0.00001

0.014

(0.0005)

6.47e­06

FRM

0.735

(0.029)

0.0004

1.114

(0.140)

0.0004

Low Doc

­0.187

(0.007)

­0.001

­0.188

(0.008)

­0.001

­0.196

(0.009)

­0.001

­0.214

(0.008)

­0.001

FICO/100

0.394

(0.007)

0.003

0.435

(0.017)

0.002

0.434

(0.017)

0.002

0.384

(0.016)

0.002

Original LTV

­0.462

(0.026)

­0.003

­0.441

(0.029)

­0.002

­0.460

(0.033)

­0.002

­0.521

(0.031)

­0.003

48

Table 3b Continued

Specification 1 Specification 2 Specification 3 Specification 4

Eqn 1 Eqn 2 Eqn 1 Eqn 2 Eqn 1 Eqn 2 Eqn 1 Eqn 2

Unemployment

­0.026

(0.002)

­0.0002

­0.022

(0.002)

­0.0001

­0.014

(0.003)

­0.00008

­0.031

(0.004)

­0.0002

PI ratio

­0.589

(0.081)

­0.004

PI ratio×

Low FICO

­0.561

(0.102)

­0.003

­0.531

(0.097)

­0.003

­0.529

(0.093)

­0.003

PI ratio×

Medium FICO

­0.734

(0.084)

­0.004

­0.698

(0.083)

­0.004

­0.693

(0.072)

­0.004

PI ratio×

High FICO

­0.354

(0.109)

­0.002

­0.294

(0.090)

­0.001

­0.351

(0.101)

­0.002

Loan Age

­0.030

(0.001)

­0.0001

­0.029

(0.001)

­0.0001

Loan Age2/100

0.039

(0.002)

0.0002

0.041

(0.002)

0.0002

Local

DemographicsYes

MSA Dummies Yes

Year Dummies Yes

Corr. b/w

ε1 and ε2

­0.186

(0.032)

­0.246

(0.049)

­0.554

(0.031)

­0.473

(0.029)

No. Obs 3649405 3508428 3314294 3269190

Log Likelihood ­118289.46 ­113156.95 ­103032.91 ­100989.96

Dependent Variable = No Default. No Default includes both continued payments and prepayments.

No random effects. Contents of each cell: estimated coefficient, standard error, marginal effects.

Standard errors are clustered by loan. 49

Table 4: Bivariate Probit with Partial Observability (Random Effects)

Specification 1 Specification 2 Specification 3 Specification 4

Eqn 1 Eqn 2 Eqn 1 Eqn 2 Eqn 1 Eqn 2 Eqn 1 Eqn 2

log(LV

)1.747

(0.123)

1.337

(0.091)

1.546

(0.089)

1.635

(0.141)

log(LV

)×

Exp_Bwd

5.533

(0.462)

5.356

(0.443)

4.805

(0.710)

Past Volatility0.042

(0.008)

0.043

(0.006)

0.030

(0.008)

IR­0.263

(0.106)

­0.233

(0.153)

MR0.013

(0.001)

0.014

(0.002)

FRM0.646

(0.046)

0.892

(0.129)

Low Doc­0.205

(0.015)

­0.205

(0.016)

­0.225

(0.018)

­0.242

(0.016)

FICO0.406

(0.015)

0.493

(0.022)

0.539

(0.023)

0.459

(0.021)

Original LTV­0.429

(0.061)

­0.379

(0.059)

­0.391

(0.062)

­0.450

(0.061)

Unemployment­0.025

(0.004)

­0.027

(0.005)

­0.016

(0.005)

­0.018

(0.008)

PI ratio­0.710

(0.021)

PI ratio×

Low FICO

­0.627

(0.025)

­0.633

(0.029)

­0.593

(0.031)

PI ratio×

Medium FICO

­0.905

(0.062)

­0.966

(0.066)

­0.882

(0.063)

