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Consumption in the Great Recession:
The Financial Distress Channel
WP 19-13
Kartik Athreya
Federal Reserve Bank of Richmond
Ryan Mather
Federal Reserve Bank of St. Louis
José Mustre-del-Río
Federal Reserve Bank of Kansas
City
Juan M. Sanchez
Federal Reserve Bank of St. Louis
Consumption in the Great Recession:
The Financial Distress Channel∗
Kartik Athreya† Ryan Mather‡
José Mustre-del-Rı́o§ Juan M. Sánchez¶
August 27, 2019
Working Paper No. 19-13
Abstract
During the Great Recession, the collapse of consumption across the
US varied greatly but systematically with house-price declines. Our
message is that household financial health matters for understanding
this relationship. Two facts are essential for our finding: (1) the decline in house prices led to an increase in household financial distress
(FD) prior to the decline in income during the recession, and (2) at
the zip-code level, the prevalence of FD prior to the recession was
positively correlated with house-price declines at the onset of the recession. We measure the power of the financial distress channel using
a rich-estimated-dynamic model of FD. We find that these channels
amplify the aggregate drop in consumption by 7% and 45%, respectively.
Keywords: Consumption, Credit Card, Mortgage, Bankruptcy, Foreclosure, Delinquency, Financial Distress, Great Recession.
JEL Classification: D31, D58, E21, E44, G11, G12, G21.
∗
We thank seminar participants at the 2018 Stockman Conference and the 2019 SED
Meetings. The views expressed herein are those of the authors and should not be attributed
to the FRB of Kansas City, Richmond, St. Louis, or the Federal Reserve System.
†
Federal Reserve Bank of Richmond; e-mail: kartik.athreya@rich.frb.org
‡
Federal Reserve Bank of St. Louis; e-mail: ryan.mather@stls.frb.org.
§
Federal Reserve Bank of Kansas City; e-mail: jose.mustre-del-rio@kc.frb.org
¶
Federal Reserve Bank of St. Louis; e-mail: juan.m.sanchez78@gmail.com.
1
1
Introduction
A substantial proportion of US households experience financial distress (FD):
they are either unable to repay a debt as initially promised, have mostly
exhausted the options to borrow quickly, or both. This paper’s goal is to
show that FD matters for macroeconomics, and in particular, for the severe
reduction in consumption seen in the Great Recession.
A definitive feature of the Great Recession was the large decline in house
prices that occurred before the recession actually began (solid line in Figure
1). As a matter of accounting, this decline immediately damaged household
balance sheets. Moreover, importantly for the argument we make, as a matter
household liquidity and solvency, this decline increased the prevalence of FD
before the beginning of the recession (dashed lines in Figure 1). This provides
the first of two channels through which FD amplified the decline of aggregate
consumption during the recession.
.15
300
Figure 1: Evolution of Aggregate House Prices and Financial Distress
200
250
House Values, Thousands $
Fraction of Debt in DQ
.05
.1
Median Home Value, Right Axis
DQ 30
0
150
DQ 90
2000
2002
2004
2006
2008
2010
Note: The shaded area represents the recession. DQ 30 and 90 here respectively specify
the fraction of debt that is at least 30 days delinquent and 90 days delinquent.
The second channel by which FD matters for aggregate outcomes comes
from the novel fact we establish: using zip-code-level data, we show that
during the Great Recession there was a positive covariance between housing
2
wealth shocks and the incidence of “initial” FD. Figure 2 shows that regions
with larger FD in 2006 faced a larger decline in house prices during 2006-12.
Percent Change in Median Home Value, 2006−12
−35
−30
−25
−20
−15
Figure 2: Regional Changes in House Prices by Financial Distress
.1
.2
.3
% of Households in FD, 2006
.4
.5
Note: FD is measured with CL80, which is the share of individuals who used 80% or
more of their credit credit limit at some point in a given year. For ease of viewing, the
data have been divided into 40 bins with respect to CL80, and each dot represents the
mean of that bin weighted by the number of households in each zip code as of 2006.
The two channels we uncover do not by themselves establish the claim
we made: that FD matters for macroeconomic dynamics. This requires a
model, as the state of being in FD is a choice. The second contribution of
the paper is to provide a framework in which FD as an endogenous object
matters for consumption dynamics. We develop a model of consumption rich
enough to encompass heterogeneity in income risk, life-cycle consumption
needs, housing, debt repayment, and, importantly, nonrepayment and formal
default (bankruptcy). We then use our model to demonstrate the channels
at work and, critically, show via counterfactuals how they determine the
response of aggregate consumption. Our conclusion is that FD amplified the
drop in aggregate consumption by up to 45 percent.
A key reason for this finding is that in the model individuals in FD tend to
have higher marginal propensities to consume (MPC) out of housing shocks.
We corroborate this model-based implication by merging data on car regis3
trations with our dataset on FD. Indeed, we find that areas with higher FD
experienced larger consumption reductions in response to exogenous house
price shocks, even controlling for regional differences in income, net wealth,
and-critically-housing leverage.1 Overall, our results suggest the Great Recession was a bit of a perfect storm: not only did it increase the share of
people in FD (who tend to be more responsive), it also disproportionately
afflicted individuals in FD (because of the positive covariance between FD
and housing shocks).
While our focus is only on consumption, that interest is driven by the
standard (Old and New Keynesian) view that at high frequencies, what happens to consumption is important for the determination of income. Our
model helps us contribute to an understanding of income movements in the
sense that it allows for an empirically accurate distribution of FD across
geographies to play a role in determining consumption dynamics in more
aggregated (zip-code-level) outcomes. Under our maintained view of shortrun output determination, this yields insight into the steep fall in income or
output during the period following the housing price collapse.
On one level, FD resembles conventional measures of liquidity constraints.
As we show, one definition defines FD in just this way. Measures of indebtedness are also plausibly natural contributors to FD: given any fixed borrowing
capacity, more debt means less ability to handle the next shock that arrives.
Similarly, by limiting access to collateral, high leverage hinders access to future credit. It was shown in the seminal work of Mian, Rao, and Sufi [2013],
and surveyed in Mian and Sufi [2010], that those who had borrowed heavily
against their homes lost most or all of their wealth as house prices fell. In the
Great Recession, the attendant sudden reduction in credit access is plausibly
linked to the large drop in aggregate consumption–and later linked to output and employment as well. As we will argue, FD is broader than either,
especially when it is defined to include information encoded in past debt
repayment decisions, something done neither by current debt nor leverage.
This is because of the presence of costs associated with formal and informal
debt default (e.g., “stigma,” collections efforts, reduced future credit access,
administrative fees), whereby those in FD face the risk of having to choose
between not repaying debt and lowering consumption.
1
Of course, the differences in FD across regions are almost certainly not exogenous.
There are unobserved differences across households in FD and households that are not in
FD. In our model, that heterogeneity is captured by discount-factor heterogeneity as in
Athreya, Mustre-del Rı́o, and Sánchez [2019].
4
Two formal definitions of FD are those developed in Athreya, Mustre-del
Rı́o, and Sánchez [2019] and follow the logic laid out at the outset. The
first is having debts past due, and the second is having exhausted a large
fraction of available credit–as measured by credit card utilization rates. In
that work, both these measures of FD are shown to be relatively common
(i.e., high incidence) but also disproportionately accounted for by a smaller
group of households persistently in FD. Thus, the empirics of FD in the U.S.
suggest that individual consumption dynamics over longer-run periods are
affected for many, with some facing much more frequent difficulties.
Financial distress–defined as we have done–offers an encompassing, easily
measured, and timely way to gauge the vulnerability of households and the
economy at large to shocks. Encompassing, because unlike other measures, it
does not require knowledge of the items on households’ balance sheets, nor of
prices that are needed to compute measures such as net worth or leverage. For
example, one may well have little measured wealth but substantial amounts
of poorly measured wealth (e.g., cash in a mattress or, more often, assets with
uncertain liquidation values) or access to supplementary credit from hard-toview sources (e.g., family or business assets that can be liquidated). Similarly,
individuals with low levels of observable net worth may not be constrained.2
By contrast, seeing an individual become significantly delinquent, or utilizing
most if not all unsecured credit, is far more telling. It is unlikely, given
the costs associated with being delinquent or utilizing typically expensive
unsecured credit, that there are hidden sources of cheap credit available or
that the household seeks to increase its net worth position in preparation
for retirement, and so on. More importantly, since the marginal cost of
credit is what determines the marginal propensity to consume (MPC), and
the latter is central to accounts of macroeconomic susceptibility to shocks,
FD is a window into both individual and aggregate MPCs. As for its ease of
measurement and timeliness, our measures of FD are built on rich (individuallevel) and frequently updated credit bureau data, precisely what Athreya,
Mustre-del Rı́o, and Sánchez [2019] exploit.
2
Think of those in middle age who are beginning wealth accumulation for retirement.
At the other end of the spectrum, those with high observable wealth or net worth may be
significantly constrained due to debt and other potentially more informal future obligations
not easily seen.
