Default Option Exercise over the Financial
Crisis and beyond*
Xudong An
1
, Yongheng Deng
2
, and Stuart A. Gabriel
3
1
Federal Reserve Bank of Philadelphia,
2
University of Wisconsin – Madison, and
3
University of
California, Los Angeles Anderson School of Management
Abstract
We document changes in borrowers’ sensitivity to negative equity and show height-
ened borrower default propensity as a fundamental driver of crisis period mortgage
defaults. Estimates of a time-varying coefficient competing risk hazard model reveal
a marked run-up in the default option beta from 0.2 during 2003–06 to about 1.5 dur-
ing 2012–13. Simulation of 2006 vintage loan performance shows that the marked
upturn in the default option beta resulted in a doubling of mortgage default inci-
dence. Panel data analysis indicates that much of the variation in default option ex-
ercise is associated with the local business cycle and consumer distress. Results
also indicate elevated default propensities in sand states and among borrowers
seeking a crisis-period Home Affordable Modification Program loan modification.
JEL classification: G21, G12, C13, G18
Keywords: Mortgage default, Option exercise, Default option beta, Time-varying coefficient
hazard model
Received August 19, 2017; accepted October 23, 2019 by Editor Amiyatosh Purnanandam.
* We thank Sumit Agarwal, Yacine Ait-Sahalia, Gene Amromim, Linda Allen, Brent Ambrose, Bob
Avery, Gadi Barlevy, Neal Bhutta, Shaun Bond, Alex Borisov, Raphael Bostic, John Campbell, Paul
Calem, Alex Chinco, John Cotter, Larry Cordell, Tom Davidoff, Moussa Diop, Darrell Duffie, Ronel
Elul, Jianqing Fan, Andra Ghent, Matt Kahn, Bill Lang, David Ling, Crocker Liu, Jaime Luque, Steve
Malpezzi, Andy Naranjo, Raven Molloy, Kelley Pace, Erwan Quintin, Tim Riddiough, Dan Ringo, Amit
Seru, Shane Sherlund, Steve Ross, Eduardo Schwartz, Joe Tracy, Alexi Tschisty, Kerry Vandell,
Paul Willen, Wei Xiong, Vincent Yao, Abdullah Yavas and conference and seminar participants at
AFA/AREUEA, Baruch College, the Federal Reserve Bank of Chicago, Cornell University, Federal
Reserve Bank of Philadelphia, Federal Reserve Board, Georgia State University, the Homer Hoyt
Institute, National University of Singapore, Tel Aviv University, Urban Economics Association, UC
Irvine, UIUC, University of Cincinnati, University of Connecticut, and University of Wisconsin for
helpful comments. The authors acknowledge financial support from the UCLA Ziman Center for
Real Estate and the NUS Institute of Real Estate Studies. The authors also gratefully acknowledge
the excellent research assistance provided by Chenxi Luo and Xiangyu Guo. The views expressed
here are not necessarily those of the Federal Reserve Bank of Philadelphia or the Board of
Governors of the Federal Reserve System. All remaining errors are our own responsibilities.
V
C
The Author(s) 2020. Published by Oxford University Press on behalf of the European Finance Association.
Review of Finance, 2021, 153–187
doi: 10.1093/rof/rfaa022
Advance Access Publication Date: 17 August 2020
Downloaded from https://academic.oup.com/rof/article/25/1/153/5893492 by guest on 19 February 2021
1. Introduction
Default on residential mortgages skyrocketed during the late-2000s giving rise to wide-
spread financial institution failure and global financial crisis. Among factors associated
with mortgage failure, analysts have pointed to the widespread incidence of negative equity,
shocks to unemployment and income, lax underwriting, extensive use of risky loan
products, and fraud, to name a few.
1
In this article, we provide new evidence of heightened
borrower sensitivity to default in response to negative equity and show that factor to be
highly salient to crisis period defaults. The run-up in borrower propensity to default,
coupled with a decline in home equity, resulted in a widespread increase in mortgage de-
fault during the 2000s crisis. Results also suggest elevated default option exercise in the
wake of the enactment of crisis-period loan modification programs, providing yet another
example of the Lucas critique.
To empirically identify changes in borrower response to negative equity, we apply a
time-varying coefficient competing risk hazard model to loan-level event-history data. We
model the conditional probability of default as a function of contemporaneous borrower
negative equity and a large number of other factors. We label the estimated coefficient
associated with negative equity as the “default option beta.”
2
Contrary to existing mort-
gage default literature, we allow the default option beta to vary over time and place.
We estimate our models using expansive microdata on loan performance during the
2000–18 period. Our primary dataset includes monthly mortgage performance history on
fixed-rate 30 year home mortgage loans from Fannie Mae and Freddie Mac (the govern-
ment-sponsored enterprises, i.e., GSEs). We corroborate findings using microdata from
private-label securitizations. Results of rolling window local estimation of the hazard
model show a marked run-up in the default option beta from 0.2 during 2003–06 to about
1.5 during 2012–13, followed by a downward retracing of roughly one-half the upward
movement in the estimated beta value through 2016 (Figure 1). The upward movement in
the default option beta led to substantially higher default probabilities for a given level of
negative equity (Figure 2). Results of simulation show that for 2006 vintage loans, the
marked upturn in the default option beta resulted in a doubling of default incidence
(Figure 3). We also find substantial geographic heterogeneity in the default option beta.
Figure 4 shows dramatic cyclical movements in the default option beta among all sampled
states. Further, while all of the state-specific default option beta time series rise with the
onset of the crisis, they differ markedly in slope and amplitude. At the peak in 2012–13, the
default option beta in hard-hit Florida, at 1.8, was one and one-half times that of Texas.
In research dating from the 1980s, mortgage default is modeled as borrower exercise of
the put option (see literature reviews by Quercia and Stegman, 1992; Kau and Keenan,
1995). Empirical findings have shown that negative equity, or the intrinsic value of the de-
fault option, is a major driver of default (see, e.g., Quigley and Van Order, 1995, Deng,
Quigley, and Van Order, 2000). Recent research, however, indicates that home equity must
1 The long list of crisis references include but are not limited to Gerardi et al. (2008); Mayer, Pence,
and Sherlund (2009); Mian and Sufi (2011); Keys et al. (2010); Mian, Sufi, and Trebbi (2010); Rajan,
Seru, and Vig (2015); Agarwal et al. (2014, 2017); An, Deng, and Gabriel (2011); Demyanyk and Van
Hemert (2011); Brueckner, Calem, and Nakamura (2012); Nadauld and Sherlund (2013); Cotter,
Gabriel, and Roll (2015); Demyanyk and Loutskina (2016), etc.
2 This nomenclature is consistent with prior literature on mortgage default (see, e.g., Deng, Quigley,
and Van Order, 2000).
154 X. An et al.
Downloaded from https://academic.oup.com/rof/article/25/1/153/5893492 by guest on 19 February 2021
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
Figure 1. Rolling window estimates of the default option beta.
Notes: Figure 1 is based on the Freddie Mac Single-Family Loan-Level Dataset and Fannie Mae Single-
Family Loan Performance Data (hereafter GSE data) accessed from the Risk Assessment, Data
Analysis, and Research (RADAR) at the Federal Reserve Bank of Philadelphia. This figure shows the
estimates of default option beta in a hazard model. The estimation is based on 3 year rolling window
samples of first-lien, full documentation, and fully amortizing 30 year FRMs acquired by the GSEs dur-
ing 2000–17. A random sample of the GSE loans is used in the estimations. The dark line shows the
point estimates, and the shaded area shows the confidence interval.
0
0.5
1
1.5
2
2.5
3
3.5
4
-20% -10% 0% 10% 20% 30% 40% 50%
Neg. eq. impact 2006 Neg. eq. impact 2012
Negave equity
Hazard
rao
Figure 2. The impact of negative equity on mortgage default probability.
Notes: This figure shows the simulated impact of negative equity on default probability in different
years. Simulations are based on the default option beta estimates shown in Figure 1.
Default Option Exercise over the Financial Crisis and beyond 155
Downloaded from https://academic.oup.com/rof/article/25/1/153/5893492 by guest on 19 February 2021
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Cumulave default rate
Duraon (quarters)
Model Actual
Figure 3. The impact of default option beta on default predictions.
Notes: We use a model estimated using the 2002–06 performance record of the 2002–04 vintages to
predict default of the 2006 vintage assuming a perfect foresight of house price movement. The red
solid line shows the actual performance of the 2006 vintage (with the actual beta), while the blue
dashed line shows the model prediction with the estimated beta using the 2002–06 performance of
the 2002–04 vintages. Over the twenty quarter horizon, the predicted default rate with the estimated
beta is only about half of the actual default rate. As a comparison, the default rate of GSE 30 year
FRMs during 2006–10 was about three times as high as that during 2002–06.
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
CA FL GA IL NY TX
Figure 4. Default option beta time series for the selected states.
Notes: Figure 4 is based on the GSE data. This figure shows the by-state point estimates of the
default option beta based on 3 year rolling window samples of loans in the selected states. The estima-
tions are based on the full sample of GSE loans, and the betas in different states are estimated separately.
156 X. An et al.
Downloaded from https://academic.oup.com/rof/article/25/1/153/5893492 by guest on 19 February 2021
turn deeply negative before most borrowers exercise the default option (see, e.g., Bhutta,
Dokko, and Shan, 2017). Indeed, numerous authors have suggested that residential default
may be less than ruthless (see, e.g., Vandell, 1993, Ambrose, Buttimer, and Capone, 1997;
Deng and Gabriel, 2006). Our results document systematic variability in the default option
exercise among a cross-section of states and over the economic cycle.
3
We explore heterogeneity in borrower propensity to default via a simple theoretical
framework. Our theoretical model builds on existing literature and assumes that borrowers
have rational expectations and engage in default to maximize wealth (see, e.g., Kau et al.,
1992; Riddiough and Wyatt, 1994b; Ambrose, Buttimer, and Capone, 1997; Campbell and
Cocco, 2015). Our model suggests borrower propensity to default can vary over time due
to factors such as changing borrower expectations on the path of the local economy, bor-
rowers’ subjective assessment of the conditional probability of foreclosure (versus work-
out), changing default transaction costs (including stigma effects), and the like. For
example, pessimism about the future trajectory of house prices could make the borrower
more sensitive to a negative equity position. Similarly, expectations of loan modification
conditional on default could also lead to elevated default option exercise.
We employ proxies for factors identified in theory to empirically assess drivers of the
observed variation in the default option beta. We find that county unemployment rate shocks,
reflecting cyclical fluctuations in the local economy, are highly predictive of variation in the de-
fault option beta. Conditional on controls for the local business cycle, we find that borrower
default propensities are sensitive to consumer distress, where our measure of distress is ortho-
gonalized to current economic fundamentals. Further, those factors are economically salient
and together could account—via their impact on the default option beta—for over two-thirds
of the increase in crisis period default risk (Figure 5). We also find evidence of a structural
break in the default option beta time series in 2009, which coincides with federal mortgage
market intervention via the Home Affordable Modification Program (HAMP). Finally, while
results do not show significantly damped default propensities among states with recourse to
borrowers’ nonhousing assets, they do indicate sizable and significantly elevated default option
betas among sand states hard hit by the 2000s housing and mortgage crisis. Together, these
factors explain over 70% of the variation in the default option beta panel.
We also seek to shed light on the structural break in default option exercise in 2009.
A difference-in-differences (DID) analysis shows that those eligible for HAMP loan
modification became significantly more sensitive to negative equity in the wake of program
implementation, relative to the non-HAMP eligible control group. This finding is consistent
with the notion that mortgage borrowers may be strategic and hence, more likely to become
delinquent when they expect lenders to modify defaulted loans (see, e.g., Guiso, Sapienza,
and Zingales, 2013; Mayer et al., 2014).
4
Our findings are robust to alternative model specifications and loan samples. While our
primary sample comprised conventional conforming loans from the GSEs, we re-estimate
the model using nonagency loans and confirm a similar pattern of default option beta vari-
ation. We assess the robustness of findings to book versus market value of negative equity,
3 In related literature on corporate default, Duffie et al. (2009) find evidence of dynamic variation in
the role of common latent factors in predicting firm-level default.