PI ratio×

High FICO

­0.792

(0.178)

­0.869

(0.175)

­0.912

(0.141)

50

Table 4 Continued

Specification 1 Specification 2 Specification 3 Specification 4

Eqn 1 Eqn 2 Eqn 1 Eqn 2 Eqn 1 Eqn 2 Eqn 1 Eqn 2

Loan Age­0.030

(0.002)

­0.027

(0.001)

Loan Age2/1000.036

(0.003)

0.036

(0.002)

Local

DemographicsYes

MSA

DummiesYes

Year Dummies Yes

Corr. b/w

ε1 and ε2

­0.171

(9.507)

­0.222

(7.701)

­0.613

(1453.45)

­0.453

(73.469)

RE Scale

Parameter

0.936

(0.012)

0.784

(0.007)

0.027

(0.010)

0.009

(0.007)

0.059

(0.010)

0.289

(0.009)

0.061

(0.014)

0.215

(0.008)

No. Obs 915936 915936 915936 915936

Log

Likelihood­29143.58 ­28910.24 ­26329.06 ­25658.72

Dependent Variable = No Default. No Default  includes both continued payments and prepayments. Contents of

each cell: estimated coefficient,  standard  error. Standard errors are clustered by  loan. Due to  the computational

burden, we use a 1/4 random sample of loans for estimation of random effects models.

51

Table 5: Marginal Effects (based on Table 3a)

Specification 1 Specification 2 Specification 3 Specification 4

1 std.

dev.

Marginal

Effects

Marginal

Effects

Marginal

Effects

Marginal

Effects

Log(LV

) 0.459 47.81% 24.16% 25.38% 8.77%

Exp_Bwd 0.118 6.58% 6.02% 2.1%

Past Volatility 1.473 9.62% 10.4% 3.06%

IR 0.096 ­0.58% ­0.19%

MR 13.195 4.46% 1.54%

FRM 1 15.08% 8.93%

Low Doc 1 ­53.10% ­58.43% ­61.84% ­70.38%

FICO/100 0.709 73.66% 91.27% 91.73% 82.97%

Original LTV 0.135 ­16.46% ­17.75% ­18.62% ­21.03%

Unemployment 1.358 ­9.39% ­11.62% ­7.96% ­11.98%

PI ratio 0.119 ­18.56%

PI ratio×

Low FICO0.169 ­28.39% ­27.17% ­27.20%

PI ratio×

Medium FICO0.164 ­35.31% ­34.05% ­34.30%

PI ratio×

High FICO0.113 ­12.18% ­10.62% ­12.49%

Local

DemographicsYes

MSA Dummies Yes

Year Dummies Yes

This table reports marginal effects (relative to the hazard of default computed at the sample means) associated with

a  one­standard­deviation  increase  in  each  regressor.  For  binary  variables,  it  is  a  unit  change  instead  of  a  one­

standard­deviation change.

52

Table 6: Comparison of 2004­ and 2006 Vintage Loans (based on Table 3a Specification 3)

2004 Mean

(1)

2006 Mean

(2)

Δ in RHS Variable

(2) – (1)

Δ in Default

Probability

Log(LV

) 0.512 0.402 ­0.109 5.264%

Exp_Bwd 0.090 ­0.035 ­0.126 0.016%

Past Volatility 2.067 1.144 ­0.922 5.653%

IR ­0.042 ­0.006 0.036 0.192%

MR* 18.393 15.992 ­2.400 0.705%

FRM 0.266 0.193 ­0.072 0.955%

Low Doc 0.461 0.439 ­0.021 ­1.138%

FICO/100 6.711 6.275 ­0.436 49.002%

Original LTV 0.769 0.802 0.033 3.993%

Unemployment 4.806 4.387 ­0.418 ­2.132%

PI ratio×

Low FICO0.053 0.102 0.049 6.948%

PI ratio×

Medium FICO0.112 0.169 0.056 10.202%

PI ratio×

High FICO0.079 0.031 ­0.047 ­3.861%

This  table  reports how  the  difference  in  each  regressor  between  2004­  and  2006 vintage  loans affects  the

probability of default, relative to the hazard of default computed at the overall sample means.