5
1.1
Related literature
In addition to the work cited above, on which we build most closely, our work
is tied to several recent papers. First, Patterson [2018] documents that individuals with higher marginal propensities to consume out of income shocks
are also those whose earnings are cyclically more sensitive. She shows that
this positive covariance is large enough to increase shock amplification by
40 percent over a benchmark in which all workers are equally exposed. Our
paper complements hers by focusing on marginal propensities to consume
out of housing wealth shocks and documenting that the covariance between
these shocks and financial distress amplifies housing shocks. Second, Herkenhoff and Ohanian [2012], Herkenhoff [2013], and Auclert and Mitman [2019]
demonstrate that the ability of households to default on debt changes macroeconomic dynamics. While Herkenhoff and Ohanian [2012] and Herkenhoff
[2013] emphasize the importance of default for the dynamics of unemployment, Auclert and Mitman [2019] consider the Keynesian channels of aggregate demand (via sticky prices and the attendant AD externalities à la
Blanchard and Kiyotaki [1987]). Campbell and Cocco [2007], Aladangady
[2017], and Aruoba, Elul, and Kalemli-Ozcan [2018] use individual-level data
to investigate the consumption response to a change in house prices. Campbell and Cocco [2007] focus on the differences between the life cycle and
homeownership. Aladangady [2017] and Aruoba, Elul, and Kalemli-Ozcan
[2018] obtain empirical results in line with our finding that greater FD is associated with higher MPCs. Those papers use zip-code-level data to highlight
the importance of household financial constraints in shaping consumption
responses. We connect these findings to FD, emphasize the importance of
the geographical distribution of FD and house price shocks, and use a lifecycle model to compute counterfactual exercises. Lastly, our finding on the
positive covariance between initial FD and subsequent house price declines at
the zip-code level is related to Piazzesi and Schneider [2016]. They document
that during the 2000s cheaper houses experienced a stronger boom-bust cycle
than more expensive ones using city-level data from Zillow. Consistent with
their fact, we find that zip-codes with higher initial FD, and subsequently
larger house price depreciations, also tend to have cheaper homes in 2006.
There are several papers analyzing the decline in consumption after house
price shocks or, more generally, during the recession. Berger, Guerrieri,
Lorenzoni, and Vavra [2018] was the first paper to study how prices affect consumption in a heterogeneous agent model with incomplete markets.
6
They show how consumption responses depend on factors like the level and
distribution of debt, the size and history of house price shocks, and the level
of credit supply. Kaplan, Mitman, and Violante [2019] build a quantitative
model with long-term mortgages and default to study which are the necessary shocks to account for the joint evolution of house prices and consumption
during the recession. Their key new component is the change in expected
house price growth. Finally, Garriga and Hedlund [2017] use a model of housing search to show that an endogenous decline in housing liquidity amplifies
the decline in consumption during the Great Recession.
The remainder of the paper is structured as follows. In Section 2, we
lay out the key facts related to the geographic variation in FD in the U.S.–
as of 2006. We then show empirically how this map contains predictive
power for the observed variation in the size of house price shocks. With
those facts established, we turn in Section 3 to our model, which as stated
above, is very rich and hence capable of incorporating the desired margins
of adjustment–and the costs associated with those adjustments. Section 4
presents the parameterization. Section 5 contains the results, and Section 6
offers concluding remarks.
2
FD and the Great Recession
This paper will make use of two main definitions of FD developed by Athreya,
Mustre-del Rı́o, and Sánchez [2019]. The first of these, labeled DQ30, gives
the percentage of people who are at least 30 days delinquent on a credit
card payment at some point during the year. The second measure, which
we label CL80, is defined as the percentage of people within a zip code who
have reached at least 80% of their credit limit over the same time interval.3
We demonstrate now that under either of our measures, FD varied substantially across geographies before the Great Recession, was correlated with
housing net worth shocks, and influenced a household’s reaction–in terms of
consumption spending–to these shocks.
3
A more complete definition of these and other definitions of FD used in this paper are
available in appendix section A.1.4.
7
2.1
Geographic Dispersion in FD by Zip Codes
FD, as we have defined it, provides a useful and timely indicator of the
financial health of a zip code that is easily accessible (in our case, via Equifax
data). Figure 3 shows that both of our measures across zip codes convey the
same message: the incidence of FD varied widely, even relatively regionally,
in 2006, were highest in the Deep South and some coastal areas, and lower in
the upper Midwest and Great Plains.4 Indeed, no state can be characterized
as having entirely high or low FD. What is more, these national pictures
mask a high degree of dispersion in individual cities. Take, for example, two
contiguous zip codes in St. Louis, Missouri: 63110 to the east and 63105
to the west. In 2006, 5.8% of households in the west were in FD (here,
by the 30-day delinquent standard) on a credit card payment, while the
incidence was almost triple that in the east, at 16.1%. When housing prices
collapsed starting in 2006, the west lost an average $31,123 of the value of
their homes, which is less than half of the average loss that occurred in our
sample. And though the east lost even less, just $22,386 on average, this
hides disproportionate loss. Taking the home value loss as a percentage of
net wealth, however, the west lost just .4% while the east lost a full 6.6%.
Clearly, then, the experiences of these two adjacent zip codes were very
different in terms of FD and wealth loss. This case is not an anomaly. In
our sample, the standard deviation of FD (here using DQ30) across counties
is .034, but the average standard deviation of FD across zip codes within a
county is roughly twice as high: a full .060. Similarly, while the standard
deviation of FD by the CL80 standard across counties is .036, the average
standard deviation among zip codes in the same county is again twice as
high, .073. Thus, aggregate statistics mask substantial heterogeneity in FD
prevailing in more disaggregated data.
The second fact we emphasize about the geography of FD is that as of
the eve of the Great Recession, the indcidence of FD exhibits a substantial
positive covariance with the size of the eventual fall in house prices. This
will be detailed in section 2.2.
The data displayed so far are, of course, purely cross-sectional. Does such
a snapshot convey the general state of consumers’ health and sensitivity to
shocks, especially over time? The answer depends on the persistence of FD.
Here, we emphasize a main finding of Athreya, Mustre-del Rı́o, and Sánchez
4
This fact is not unique to 2006; similar maps from other years up to the present day
reveal the same.
8
(a) DQ30
(b) CL80
Figure 3: National Maps of FD Dispersion in 2006
Source: FRBNY Consumer Credit Panel/Equifax.
9
[2019], who showed, using data at the individual level, that FD is remarkably
persistent under similar measures. For example, conditional on being in FD
today, an individual is roughly four times more likely to be in FD two years
from now as compared to the average person. Thinking, then, of a zip code
as a collection of such individuals, these measures provide a relatively stable
indicator of FD characteristics across time.
The foregoing supports our focus on cross-sectional measures across granular geographies. As we noted above, variation in outcomes across zip codes
is substantial. Table 1 summarizes the characteristics of zip codes by the
incidence of FD. Perhaps naturally, FD is inversely related to a variety of
other measures of economic health, wealth, and human capital.
Areas with high FD tended in 2006 to have lower incomes, net wealth,
and home values. Their lower wealth prevents them from sustaining higher
levels of debt, both in terms of housing debt and, perhaps more surprisingly,
credit card debt. This arises because despite using a higher proportion of
their available credit, zip codes with high FD also tend on average to have
significantly lower credit limits. On the other side, zip codes with low FD
enjoy the double bonus of having both a high credit limit and having used
a lower portion of that limit. Clearly, then, from an ex-ante perspective,
the latter is better situated to weather financial losses. In terms of human
capital, people in the highest FD quintile are less than half as likely to have
earned a high school diploma as those in the zip code drawn from the lowest
FD quintile.
The preceding is highly suggestive of the connection between FD and
broader financial health at the local level. Nonetheless, given that the probability of a person being in FD declines dramatically over the life cycle,5 it
might be worried that we are merely picking up differences in age across zip
codes. There is indeed some of this effect, but the difference in mean age
between the top and bottom quintile is just slightly over two years. Second,
the work of Mian, Rao, and Sufi [2013] is important to acknowledge here.
Their findings might suggest that in looking at FD, we are merely repackaging leverage. An important part of our empirics is that this is not what
is happening. We see from Table 1 that there is no consistent relationship
between housing leverage and FD. If anything, housing leverage seems to be
decreasing in FD. This is displayed more explicitly in Figure 4.
5
Athreya, Mustre-del Rı́o, and Sánchez [2019] document that the percentage of people
in FD declines by over 40% from age 25 until age 55.