4 Piskorski and Tchistyi (2011) also argue that bailing out the most distressed borrowers in the crisis
period encourages irresponsible financial behavior during the boom. Ghent and Kudlyak (2011) find
that borrowers in nonrecourse states are more sensitive to negative equity.
Default Option Exercise over the Financial Crisis and beyond 157
Downloaded from https://academic.oup.com/rof/article/25/1/153/5893492 by guest on 19 February 2021
controls for the nonlinearity of negative equity, and size of the estimation rolling window
(e.g., 2 years vs. 3 years). We further evaluate robustness in the default option beta among
borrowers less likely to be liquidity constrained. In addition, we test specifications of the
model that account for default burnout. Finally, we estimate the model using annual
cohorts to assess whether changes in the mix of borrowers may have contributed to the
observed variation in the default option beta. Results throughout indicate a similar counter-
cyclical pattern of default option beta over the crisis period and beyond.
Our findings contribute to the literature in several important ways. First, results provide
new insights into the cyclical pattern of borrower default during the financial crisis and be-
yond. Among relevant crisis-related analyses (see, e.g., Mian and Sufi, 2009; Keys et al.,
2010; Piskorski, Seru, and Witkin, 2015; Rajan, Seru, and Vig, 2015, among many others),
temporal shifts in default behavior among mortgage borrowers have received only limited
attention. Here we show that changes in the propensity to exercise the mortgage default
option were material to the crisis.
Second, our findings raise important issues of modeling and management of mortgage
default risk in an ever-changing market environment. As evidenced in recent studies,
statistical models may substantially underestimate default risk in the presence of economic
fluctuations, policy intervention, and behavioral change (see, e.g., An et al., 2012; Rajan,
Seru, and Vig, 2015). Indeed, the assumption of a fixed and static default option beta may
result in significant underprediction of default risk (An et al., 2012). The time-varying
coefficient hazard model better characterizes ongoing evolution in borrower default
behavior so as to enhance risk management.
Third, our study adds to the growing literature on strategic default (see, e.g., Riddiough
and Wyatt, 1994a; Guiso, Sapienza, and Zingales, 2013; Mayer et al., 2014). Mortgage
0
0.5
1
1.5
2
2.5
3
3.5
4
-20% -10% 0% 10% 20% 30% 40% 50%
Neg. eq. Neg. eq. reces.
Neg. eq. reces. + low sen. Neg. eq. reces. + low sen. + post2009Q3
Hazard rao
Negave equity
Figure 5. Decomposition of the various drivers of default option beta.
Notes: This figure shows the simulated impact of negative equity on default probability to illustrate
the impact of the various drivers of the default option beta. Simulations are based on the estimates
shown in Table V.
158 X. An et al.
Downloaded from https://academic.oup.com/rof/article/25/1/153/5893492 by guest on 19 February 2021
default is more than a one-sided process and often involves strategic interaction between
borrowers and lenders. Our results suggest that in anticipation of lender or servicer actions,
borrowers’ willingness to exercise the default option may change as well.
Finally, our study has important implications for crisis-period federal policy. While
HAMP saved many defaulted borrowers from foreclosure (see, e.g., Agarwal et al., 2017),
our findings suggest this program also may have had an unintended consequence of induc-
ing some borrowers to enter into delinquency. While we are silent on the ultimate impact of
HAMP on borrower well-being and social welfare, it appears that the efficacy of HAMP in
mitigating home foreclosure may have been diminished by an increase in default option ex-
ercise among borrowers seeking a HAMP loan modification.
While our analysis does not include the period of the 2020 COVID-19 (coronavirus
disease 2019) pandemic, we suspect that relevant mortgage policy interventions, including
government-backed loan forbearance and moratoria on foreclosure, likely resulted in
damped default option exercise among distressed borrowers and in areas hit hard econom-
ically by the pandemic. In contrast, the absence of such policy treatments likely gave rise to
elevated default option betas among similarly situated borrowers holding untreated non-
conforming mortgages. We leave that analysis to future research.
The remainder of the article is organized as follows: in the next section, we discuss our
data; in Section 3, based on hazard model estimates, we document the time series and
cross-sectional variations in the default option beta; in Section 4, we explore factors that
drive variations in the default option beta; and Section 5 provides concluding remarks.
2. Data
2.1 Data Sources
Our primary dataset consists of loan-level information in the Freddie Mac’s Single-Family
Loan-Level Dataset and Fannie Mae’s Single-Family Loan Performance Data (hereafter
Freddie Mac data and Fannie Mae data, respectively, and GSE data altogether).
5
The GSE
data comprised over 50 million loans, on which we focus on the roughly 42 million fixed-
rate 30 year mortgage loans acquired by the GSEs over the 2000–16 period. The sheer size
of the dataset, as well as the richness of its content, is unparalleled. It provides detailed in-
formation on borrower and loan characteristics at origination, including the borrower’s
credit score, origination loan balance, note rate, loan term, loan-to-value (LTV) ratio, debt-
to-income (DTI) ratio, loan purpose (home purchase, rate/term refinance, cash-out refi-
nance), occupancy status, prepayment penalty indicator, and the like. The GSE data also
track the performance (default, prepayment, mature, or current) of each loan every month,
which is crucial to our default risk modeling.
We merge the loan-level data with proxies for the labor market, housing, and other
macroeconomic conditions. For example, to obtain a measure of negative equity for each
loan in each quarter, we merge the loan event history with a county-level house price index
(HPI) from CoreLogic. We also utilize the HPI to compute time-varying house price return
volatility, which either enters the model as a standalone variable or via a volatility-
adjusted default option value term. To calculate the prepayment option value for each
5 See http://www.fanniemae.com/portal/funding-the-market/data/loan-performance-data.html as
well as http://www.freddiemac.com/news/finance/sf_loanlevel_dataset.html. We standardize the
variables and formats between the Fannie Mae and Freddie Mac datasets.
Default Option Exercise over the Financial Crisis and beyond 159
Downloaded from https://academic.oup.com/rof/article/25/1/153/5893492 by guest on 19 February 2021
loan in each quarter, we merge mortgage interest rates from the Freddie Mac Primary
Mortgage Market Survey to our loan event history. In addition, we supplement our mort-
gage data with macroeconomic variables, including the county-level unemployment rate
from Bureau of Labor Statistics (BLS), Treasury bond rate from the Federal Reserve
Board, and consumer distress index from St. Louis Fed. For purposes of robustness, we
also estimate our models using loan-level data from BlackBox Logix (BBX) for nonagency
securitized mortgages.
6
Additional information on data and variable construction is found
later in the article.
2.2 Sample and Descriptive Statistics
In our main analysis, we focus on first-lien, full documentation, and fully-amortizing
30 year fixed-rate mortgage (FRM) loans acquired by the GSEs during 2000–16 for
Washington DC and nine representative states, including Arizona, California, Florida,
Georgia, Illinois, Massachusetts, Michigan, New York, and Texas.
7
Our focus on narrowly
defined loans and borrowers (only 30 year FRMs) allows us to draw inference on default
behavior from a relatively homogeneous sample. The distribution of loans among sampled
U.S. states allows ample cross-sectional variation in our time series measures. We limit the
analysis to larger states to ensure we have adequate loan samples for subsequent estimation
of a panel data model based on state-level rolling window default option betas. Our sample
contains 42,093,277 individual mortgage loans.
In Table I, we report descriptive statistics of loan and borrower characteristics.
The average loan amount at origination is $199,681, and the average note rate is 5.52%.
The mean borrower’s credit score is 737, and approximately three-quarters of the loans are
for single-family properties. Cash-out refinance, and rate/term refinance mortgages com-
prised 26% and 30% of the sample, respectively. Owner-occupied loans comprise 90% of
our sample, whereas investment property loans constitute 6%. About 23% of our sampled
loans were originated pre-2003, and 28% of sampled loans were originated during the
2003–07 precrisis boom period, whereas one-half of sampled loans were originated during
the Great Recession and its aftermath through 2016. The average combined LTV is 75%.
We also calculate a mean total DTI ratio of 25%. All sample loans are underwritten with
full documentation. Over the sample period, 68% of loans prepay, whereas 6% of loans
terminate in default. At the time of data collection (March 2018), about 26% of our loans
were still performing and hence were censored observations in our model.
3. Rise in Mortgage Default Propensities
3.1 Default Hazard Models
We follow the existing literature in estimating the competing risks of mortgage default and
prepayment in a proportional hazard framework (see, e.g., Deng, 1997, Deng, Quigley,
6 The BBX data are accessed through UCLA’s Ziman Center for Real Estate and the James A.
Grasskamp Center for Real Estate at the Wisconsin School of Business. The data contain roughly
22 million loans. We focus on the fixed-rate fully amortizing mortgages.
7 THE 15 year loans are excluded. A series of filters is also applied: we exclude loans with missing
or wrong information on loan origination date, original loan balance, borrower credit score, LTV
ratio, or DTI ratio.
160 X. An et al.
Downloaded from https://academic.oup.com/rof/article/25/1/153/5893492 by guest on 19 February 2021
and Van Order, 2000; ). As noted above, the hazard model is convenient primarily because
it allows us to work with the full sample of loans despite the censoring of some observa-
tions. The specification of the model is motivated by option theory, which predicts that ra-
tional mortgage borrowers will exercise the default or prepayment option to maximize
their wealth. Theory suggests that mortgage borrowers will exercise the default option
when the value of the mortgage exceeds the value of the collateral. Similarly, borrowers
will exercise the prepayment option when the market value of the mortgage exceeds its
Table I. Summary statistics of the loan sample
Notes: Table I is based on the Freddie Mac Single-Family Loan-Level Dataset and Fannie Mae
Single-Family Loan Performance Data (hereafter GSE data) accessed from RADAR at the
Federal Reserve Bank of Philadelphia. GSE loans included here are first-lien, full-documenta-
tion, and fully amortizing 30 year FRMs acquired by the GSEs during 2000–16. We exclude
loans with missing or obviously wrong information on loan origination date, original loan bal-
ance, borrower credit score, LTV ratio, or DTI ratio. The data cutoff date is March 2018. Default
is defined as 60 day delinquency. Prepayment refers to early repayment of a loan as a result of
borrower move or refinancing for lower interest rates, different loan terms, or cash out. Current
(censor) means that the loan is performing at the date of the data cutoff date. For definitions of
variables, see http://www.fanniemae.com/portal/funding-the-market/data/loan-performance-
data.html and http://www.freddiemac.com/news/finance/sf_loanlevel_dataset.html. RADAR has
normalized the fields and codes across the two datasets when possible.
Variable Mean STD Min. Median Max.
Original loan amount 199,681 109,602 5,000 176,000 1,470,000
Note rate (%) 5.52 1.26 1.88 5.63 13.50
LTV ratio (%) 74 15 25 79 97
Combined LTV (%) 75 15 25 79 200
Borrower credit score 737 54 300 748 850
DTI ratio (%) 34 11 9 34 61
First-time home buyer 13.2 – 0 – 1
Single family 73.3 – 0 – 1
Condominium 8.6 – 0 – 1
Planned-unit development 18.1 – 0 – 1
Owner occupied 89.5 – 0 – 1
Second home 4.1 – 0 – 1
Investment property 6.4 – 0 – 1
Home purchase 44.9 – 0 – 1
Cash-out refinance 25.7 – 0 – 1
Rate/term refinance 29.5 – 0 – 1
Originated prior to 2003 23.3 – 0 – 1
Originated 2003–07 28.2 – 0 – 1
Originated 2008–12 24.9 – 0 – 1
Originated after 2012 23.6 – 0 – 1
Defaulted 5.95 – 0 – 1
Prepaid 68.02 – 0 – 1
Current 26.03 – 0 – 1
Total number of loans 42,093,277
Default Option Exercise over the Financial Crisis and beyond 161
Downloaded from https://academic.oup.com/rof/article/25/1/153/5893492 by guest on 19 February 2021
book value. These two options compete against each other.
8
Among other drivers of de-
fault, recent research has underscored the importance of crisis-period income and liquidity
shocks as default triggers (see, e.g., Foote, Gerardi, and Willen, 2008; Elul et al., 2010;
Gyourko and Tracy, 2014; Campbell and Cocco, 2015; Gerardi et al., 2015 for the double
trigger argument).