* conditional on being an ARM.

53

Table 7: Univariate Probit

Spec 1 Spec 2 Spec 3 Spec 4 Spec 5 Spec 6

log(LV

)

0.296

(0.016)

0.0036

0.234

(0.017)

0.002

­0.286

(0.047)

­0.002

0.191

(0.014)

0.0012

­0.692

(0.049)

­0.012

log(LV

)×

Exp_Bwd

0.526

(0.070)

0.0064

0.676

(0.070)

0.006

­0.104

(0.060)

­0.0007

log(LV

)×

Exp_HMS

0.432

(0.044)

0.004

0.750

(0.049)

0.013

Past Volatility

0.117

(0.005)

0.0014

0.089

(0.005)

0.0008

0.059

(0.006)

0.0005

0.050

(0.006)

0.0003

0.017

(0.006)

0.0002

log(LV

)×

Past Volatility

­0.057

(0.009)

­0.00069

­0.035

(0.010)

­0.0003

­0.028

(0.009)

­0.0002

­0.0024

(0.0088)

­0.00002

­0.030

(0.009)

­0.00051

IR

­0.571

(0.026)

­0.0069

­0.113

(0.029)

­0.001

­0.456

(0.035)

­0.004

­0.564

(0.041)

­0.0036

­0.288

(0.040)

­0.0049

MR

0.011

(0.0003)

0.0001

0.004

(0.0003)

0.00004

0.003

(0.0003)

0.00003

0.0043

(0.0004)

0.00003

0.0062

(0.0003)

0.0001

FRM

0.413

(0.007)

0.0043

0.283

(0.008)

0.002

0.255

(0.008)

0.002

0.290

(0.011)

0.0016

0.404

(0.010)

0.0063

Low Doc

­0.172

(0.005)

­0.002

­0.175

(0.006)

­0.001

­0.170

(0.006)

­0.001

­0.193

(0.008)

­0.0013

­0.172

(0.007)

­0.0031

FICO/100

0.316

(0.013)

0.0038

0.295

(0.009)

0.002

0.296

(0.012)

0.002

0.343

(0.010)

0.0022

0.309

(0.009)

0.0052

54

Table 7 Continued

Spec 1 Spec 2 Spec 3 Spec 4 Spec 5 Spec 6

Original LTV

­0.812

(0.022)

­0.009

­0.515

(0.029)

­0.005

­0.536

(0.029)

­0.005

­0.620

(0.033)

­0.0039

­0.667

(0.032)

­0.011

Unemployment

­0.021

(0.001)

­0.0002

­0.004

(0.002)

­0.00004

­0.012

(0.003)

­0.0001

­0.026

(0.004)

­0.0002

­0.033

(0.004)

­0.0005

PI ratio×

Low FICO

­0.487

(0.061)

­0.0059

­0.500

(0.039)

­0.005

­0.479

(0.048)

­0.004

­0.543

(0.030)

­0.0034

­0.639

(0.035)

­0.011

PI ratio×Medium

FICO

­0.632

(0.049)

­0.0077

­0.692

(0.039)

­0.006

­0.638

(0.045)

­0.006

­0.718

(0.029)

­0.0046

­0.863

(0.030)

­0.015

PI ratio×

High FICO

­0.533

(0.096)

­0.0064

­0.619

(0.079)

­0.006

­0.586

(0.101)

­0.005

­0.689

(0.047)

­0.0044

­0.813

(0.054)

­0.014

Loan Age

­0.023

(0.0007)

­0.0002

­0.023

(0.0008)

­0.0002

­0.028

(0.001)

­0.00018

­0.027

(0.0009)

­0.0004

Loan Age2/100

0.031

(0.001)