10
Table 1: Descriptive Statistics by Quintile of FD, 2006
Quintiles of CL80
1
2
3
4
5
Income Per Household $000
Net Wealth Per Household $000
Median Home Value $000
108.1
990.9
388.7
85.84
704.4
334.1
Wealth
71.52 62.66
488.3 382.9
296.8 258.8
55.51
285.5
236.1
Less Than HS
HS
College
Age
9.540
21.54
68.92
45.01
Human Capital
12.35 14.91 16.51
24.03 25.70 27.37
63.62 59.38 56.13
44.37 43.82 43.64
18.13
29.00
52.87
43.29
Debt and Delinquency
% that Own a Home
0.717 0.677 0.652 0.644 0.628
% with Housing Debt
0.502 0.455 0.424 0.397 0.369
Housing Debt per Home Owner $000 208.5 176.8 156.2 132.8 118.5
CC Debt Per Household $000
5.100 4.851 4.494 4.323 4.094
Housing Leverage
0.475 0.481 0.474 0.450 0.443
CL80
0.126 0.186 0.227 0.270 0.342
% with Housing Debt and FD
0.097 0.145 0.179 0.226 0.294
Note: Here “housing” debt refers to a mortgage or home equity line of credit. Housing
leverage is then measured as housing debt divided by the total housing wealth in each
geography. All means are weighted by the number of households, save housing debt per
homeowner, which naturally is weighted by homeowners. “% with Housing Debt and
FD” gives the percentage of those with housing debt who are also in FD under the CL80
criterion.
11
.42
Housing Leverage Ratio
.44
.46
.48
.5
Figure 4: Correlation of Housing Leverage with FD (CL80) in 2006
.1
.2
.3
.4
CL80
Note: Housing leverage is here measured as housing debt (including mortgages and home
equity lines of credit) divided by the total housing wealth in each geography. For ease of
viewing, the data have been divided into 20 bins with respect to CL80, and each dot
represents the mean of that bin weighted by the number of households in each zip code
as of 2006.
12
Finally, given that we intend to look at the interaction between FD and
housing shocks, it may be worried that the differences in FD across zip codes
are driven mainly by people who do not own homes, especially because those
in high FD zip codes are somewhat less likely to own the home in which
they live. To examine this, we identify within the Equifax data whether
someone owns a home by whether they have either a mortgage or a home
equity line of credit. Of course, this method does not allow us to identify
homeowners who have completely paid off their homes and have no home
equity lines of credit. The “% with Housing Debt” row is included to show
the extent of this omission and reveals that our proxy for homeownership in
Equifax usually underestimates the percentage of households that own the
home they live in by about a third. This is in line with estimates of the
percentage of homeowners who have paid off their mortgages.
The last line of the table then shows that when we consider the fraction
of people identified in this way to both own a home and be in FD, the
resulting differences between quintiles are similar in magnitude to those of
FD considered directly. What is more, the omission of homeowners who do
not have housing debt leads this final row to be an underestimate. Adding a
third to the bottom row, which would be the approximate bias if homeowners
without housing debt had the same distribution of FD as homeowners with
housing debt, exceeds the difference between that and the unconditional
percentage in FD for every quintile. Thus, it is highly unlikely that our
results are being driven by people who do not own homes.
2.2
The Relationship between Housing Shocks and Financial Distress
A central feature of the Great Recession was the unprecedented size and geographic scope of declines in house prices. Figure 5 exemplifies this dynamic.
Each line plots the evolution of median home prices at the zip code level
grouped by quintile of financial distress. The lines suggest that by 2009,
regardless of FD, median home prices declined on average by 20% relative
to their 2006 levels. However, these lines also show a fairly systematic relationship between FD in 2006 and subsequent home price declines: zip codes
with higher FD in 2006 experienced large median home price declines.
In considering the implications of this drop in house prices for household balance sheets, it is useful to convey the lost housing wealth as a frac-
13
Figure 5: Evolution of House Prices by Quintiles of FD
Note: Weighted by owner-occupied housing units at the zip code level.
14
tion of net wealth. We follow Mian, Rao, and Sufi [2013] in defining net
wealth N W as the sum of housing wealth H and financial wealth F W less
debt D. In their framework, the housing net worth shock is then defined
H,i
i
i
as ∆log(p06−09 )H06
/N W06
using an appropriate housing price index pH,i . Our
methodology for constructing these and other variables at the zip code and
county levels is thoroughly described in appendix section A.1.
Figure 6 documents the major fact to be established in this section: the
incidence of the housing wealth shock upon zip codes was highly positively
correlated with household FD. That is, higher FD in 2006 was associated
with larger declines in housing wealth shocks in the ensuing three years of
significant recession. This fact is robust to numerous other measurements
of FD, including DQ30 and CL80 conditional on homeownership. Appendix
section A.2 shows the associated graphs for those cases.
Figure 6: Housing Wealth Shocks (2006-09) and FD (CL80) in 2006
Shock and FD (CL80)
−20
0
20
40
By quintiles of FD in 2006
1
2
3
4
FD
Housing Net Worth Shock
5
Sources: IRS SOI, CoreLogic HPI, FRBNY Consumer Credit Panel/Equifax, Census
Bureau. “FD” quintile means are weighted by the number of households in each zip code
as of 2006, and “housing net worth shock” quintile means are weighted by 2006 net
wealth.
To understand what is driving this correlation, consider the following
decomposition: we can separate the housing net wealth shock into two component parts, the change in home prices and the share of wealth that was
held in housing in 2006. We rewrite the shock definition as
15
∆log(pH,i )H i
i
∆log(pH,i
06−09 )H06
06−09
06
=
i
i
N W06
H06
{z
}
|
chg. in house prices
Hi
06
i
N W06
| {z }
share of wealth in housing
Setting each component in turn at its sample mean to isolate variation in
the other, we uncover the relative importance of each component to the
overall housing net worth shock. Figure 7 plots the resulting relationship
and shows that the effects of each are meaningfully correlated with FD. In
other words, the observed relationship between housing price shocks during
the Great Recession and FD would have existed regardless of whether changes
in home prices or the share of wealth people held in their homes were held
fixed across the country. This again points to a sort of “double whammy”
borne by communities with high levels of FD: they held a higher portion
of household wealth in their homes and faced steeper price losses on those
homes.
Figure 7: Decomposition of 2006-09 House Price Shock
Sources: IRS SOI, CoreLogic HPI, FRBNY Consumer Credit Panel/Equifax, Census
Bureau. Group means are weighted by net wealth in each zip code as of 2006.
16
In sum, the results from this section reveal that the Great Recession was
novel from the point of view of FD both because of the high incidence of
distress, but also, and perhaps more importantly, because of the positive
correlation between FD prior to the recession and subsequent house price
declines. Importantly, we show this positive correlation is not a simple artifact of a third variable (e.g., housing leverage), but rather a peculiarity of the
U.S. economy at the onset of the Great Recession. Central to our main thesis is how financial distress affects the pass-through of housing shocks into
consumption? Relatedly, how important was the documented relationship
between financial distress and house price shocks in determining this passthrough? Since the latter question is a counterfactual exercise it requires a
fully specified model to which we turn next.
17
3
A Dynamic Model of Financial Distress
The results from the previous section show that prior to the Great Recession
the U.S. economy was characterized by an elevated level of financial distress,
which was nonuniformly distributed across regions in the country. More
interestingly, the decline in house prices that precipitated the Great Recession
was also nonuniformly distributed across the U.S.; it was more severe in
regions with higher initial FD. Because financial distress is an endogenous
choice, a model is required to fully answer the question at hand, which is
how FD affected the transmission of housing shocks into consumption. In
this section, we present such a model. In the subsequent sections, we use this
model as a laboratory to assess the role played by financial distress in the
response of consumption to housing shocks and quantifying the importance
of the positive correlation between initial distress and house price shocks.
3.1
Benchmark Model
There is a continuum of finitely lived individuals who are risk-averse and
discount the future exponentially. All individuals survive to the next period
with probability ρn , which depends on age n. Each agent works for a finite
number of periods and then retires at age W . Agents are subject to idiosyncratic risk to their income y (which will be specified below). Each period,
agents choose non-durable consumption c, housing h, and financial assets (or
debt) a0 . Lastly, the model allows for preference heterogeneity of a restricted
form: individuals will differ in how they discount the future. Specifically, a
share pL of the population has a discount factor of βL , while the remaining
share has a discount factor of βH ≥ βL . The distribution of discount factors
will be estimated to be consistent with select household balance sheet facts,
following Athreya, Mustre-del Rı́o, and Sánchez [2019]. We next detail the
agent’s choices in the asset and real estate markets.
Agents enter each period either as nonhomeowners or homeowners. Rental
houses are of size hR , while owner-occupied houses vary in discrete sizes
h0 ∈ {h1 , h2 , . . . , hH }. To finance the purchase of nonrental houses, agents
borrow using mortgages b0 . Importantly, borrowing capacity in the mortgage market is endogenously given by a zero-profit condition on lenders due
to limited commitment of agents’ ability to repay mortgages (as detailed
below).
If agents choose to save (a > 0) in the financial asset a, they are paid
18
a risk-free rate r. However, when agents borrow (a ≤ 0), the price of their
debt q also depends on their borrowing, because debt may be repudiated and
lenders must break even. Debt repudiation can occur in one of two ways.