9
As discussed below, we also include proxies of income shocks in our
model specification.
As in much of the literature, we define default as mortgage delinquency in excess of 60
days. An important consideration in this definition of default is that lenders and servicers
typically intervene in the default process only after 60 day delinquency; as such, the 60 day
delinquency event reflects the borrower decision-making, as is the focus of this article.
Prepayment refers to early repayment of a loan as a result of borrower relocation or refi-
nancing for purposes of a lower interest rate, different loan terms, or cash out.
The literature typically assumes the hazard rate of mortgage loan termination at period
T since origination is of the form
h
k
i
ðT; Z
0
i;t
Þ¼h
k
0
ðTÞ expðZ
0
i;t
b
k
Þ (1)
where k indicates default or prepayment, T is duration time, t indicates calendar time, i is
the individual loan, and Z
0
i;t
is a vector of covariates for loan i that includes all identifiable
risk factors.
10
Here, h
k
0
ðTÞ is the baseline of the hazard function. In the proportional hazard
model, changes in covariates shift the baseline hazard rate proportionally without other-
wise affecting the duration pattern of default or prepayment. Covariates include proxies for
default and prepayment option values, borrower credit score, payment (debt) to income
ratio, loan amount, and a host of other loans, borrower, and locational characteristics.
In our analysis, we allow the coefficient of the default option in the hazard model to be
time-varying so as to focus on possible intertemporal variation in the sensitivity of borrow-
er default probability to negative equity. Therefore, our model becomes a time-varying co-
efficient (partially linear) model of the form:
h
k
i
ðT; Z
0
i;t
Þ¼h
k
0
ðTÞ expðZ
0
i;t
b
k
t
Þ (2)
To estimate a time-varying coefficient hazard model, we adopt the rolling window local
estimation approach from the statistics literature (see, e.g., Cleveland, Grosse, and Shyu,
1991; Fan and Zhang, 1999). The idea is that the time-varying coefficient model can be
treated as locally linear, allowing us to assume the coefficients are smooth for each short
time window and to apply the usual estimation method to obtain a local estimator.
11
In
that regard, we form quarterly three-year rolling windows to construct our local estimation
samples. As discussed below, we also assess the robustness of results to the size of the roll-
ing window.
8 Kau et al. (1992) and Kau and Keenan (1995) have outlined the theoretical relationships among the
options, and Schwartz and Torous (l993) have demonstrated their practical importance.
9 According to the double-trigger argument, negative equity is a necessary but not sufficient condi-
tion for mortgage default. That argument further stresses the importance of income shocks to de-
fault. Low (2015) presents evidence on positive equity and default.
10 Notice that the loan duration time T (tau) is different from the calendar time t, which allows identi-
fication of the model.
11 More sophisticated methods include a two-step procedure presented in Fan and Zhang (1999)
and Fan and Zhang (2008).
162 X. An et al.
Downloaded from https://academic.oup.com/rof/article/25/1/153/5893492 by guest on 19 February 2021
The hazard model is estimated using loan event-history. We construct the quarterly per-
formance history of each loan based as reported in the GSE data, as well as a number of
time-varying explanatory variables. Negative equity is defined as the percentage difference
between the book value of the loan and the market value of the property relative to the
market value of the property.
12
The default option is defined as the cumulative distribution
function value of negative equity over county house price return volatility.
13
In an alterna-
tive specification, we replace the default option variable with spline functions of negative
equity and a standalone house price return volatility term. Results are robust to that trans-
formation and are reported in Appendix figures and tables. The market value of the prop-
erty is calculated based on property value at the time of loan origination plus/minus any
change therein as indicated by a local HPI. The prepayment option value is computed as
the contemporaneous difference between the market value of the loan and its book value.
The book value of the loan is the remaining mortgage balance (from the loan amortization
schedule) whereas the market value of the loan is computed based on the remaining mort-
gage payments discounted at the current prevailing mortgage interest rate in the market
(see, e.g., Deng, Quigley, and Van Order, 2000). We also use the change in the state
unemployment rate from loan origination through termination or censor of the loan to
approximate income shocks.
14
Sample statistics of the time-varying covariates are reported
in Table II.
Time-fixed covariates included in the hazard model include loan and borrower charac-
teristics such as borrower credit score, LTV ratio (LTV), DTI ratio, loan amount, loan
purpose, property type, occupancy type, first-time buyer status, and the like. We also
include state-fixed effects and vintage-fixed effects. State-fixed effects account for the
possible impact of varying state foreclosure laws on default probability, among other
things, whereas vintage-fixed effects control for unobserved changes over time in under-
writing standards. To account for potential nonlinearities, we include square terms of such
key variables as a change in the local unemployment rate and the default and prepayment
option values. Moreover, for variables such as borrower credit score, LTV, DTI, and loan
amount, we use granular buckets.
3.2. Default Option Beta Time Series
Prior to the presentation of our rolling window estimates and to assure the reasonableness
of model specification, we examine a pooled-sample baseline model. Estimates of the base-
line model are reported in Table III. Standard errors clustered at the loan-level are reported
in the table as well. As is evident, model coefficients conform to economic intuition and
findings in the existing literature (see, e.g., Deng, Quigley, and Van Order, 2000; Deng and
Gabriel, 2006). For example, the default option value is positively related to default risk.
That relationship is nonlinear, as reflected by the significance of the default option square
term.
12 As a robustness check, we use the market value instead of the book value of the mortgage to cal-
culate negative equity. The resulting default option beta demonstrates similar time variation.
13 House price return volatility is a scaling factor.
14 Butta, Dokko, and Shan (2016) use local credit card delinquency rates as an alternative measure
of income shocks. We test such an alternative as well as a zip code-level income change meas-
ure based on IRS data and find our results to be robust to those alternative specifications.
Default Option Exercise over the Financial Crisis and beyond 163
Downloaded from https://academic.oup.com/rof/article/25/1/153/5893492 by guest on 19 February 2021
Table II. Summary statistics of the event history sample
Notes: Table II is based on the performance history of loans described in Table I. Negative equity (book) is the difference between the book value of the loan
and the market value of the property over the market value of the property. Negative equity (market) is the difference between the market value of the loan and
the market value of the property over the market value of the property. Default option is the cumulative distribution function value of negative equity over house
price return volatility. Prepayment option is the difference between the market value of the loan and the book value of the loan. The market value of the property
is calculated based on property value at origination plus change therein, as indicated by a local HPI. For more details, see Deng, Quigley, and Van Order (2000).
The book value of the loan is the remaining balance, and market value is calculated as the present value of the remaining mortgage payments using the current
prevailing mortgage interest rate as the discount rate. For loans with junior lien(s), the book and the market values of the loan account for the junior lien(s).
Change in unemployment rate is from loan origination to the performance date. HPI is from CoreLogic. The mortgage interest rate is from the St. Louis Fed. The
unemployment rate is from the BLS.
Defaulted Prepaid Current
Variable Mean STD Min. Median Max. Mean STD Min. Median Max. Mean STD Min. Median Max.
Default option (book) 0.21 1.11 0.00 0.00 1.00 0.05 2.27 0.00 0.00 1.00 0.04 4.64 0.00 0.00 1.00
Default option (market) 0.33 1.31 0.00 0.03 1.00 0.11 3.75 0.00 0.00 1.00 0.07 6.51 0.00 0.00 1.00
Prepayment option 0.11 0.30 0.12 0.11 0.45 0.10 1.27 0.12 0.10 0.45 0.05 2.45 0.13 0.04 0.44
Negative equity (book) 0.17 0.84 0.93 0.20 1.57 0.33 2.69 0.91 0.32 1.23 0.36 5.95 0.93 0.36 1.35
Negative equity (market) 0.08 1.02 0.92 0.13 1.91 0.26 3.28 0.90 0.27 1.53 0.33 6.84 0.92 0.34 1.67
HPA volatility 0.08 0.11 0.00 0.08 0.25 0.07 0.48 0.01 0.07 0.25 0.07 0.99 0.00 0.07 0.25
Change in unemp. rate 2.22 9.87 17.10 1.90 20.20 0.52 36.91 14.30 0.40 19.40 0.13 79.41 17.50 0.20 20.20
Number of loan quarters 612,490,108
164 X. An et al.
Downloaded from https://academic.oup.com/rof/article/25/1/153/5893492 by guest on 19 February 2021
Table III. MLE estimates of the baseline competing risks hazard model
Notes: Table III is based on the GSE data. These are MLE estimates of the competing risks haz-
ard model for default and prepayment based on a random sample of the event history data
described in Table II. The hazard model is in the form of h
k
i
ðT ; Z
0
i;t
Þ¼h
k
0
ðT ÞexpðZ
0
i;t
b
k
Þ, where k
indicates default or prepayment, T indicates duration time, t indicates calendar time, i indicates
individual loan, and Z
0
i;t
are the risk factors reported in this table. The baseline h
k
0
ðT Þ is esti-
mated nonparametrically and not reported here. State- and vintage-fixed effects are not
reported here, either, but they are available upon request. Variable definitions are discussed in
Tables I and II. Standard errors are clustered at the loan-level. ***, **, and * indicate 0.1%, 1%,
and 5% significance, respectively.
Dependent variable:
default/prepay hazard
Default Prepayment
Estimate SE Estimate SE
Default option (book) 0.747*** 0.015 0.058*** 0.014
Default option squared 0.091*** 0.005 0.078*** 0.006
Prepayment option 0.273*** 0.007 0.987*** 0.008
Prepayment option squared 0.083*** 0.003 0.006 0.004
Change in unemp. rate 0.174*** 0.006 0.185*** 0.006
Change in unemp. rate squared 0.027*** 0.003 0.003 0.003
LTV < 60 0.385*** 0.014 0.059*** 0.011
LTV 60–70 0.130*** 0.014 0.017 0.012
LTV 80–90 0.090*** 0.012 0.039*** 0.010
LTV > 90 0.355*** 0.014 0.082*** 0.013
Credit score < 580 0.744*** 0.037 0.035 0.049
Credit score 580–620 0.376*** 0.020 0.037 0.026
Credit score 660–700 0.486*** 0.013 0.051*** 0.015
Credit score 700–740 0.975*** 0.013 0.104*** 0.015
Credit score 740–780 1.531*** 0.013 0.159*** 0.014
Credit score > 780 2.062*** 0.015 0.154*** 0.015
DTI < 20 0.344*** 0.017 0.009 0.013
DTI 20–30 0.217*** 0.011 0.008 0.009
DTI 40–50 0.213*** 0.011 0.027** 0.010
DTI> 50 0.335*** 0.014 0.048*** 0.013
Loan amount < 10K 0.199*** 0.015 0.577*** 0.013
Loan amount 10–15K 0.007 0.015 0.282*** 0.012
Loan amount 15–20K 0.048** 0.015 0.117*** 0.012
Loan amount 25–30K 0.030 0.019 0.095*** 0.015
Loan amount 30–35K 0.096*** 0.023 0.104*** 0.018
Loan amount > 35K 0.181*** 0.023 0.314*** 0.016
First-time home buyer 0.063*** 0.015 0.109*** 0.013
Condominium
0.109*** 0.016 0.015 0.013
Planned-unit development 0.104*** 0.014 0.068*** 0.011
Investment property 0.105*** 0.017 0.198*** 0.015
Second home 0.202*** 0.025 0.108*** 0.018
Cash out refinance 0.429*** 0.012 0.130*** 0.010
Rate/term refinance 0.256*** 0.012 0.089*** 0.010
State FE Yes Yes
Vintage FE Yes Yes
Flexible baseline function Yes Yes
N 1,034,009
Default Option Exercise over the Financial Crisis and beyond 165
Downloaded from https://academic.oup.com/rof/article/25/1/153/5893492 by guest on 19 February 2021
Similarly, as expected, the value of the prepayment option is positively related to the
risk of prepayment. Consistent with the competing risk model specification, the estimated
coefficients of the default option and prepayment option values also are statistically signifi-
cant in the prepayment and default hazard models, respectively. As evidenced in Table III,
coefficients on LTV buckets in the default equation are significant throughout and increase
monotonically over LTV levels. Further, lower levels of LTV are associated with negative
default risk, whereas substantial positive coefficients are estimated for the higher LTV cate-
gories. In a similar vein, the estimated coefficients on the credit score categorical terms de-
cline monotonically with credit score bucket. As expected, while coefficients associated
with lower credit score categories are positive and significant in the determination of de-
fault risk, those estimates turn negative, sizable, and significant for the higher credit score
buckets. Also, monotonic and increasing coefficients are estimated for the DTI categorical
terms in the default hazard. Almost all other controls enter the specified competing risk
equations with anticipated signs and a high level of statistical significance.