0.0003

0.035

(0.001)

0.0003

0.038

(0.001)

0.00024

0.040

(0.002)

0.0006

Local

DemographicsYes Yes Yes

YEAR Dummies Yes Yes Yes

RE Rho No RE No RE No RE No RE 0.106 No RE

No. Obs 3444360 3444334 3444334 3269190 3390424 1642033

Pseudo R2 0.0395 0.0378 0.0669 0.0776 0.0772 0.0975

Log Likelihood ­110150.6 ­110339.6 ­107004.4 ­100540.7 ­104208.4 ­87451.9

Dependent Variable = No Default. Contents of each cell: estimated coefficient, standard error, marginal effects.

Standard errors are clustered by loan. For Specifications 1­5, No Default includes both continued payments and

prepayments. For Specification 6, No Default includes continued payments only.

55

Table 8: Competing Hazards Model

Specification 1

No Unobserved

Heterogeneity

Specification 2

2 Unobserved Types

Specification 3

2 Unobserved Types

Specification 4

2 Unobserved Types

Default Prepay Default Prepay Default Prepay Default Prepay

Log(LV

)

­2.149

(0.037)

0.116

0.155

(0.011)

1.168

­1.838

(0.042)

0.159

0.477

(0.014)

1.611

­0.237

(0.117)

0.789

­0.204

(0.037)

0.815

­0.271

(0.119)

0.763

­0.164

(0.038)

0.849

(log(LV

))2

0.280

(0.004)

1.323

0.015

(0.003)

1.015

0.268

(0.005)

1.307

­0.025

(0.003)

0.975

0.176

(0.006)

1.193

­0.060

(0.004)

0.942

0.179

(0.006)

1.196

­0.048

(0.004)

0.953

log(LV

)×

Exp_Bwd

­4.227

(0.161)

0.015

1.731

(0.034)

5.648

­4.148

(0.164)

(0.016)

1.651

(0.034)

5.212

log(LV

)×

Exp_HMS

­0.788

(0.088)

0.455

0.567

(0.027)

1.762

­0.772

(0.090)

0.462

0.503

(0.029)

1.654

IR

1.579

(0.083)

4.850

0.948

(0.036)

2.580

0.496

(0.092)

1.642

0.841

(0.042)

2.319

0.599

(0.092)

1.820

0.784

(0.042)

2.190

MR

­0.312

(0.011)

0.732

­0.189

(0.004)

0.827

­0.213

(0.013)

0.808

­0.150

(0.005)

0.860

­0.189

(0.013)

0.828

­0.146

(0.005)

0.864

FRM

­1.403

(0.028)

0.245

­0.965

(0.011)

0.381

­1.076

(0.030)

0.341

­0.815

(0.012)

0.443

­0.971

(0.029)

0.379

­0.821

(0.012)

0.440

Low Doc

0.553

(0.019)

1.738

0.156

(0.008)

1.169

0.541

(0.019)

1.718

0.128

(0.009)

1.137

FICO

­0.828

(0.015)

0.437

­0.134

(0.006)

0.879

­0.898

(0.016)

0.407

­0.132

(0.006)

0.877

56

Table 8 Continued

Specification 1

No Unobserved

Heterogeneity

Specification 2

2 Unobserved Types

Specification 3

2 Unobserved Types

Specification 4

2 Unobserved Types

Default Prepay Default Prepay Default Prepay Default Prepay

Original LTV

1.414

(0.099)

4.111

0.672

(0.030)

1.960

0.848

(0.099)

2.335

0.861

(0.003)

2.366

PI ratio

2.205

(0.069)

9.061

1.143

(0.031)

4.108

2.179

(0.071)

8.84

1.095

(0.033)

2.988

Refinance,

Cash

­0.525

(0.020)

0.592

0.126

(0.010)

1.134

Refinance,

No cash

­0.512

(0.028)

0.599

­0.028

(0.013)