First, the agent may simply cease payment. This is known as delinquency
(DQ) or informal default. With delinquency, a households debt is not necessarily forgiven, however. Instead, debts are forgiven with probability η. The
probabilistic elimination of debts is meant to capture the presence of creditors periodically giving up on collections efforts. With probability 1-η, then,
a households rolled-over debt is not discharged, and, in this case, the household pays a penalty rate, rR , of interest higher than the average rate paid by
borrowers. Moreover, in any period of delinquency, we prohibit saving, and
since the agent did not borrow but in fact failed to repay as promised, their
consumption equals income. Second, as is standard in models of unsecured
debt, agents may invoke formal default via a procedure that represents consumer bankruptcy (BK). If this is the path chosen, all debts are erased, and
in the period of filing for bankruptcy, consumption equals income net of the
monetary cost f of filing for bankruptcy.
To better understand the structure of the model, Figures 8 and 9 provide
a simple visual description of the choices faced by agents who enter a period
as nonhomeowners or homeowners, respectively.
Figure 8: Decision tree of a nonhomeowner
RP , pay/save a
RBK , default on a
R, rent hR
RDQ , become delinquent on a
N , nonhomeowner
with (a, y)
Choose h0 and m0 ; pay/save a
B, buyer
Figure 8 shows that a nonhomeowner N with assets a and income y can
choose to either rent R or become a homebuyer B. If the agent chooses to
rent, then she must decide whether to pay/save RP her financial assets
a,
P P , pay/save
assets a
19 m
P , pay
P BK , default on a
P DQ , become delinquent on a
F , refinance
Pay/save assets a
RP , pay/save a
RBK , default on a
R, rent h
R
formally default on them
RBK , or cease repayment and therefore become
DQ
DQ , become
delinquent
. Alternatively, if theRagent
chooses
to become
a homebuyer,
N , non-R
delinquent
on a
then homeowner
she must choose the size of the house to by h0 and the mortgage to
with (a, y)
finance it m0 . We assume that in the period of purchasing a home, agents
are not able to repudiate
a in
anym0form.
B, buyer financial debt
Choose
h0 and
; pay/save a
Figure 9: Decision tree of a homeowner
P P , pay/save assets a
P BK , default on a
P , pay m
P DQ , become delinquent on a
F , refinance
m for m0
Pay/save assets a
DP , pay/save a
H, homeowner
with (a, y, h, m)
D, default on
m and rent hR
DBK , default on a
DDQ , become delinquent on a
SR , sell h
and rent hR
Pay/save a
Choose h0 and m0 ; pay/save a
SB , sell h
Next, Figure 9 shows the choices available to an existing homeowner H
with assets a, income y, living in a house of size h, and paying a mortgage
m. Homeowners have five options. First, they can choose to pay P their
1 whether to pay/save P P their financial
mortgage m. Then, they must decide
assets a, formally default on them P BK , or become delinquent P DQ . Second,
a homeowner can refinance F their existing mortgage m to obtain a new one
20
m0 . Much like a homebuyer, we assume that in the period of refinancing
a mortgage, agents are not able to repudiate financial debt a in any form.
Third, homeowners can choose to default D on their mortgage. As a result of this mortgage default, these agents immediately become renters and
therefore can also choose to repay DP or repudiate their financial debt via
delinquency DDQ or bankruptcy DBK . Fourth, homeowners can choose to
sell their house and become renters S R . We assume that in the period of
selling a home, agents are not able to repudiate financial debt a in any form.
Lastly, homeowners can choose to sell their house h and buy a new house of
size h0 with a new mortgage m0 . Effectively, this implies the same optimization problem as that facing a homebuyer, detailed above, and so agents are
not able to repudiate financial debt a.
In the next subsections, we sketch each decision problem and provide
some additional details. A formal description of the recursive problems is
presented in Appendix C.
3.1.1
Nonhomeowners
If the agent does not own a house, she must decide whether to rent a home,
R, or buy one, B. Agents who rent can meet their existing financial obligations (or save), become delinquent on current financial debts, or formally
default (bankruptcy). Meanwhile, agents who purchase a house must choose
the size of the house and a corresponding mortgage and pay existing financial
debts. We describe these problems below.
Renter and no financial asset default. A renter of discount factor type
j, with income y, who decides not to default on financial assets can only
choose next period’s financial assets a0 . Hence, the agent’s budget constraint
reads:
a
c + qj,n
(hR , 0, a0 , y)a0 = y + a.
Here y denotes income and q a is the price (i.e., discount) applied to financial
assets. As noted above, the fact that agents can repudiate debt means that
its price will reflect default incentives, which in turn depend on the agent’s
state-vector, and hence on housing, income, and their discount factor type.
Renter and bankruptcy. A renter of type j with income y, who decides
21
to formally default on financial assets a faces the following trivial budget
constraint: c = y − (filing fee), where f iling f ee is the bankruptcy filing
fee.
Renter and delinquency. An agent who is a renter and decides to skip
payments (i.e., become delinquent) on financial assets a faces the following
constraints:
c = y,
a0 = 0, with prob. γ,
a0 = (1 + rR )a, with prob. 1 − γ.
Here, γ is the probability of discharging delinquent debt, and rR is the rollover interest rate on delinquent debt.
Homebuyer. An agent who is buying a house and income y and assets
a must choose next period’s financial assets a0 , the size of their house h0 ,
and the amount to borrow for the house m0 . For a given tuple of income,
assets, savings, house size, and mortgage size, the agent faces the following
constraints:
a
m
c + qj,n
(h0 , m0 , a0 , y)a0 = y + a + qj,n
(h0 , m0 , a0 , y)m0 − Im0 >0 ξM − (1 + ξB )ph0 ,
m
qj,n
(h0 , m0 , a0 , y)m0 ≤ λph0 .
Here, p is the price of a house, and q m is the price of a mortgage. The mortgage price depends on the house size, mortgage amount, income, and the
agent’s discount factor type j. The second equation is a loan-to-value (LTV)
constraint implying that the LTV ratio cannot exceed an amount λ.
3.1.2
Homeowner
A homeowner’s problem is more complex. On the financial asset dimension,
homeowners must decide to default or repay their financial assets. On the
housing dimension, homeowners can : (i) pay their current mortgage, (ii) refinance their mortgage, (iii) default on their mortgage, or (iv) sell their house
22
and buy another one, or (v) become a renter. We describe these problems
next.
Mortgage payer and no financial asset default. Agents who decide
to pay their mortgage and their financial assets face the following budget
constraint:
a
c + qj,n
(h, m(1 − δ), a0 , y)a0 = y + a − m.
(1)
Notice that the bond prices these agents face depend on the size of their
house h, tomorrow’s mortgage size m(1 − δ), the financial assets borrowed
or saved a0 , income, and the agent’s discount factor type j. The parameter
δ captures the rate at which mortgage payments decay.
Mortgage payer and bankruptcy. Agents who decide to pay their mortgage but formally default on their financial assets have the following budget
constraint c = y − (filing fee) − m, where f iling f ee is the bankruptcy filing
fee and m is the current mortgage payment.
Mortgage payer and delinquency. Households who decide to pay their
mortgage but informally default on their financial assets face the following
constraints:
c = y − m,
a0 = 0, with prob. γ,
a0 = (1 + rR )a, with prob. 1 − γ.
Mortgage refinancer. An agent who chooses to refinance cannot default
on financial assets a, must prepay their current mortgage, choose next period’s financial assets a0 , and choose the amount to borrow b0 with their new
mortgage. This problem can be thought of as a special case of a homebuyer
who is “rebuying” their current home of size h but who has cash-on-hand
equal to income y, plus financial assets a, minus fees from prepaying their
current mortgage m. Thus, the constraints for this problem are:
23
a
m
c + qj,n
(h0 , m0 , a0 , y)a0 = y + a − qn∗ m + qj,n
(h0 , m0 , a0 , y)m0 − Im0 >0 ξM ,
m
(h0 , m0 , a0 , y)m0 ≤ λph0 .
qj,n
Here, qn∗ m is the value of prepaying a mortgage of size m with n remaining
periods worth of payments. Following Hatchondo, Martinez, and Sánchez
[2015] the pricing function q ∗ is:
1−
qn∗
=
1−δ
1+r
1−
n+1
, for n ≥ 1,
1−δ
1+r
where δ is the rate at which mortgage payments decay.
Mortgage defaulter and no financial asset default. An agent who
defaults on her mortgage and chooses not to default on her financial assets a
immediately becomes a renter and must choose next period’s financial assets
a0 . Thus, the budget constraint she faces is identical to that of a renter who
a
pays her financial assets: c + qj,n
(hR , 0, a0 , y)a0 = y + a.
Mortgage defaulter and bankruptcy. Using the same reasoning as
above, we can write the problem as a mortgage defaulter who chooses bankruptcy
(on financial assets) as the problem of renter who files for bankruptcy. Thus,
the budget constraint is simply:c = y − f iling f ee.
Mortgage defaulter and delinquency. Lastly, we can write the problem as a mortgage defaulter who chooses delinquency (on financial assets) as
the problem of renter who is also delinquent on existing debt:
c = y,
a0 = 0, with prob. γ,
a0 = (1 + rR )a, with prob. 1 − γ.