As discussed above, our focus is on the time variation in the default option beta. In that
regard, we use the cumulative distribution function value of negative equity over house
price return volatility to represent the default option value.
15
Given the presence of the
square term in default option value, the default option beta is calculated as the coefficient
of the default option term plus two times the coefficient of the default option square term
times the mean value of the default option term—the first-order partial derivative of the de-
fault hazard rate with respect to the value of the default option.
In Figure 1, we display rolling window estimates of the default option beta from
Equation (2). We plot both the estimated beta together with its confidence band. Clearly
evidenced are sizable and significant intertemporal variations in the estimated beta. In that
regard, the default option beta rose gradually from about 0.2 during 2003–06 to almost 1.3
in 2009. That estimate continued to trend up in the immediate aftermath of the crisis to
peak at about 1.6 during 2012–13. Subsequent to that, a clear trending down in the default
option beta was evidenced; nonetheless, as recently as 2016Q2, the estimated beta
remained elevated at close to 1.0. Overall, results indicate statistically significant counter-
cyclical movement in the default option beta over the 2003–16 timeframe of the analysis.
16
To assure robustness of results to loan samples, we re-estimated our models using non-
agency securitized loans from BBX in place of our GSE loan sample. Results indicate the
time series pattern in the default option beta is robust to the loan sample.
17
To provide insights as to the economic significance of changes in the mean estimated de-
fault option beta, we plot in Figure 2, the impact of borrower negative equity on default
probability in the years 2006 and 2012. Interestingly, a sizable increase in negative equity
had a limited impact on default probability in 2006. In marked contrast, by 2012, the im-
pact of negative equity on loan default probability was sizable. In that year, a loan with
30% negative equity had over a roughly 170% chance of entering into default as compared
to a loan with 10% negative equity. In addition, a loan with 40% negative equity had over
a 190% chance of entering into default as compared to a loan with 10% negative equity.
15 See, for example, Deng, Quigley, and Van Order (2000); Deng and Gabriel (2006).
16 As shown in Appendix Figure A1, a similar and marked cyclical trend is evidenced in the negative
equity spline beta estimates.
17 Some of these results appear in prior versions of our article. Additional results are available upon
request.
166 X. An et al.
Downloaded from https://academic.oup.com/rof/article/25/1/153/5893492 by guest on 19 February 2021
Loans with negative equity in the range of 10–30% witnessed an increase in the default
hazard ratio of 60–150% between 2006 and 2012.
To gain further insights regarding the economic significance of those findings, we use
model estimates from 2002 to 2004 vintage loans to predict default in the 2006 vintage.
18
Per the above, if the default option beta was lower in 2002–04, a model estimated with
data from those years will underpredict default in the 2006 vintage. In order to isolate the
impact of changes in the default option beta from that in the default option value itself, we
assume perfect foresight in house price movement for the 2006 vintage. The red solid line
in Figure 3 shows the actual performance of the 2006 vintage with the correct default op-
tion beta. The blue dashed line in the same figure shows the model prediction with the esti-
mated default option beta from the 2002 to 2004 vintage. Over a twenty quarter horizon,
the predicted default rate with the 2002–04 beta is only about half of the actual default
rate. As a comparison, the default rate of GSE 30 year FRMs during 2002–06 was about
one-third that of 2006–10. Taken together, along with the decline in home equity, the up-
turn in the default option beta figured importantly in the run-up in default.
As is evident in Figure 1, the estimated movement over time in the default option beta
appears to be strongly correlated with cyclical fluctuations in house prices and the broader
economy. During the precrisis boom years and in the context of strong housing market per-
formance, the estimated beta was small in magnitude. As boom turned to bust, the default
option beta rose markedly. Finally, in the wake of the postdownturn expansion and as eco-
nomic conditions improved, the household propensity to exercise the default option again
declined.
For purposes of robustness, we replace the default option term with spline functions of
negative equity and a standalone house price return volatility term. Results shown in
Appendix Table A1 are consistent with the findings of our primary specification. For ex-
ample, the spline function shows that negative equity is positively related to default prob-
ability, and the relation is nonlinear. Moreover, house price return volatility is negatively
associated with default probability, consistent with findings in classical models of default
risk that show that borrowers delay defaulting on their loan when asset volatility unexpect-
edly increases. Using the model shown in Appendix Table A1, we conduct rolling window
estimation of the model. Results show a marked increase in the negative equity beta during
2009–13 for borrowers with negative equity.
19
Interestingly, for borrowers with significant
positive equity in their home, the relation between default probability and the depth of
equity remains stable over the full sample period.
Among other robustness checks, we estimate the rolling window model using different
window sizes (24 months vs. 36 months). The results are robust to that transformation.
Note also that the use of HPI to calculate negative equity may result in measurement error
relative to the idiosyncratic house price change that a given homeowner might experience.
This measurement error could bias the estimated default option betas. To the extent that
this measurement error varies over time, the same borrower behavior could manifest with a
changing beta. To assess the salience of this issue, we regressed individual house price
returns (based on repeated CoreLogic real estate deeds transactions data) on the CoreLogic
18 See An et al. (2012) for a similar simulation.
19 Appropriately accounting for nonlinearity helps to provide assurance that we are assessing the
effects of changes in borrower tendency to default for a given level of negative equity, rather
than time-variant changes in the distribution of negative equity.
Default Option Exercise over the Financial Crisis and beyond 167
Downloaded from https://academic.oup.com/rof/article/25/1/153/5893492 by guest on 19 February 2021
zip code level HPI returns.
20
Appendix Figure A3 provides a metric of house price measure-
ment error over our study period as represented by the mean absolute error (MAE) of that
regression. As is evident, the annual variation in the house price measurement error does
not coincide with the temporal variation in the default option beta as shown in Figure 1.
3.3 State Default Option Beta Panel
We further evaluate spatial heterogeneity in the default option beta time series across select
states. To do so, we stratify the sample by state and estimate the rolling window model. To
obtain a better picture of the spatial heterogeneity in the state-specific default option beta
estimates, we plot the beta time series for six states—including California, Florida,
Georgia, Illinois, New York, and Texas—in Figure 4. As is evident, all sampled states dis-
play significant cyclical movement in the default option beta over the boom, bust, and crisis
aftermath. For example, California, Florida, Georgia, and Illinois demonstrate two succes-
sive periods of upward movement in the default option beta between 2006 and 2012 prior
to more recent trending down in those series. While all sampled states exhibited a peak in
the default option beta series in 2012, the amplitude of those cycles varied across states.
Indeed, the run-up over the crisis period and its aftermath in beta were substantially
damped in Texas and New York relative to elevated levels computed for Florida.
4. What Drives Variations in Default Propensities?
4.1 A Theoretical Framework
As evidenced above, variations in the negative equity beta are sizable both in the time series
and in the cross-section. Below, we explore some explanations of these variations. We start
with a simple theoretical framework to inform the empirical analysis.
The mortgage termination literature emanates from an option-based contingent claims
framework whereby mortgage default and prepayment are options to put and call the con-
tract, respectively (see, e.g., Kau et al., 1992; Schwartz and Torous, 1992; Ambrose,
Buttimer, and Capone, 1997). Recent literature has extended early papers in the context of
a more general household utility/wealth maximization framework. In the broader model,
mortgage borrowers exercise the default option to maximize utility/wealth, subject to li-
quidity constraints and other exogenous shocks (see, e.g., Campbell and Cocco, 2015;
Corbae and Quintin, 2015).
As in the literature, we characterize mortgage loans as debt contracts with a compound
default (put) option, such that a borrower who does not default in a given period has the
right to default in the future. Consider a mortgage borrower who faces a decision at time t
of whether to continue to make the mortgage payment or to default on the loan. Assume
the property value is H
t
and the remaining mortgage balance is M
t
(negative equity is thus
H
t
M
t
). Default eliminates borrower’s negative equity.
Building on Riddiough and Wyatt (1994b) and others, we allow for the possibility of a
loan workout in the wake of default. Accordingly, if the borrower chooses to default, there are
two possible outcomes, including foreclosure with probability p
t
, and workout with probabil-
ity ð1 p
t
Þ. If foreclosed, the borrower incurs tangible transaction costs R
t
, which include
moving costs and credit impairment (Cunningham and Hendershott, 1984). There are also
20 In this analysis, only the top fifty zip codes ranked by number of housing transactions are
included.
168 X. An et al.
Downloaded from https://academic.oup.com/rof/article/25/1/153/5893492 by guest on 19 February 2021
intangible foreclosure transaction costs S
t
, which include stigma effects and possible psychic
costs (Kau and Keenan, 1995; White, 2010). If instead, the bank agrees to work out the loan,
the borrower will receive a benefit of V
t
in terms of payment reduction (reduced interest rate,
term extension, and the like) and/or write-off of some portion of principal balance.
Let B
t
denote the benefit to the borrower of default. Then
B
t
¼ p
t
H
t
M
t
ðÞ
R
t
S
t
1 þ r
t
ðÞ
1
E
t
B
tþ1
hi
þ 1 p
t
ðÞ
V
t
;
where B
tþ1
¼ p
tþ1
H
tþ1
M
tþ1
ðÞ½ (3)
Equation (3) shows that the default benefit consists of two parts: the first part is net
benefit from possible foreclosure, including the extinguishment of negative equity (H
t
M
t
),
incurrence of transaction costs (R
t
þ S
t
), and loss of the option to default in the next period
with a value of E
t
B
tþ1
discounted back to the current period with a discount rate r
t
; and the
second part is the net benefit of possible work out, V
t
. The total benefit is just a weighted
average of these two parts.
Upon loan maturity at time T, the net benefit becomes
B
T
¼ p
T
H
T
M
T
ðÞ
R
T
S
T
½
þ 1 p
T
ðÞ
V
T
; (4)
as there is no remaining next period default option.
It has long been recognized that certain exogenous shocks, such as loss of job could trig-
ger default. Vandell and Thibodeau (1985) describe such an outcome as suboptimal default,
whereas Campell and Cocco (2015) and Corbae and Quintin (2015) model default result-
ing from income shocks in the context of a utility/wealth maximization problem. More gen-
erally, such trigger events may be described in terms of borrower budget constraints. For
the borrower to be able to continue making monthly payments, her income must be ad-
equate to cover her mortgage payment, other debt payments, and consumption,
Y
t
P
t
þ D
t
þ C
t
; (5)
where Y
t
denotes the borrower’s income, P
t
is the mortgage payment, D
t
is other debt pay-
ment and C
t
is consumption.
There is the possibility of borrower insolvency such that her income falls short of
required debt payments and consumption. In such circumstances, the borrower can sell the
property to pay off the loan and thus avoid default. However, there may be substantial
transaction costs associated with a fire sale of the property, including real estate agent com-
missions and psychic distress. Alternatively, the borrower can choose to default to avoid
such transaction costs. We denote such transaction costs as W
t
. Further, we denote the
probability that the borrower becomes insolvent as q
t
. The ultimate benefit of default to
the borrower at decision point t is then
G
t
¼ 1 q
t
ðÞ
B
t
þ q
t
ðW
t
þ B
t
Þ¼B
t
þ q
t
W
t
: (6)
The default condition is G
t
0.
The model solution requires information about the full dynamics of house prices, mort-
gage interest rates, transaction costs, borrower income, other debt payments, consumption,
the conditional probability of foreclosure given loan default, and benefits of a loan
workout. While a closed-form solution is unlikely, we are able to make some inferences
that inform the empirical analysis.