0.972

Loan Age

1.478

(0.092)

4.384

0.949

(0.044)

2.583

Loan

Age2/100

­0.197

(0.014)

0.822

­0.153

(0.007)

0.858

Local

DemographicsYes Yes

(ηp1, ηd1,

ηp2, ηd2)

(­2.9, ­3.82,

­5.38, ­7.42)

SE (0.01, 0.03,

0.03, 0.06)

(­2.96, ­1.08,

­5.08, ­4.33)

SE (0.05, 0.13,

0.06, 0.14)

(­4.22, 0.46,

­6.55, ­2.75)

SE (0.09, 0.19,

0.10, 0.20)

Pr. of Type 1 0.261 (0.002) 0.248(0.004) 0.256 (0.003)

No. Loans 177420 177420 177420 177420

Log

Likelihood­ 545233.004 ­ 538260.594 ­532946.781 ­531382.845

Contents of each cell: estimated coefficient, standard error, hazard ratio. Hazard ratios are exponentiated coefficients and have

the interpretation of hazard ratios for a one­unit change in X. 57

Table A1: Univariate Probit with Quarterly Observations

Specification 1 Specification 2 Specification 3

log(LV

)

0.244

(0.011)

0.0071

0.267

  (0.018)

0.0070

0.204

(0.017)

0.0051

log(LV

)×

Exp_Bwd

1.409

(0.067)

0.041

0.555

(0.074)

0.015

­0.223

(0.077)

­0.0056

Past Volatility

0.121

(0.006)

0.0032

0.084

(0.006)

0.0021

log(LV

)×

Past Volatility

­0.052

(0.010)

­0.0014

­0.014

(0.010)

­0.00034

IR

­0.080

(0.035)

­0.0021

­0.511

(0.041)

­0.013

MR

0.0048

(0.0004)

0.00013

0.0036

(0.0004)

0.000092

FRM

0.311

(0.009)

0.0073

0.279

(0.010)

0.0063

Low Doc

­0.185

(0.006)

­0.0057

­0.198

(0.007)

­0.0055

­0.195

(0.007)

­0.0052

FICO/100

0.359

(0.010)

0.011

0.338

(0.011)

0.0088

0.335

(0.012)

0.0084

58

Table A1 Continued

Specification 1 Specification 2 Specification 3

Original LTV

­0.603

(0.029)

­0.018

­0.598

(0.032)

­0.016

­0.623

(0.032)

­0.016

Unemployment

­0.028

(0.002)

­0.00083

­0.0079

(0.0024)

­0.00021

­0.025

(0.004)

­0.00063

PI ratio×

Low FICO

­0.627

(0.030)

­0.018

­0.563

(0.042)

­0.015

­0.537

  (0.048)

­0.013

PI ratio×

Medium FICO

­0.797

(0.039)

­0.023

­0.773

(0.046)

­0.020

­0.724

(0.051)

­0.018

PI ratio×

High FICO

­0.732

(0.076)

­0.021

­0.726

(0.091)

­0.019

­0.700

(0.106)

­0.018

Loan Age

­0.021

(0.0008)

­0.00055

­0.022

(0.0009)

­0.00056

Loan Age2/100

0.028

(0.002)

0.00073

0.034

(0.002)

0.00085

Local Demographics Yes

YEAR Dummies Yes

No. Obs 1284073 1212730 1193639

Pseudo R2 0.0559 0.0757 0.0851

Log Likelihood ­97064.66 ­88143.61 ­85911.14

Contents  of  each  cell:  estimated  coefficient,  standard  error,  marginal  effects. Quarters

computed starting from month of  initial observation for each loan (e.g.,  for a loan first

appearing  in the data in 11/2007, the first quarter  is 11/2007 – 01/2008.)    Right­hand­

side variables are averages over quarters.