24
Seller to renter. Recall, a home seller who decides to rent cannot default on financial assets. Hence, this problem is simply that of a renter with
financial assets equal to a plus the gains from selling their current house.
Thus, the agent’s budget constraint reads:
a
(hR , 0, a0 , y)a0 = y + a + ph(1 − ξS ) − qn∗ m.
c + qj,n
(2)
Here, the term 1 − ξS is a transaction cost from selling a house with value
ph, and qn∗ m is the value of prepaying a mortgage of size m with n periods left.
Seller to other house. Finally, a seller who decides to buy another house
must also pay her financial obligations. Therefore, this agent’s problem is
just a special case of a homebuyer with cash on hand equal income plus current financial assets plus gains from selling the current house. As a result,
we can write the constraints for this problem as:
a
m
c + qj,n
(h0 , m0 , a0 , y)a0 = y + a + ph(1 − ξS ) − qn∗ m + qj,n
(h0 , m0 , a0 , y)m0
− Im0 >0 ξM − (1 + ξB )ph0 ,
m
qj,n
(h0 , m0 , a0 , y)m0 ≤ λph0 .
3.1.3
Mortgage prices
When an agent of type j, with income y and financial savings a0 , asks for a
mortgage that promises to pay m0 next period, the amount she borrows is
m
given by m0 qj,n
(h0 , m0 , a0 , y), where:
qnm (h0 , m0 , a0 , y) =
m
m
m
qpay,j,n
+ qprepay,j,n
+ qdef
ault,j,n
.
1+r
(3)
This equation reveals that the price of a mortgage depends on the likelihood that tomorrow this mortgage will be repaid (first term), prepaid (second term), or defaulted on. Recall, mortgage payment can occur alongside
25
financial debt payment, default, or delinquency. Meanwhile, mortgage prepayment occurs whenever the agent refinances, sells her current house and
rents, or sells her current house and buys another house. In all of these prepayment scenarios, financial debts cannot be repudiated. Lastly, mortgage
default can occur alongside financial debt payment, default, or delinquency.
Hence, under this formulation, mortgage prices internalize how financial asset
positions today and tomorrow affect the probability of mortgage default.
3.1.4
Bond prices
When an agent of type j, income y, house size h0 , and mortgage size m0 issues
debt and promises to pay a0 next period, the amount it borrows is given by
a
a0 qj,n
(h0 , m0 , a0 , y), where:
a
qj,n
(h0 , b0 , a0 , y) =
a
a
qpay,j,n
+ qDQ,j,n
.
1+r
(4)
a
. Conditional on
First, consider the price of payment tomorrow, qpay,j
being a nonhomeowner, this occurs in two scenarios: renter, no financial
asset default, and homebuyer. Conditional on being a homeowner, payment
occurs in five scenarios: mortgage payer, no financial asset default; mortgage
refinancer; mortgage defaulter, no financial asset default; seller to renter; and
seller to buyer. Regardless of home status, in all of these cases creditors get
paid the same amount per unit of debt issued by the household.
a
. Conditional
Next, consider the price given delinquency tomorrow, qDQ,j
on being a nonhomeowner, this occurs only when renters choose delinquency.
Meanwhile, conditional on being a homeowner, this occurs in two cases:
mortgage payer, delinquency; and mortgage defaulter, delinquency. In all
of these cases debt gets rolled-over at a rate (1 + rR ) with probability (1 − γ).
Importantly, though, tomorrow’s price of this rolled-over debt will depend
on housing status tomorrow. Hence, this bond pricing formula reveals that
bond prices interact with housing status as the latter affects the likelihood
of financial debt payment, default, and delinquency in the future.
3.2
Parameterization
Our approach to model parameterization is standard. We first directly set
values for a subset of the most standard parameters. Second, given these
26
first-stage values, we estimate the remaining parameters so that the modelsimulated data match some key empirical features.
3.2.1
Assigning first-stage parameters
Table 2 collects the parameters set externally. A period in the model refers
to a year; households enter the model at age 25, retire at age 65, and die
no later than age 82. We set the risk-free interest rate at 3%. In addition, we externally calibrate the parameters governing the income process,
bankruptcy filing costs, retirement, and mortality. We also externally set the
initial distribution of wealth-to-earnings to match the distribution of wealthto-earnings of 25-year-olds in the Survey of Consumer Finances between 1998
and 2016.
The utility u derived from consumption c and from living in a house of
size h displays a constant elasticity of substitution between the two goods:
u(c, h) =
((1 − θ)c1−1/α + θh1−1/α )(1−γ)/(1−1/α)
1−γ
where: γ denotes the risk aversion parameter, α governs the degree of
intra-temporal substitutability between housing and nondurable consumption goods, and θ determines the expenditure share for housing. Following
Hatchondo, Martinez, and Sánchez [2015], we set γ to 2, α to 0.5, and θ to
0.11.
As previously mentioned, we follow Athreya, Mustre-del Rı́o, and Sánchez
[2019] and assume agents can either be patient βH or impatient βL ≤ βH .
For simplicity, and following Athreya, Mustre-del Rı́o, and Sánchez [2019],
we set βH = 1.00, which leaves βL and the share of impatient types sL as
parameters to be determined.
The penalty rate for delinquent debt is set at 20% annually, following
Livshits, MacGee, and Tertilt [2007]. Bankruptcy filing costs are at 2.8%
of average income, or roughly $1,000, again following Livshits, MacGee, and
Tertilt [2007].
Turning to the income-process parameters, we consider restricted-incomeprofile (RIP) type income processes following Kaplan and Violante [2010].
During working ages, income has a life-cycle component, a persistent component, and an i.i.d component:
i
i
log(yn,t
) = l(n) + zn,t
+ in,t
27
where: l(n) denotes the life-cycle component, in,t is a transitory compoi
nent, and zn,t
is a persistent component that follows:
i
i
zn,t
= zn,t−1
+ ein,t .
We assume in,t and ein,t are normally distributed with variances σ2 and σe2 ,
respectively.
While in retirement, the household receives a fraction of the last realization of the persistent component of its working-age income using the replacei
ment ratio formula: max{A0 + A1 exp(zW
1 ), A2 }. In order to be consistent
with U.S. replacement ratios, we calibrate A0 , A1 , and A2 such that the
replacement ratio declines with income, from 69% to 14%, with an average replacement rate of 47%. The age-specific survival probabilities follow
Kaplan and Violante [2010].
Table 2: Externally set parameters
Parameter
l
W
ρn
a0
σ2
σe2
r
γ
α
θ
βH
ξB
ξS
ξ̄S
ξM
δ
A0
A1
A2
λ
f
rR
3.2.2
Value
–
65
–
–
0.063
0.0166
0.03
2
0.5
0.11
1.00
0.03
0.03
0.22
0.15
0.02
0.7156
0.04
0.14
1
0.028
0.2
Definition
Life-cycle component of income
Retirement age
Mortality age profile
Initial financial asset distribution
Variance of
Variance of e
Risk-free rate
Risk aversion
Elasticity of substitution
Consumption weight of housing
Discount factor of patient types
Cost of buying a house, households
Cost of buying a house, households
Cost of selling a house, banks
Cost of signing a mortgage
Payments decay
Replacement ratio
Replacement ratio
Replacement ratio
LTV limit
Cost of filing for bankruptcy/ average income
Roll-over rate on delinquent debt
Basis
Kaplan and Violante [2010]
U.S. Social Security
Kaplan and Violante [2010]
Survey of Consumer Finances 1998-2016
Kaplan and Violante [2010]
Kaplan and Violante [2010]
Standard
Standard
Standard
Hatchondo, Martinez, and Sánchez [2015]
Athreya, Mustre-del Rı́o, and Sánchez [2019]
Gruber and Martin [2003]
Gruber and Martin [2003]
Pennington-Cross [2006]
U.S. Federal Reserve
Average inflation
U.S. Social Security
U.S. Social Security
U.S. Social Security
Positive down payment
Livshits, MacGee, and Tertilt [2007]
Livshits, MacGee, and Tertilt [2007]
Estimating the remaining parameters
The remaining parameters to be determined are: βL the discount factor of
impatient types, sL the share of impatient types in the population, η the
28
probability of delinquent debt being fully discharged, hR the size of rental
houses, p the mean house price, and λ the loan-to-value ratio limit. We
estimate these parameters so that model-simulated data replicate some key
features of the data pertaining to homeownership, financial wealth, and FD.
Table 3 presents the model’s performance in matching the empirical targets. As can be seen from this table, the model does a good job of matching
salient features of the financial asset distribution, homeownership, home values relative to income, and initial loan-to-value ratios, which are critical to
get an empirically plausible housing leverage distribution. Additionally, the
model also matches average mortgage default rates and FD via delinquency
or bankruptcy.