Default Option Exercise over the Financial Crisis and beyond 169
Downloaded from https://academic.oup.com/rof/article/25/1/153/5893492 by guest on 19 February 2021
First, consider the probability of default. Per Equation (3), a borrower benefit from de-
fault is the extinguishment of negative equity (H
T
M
T
). The probability of default then
varies positively with that term. The probability of default also varies with the borrower’s
expectation of house prices and interest rates over the life of the loan, reflected in the
B
tþ1
term. Finally, default probability is a function of transaction costs, borrower assess-
ment of the likelihood of receiving a workout and magnitude of workout benefit, and bor-
rower probability of insolvency.
Further, per above, the sensitivity of default probability to negative equity, which is the
first-order partial derivative of default probability with respect to negative equity, should
be a function of the borrower’s expected conditional probability of foreclosure p
t
. It should
also be a function of borrower expectations of future house prices and mortgage interest
rates.
21
This is because B
t
depends on E
t
B
tþ1
, which varies with current H
t
as well as
expected changes in house prices and mortgage interest rates.
22
To summarize, the above model suggests that negative equity is a key driver of loan de-
fault. Further, as suggested above, the borrower’s sensitivity to negative equity can vary
with changing borrower expectations, the conditional probability of foreclosure (or work-
out), and other factors.
4.2 Panel Data Regression of State-Level Default Option Beta
In this section, informed by the above theoretical framework, we study underlying factors
that drive variation in the estimated default option betas. Recall that our rolling window
hazard model estimates yield a panel of default option betas by state and by quarter. As dis-
cussed above, we hypothesize that potential drivers of the default option beta include such
factors as borrower changing market expectations, the future path of house prices, and the
conditional probability of foreclosure.
We proxy for borrower expectations using measures of the local business cycle and con-
sumer sentiment. Both terms are available at the state level. Following Korniotis and
Kumar (2013), we use the unemployment rate innovation as a measure of the local business
cycle. It is computed using the BLS current quarter unemployment rate divided by its four-
quarter moving average. Also, borrowers might use past evidence of house price appreci-
ation to gauge future returns. For this reason, we consider a lagged house price return term
based on the CoreLogic HPI.
We use a consumer distress index to proxy sentiment. The index comes from
CredAbility, and we access it through the St. Louis Fed Federal Reserve Economic Data
(FRED). It is a quarterly comprehensive measure of the average American household’s fi-
nancial condition. CredAbility uses more than sixty-five variables from government, public,
and private sources to convert a complex set of factors into a single index of consumer dis-
tress. Given that this distress index in part reflects economic fundamentals, which might be
already reflected by unemployment rate innovation, we first regress the state-level
CredAbility consumer distress index on state-level unemployment rate innovations as well
as time- and state-level fixed effects to obtain a distress index orthogonalized to fundamen-
tals. We then use the orthogonalized distress index in our analysis.
21 Here, we assume negative equity is independent of borrower insolvency probability, q
t
, and trans-
action costs (a combination of R
t
, S
t
, and W
t
).
22 More formally if we assume house price follows a geometric Brownian motion with time varying
drift, such a relation will be obvious from the first-order derivative calculation.
170 X. An et al.
Downloaded from https://academic.oup.com/rof/article/25/1/153/5893492 by guest on 19 February 2021
There is no consensus on how to measure borrowers’ subjective assessment of the likeli-
hood of loan modification (vs. foreclosure) conditional on default. Our approach is to test
for structural breaks in default option exercise coincident to the enactment of major crisis-
period loan modification programs, as existing literature suggests elevated borrower stra-
tegic default in the wake of such loan modification programs (see, e.g., Mayer et al., 2014).
Note that our theory suggests that while borrower income shocks are an important
driver of default probability, they should not directly affect the default option beta.
However, to account for the possibility that our first-stage hazard model does not fully con-
trol for this factor, we include average gross income growth from the Internal Revenue
Service (IRS) in our panel data regression as well.
We also include categorical controls for recourse states and sand states. In recourse
states, lenders may pursue deficiency judgments against borrowers to the extent foreclosure
proceeds fail to fully compensate for losses. It is hypothesized that even the legal threat of
recourse to borrower nonhousing assets may change borrower default behavior. Ghent and
Kudlyak (2011) find that borrowers in nonrecourse states are more sensitive to negative
equity. As regards sand states, that nomenclature was adopted during the late 2000s to
identify those states that experienced a marked boom-bust cycle in housing and were at the
epicenter of the crisis.
We present the results of our panel data regression in Table IV. The dependent variable
is the by-quarter estimate of the default option beta from the hazard model of default for
each state in rolling windows (hence a panel of betas). In Model 1, we include among ex-
planatory terms the state unemployment rate innovation, the orthogonalized state con-
sumer distress index, and a time dummy. State unemployment rate innovation is positive
and significant, indicating an elevated default option beta in the context of a weaker local
economy. The orthogonalized Metropolitan Statistical Area (MSA) consumer distress index
is negative and significant, suggesting elevated default option exercise in the context of
higher levels of consumer distress. The time dummy is positive and significant, indicating
an elevated default option beta post-2009Q3. We tested a number of other breaking points,
but find post-2009Q3 provides the best fit of the data. Later in the article, we test whether
this result is related to the borrower’s changing view of the likelihood of receiving a loan
workout in the wake of the enactment of a major mortgage modification program. Finally,
in our sample, the categorical term identifying recourse states is not a significant factor in
determination of the default option beta. The four variables combined explain about 68%
of the variations in default option beta.
In Model 2, we substitute a categorical control for sand states in place of that for re-
course states. As expected, after controlling for state unemployment conditions, the ortho-
gonalized state distress index, and the post-2009 policy treatment, findings indicate a
significantly elevated default option beta among hard-hit sand state areas. Further, other
results are robust to the inclusion of that term. In Model 3, we include a full vector of state
fixed effects instead of the recourse or sand state categorical terms. As is evident, findings
are robust to the inclusion of state fixed effects; further, that specification explains a full
three-fourths of the variation in the default option beta.
In Models 4–6, we replace the state unemployment rate innovation and orthogonalized
state distress index terms with proxies for house price expectations and income shocks. We
calculate house price return based on the CoreLogic HPI data and use its lagged term as a
proxy for house price expectations. Borrower income shocks are approximated by the
change in IRS zip code-level average adjusted gross income aggregated to the state level.
Default Option Exercise over the Financial Crisis and beyond 171
Downloaded from https://academic.oup.com/rof/article/25/1/153/5893492 by guest on 19 February 2021
Table IV. OLS estimates of the panel data model of the mortgage default option beta
Notes: Table IV reports the OLS estimates of the panel data model of the default beta, which is similar to what is shown in Figure 4. The dependent variable is
the default option beta estimate from the hazard model for default (the first-stage analysis) for each state in each rolling window (thus a panel of betas). Loans
included in the first-stage hazard model estimation are GSE loans described in Table I. Due to the availability of the consumer distress index, our sample cutoff
date here are March 2013, and we focus on nine representative states and the District of Columbia: Arizona, California, DC, Florida, Georgia, Illinois,
Massachusetts, Michigan, New York, and Texas. Recourse states in our sample include DC, Florida, Georgia, Illinois, Massachusetts, Michigan, New York, and
Sand states refer to Arizona, California, and Florida. Unemployment rate innovation is the current quarter unemployment rate divided by its four-quarter moving
average and is based on BLS data. Consumer distress index is a quarterly comprehensive measure of the average American household’s financial condition
compiled by CredAbility and made available by the St. Louis Fed. Orthogonalized consumer distress index is the residual from a regression where the state-level
consumer distress index is regressed on the state-level unemployment rate innovation, state-fixed effect, and year-fixed effect. In addition, the HPI return is cal-
culated based on the CoreLogic home price index; change in average AGI is based on IRS data. For the structural break, we test a number of alternative breaking
points but find 2009Q3 is the best breaking point based on model fit. Other variable definitions are discussed under Tables I and II. ***, **, and * indicate 0.1%,
1%, and 5% significance, respectively.
Dependent variable:
default option beta
Model 1 Model 2 Model 3 Model 4 Model 5 Model 6 Model 7 Model 8
Estimate SE Estimate SE Estimate SE Estimate SE Estimate SE Estimate SE Estimate SE Estimate SE
Intercept 0.232*** 0.013 0.205*** 0.009 0.245*** 0.008 0.217*** 0.009 0.212*** 0.009
Unemp. rate innovation 0.062*** 0.006 0.061*** 0.006 0.062*** 0.006 0.032*** 0.009 0.041*** 0.008
Orth cons distress index 0.023*** 0.006 0.022*** 0.006 0.013* 0.007 0.013* 0.006 0.012* 0.006
Post-2009Q3 0.386*** 0.014 0.385*** 0.013 0.387*** 0.012 0.343*** 0.014 0.342*** 0.013 0.346*** 0.012 0.360*** 0.014 0.369*** 0.013
Lagged HPA 0.071*** 0.007 0.072*** 0.007 0.064*** 0.006 0.045** 0.010 0.033** 0.009
Income growth 0.010 0.007 0.011 0.007 0.009 0.006 0.011 0.007 0.008 0.006
Recourse state 0.019 0.014 0.018 0.014
Sand state 0.048*** 0.014 0.058*** 0.014 0.052*** 0.013
State FE No No Yes No No Yes No Yes
N 410 410 410 410 410 410 410 410
Adjusted R
2
0.683 0.691 0.755 0.685 0.696 0.749 0.707 0.763
172 X. An et al.
Downloaded from https://academic.oup.com/rof/article/25/1/153/5893492 by guest on 19 February 2021
Model 4 is identical to Model 1 except for that substitution. Results of Models 4–6 show
that lagged HPI return is significant and negative in explanation of the default option
beta.
23
To the extent, lagged HPI return is a measure of borrower expectations, this result
suggests that the default option betas are damped in the context of elevated expectations of
house price returns. Consistent with our theory, while the income shock is a positive and
significant factor in the first-stage hazard model for default probability, that same factor is
insignificant in determination of the default option beta. In other words, borrower insolv-
ency probability is a determinant of default probability but not necessarily an important
factor in explaining borrower default propensities.
24
Findings associated with the estimated
recourse and sand states categorical terms (see Models 4 and 5, respectively) are consistent
with those described above and robust to this specification.
Finally, in Model 7, we include all five factors as well as the sand state categorical term
and in Model 6 we substitute state fixed effects for the sand state control. The results of
those full specifications are consistent with those of the above models. In sum, results of
panel data analysis are consistent with theory and show that those proxies for local business
cycle, sentiment, and house price expectations capture some of the variances in the default
option beta. Further, as evidenced, default propensities as embodied in the default option
beta are elevated among sand states. Model 8 includes state fixed effects and provides con-
sistent results regarding the impact of local business cycle, sentiment, and house price
expectations. While the model explains over 70% of the variation in the default option
beta, we do not rule out other possible explanations such as the increased social acceptance
of default option exercise (see, e.g., Guiso, Sapienza, and Zingales, 2013).
4.3 Hazard Model with Interaction Terms
The literature on varying coefficient models suggests that if we know the determinants of
time variation in the default option beta, we can simply include interaction terms between
the covariate and those factors and estimate the model in linear form (see, Cai et al., 2008).
In this case, the model becomes
h
k
i
ðT; Z
0
i;t
Þ¼h
k
0
ðTÞ exp½at
ðÞ
Z
0
i;t
b (7)
Here at
ðÞ
is the time series factor that determines the time-varying coefficient. As the
focus of this article is the time-varying coefficient of the default option, we hold constant
the coefficients of the other covariates in our interaction model.
25
As such, we have
at
ðÞ
Z
0
i;t
b ¼ b
1
u
t
x
i;t
þ W
0
i;t
c; (8)
where we decompose Z
i;t
into the default option x
i;t
and the other covariates W
i;t
. Here b
1
measures how the sensitivity of borrower default to default option value varies with time
series factors u
t
, which include business cycle, sentiment, and other indicators that we dis-
cuss in the next section.
23 Here HPI return is calculated as log(HPI
t
/HPI
t-4
), and we use one-quarter lag.
24 Certainly, due to data limitations, our measure of income shock is not perfect. If exact information
about borrower-level income and its change becomes available in the future, one can further test
this hypothesis.