59

Table A2: Bivariate Probit with Partial Observability using Exp_ Fwd

Specification 1 Specification 2 Specification 3 Specification 4

Eqn 1 Eqn 2 Eqn 1 Eqn 2 Eqn 1 Eqn 2 Eqn 1 Eqn 2

Log(LV

)

1.029

(0.122)

0.00043

0.974

(0.073)

0.0004

1.040

(0.101)

0.0002

1.011

(0.091)

0.0002

log(LV

)×

Exp_Fwd

6.462

(0.554)

0.0027

4.980

(0.243)

0.0023

5.100

(0.419)

0.00097

4.880

(0.434)

0.0011

Past Volatility

­0.0617

(0.0113)

­0.00002

­0.0376

(0.0137)

­0.00001

­0.0676

(0.0162)

­0.00001

­0.0702

(0.0162)

­0.00001

log(LV

)×

Past Volatility

0.7906

(0.0561)

0.00033

0.677

(0.066)

0.0003

0.670

(0.084)

0.00013

0.688

(0.084)

0.00015

IR

­0.239

(0.051)

­0.0001

­0.227

(0.070)

­0.00004

0.145

(0.116)

0.00003

log(LV

)×

IR

­1.609

(0.460)

­0.0003

MR

0.0140

(0.0005)

6.4e­6

0.0145

(0.0006)

2.8e­6

0.0143

(0.0006)

3.1e­6

FRM

0.744

(0.030)

0.0002

1.105

(0.127)

0.00019

1.028

(0.108)

0.0002

Low Doc

­0.1830

(0.0080)

­0.0013

­0.192

(0.009)

­0.0012

­0.211

(0.008)

­0.0016

­0.212

(0.008)

­0.0016

FICO/100

0.4314

(0.0175)

0.003

0.432

(0.017)

0.0025

0.381

(0.016)

0.0026

0.383

(0.016)

0.0026

60

Table A2 Continued

Specification 1 Specification 2 Specification 3 Specification 4

Eqn 1 Eqn 2 Eqn 1 Eqn 2 Eqn 1 Eqn 2 Eqn 1 Eqn 2

Original LTV

­0.434

(0.028)

­0.003

­0.454

(0.032)

­0.0027

­0.500

(0.029)

­0.0035

­0.503

(0.030)

­0.0035

Unemployment

­0.0290

(0.0025)

­0.00020

­0.0200

(0.0029)

­0.0001

0.0285

(0.0042)

­0.0002

­0.0283

(0.0042)

­0.00019

PI ratio×

Low FICO

­0.564

(0.097)

­0.0039

­0.537

(0.094)

­0.0032

­0.523

(0.088)

­0.0036

­0.522

(0.088)

­0.0036

PI ratio×

Medium FICO

­0.719

(0.076)

­0.0049

­0.692

(0.075)

­0.0041

­0.679

(0.066)

­0.0047

­0.678

(0.066)

­0.0047

PI ratio×

High FICO

­0.371

(0.107)

­0.0025

­0.320

(0.089)

­0.0019

­0.359

(0.097)

­0.0025

­0.356

(0.097)

­0.0025

Loan Age

­0.0299

(0.0011)

­0.0001

­0.0293

(0.0010)

­0.0002

­0.0298

(0.0010)

­0.00021

Loan Age2/100

0.0396

(0.0023)

0.0002

0.0408

(0.0020)

0.00028

0.0420

(0.0022)

0.00029

Local

DemographicsYes Yes

MSA Dummies Yes Yes

Year Dummies Yes Yes

Corr. b/w

ε1 and ε2

­0.222

(0.033)

­0.611

(0.029)

­0.511

(0.035)

­0.510

(0.034)

No. Obs 3646195 3444334 3390424 3390424

Log Likelihood ­117246.9 ­106871.7 ­104540.4 ­104535.0

Dependent Variable = No Default. No Default includes both continued payments and prepayments.

No random effects. Contents of each cell: estimated coefficient, standard error, marginal effects.

Standard errors are clustered by loan. 61