Table 3: Calibration targets
Calibration target
Source
Data
Model
Mean (savings/inc)
SCF 2007
1.98
Homeownership rate (in %)
SCF 2007 68.00
Mortgage default rate (in %)
JKM [2013] 0.50
Bankruptcy rate (in %)
LMT [2007] 0.84
Mean DQ rate (in %)
Equifax
14.40
Mean (home value / income), owners SCF 2007
3.81
Mean LTV, owners
MIRS 2006 0.76
1.93
68.76
0.51
0.85
13.85
3.89
0.70
29
Table 4 presents the model’s implied parameter values. Similar to Athreya,
Mustre-del Rı́o, and Sánchez [2019], the model requires a significant amount
of discount factor heterogeneity to generate sufficient financial distress while
also generating an empirically plausible financial wealth distribution. Additionally, the model requires a reasonably high discharge probability of delinquent debt to make the informal default margin attractive relative to formal
bankruptcy. Lastly, the model does not require a very tight loan-to-value
constraint in order to generate empirically plausible loan-to-value ratios.
Table 4: Model parameter estimates
Parameter
Value
Low discount factor βL
0.51
(0.12)
0.59
(0.21)
1.17
(0.14)
6.25
(0.52)
0.32
(0.82)
0.90
(0.42)
Discharge prob. γ
Rental house size hR
House prices pH
share of pop. of type L
LTV λ
Notes: Asymptotic standard errors appear in parentheses.
30
4
Quantitative Exercises
We can now use the model to better understand how the relationship between
financial distress and housing wealth affected the dynamics of consumption
during the Great Recession. This requires, first of all, that we generate
within the model a stylized Great Recession. We then proceed to inspect the
micro-level mechanisms at work in our model and confirm they are at play
in the data.
4.1
Engineering a recession
A central aspect of the Great Recession was that it was characterized by a
large drop in home prices followed by a decline in income. Taking both as
exogenous and unanticipated, we replicate these events in our model. We
find that each of these two shocks amplify the other and that the magnitude
of amplification critically depends on the covariance between house price
shocks and financial distress. Thus, our model, even though in no direct
way engineered to generate such features, produces outcomes much like our
empirical findings.
Specifically, we first subject the stationary distribution of the economy
to an unanticipated (but permanent) house price decline. Importantly, to
mimic the empirics from the previous sections, we assume that house price
shocks are positively correlated with financial distress, but on average lead
to a 10% decline in house prices.6 In the period immediately following the
house price shock, we further subject the economy to an unanticipated (again,
permanent) 3% income decline, which is uniformly experienced across all
individuals. We then compute the drop in aggregate consumption. The top
row of Table 5 summarizes the results.
The first row of Table 5 suggests that the Great Recession, as captured in
these two shocks, caused a significant decline in aggregate consumption. We
see in our experiment that an average house price decline of 10%, followed by
a 3% decline in income, results in a 3.4% decline in aggregate consumption
(Row 1). Importantly, however, this headline number depends on correlation
between house price shocks and FD, the key empirical finding from the previous section. Row (2) of this table shows that if the 10% house price decline
6
In these exercises the house price decline for individuals in FD is roughly three times
larger than the house price decline for individuals not in FD, which roughly matches the
housing shocks faced by zip codes in the top quintile of FD versus first and second quintiles.
31
Table 5: Engineering a recession
Scenario
Av. % change
in C
(1) Corr. house shock then income shock
-3.4
(2) Uniform house shock then income shock
-2.9
-1.6
(3) Income shock alone
(4) Corr. house shock alone
-1.6
-1.1
(5) Uniform house shock alone
Av. % change
in FD
4.2
3.7
0.0
4.1
3.5
Notes: Here the average percentage change in consumption (FD) is the percentage change
relative to the steady-state level of consumption (FD) averaged between the year of the
initial shock and the next two years after the shock.
is uniformly experienced by all individuals regardless of FD, the resulting decline in aggregate consumption is less at 2.9%. Thus, the positive covariance
between house price shocks and FD leads to an additional 0.5 percentage
point drop in aggregate consumption when these shocks precede an income
shock. Alternatively, we can focus on the role of house shocks alone (and the
covariance structure) by comparing Rows (4) and (5). Here too we find that
housing shocks correlated with FD lead to an additional 0.5 percentage point
drop in aggregate consumption relative to a case when housing shocks are
uncorrelated with FD. Thus, what we label as the covariance channel of FD
amplifies the drop in consumption due to house prices by 45% (i.e., 0.5/1.1).
While the previous calculations highlight the importance of the covariance between house price shocks with FD, they do not address how house
price shocks and income shocks interact and amplify each other. To quantify the amplification/timing aspect, we can compare the individual effects
of housing shocks or income shocks alone with their joint effect. For example, adding Rows (3) and (4) combines the independent effects of income
and correlated housing shocks. They result in a 3.2 percentage point drop
in aggregate consumption, which is 0.2 percentage point less than what is
reported in Row (1), when the correlated housing shock precedes the income
shock. For uncorrelated housing shocks we can perform a similar calculation
by adding Rows (3) and (5) and comparing the result to Row (2). Adding
the two independent effects leads to a 2.7 percent decrease in aggregate consumption, which again is 0.2 percentage point less relative to the case when
the uniform housing shock precedes the income shock. Thus, what we label
as the amplification or timing channel of FD accounts for an amplification
32
of 6 to 7% (i.e., 0.2/3.2 or 0.2/2.7) in the drop in aggregate consumption,
depending on whether housing shocks are correlated or not.
Finally, the second column of Table 5 shows how the aggregate level of
FD responds to each of the shocks. The main conclusion from this column
is that FD mostly reacts to changes in house prices but not changes in income. Indeed, Row (3) shows that income shocks alone generate essentially
no change in FD, whereas Rows (4) and (5) suggest FD reacts strongly to
house price shocks, whether they are correlated with FD or not. To put Rows
(4) and (5) into perspective, recall the steady-state level of FD is approximately 14%. So, these percentage point differences are about 25 to 29% of
the steady-state level of FD.
Overall, the results from this subsection highlight three things. First,
the observed covariance between house price shocks and FD is quantitatively
important for generating drops in consumption compared to a scenario where
house price shocks are uniformly distributed across individuals regardless
of distress. Our calculations suggest correlated house price shocks increase
the drop in consumption relative to the uniform case by 45% (equivalent to
0.5 percentage points). Second, our model implies a nontrivial role for the
interaction between house price shocks and income shocks. Indeed, a naive
addition of the independent effects of these two shocks misses between 67% of the total drop in consumption (equivalent to 0.2 percentage points)
when the two shocks are combined. Third, the aggregate level of FD reacts
strongly to house price shocks but not to income shocks. Thus, this suggests
increases in FD are associated with large consumption drops. In the next
section, we discuss the direct link between FD and changes in consumption.
4.2
Inspecting the mechanism: the importance of FD
A key conclusion from the results in the previous subsection is that the covariance between FD and house price shocks significantly matters for the
response of aggregate consumption. In this section, we show that this occurs for two reasons. First, as previously described, the level of FD is very
responsive to house price shocks. Second, and more importantly, individuals
in FD in general have more elastic consumption responses to shocks. Thus,
with these two results it should come as little surprise that when house price
shocks land more heavily on people in FD, the response of consumption is
greater.
To see that individuals in FD tend to have more elastic consumption re33
sponses to shocks, consider Figure 10, which plots the marginal propensities
to consume (MPC) out of housing shocks for the two types of shocks we consider. The left panel of this figure plots the MPCs when shocks are correlated
with FD, whereas the right panel plots MPCs when housing shocks are uncorrelated with FD. Focusing on the left panel, the first two bars show that
individuals who in steady state are in FD have an MPC out of housing shocks
of roughly 11 cents (in model units of nondurable consumption) for every dollar of housing wealth lost. In contrast, individuals who in steady state are
not in FD have an MPC out of housing shocks of roughly 7 cents for every
dollar of housing wealth lost. Overall, when housing shocks are correlated
with FD, our model implies an MPC out of housing wealth of nearly 8 cents,
which is very close to the IV-estimate of the MPC out of housing wealth
reported by Mian et al. [2013] of 7.2 cents (depicted by the solid horizontal
line). The right panel of Figure 10 shows that qualitatively the same patterns emerge when housing shocks are uncorrelated, but quantitatively the
numbers differ. Indeed, even when housing shocks are independent of FD,
individuals in FD tend to have higher MPCs than those not in FD. However,
the magnitudes are larger. Individuals in FD have an MPC of roughly 16
cents, about 5 cents higher than in the case with correlated housing shocks.
Meanwhile, individuals not in FD have an average MPC of roughly 10 cents,
which is about 3 cents larger than in the case with correlated housing shocks.
That the MPCs rise with uniform housing shocks, particularly for those in
FD, reveals that in our model MPCs are a nonlinear function of the size of
the shock: higher for for smaller shocks, and lower for bigger shocks.
Table 6 shows that the decline in consumption for people in FD is particularly salient for homeowners, using the case of a uniform 10% house price
decline as an example. As can be seen from the first row of this table, the
average percent change for homeowners in FD ranges from -4.5 to -5.5 percent depending on the severity of FD. This contrasts sharply with the much
smaller average increases in consumption for homeowners not in FD and the
muted response of nonhomeowners in general.7
7
This is consistent with Aladangady [2017], who finds a negligible response of renters
to house price shocks.