25 We conduct some tests whereby we relax this assumption and allow all the covariates to vary
over time. Significant variation is evidenced only in the case of the default option.
Default Option Exercise over the Financial Crisis and beyond 173
Downloaded from https://academic.oup.com/rof/article/25/1/153/5893492 by guest on 19 February 2021
We now turn to the estimation of the competing risks proportional hazard model with
interaction terms. In contrast to the 3 year moving window estimates displayed in Figure 1,
here we pool all observations in the estimation of the hazard model. We focus on the
hypothesized drivers of the default option beta explored in Section 4.2, namely unemploy-
ment rate innovations, orthogonalized MSA consumer distress index, and a time dummy
for a possible structural break in 2009.
Model estimates for the default equation are reported in Table V. While the regressions
include a large number of loans, borrower, and locational controls, we focus on the table
on the interaction terms. In the first column, results are based on the full sample. As is con-
sistent with results in the panel data model, the estimated default option beta is higher for
states and time periods with higher unemployment rate innovations. In other words, bor-
rower sensitivity to negative equity varies with the economic cycle—borrowers are more
sensitive to negative equity and are more likely to pull the trigger on default in bad times.
Further, findings indicate that innovations in the unemployment rate are themselves
positively associated with default probability. As is also consistent with results of panel esti-
mation, lower levels of orthogonalized state-level consumer sentiment are associated with
higher likelihoods of loan default. We similarly find evidence of a structural break in de-
fault likelihood and behavior in 2009Q3. All things equal, borrowers are more likely to de-
fault after the third quarter of 2009; further, borrowers become more sensitive to negative
equity at that time.
26
As discussed below, that timing is coincident to implementation of a
major loan modification program (HAMP) that likely affected borrower priors regarding
receipt of a favorable loan modification conditional on loan default.
As discussed above, recent research has underscored the importance of crisis-period in-
come and liquidity shocks as a default trigger. One may inquire as to whether residual in-
come and liquidity effects not controlled for by our income change proxies bias our results.
While our panel beta regression results show that is not likely the case, as the income
change term is not significant in the regression, we conduct further analysis below to show
that variations in the estimated default option beta are not explained by the residual income
effect. First, we stratify the sample based on the borrower DTI ratio and re-estimate the
model using the bottom quartile of borrowers with DTI ratios below 29%. We hypothesize
that those borrowers are least likely to have liquidity issues and hence are less sensitive to
income shocks. Results in the middle column of Table V show that even among the bor-
rowers who are least likely to be liquidity constrained, there remain significant variations in
the default option beta with unemployment rate innovations, orthogonalized state con-
sumer distress index, and the 2009Q3 time dummy.
As shown in Table V, we also assess the robustness of results among loan samples
sorted by neighborhood income growth. The positive income growth subsample includes
loans in zip codes experiencing positive income growth. The sorting of loans is dynamic
so that the same loan can fall into different categories based on current income growth
in the zip code. We hypothesize that liquidity constraints should be the least binding in
neighborhoods with positive income growth. Results confirm the robustness of drivers
of the variation in negative equity even among the neighborhoods with positive income
growth.
26 We use the Wald test discussed in Andrews (1993) and test a number of alternative dates for the
structural break and find 2009Q3 is the most significant structural break point.
174 X. An et al.
Downloaded from https://academic.oup.com/rof/article/25/1/153/5893492 by guest on 19 February 2021
Table V. Default option exercise and business cycle, sentiment and structural break
Notes: Table V reports the MLE estimates of the competing risks hazard model for default and prepayment based on a random sample of the event history data
described in Table II. Unemployment rate innovation is the current quarter unemployment rate divided by its four-quarter moving average and is based on BLS
data. Consumer distress index is a quarterly comprehensive measure of the average American household’s financial condition compiled by CredAbility and
made available by the St. Louis Fed. Orthogonalized consumer distress index is the residual from a regression where the state-level consumer distress index is
regressed on the state-level unemployment rate innovation, state-fixed effect, and year-fixed effect. Due to the availability of the consumer distress index, our
sample cutoff date here is March 2013, and we focus on nine representative states and the District of Columbia: Arizona, California, DC, Florida, Georgia, Illinois,
Massachusetts, Michigan, New York, and Texas. For the structural break, we test a number of alternative breaking points but find 2009Q3 is the best breaking
point based on model fit. The low-DTI subsample is loans with DTI less than 29% (the lower quartile). The positive income growth subsample is loans in zip code
that experience positive income growth. The sorting of loans is dynamic so that the same loan can fall into different categories based on the current income
growth in the zip code. Income growth is calculated based on IRS AGI data. Other variable definitions are discussed in Tables I and II. Standard errors are clus-
tered at the loan-level. ***, **, and * indicate 0.1%, 1%, and 5% significance, respectively.
Dependent variable: default hazard All loans Low DTI Positive inc. growth
Estimate SE Estimate SE Estimate SE
Default option unemployment rate innovation 0.038*** 0.009 0.035** 0.012 0.159*** 0.044
Default option orthogonalized consumer distress 0.039*** 0.009 0.030* 0.012 0.008* 0.004
Default option post-2009Q3 0.106*** 0.022 0.136*** 0.030 0.133*** 0.029
Default option 0.743*** 0.026 0.863*** 0.038 0.793*** 0.076
Default option squared 0.114*** 0.012 0.123*** 0.016 0.311*** 0.042
Unemployment rate innovation 0.300*** 0.010 0.261*** 0.012 0.405*** 0.018
Orthogonalized consumer distress index 0.180*** 0.007 0.167*** 0.008 0.024*** 0.001
Post-2009Q3 0.211*** 0.029 0.092* 0.037 0.062*** 0.014
Control variables Prepayment option, prepayment option squared, change in unemployment rate, change in unemployment rate
squared, LTV buckets, FICO buckets, DTI buckets, loan amount buckets, fist-time home buyer indicator,
property type, occupancy type, loan purpose, state FE, vintage FE
N 397,750 103,992 252,605
Default Option Exercise over the Financial Crisis and beyond 175
Downloaded from https://academic.oup.com/rof/article/25/1/153/5893492 by guest on 19 February 2021
We conduct a series of additional robustness checks. In so doing, we augment our model
specification to assess the effects of a “Woodhead”
27
measure (missed default opportuni-
ties). Results in Appendix Tables A2 show our findings regarding drivers of beta changes
are highly robust to that specification. Also, we estimate the model using annual cohorts.
This test addresses the concern that a changing mix of borrowers might have contributed to
the observed changes in the default option beta, even after controlling for a large set of bor-
rower characteristics. As displayed in Appendix Table A3, the estimated default option
betas are robust to the cohort specification, so as to underscore the primary findings of the
article.
Finally, to ensure our results are not merely driven by a specific sample of mortgage
loans, we also rerun our analysis using alternative loan samples. Specifically, we re-estimate
our models using a sample of private-label securitized mortgage loans from BBX. In that ex-
ercise, we run separate models by loan type for subprime, Alt-A, and prime jumbo loans as
well as a model with all loans pooled. We find consistent results.
28
We further conduct decomposition analysis to assess the economic significance of fac-
tors identified in the panel model. We do so by taking the aforementioned hazard model
results and simulating the impact of each factor on the default option beta and default
probability. The results are presented in Figure 5. The baseline results (blue line) show the
impact of negative equity on the hazard rate of default in a benign economic environment.
Consistent with Figure 2, the default hazard rate increases with negative equity, but the
marginal impact is modest. Moving on to the red line, here we assume a recession environ-
ment indicated by a sharp increase in the unemployment rate. As is evident, the sensitivity
of borrowers to negative equity increases significantly. Finally, we incrementally add the
sentiment factor (green line) and the 2009 structural break (purple line). Overall, among
primary drivers, local business cycle and consumer sentiment were each associated with
roughly 30–40% of the increase in default risk due to their impact on the default option
beta, while the 2009 structural break contributed the remaining 20–30%, depending on the
magnitude of borrower negative equity.
4.4 HAMP Program Effects
In the wake of the housing crisis, numerous government mortgage modification programs
were enacted with the aim of mitigating home foreclosure. Among the most notable was
the federal HAMP, which was implemented in the first quarter of 2009. The HAMP pro-
gram used federal subsidies to incentivize lenders to modify loans rather than foreclose on
defaulted borrowers. In the spirit of the “Lucas Critique,” we suspect that the enactment of
a major foreclosure abeyance program may have influenced the default behavior of mort-
gage borrowers, for example, borrowers may have become more likely to default to the ex-
tent a loan modification was forthcoming.
The existing literature provides ample evidence on strategic default. Riddiough and
Wyatt (1994b) and Guiso, Sapienza, and Zingales (2013) argue that a borrower’s delin-
quency decision may depend on the anticipated lender response (e.g., the likelihood of fore-
closure conditional on delinquency). Mayer et al. (2014) provide evidence of increased
borrower willingness to strategically default in response to a lender loan modification
27 See Deng and Quigley (2001) for a discussion.
28 Some of the results were shown in an earlier version of our article, while others are available
upon request.
176 X. An et al.
Downloaded from https://academic.oup.com/rof/article/25/1/153/5893492 by guest on 19 February 2021
program. As discussed above, in Table V, we report on estimation of elevated default prob-
abilities post-2009Q3. The structural break coincides with the timing of HAMP implemen-
tation.
29
Further, results show a sizable and significantly elevated default option beta for
the post-2009 period. Below we report on the related corroborating DID analysis.
For a loan to qualify for modification under the HAMP program, a number of criteria
must be met. First, only owner-occupied loans were eligible for modification under HAMP.
Second, the loan must have been originated prior to January 2009. Third, the remaining
balance on the loan must be less than $729,500. Fourth, the borrower’s DTI ratio at the
time of modification was required to be in excess of 31% as the intent of the modification
was to reduce borrowers’ monthly housing payments to no more than 31% of gross month-
ly income. Finally, there was a HAMP implementation window, which originally was set to
be from March 2009 to December 2012 but later was extended through 2016. We utilize
the above eligibility rules to conduct DID analysis of changes in borrower default option
exercise in the wake of the enactment of the HAMP program. Agarwal et al. (2017) use this
strategy to identify the impact of HAMP on loan renegotiations.
30
Similar to Agarwal et al. (2017), our DID control group comprised investor property
loans that did not qualify for modification under HAMP, whereas our treatment group
includes owner-occupied loans that may be qualified for HAMP pending other conditions.
We use the 2009Q3 as the treatment date. To avoid confounding effects and consistent
with HAMP program terms, we limit the sample to loans with a remaining balance below
the HAMP threshold of $729,500. For similar reasons, we also exclude loans with a DTI
ratio below 44%.
31
All of our loans were originated prior to January 2009. Note that our
DID test does not require a perfect identification of HAMP eligible loans or loans eventual-
ly modified via HAMP.
32
As long as one group of borrowers had a higher probability of
receiving a HAMP modification than the other group based on ex ante borrower expecta-
tions, we should be able to identify HAMP effects via our DID test.
Given well-known challenges in applying DID framework in the context of nonlinear
models such as the Cox hazard model (Ai and Norton, 2003; Karaca-Mandic, Norton, and
Dowd, 2012), we instead conduct our DID analysis using a generalized least squares esti-
mation of a linear default model. Table VI presents our DID regression results. The DID re-
gression takes the form
Y ¼ b
1
T þ b
2
TAfter þ b
3
After
x þ Z
0
c þ e; (9)
where T represents the treatment group, After represents the period after which the policy
was implemented, and the Z vector represents a vector of control variables. The dependent
variable Y takes the value of “1” if a loan defaults in a particular quarter and “0” other-
wise. Note first in Appendix Figure A2, the parallel trends exhibited in the default option
29 While implementation of HAMP commenced in 2019Q1, substantial modification volume dates only
from late 2009 and early 2010.
30 In contrast to Agarwal et al. (2017), our analysis focuses on borrower delinquency rather than
loan modification.
31 We do not have information on the front-end (payment-to-income) ratio in the GSE data. However,
we use a 44% back-end ratio cutoff is to ensure that the loans included in the analysis are all
HAMP eligible.
32 Not all HAMP applications that met those five criteria were approved and some fell out of the pro-
gram after the trial period.