34
Figure 10: MPC out of Housing Wealth in Model-Simulated Data
(a) Shock Covarying with β
(b) Uniform Shock
Note: The dark horizontal line corresponds to the MPC out of a dollar change in
housing wealth found by Mian et al. [2013] in their instrumental variable estimation. As
before, we report the “Average MPC” between the period of the shock and the period
after relative to a counterfactual in which the steady state had continued. “FD in Steady
State” refers to being in FD in either the first or second period of that counterfactual.
Table 6: Consumption Responses to a Housing Shock by Financial Distress
and Homeownership.
FD Group Av. % chg. share of share FD in
in C
pop
βL
shock
Homeowners in Year of Shock
High FD
-5.5
5.7
93.9
44.4
Low FD
-4.5
18.7
74.9
52.6
No FD
1.4
53.8
1.78
2.0
Nonhomeowners in Year of Shock
High FD
0.4
10.5
99.6
53.5
Low FD
2.5
1.8
61.2
30.9
No FD
-1.7
9.5
0.1
0.1
Note: The “No FD” group includes individuals who have not been in FD for the last six time periods.
Among those with some FD over the last six time periods, the 50th percentile of time spent in FD was
found, and agents were divided into “high” and “low” FD based upon that threshold. Note that because
this grouping is done based on the last six time periods, agents who have been in the model for fewer
than six periods are omitted.
Table 7 goes further into detail to understand the interaction between
homeowners and FD status in shaping their consumption response to house
price shocks. Specifically, this table presents the average consumption re35
sponses conditional on the optimal response absent the house price shock
(i.e., in steady-state) and conditional on the optimal response given the house
price shock. For example, among homeowners in the year of the shock, the
first row denoted by “Pay/Pay” displays the average consumption response
by individuals who in steady state pay their mortgage and still pay their
mortgage after the house price shock hits. Because Table 7 is meant to
illustrate the mechanisms at hand and because there are many possible combinations of steady-state/shock decisions, we choose to present only the most
quantitatively salient ones.
The key message from the top panel of this table is that among homeowners the refinance channel is critical for generating large declines in consumption for financially distressed homeowners. Note that individuals who in
steady-state refinance but given the shock pay their mortgage (Refi/Pay) see
their consumption decline by on average 5.7%. Recall, these are responses to
a 10% uniform house price shock, suggesting the pass-through of this shock
into nondurable consumption is over 50%. In the steady state of the model,
these individuals are using the refinance channel to extract equity from their
houses to finance nondurable consumption. Importantly, because a large
share of these individuals are effectively impatient (81% of them have low
discount factors) and have a history of being in FD, they face high borrowing
costs in the unsecured credit market; hence, they turn first to refinancing.
Once house prices decline, these individuals lose home equity and the refinance option becomes unavailable to them. As a consequence, many of these
individuals continue (or enter) in FD, face even higher borrowing costs (because now their net worth position is even worse), and cut their consumption
dramatically. Also note that individuals who refinance regardless (Refi/Refi)
also cut their consumption in response to the house price shock but by much
less since fewer of these individuals are in FD to begin with.
The bottom panel of Table 7 helps to clarify the mechanisms behind the
more modest responses to house price shocks of nonhomeowners. The bulk
of nonhomeowners not only do not own a house, but also do not plan to buy
one in steady-state or when house prices decline. We denote this group as
(Don’t Buy/Don’t Buy). Naturally, perhaps, their consumption moves very
little when the shock hits: the shock is essentially irrelevant. Nonhomeowners
who eventually are likely purchase a house regardless of the house price shock,
whom we denote as (Buy/Buy), increase their nondurable consumption quite
substantially because now houses are cheaper. Lastly, and in contrast to the
previous group, nonhomeowners who purchase a house because of the house
36
Table 7: Consumption Responses to a House Price Shock by Detailed Homeownership.
Steady State / Shock
Av. % chg. share of share
in C
pop
βL
Homeowners in Year of Shock
Pay/Pay
-0.9
45.4
14.7
Refi/Pay
-5.7
11.5
80.8
Refi/Refi
-1.8
6.1
10.2
Sell then Buy/Sell then Buy
5.1
1.2
21.1
Nonhomeowners in Year of Shock
Buy/Buy
6.0
2.5
38.9
Don’t Buy/Buy
-7.7
1.2
33.8
Don’t Buy/Don’t Buy
-1.1
27.3
47.5
Note: The first column categorizes individuals by their decisions under the steady state and their new
decisions under the shock. “Pay” and “Refinance” refer to paying or refinancing the mortgage. “Sell”
and “Buy” here refer to selling or buying homes. Some small categories have been omitted for brevity.
Av. % Change gives the percentage change from steady state between the year of the shock and the year
after the shock.
price shock (Don’t Buy/Buy) decrease their nondurable consumption quite
substantially because even though houses are cheaper, their financial asset
position still requires them to cut back on nondurable consumption to finance
housing.
To summarize, this subsection reveals three critical facts that help understand the aggregate consumption changes described in the previous section.
First, in our model, individuals in FD tend to have larger consumption responses to changes in house prices. Second, this is disproportionately due
to homeowners in FD. Third, the main reason why homeowners in FD react
strongly is because the refinance channel dries up with house price declines:
individuals who tend to smooth consumption by refinancing their mortgages
are also systematically more likely to be in FD. When house prices fall, they
lose home equity and therefore can no longer smooth consumption by refinancing. As a result, their consumption falls.
37
4.3
Are Financially Distressed Households Really More
Responsive to Housing Shocks?
The results from the previous two subsections show that in our model at an
aggregate level, higher FD is associated with larger consumption declines.
At the individual level, agents cut their consumption more drastically not
because of their FD status per se, but rather because of what this status
summarizes. Using the case of homeowners as an example, those in FD are
mostly impatient types with long histories of facing high borrowing costs
in the unsecured credit market. As a result, their consumption is mainly
financed through other means like mortgage refinancing. When housing and
income shocks arrive, these means vanish and they respond by aggressively
cutting consumption.
While we lack sufficiently detailed data at the individual level to corroborate this mechanism, we can still ask at a more aggregate level whether
consumption in regions with higher FD actually responds more to housing
price shocks? We argue that the answer is “yes.” To this end, we estimate
the marginal propensity to consume (MPC) out of housing shocks following
the seminal work of Mian, Rao, and Sufi [2013]. In particular, we want to determine whether MPCs vary in a significant fashion by FD holding constant
other regional features like income, wealth, etc.
Formally, we estimate regressions of the form:
∆Cti = α + β1 ∆HVti + β2 F Dti + β3 (∆HVti × F Dti ) + β4 Xti + it .
(5)
Here, ∆Cti represents the dollar change in consumption in geographic region
i between t and t + 1; ∆HVti is the change in house value; F Dti is the level
of financial distress in region i at time t; Xti is a vector of other regional
covariates that can be both in levels and changes; and it represents classical
measurement error. The coefficients of central interest are: (i) β2 , the coefficient on financial distress, and (ii) β3 , the interaction between financial
distress and housing shocks. To mitigate endogeneity problems, we follow
Mian, Rao, and Sufi [2013] and instrument for changes in house value using housing supply elasticities as in Saiz [2010]. Additionally, we focus on
new auto purchases as our measure of consumption at the county level. In
terms of timing, all initial levels are measured in 2006, while all changes are
measured between 2006 and 2009.
Table 8 reports the second-stage results of estimating equation (5). All
columns reveal statistically significant coefficients at the 0.001 level for house
38
price shocks (i.e., the change in home value between 2006 and 2009) and
the interaction of these shocks with financial distress. Comparing across
columns suggests that our estimated coefficients are robust to the definition
of financial distress we use (e.g., DQ30, CL80, or a combination of the two).
Importantly, because our regression includes interaction terms it is easiest to
interpret these coefficients with some examples.
Table 8: Auto spending at the county level (IV)
∆06−09 Home Value
DQ30 (current year)
∆06−09 Home Value × DQ30 (current year)
CL80 (current year)
∆06−09 Home Value × CL80 (current year)
CL80 and DQ30 (current year)
∆06−09 Home Value × CL80 and DQ30 (current year)
Observations
∆06−09 Auto Spending
(1)
(2)
(3)
-0.367***
-0.459***
-0.403***
(0.09)
(0.10)
(0.10)
-60.302
(31.47)
1.722***
(0.40)
-95.053***
(27.23)
1.611***
(0.34)
-87.530**
(33.51)
1.700***
(0.43)
623
623
623
Notes: Controls include change in income and change in financial wealth and the interaction of these
variables with the alternative variables of FD. We additionally control for the percent of households that
owned homes in 2006 and include a constant. All regressions are weighted by the number of
owner-occupied housing units in the county as of 2006. Standard errors appear in parentheses.
Sources: IRS SOI, CoreLogic HPI, IHS Markit, FRBNY Consumer Credit Panel/Equifax, Census
Bureau.