Default Option Exercise over the Financial Crisis and beyond 177
Downloaded from https://academic.oup.com/rof/article/25/1/153/5893492 by guest on 19 February 2021
beta time series among the treated (owner-occupied) and control (investor) loans pretreat-
ment. However, as shown in Table VI, post-2009Q3, the treated owner-occupied loans ex-
hibit a statistically elevated default option beta. These findings are consistent with the
hypothesis that the federal program may have inadvertently resulted in elevated default pro-
pensities among borrowers in that group. The time window of our loan performance
records is 2007Q3–2011Q3. In an alternative specification, we conduct a DID analysis
where we utilize a narrower 2008–10 version of the test window. The alternative specifica-
tion yields similar results (see column 2 of Table VI).
We further conduct a number of placebo tests of our DID test. As shown in Table VII,
we first run the linear default model with a random breakpoint (2008Q3) where there is no
policy change so as to evaluate whether the DID regression results might simply reflect un-
controlled differences between our control and treatment groups. In the second placebo
test, both the “treatment” and control groups are loans with DTI below 29% and thus are
both HAMP ineligible. Results in Table VII indicate a lack of significance associated with
the treatment group beta in either placebo test.
Table VI. DID tests of the HAMP eligibility effect
Notes: Table VI reports the generalized least square (GLS) estimates of a linear default model
that uses the DID approach to test the HAMP eligibility effect on borrower default option exer-
cise. The DID test is in the form of Y ¼ (b
1
T þ b
2
T * After þ b
3
After)x þ Z
0
c, represents the treat-
ment group, After represents the period after which the policy was implemented, and the Z
vector represents a vector of control variables described in the table. Loans included in the test
are limited to those originated before January 2009 with DTI ratio above 44% and a remaining
balance of no more than $729,500. The HAMP payment-to-income ratio cutoff is 31%, but we
only observe DTI in our data, so we choose DTI cutoff of 44% to ensure the debt service ratio of
the selected loans is high enough to meet HAMP requirement. The treatment group is owner-
occupied property loans, which satisfy the HAMP occupancy requirement. The control group is
investor property loans that are not HAMP eligible. The event date is 2009Q3. In the first test,
the time window of our loan performance records is from 2007Q3 to 2011Q3, while in the se-
cond test, the time window is from 2008Q3 to 2010Q3. Standard errors are clustered at the
loan-level. ***, **, and * indicate 0.1%, 1%, and 5% significance, respectively.
Dependent variable: 0/1
default indicator
2007–11 data 2008–10 data
Estimate SE Estimate SE
Treatment group beta 0.007* 0.003 0.008 0.005
Treatment group Post
event beta
0.002** 0.001 0.004** 0.002
Post event beta 0.011*** 0.003 0.008** 0.003
Control variables Default option, default option squared, default option unemployment rate
innovation, default option orthogonalized consumer distress index,
unemployment rate innovation, orthogonalized consumer distress index,
post-2009Q3, prepayment option, prepayment option squared, change in
unemployment rate, change in unemployment rate squared, LTV buckets,
FICO buckets, DTI buckets, loan amount buckets, fist-time home buyer
indicator, property type, occupancy type, loan purpose, state FE, vintage FE
N 14,226 9,258
178 X. An et al.
Downloaded from https://academic.oup.com/rof/article/25/1/153/5893492 by guest on 19 February 2021
We acknowledge that it is challenging to ascertain the exact impact of HAMP as we do
not have a perfect counterfactual. However, our aforementioned results suggest that such a
nationwide program coupled with intense media coverage of default and default assistance
programs could have affected borrower behavior, as we argue in this article.
5. Conclusion
In the wake of the late-2000s implosion in house values, mortgage default skyrocketed.
While crisis period default commonly has been ascribed to the sizable run-up in borrower
negative equity, we show those loan terminations also were importantly precipitated by ele-
vated default option exercise. Results of time-varying coefficient hazard model estimation
indicate that for a given value of the mortgage default option, borrower propensity to de-
fault rose markedly during the period of the financial crisis, especially in hard-hit states.
Panel data analysis indicates that much of the variation in default option exercise can be
explained by the local business cycle, consumer distress, and federal policy intervention.
Our findings have implications for mortgage underwriting and pricing. From the per-
spective of credit risk management, results underscore the importance of model instability
and the appropriateness of time-varying coefficient models. Our study also provides guid-
ance on factors governing cross-section and time series variation in estimated default option
betas. Mortgage originators, investors, and regulators need to account for such shifts in pre-
dicted default behavior in their business planning and practice. Indeed, while the analysis is
beyond the timeframe of our study, our findings suggest substantial evolution in borrower
Table VII. Placebo test of the DID test of the HAMP eligibility effect
Notes: Table VII reports the GLS estimates of a linear default model. The tests here are in the
same form as those in Table VI except that in the first test we pick a random breakpoint
(2008Q3) where there is no policy change, and in the second test both the “treatment” group
and the control group are loans with DTI below 29% and thus are both HAMP ineligible. Loans
included in the test are also limited to those originated before January 2009 with a remaining
balance of no more than $729,500. Standard errors are clustered at the loan-level. ***, **, and
* indicate 0.1%, 1%, and 5% significance, respectively.
Dependent variable: 0/1
default indicator
Irrelevant event date Low DTI sample
Estimate SE Estimate SE
Treatment group beta 0.005 0.003 0.004* 0.002
Treatment group Post
event beta
0.001 0.002 0.002 0.002
Post event beta 0.003 0.002 0.003* 0.002
Control variables Default option, default option squared, default option unemployment rate
innovation, default option orthogonalized consumer distress index,
unemployment rate innovation, orthogonalized consumer distress index,
post 2009Q3, prepayment option, prepayment option squared, change in
unemployment rate, change in unemployment rate squared, LTV buckets,
FICO buckets, DTI buckets, loan amount buckets, first-time home buyer
indicator, property type, occupancy type, loan purpose, state FE, vintage FE
N 16,492 9,985
Default Option Exercise over the Financial Crisis and beyond 179
Downloaded from https://academic.oup.com/rof/article/25/1/153/5893492 by guest on 19 February 2021
response to negative equity in the wake of the 2020 COVID-19 pandemic and related mort-
gage policy interventions. We leave that analysis to future research.
Our findings also have implications for macroprudential policy. In that regard, there
has been substantial debate on whether the government should bail out borrowers via mort-
gage modification. Arguments against such programs point to borrower moral hazard,
whereby anticipated bailout of distressed borrowers may encourage irresponsible financial
behavior. Our findings suggest that federal foreclosure prevention and loan workout pro-
grams during the 2000s global financial crisis may have inadvertently incented higher levels
of default propensity, in turn suggesting adverse, unintended consequences of policies
designed to mitigate mortgage failure.
Data Availability
The data underlying this article were provided by Fannie Mae, Freddie Mc, CoreLogic
Analytics, and the Federal Reserve Bank of Philadelphia under license. Data will be shared
on request to the corresponding author with the permission of the aforementioned entities.
180 X. An et al.
Downloaded from https://academic.oup.com/rof/article/25/1/153/5893492 by guest on 19 February 2021
Appendix
Table A1. Negative equity and house price return volatility in the competing risks hazard model
Notes: Instead of using the default option calculated based on the equity position and house
price return volatility in the model, we use negative equity and house price return volatility as
standalone variables. A spline function is used for negative equity with cutoffs at 30%, 10%,
10%, and 30%. Standard errors are clustered at the loan-level. ***, **, and * indicate 0.1%, 1%,
and 5% significance, respectively.
Dependent variable:
default/prepay hazard
Default Prepayment
Estimate SE Estimate SE
Negative equity <30% 5.088*** 0.079 2.062*** 0.065
Negative equity 3010% 5.085*** 0.121 1.482*** 0.105
Negative equity 1010% 4.407*** 0.395 0.588 0.397
Negative equity 1030% 2.936*** 0.259 2.070*** 0.289
Negative equity >30% 2.107*** 0.143 1.511*** 0.168
House price return volatility 0.005* 0.002 0.079*** 0.007
Call option 0.180*** 0.013 0.908*** 0.011
Call option squared 0.072*** 0.007 0.038*** 0.007
Change in unemp. Rate 0.026* 0.012 0.293*** 0.011
Change in unemp. rate squared 0.038*** 0.007 0.009 0.005
LTV < 60 0.487*** 0.034 0.504*** 0.023
LTV 60–70 0.146*** 0.031 0.175*** 0.021
LTV 80–90 0.089*** 0.023 0.162*** 0.018
LTV > 90 0.072* 0.028 0.423*** 0.024
Credit score < 580 0.805*** 0.084 0.064 0.085
Credit score 580–620 0.391*** 0.038 0.004 0.043
Credit score 660–700 0.465*** 0.026 0.068* 0.026
Credit score 700–740 0.961*** 0.025 0.099*** 0.025
Credit score 740–780 1.490*** 0.025 0.163*** 0.025
Credit score > 780 1.986*** 0.027 0.189*** 0.026
DTI < 20 0.367*** 0.039 0.042 0.022
DTI 20–30 0.200*** 0.021 0.001 0.016
DTI 40–50 0.215*** 0.020
0.016 0.016
DTI> 50 0.349*** 0.027 0.035 0.024
Loan amount <10K 0.287*** 0.030 0.529*** 0.023
Loan amount 10–15K 0.023 0.028 0.270*** 0.021
Loan amount 15–20K 0.032 0.029 0.104*** 0.021
Loan amount 25–30K 0.021 0.036 0.093*** 0.026
Loan amount 30–35K 0.054 0.041 0.074* 0.030
Loan amount >35K 0.058 0.044 0.263*** 0.029
First-time home buyer 0.104*** 0.028 0.145*** 0.022
Condominium 0.133*** 0.029 0.051* 0.023
Planned-unit development 0.086*** 0.026 0.070*** 0.019
Investment property 0.194*** 0.032 0.118*** 0.025
Second home 0.143** 0.045 0.075* 0.032
Cash out refinance 0.440*** 0.023 0.100*** 0.018
Rate/term refinance 0.277*** 0.022 0.091*** 0.017
State FE Yes Yes
Vintage FE Yes Yes
Flexible baseline function Yes Yes
N 1,034,009
Default Option Exercise over the Financial Crisis and beyond 181
Downloaded from https://academic.oup.com/rof/article/25/1/153/5893492 by guest on 19 February 2021
Table A2. Default burnout and option exercise
Notes: Appendix Table A2 reports the MLE estimates of the competing risks hazard model for
default and prepayment based on a random sample of the event history data described in
Table II. The specification is the same as those in Table V except that we include an additional
variable, “Woodhead,” which is measured as the number of missed default opportunities since
loan origination by comparing negative equity and the payment status in each period. Standard
errors are clustered at the loan level. ***, **, and * indicate 0.1%, 1%, and 5% significance,
respectively.
Dependent variable:
default hazard
Estimate SE
Put option woodhead 0.086** 0.020
Put option unemployment
rate innovation
0.042*** 0.005
Put option orthogonalized
consumer distress index
0.030** 0.008
Put option post-2009Q3 0.028*** 0.005
Put option 0.932*** 0.037
Put option squared 0.166*** 0.022
Woodhead 0.303*** 0.082
Unemployment rate innovation 0.310*** 0.013
Orthogonalized consumer dis-
tress index
0.201*** 0.010
Post-2009Q3 0.206*** 0.043
Control variables Call option, call option squared, change in unemployment rate,
change in unemployment rate squared, LTV buckets, FICO
buckets, DTI buckets, loan amount buckets, fist-time home
buyer indicator, property type, occupancy type, loan purpose,
state FE, vintage FE
N 348,659
182 X. An et al.
Downloaded from https://academic.oup.com/rof/article/25/1/153/5893492 by guest on 19 February 2021
Table A3. Vintage hazard model results
Notes: Appendix Table A3 reports the MLE estimates of the competing risks hazard model for default and prepayment based on a random sample of the event
history data described in Table II. The model specification is exactly the same as in Table V, but here we run the model for each of the selected vintages.
Standard errors are clustered at the loan level. ***, **, and * indicate 0.1%, 1%, and 5% significance, respectively.
Dependent variable: default hazard 2003 2005 2007
Estimate SE Estimate SE Estimate SE
Put option unemployment rate innovation 0.027** 0.008 0.062*** 0.016 0.018* 0.007
Put option orthogonalized consumer distress index 0.062*** 0.017 0.042* 0.018 0.032 0.022
Put option post-2009Q3 0.076** 0.021 0.054* 0.020 0.007 0.038
Put option 0.846*** 0.056 1.106*** 0.033 1.036*** 0.032
Put option squared 0.077*** 0.012 0.165*** 0.027 0.002 0.026
Unemployment rate innovation 0.034 0.021 0.152*** 0.029 0.171*** 0.032
Orthogonalized consumer distress index 0.243*** 0.010 0.188*** 0.013 0.188*** 0.019
Post-2009Q3 0.008 0.069 0.120* 0.046 0.219*** 0.062
Control variables Call option, call option squared, change in unemployment rate, change in unemployment rate squared, LTV
buckets, FICO buckets, DTI buckets, loan amount buckets, fist-time home buyer indicator, property type,
occupancy type, loan purpose, state FE, vintage FE
N 324,370 261,918 248,852
Default Option Exercise over the Financial Crisis and beyond 183
Downloaded from https://academic.oup.com/rof/article/25/1/153/5893492 by guest on 19 February 2021
Figure A1. Negative equity spline beta estimates.
Notes: Instead of using the default option calculated based on the equity position and house price re-
turn volatility in the model, we use negative equity and house price return volatility as standalone vari-
ables. A spline function is used for negative equity with cutoffs at 30%, 10%, 10%, and 30%. During
2003 and 2007, the betas for certain segments of the spline function are not estimated due to too few
loans with negative equity in those segments.
0
0.005
0.01
0.015
0.02
0.025
0.03
Owner Investor
Figure A2. Parallel trend test for the DID test.
Notes: This figure plots the parallel trend test results for the DID test reported in Table VI. It shows the
default option betas of investor loans and owner loans, respectively, prior to and after HAMP. These
are estimates of a linear default model similar to those in Table VI. The difference between the two
groups of loans was stable prior to HAMP, as shown here.
184 X. An et al.
Downloaded from https://academic.oup.com/rof/article/25/1/153/5893492 by guest on 19 February 2021
References
Agarwal, S., Amromin, G., Ben-David, I., Chomsisengphet, S., and Evanoff, D. D. (2014):
Predatory lending and the subprime crisis, Journal of Financial Economics 113, 29–52.
Agarwal, S., Amromin, G., Ben-David, I., Chomsisengphet, S., Piskorski, T., and Seru, A. (2017):
Policy intervention in debt renegotiation: evidence from the home affordable modification pro-
gram, Journal of Political Economy 125, 654–712.
Ai, C. and Norton, E. C. (2003): Interaction terms in logit and probit models, Economics Letters
80, 123–129.
Ambrose, B. W., Buttimer, R. J. Jr, and Capone, C. A. (1997): Pricing mortgage default and fore-
closure delay, Journal of Money, Credit and Banking 29, 314 10.2307/2953696
An, X., Deng, Y., and Gabriel, S. A. (2011): Asymmetric information, adverse selection and the
pricing of CMBS, Journal of Financial Economics 100, 304–325.
An, X., Deng, Y., Rosenblatt, E., and Yao, V. W. (2012): Model stability and the subprime mort-
gage crisis, Journal of Real Estate Finance and Economics 45, 545–568.
Andrews, D. (1993): Tests for parameter instability and structural change with unknown change
point, Econometrica 61, 821–856.
Brueckner, J. K., Calem, P. S., and Nakamura, L. I. (2012): Subprime mortgages and the housing
bubble, Journal of Urban Economics 71, 230–243.
Bhutta, N., Dokko, J., and Shan, H. (2017): Consumer ruthlessness and mortgage default during
the 2007 to 2009 housing bust, Journal of Finance 72, 2433-2466.
Cai, J., Fan, J., Jiang, J., and Zhou, H. (2008): Partially linear hazard regression with
varying-coefficients for multivariate survival data, Journal of Royal Statistical Society B 70,
141–158.
Campbell, J. Y. and Cocco, J. F. (2015): A model of mortgage default, Journal of Finance 70,
1495–1554.
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015
Figure A3. House price measurement error over our study period.
Notes: Using the CoreLogic real estate deeds data and HPI, we regress individual house price returns
(based on repeated transactions) on HPI return. This figure plots the MAE of such a regression. Only
the top fifty zip codes ranked by the number of housing transactions are included. The chart shows
that the magnitude of house price measurement error does not coincide with the variation in default
option beta, as shown in Figure 1.
Default Option Exercise over the Financial Crisis and beyond 185
Downloaded from https://academic.oup.com/rof/article/25/1/153/5893492 by guest on 19 February 2021
Cleveland, W. S., Grosse, E., and Shyu, W. M. 1991. Local regression models, in J. M. Chambers,
and T. J. Hastie (eds.), Statistical Models in S. Wadsworth/Brooks-Cole, Pacific Grove, CA, pp.
309–376.
Corbae, D. and Quintin, E. (2015): Leverage and the foreclosure crisis, Journal of Political
Economy 123, 1–65.
Cotter, J., Gabriel, S., and Roll, R. (2015): Can metropolitan risk be diversified? A cautionary tale
of the housing boom and bust, Review of Financial Studies 28, 913–936.
Cunningham, D. F. and Hendershott, P. H. (1984): Pricing FHA mortgage default insurance,
Housing Finance Review 13, 373–392.
Demyanyk, Y. and Loutskina, E. (2016): Mortgage companies and regulatory arbitrage, Journal
of Financial Economics 122, 328–351.
Demyanyk, Y. and Van Hemert, O. (2011): Understanding the subprime mortgage crisis, Review
of Financial Studies 24, 1848–1880.
Deng, Y. (1997): Mortgage termination: an empirical hazard model with stochastic term structure,
Journal of Real Estate Finance and Economics 14, 309–331.
Deng, Y. and Gabriel, S. A. (2006): Risk-based pricing and the enhancement of mortgage credit
availability among underserved and higher credit-risk populations, Journal of Money, Credit
and Banking 38, 1431–1460.
Deng, Y. and Quigley, J. M. (2001): Woodhead behavior and the pricing of residential mortgages.
SSRN Working paper 288694.
Deng, Y., Quigley, J. M., and Van Order, R. (2000): Mortgage terminations, heterogeneity and
the exercise of mortgage options, Econometrica 68, 275–308.
Duffie, D., Eckner, A., Horel, G., and Saita, L. (2009): Frailty correlated default, Journal of
Finance 64, 2089–2124.
Elul, R., Souleles, N. S., Chomsisengphet, S., Glennon, D., and Hunt R. (2010): What “triggers”
mortgage default?, American Economic Review 100, 490–494.
Fan, J. and Zhang, W. (1999): Statistical estimation in varying coefficient models, Annals of
Statistics 27, 1491–1518.
Fan, J. and Zhang, W. (2008): Statistical methods with varying coefficient models, Statistics and
Its Inference 1, 179–195.
Foote, C., Gerardi, K. S., and Willen, P. S. (2008): Negative equity and foreclosure: theory and evi-
dence, Journal of Urban Economics 64, 234–245.
Gerardi, K., Herkenhoff, K. F.O’Hanian, L. E., and Willen, P. S. (2015): Can’t pay or won’t pay?
Unemployment, negative equity, and strategic default. FRB Atlanta Working paper.
Gerardi, K., Lehnert, A.Sherlund, S. M., and Willen, P. (2008): Making sense of the subprime cri-
sis, Brookings Papers on Economic Activity 2008, 69–145.
Ghent, A. C. and Kudlyak, M. (2011): Recourse and residential mortgage default: evidence from
U.S. States, Review of Financial Studies 24, 3139–3186.
Guiso, L., Sapienza, P., and Zingales, L. (2013): The determinants of attitudes toward strategic de-
fault on mortgages, Journal of Finance 68, 1473–1515.
Gyourko, J. and Tracy, J. (2014): Reconciling theory and empirics on the role of unemployment in
mortgage default, Journal of Urban Economics 80, 87–96.
Karaca-Mandic, P., Norton, E. C., and Dowd, B. (2012): Interaction terms in non-linear models,
Health Service Research 47, 255–274.
Kau, J. B., and Keenan, D. C. (1995): An overview of the option-theoretic pricing of mortgages,
Journal of Housing Research 6, 217–244.
Kau, J. B., Keenan, D. C., Mueller, W. J., III, and Epperson, J. F. (1992): A generalized valuation
model for fixed-rate residential mortgages, Journal of Money, Credit, and Banking 24, 279–299.
Keys, B. J., Mukherjee, T., Seru, A., and Vig, V. (2010): Did securitization lead to lax screening?
Evidence from subprime loans, Quarterly Journal of Economics 125, 307–362.
186 X. An et al.
Downloaded from https://academic.oup.com/rof/article/25/1/153/5893492 by guest on 19 February 2021
Korniotis, G. M. and Kumar, A. (2013): State-level business cycles and local return predictability,
Journal of Finance 68, 1037–1096.
Low, D. (2015): Mortgage default with positive equity. NYU Working paper.
Mayer, C., Morrison, E., Piskorski, T., and Gupta, A. (2014): Mortgage modification and stra-
tegic behavior: evidence from a legal settlement with countrywide, American Economic Review
104, 2830–2857.
Mayer, C., Pence, K., and Sherlund, S. M. (2009): The rise in mortgage defaults, Journal of
Economic Perspectives 23, 27–50.
Mian, A. and Sufi, A. (2009): The consequences of mortgage credit expansion: evidence from the
U.S. mortgage default crisis, Quarterly Journal of Economics 124, 1449–1496.
Mian, A. and Sufi, A. (2011): House prices, home equity-based borrowing, and the US household
leverage crisis, American Economic Review 101, 2132–56.
Mian, A., Sufi, A., and Trebbi, F. (2010): The political economy of the U.S. mortgage default crisis,
American Economic Review 100, 67–98.
Nadauld, T. D. and Sherlund, S. M. (2013): The impact of securitization on the expansion of sub-
prime credit, Journal of Financial Economics 107, 454–476.
Piskorski, T., Seru, A., and Witkin, J. (2015): Asset quality misrepresentation by financial interme-
diaries: evidence from RMBS market, Journal of Finance 70, 2635–2678.
Piskorski, T. and Tchistyi, A. (2011): Stochastic house appreciation and optimal mortgage lend-
ing, Review of Financial Studies 24, 1407–1446.
Quercia, R. G. and Stegman, M. A. (1992): Residential mortgage default: a review of the litera-
ture, Journal of Housing Research 3, 341–379.
Quigley, J. M. and Van Order, R. (1995): Explicit tests of contingent claims models of mortgage
default, Journal of Real Estate Finance and Economics 11, 99–117.
Rajan, U., Seru, A., and Vig, V. (2015): The failure of models that predict failure: distance, incen-
tives and defaults, Journal of Financial Economics 115, 237–260.
Riddiough, T. J. and Wyatt, S. B. (1994a): Wimp or tough guy: sequential default risk and signal-
ing with mortgages, Journal of Real Estate Finance and Economics 9, 299–321.
Riddiough, T. J. and Wyatt, S. B. (1994b): Strategic default, workout, and commercial mortgage
valuation, Journal of Real Estate Finance and Economics 9, 5–22.
Schwartz, E. S. and Torous, W. N. (1992): Prepayment, default, and the valuation of mortgage
pass-through securities, Journal of Business 65, 221–239.
Vandell, K. D. (1993): Handing over the keys: a perspective on mortgage default research, Real
Estate Economics 21, 211–246.
Vandell, K. D. and Thibodeau, T. (1985): Estimation of mortgage defaults using disaggregate loan
history data, Journal of the American Real Estate and Urban Economics Association 13,
292–316.
White, B. T. (2010): Underwater and not walking away: shame, fear, and the social management
of the housing crisis, Wake Forest Law Review 45, 971.
Default Option Exercise over the Financial Crisis and beyond 187
Downloaded from https://academic.oup.com/rof/article/25/1/153/5893492 by guest on 19 February 2021
Downloaded from https://academic.oup.com/rof/article/25/1/153/5893492 by guest on 19 February 2021