Figure 12 shows how the coefficients in Column (2) of Table 8 translate
into differing MPCs by level of financial distress. The dark set of bars represent the average MPC out of a dollar change in home values (between 2006
and 2009) for counties in a given quintile of financial distress as measured
by our CL80 measure. The lighter set of bars represent the corresponding
average MPCs under a specification where we also control for leverage. The
key observation from this figure is that MPCs rise quite dramatically with
financial distress, and this is true even after we account for differences in
leverage across low and high FD regions. Using the dark bars as an example,
while the top quintile of financial distress has an MPC out of a dollar change
in housing value of 15.3 cents, the representative individual from the bottom
quintile of FD has an MPC that is essentially zero (-1.7 cents).
39
Figure 12: Marginal Propensity to Consume out of a Dollar change in home
prices by Quintile of CL80 in 2006.
Notes: Group means are weighted by the number of owner-occupied housing units per
county as of 2006. The horizontal line corresponds to the mean MPC out of autos
estimated by MRS13.
Overall, these empirical results support the quantitative mechanisms highlighted in the previous subsections. Moreover, they are also consistent with
the recent literature on consumption responses to house price shocks as exemplified by Mian et al. [2013] and Aladangady [2017], among others. However, these results are not intended to establish a causal relationship between
financial distress and observed consumption declines. Indeed, our model suggests financial distress is a useful summary statistic capturing a history of
high borrowing costs induced, in part, by impatience. Rather, these results
corroborate our model’s quantitative implications.
40
5
Conclusions
In this paper, we uncover a previously unknown channel–financial distress–
that we argue mattered significantly for observed consumption dynamics during the Great Recession. Our contribution is to provide both empirics and
quantitative theory. Empirically, we show that prior to the Great Recession,
consumers were very differentially positioned with respect to their status in
the credit market. Specifically, zip-code-level data show large variation in
the proportion of individuals either delinquent on debts or having nearly
exhausted stated credit limits. Additionally, we demonstrate that regions
with a higher incidence of FD prior to the Great Recession systematically
suffered larger house price declines at the onset of the recession. We then
develop a rich dynamic model of consumption and credit use that allows for
variation in homeownership, debt repayment behavior, and creditor response
to consumer default risk. We use the model to show that FD amplified the
drop in aggregate consumption by up to 45 percent. A key reason for this
finding is that in the model individuals in FD tend to have higher marginal
propensities to consume (MPC) out of housing shocks. Thus, the aftermath
of the Great Recession should come as little surprise. Not only did the share
of people in FD increase, people in FD were also disproportionately buffeted
by the worst housing shocks.
In identifying FD, or proximity to it, as a key amplifier of shocks, our
findings reinforce the message first discovered and conveyed by Mian et al.
[2013] and Mian and Sufi [2010] that macroeconomic outcomes run through
household balance sheets and credit health. The shock of relevance here, that
of a sharp unanticipated drop in house prices, makes the lessons of our model
somewhat general. As Mian and Sufi [2010] have argued, housing busts lie
behind the most severe downturns that most economies experience. Our
work emphasizes that measures which capture individuals’ difficulties with
creditors, which we coin financial distress, are valuable in gauging macroeconomic vulnerability and provide information in addition to that encoded
in leverage or net worth. Our findings suggest that macroprudential policy
may be well advised to track either or both of the measures of FD we have
provided. Such measures, as we show, contain granular information relevant
to forecasting not only the severity of damage to regional consumption, and
in the short run, regional incomes arising from shocks to asset prices, but the
size of the shocks themselves.
41
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43
A
A.1
Empirical Results
Data
Summary statistics for our data are shown in Table 9.
Table 9: Descriptive Statistics
Count
Mean
Housing Net Worth Shock, 2006-9
Financial Net Worth Shock, 2006-9
Change in home value (ths $), 2006-9
Net Worth per Household (ths $), 2006
Income Per Household, (ths $), 2006
No. of hhds per county (ths), 2006
Housing Leverage Ratio, 2006
∆ auto spending per hhd (ths $), 2006-9
Housing Supply Elasticity, Saiz
Fraction in CL80, 2006
Fraction in DQ30, 2006
1083
1083
1083
1083
1083
1083
1083
1083
623
1083
1083
-0.073
-0.10
-60.73
522.96
73.68
429.5
0.487
-2.47
1.78
.237
.149
Housing Net Worth Shock, 2006-9
Financial Net Worth Shock, 2006-9
Change in home value (ths $), 2006-9
Net Worth per Household (ths $), 2006
Income Per Household (ths $), 2006
No. of hhds per Zip Code (ths), 2006
Housing Leverage Ratio, 2006
Fraction in CL80, 2006
Fraction in DQ30, 2006
6901
6901
6901
6901
6901
6901
6901
6901
6901
-0.12
-0.10
-67.65
556.45
76.00
13.03
0.46
.234
.144
S.D.
p25
p50
p75
County-level
0.10
-0.109
0.01
-0.109
84.96 -78.219
377.04 295.81
26.15
55.993
641.8
77.193
0.123
0.399
11.17
-8.564
0.99
0.975
.036
.213
.034
.126
-0.035
-0.102
-24.070
427.23
69.126
211.961
0.469
0.519
1.606
.236
.147
-0.008
-0.095
-4.122
622.69
82.413
486.391
0.570
4.850
2.340
.264
.171
Zip-code level
0.21
-0.17
0.02
-0.11
94.41
-99.63
847.86 203.05
50.95
47.58
5.78
8.91
0.19
0.34
.077
.180
.064
.097
-0.05
-0.10
-29.01
339.09
62.76
12.35
0.44
.231
.140
-0.01
-0.09
-4.71
593.87
87.40
16.33
0.55
.284
.185
Note: All statistics are weighted by the number of households in the first quarter of 2006 for each geography. p25, p50,
and p75 respectively give the 25th, 50th, and 75th percentiles.
Sources: IRS SOI, CoreLogic HPI, FRBNY Consumer Credit Panel/Equifax, Census Bureau, Zillow, Federal Flow of
Funds.
A.1.1
Building a geographically representative sample
Building a geographically representative sample over all the years considered
in this study from Equifax presents a slight challenge: small random samples
from FRBNY CCP/Equifax will give good estimates at the national level,
44
and even for the largest zip codes, but poor estimates for the smallest zip
codes. Using much larger random samples could fix this issue, but the resulting datasets become difficult to process. Instead, then, we divide the zip
codes for which we have IRS SOI data into 10 groups by population size and
over sample areas with lower population.
Specifically, we pull a 75% sample of individual Equifax records from the
smallest zip codes by population and decrease that percentage linearly until
pulling a 5% sample of Equifax records for the largest zip codes. In order to
remain in our sample for a given quarter, individuals must be between 25 and
65 years old, inclusive.8 Then, we correct for over sampling by reweighting
using population data from the 2000 and 2010 Census.
For the maps in Figure 3, we use this same method but with a larger
sample, pulling 100% of individual Equifax records for the smallest zip codes
by population and decreasing that percentage linearly until pulling a 50%
sample of the largest zip codes.
A.1.2
Household Net Wealth
The household wealth portion of our dataset was constructed at the zip
code and county levels using a method almost identical to that of MRS13.
Net wealth is defined as the sum of housing wealth H and financial wealth
F W less debt D, where F W can be further broken down into stocks S
and bonds B. H is calculated as the median home value multiplied by the
number of owner-occupied housing units in each geography. We use Zillow
data for home values and Census data on owner-occupied housing units.9
This is done separately for zip codes and for counties. With a measure of
total housing wealth in a geography thus defined, we calculate the housing
leverage ratio as the total housing debt in a geography divided by the total
housing wealth. Total housing debt is the mean housing debt, including
both mortgages and home equity lines of credit10 recorded in Equifax, in
8
Age is calculated using an individual’s recorded birth year, and so any records not
including a birth year are also excluded.
9
To fill in the missing years in Census data, we interpolate owner-occupied housing
units linearly for each zip code and county from 2000 to 2010. MRS13 did not use Zillow
data for home values and instead relied entirely on home price information from the 2000
Census tracked upward through time by the Core Logic price index. Using Zillow data
affords us the advantage of much wider data coverage.
10
This includes both the home equity installment balance and the home equity revolving
balance.
45
each geography multiplied by the number of households in that geography,
taken from the Census.
In the model calibration, we will at certain points use information from
Equifax on whether a person has mortgage or HELOC debt as a proxy for
whether they own a home. The advantage of this proxy is that because we
observe it at the individual level in Equifax, we can directly calculate the
percentage of people who are both under financial distress and have housing
debt. Its accuracy for this purpose is discussed in Section 2.1.
To construct F W , we began by using IRS Summary of Income (SOI)
data to calculate the fraction of national interest and dividends held by a
given zip code. Then, each zip code was apportioned a share of the national
stocks and bonds recorded in the Federal Flow of Funds11 corresponding to
that fraction. F W at the county level is simply calculated as the sum of F W
in its component zip codes.12 D is calculated in a similar fashion to F W .
First, we calculate the fraction of the total debt balance in our sample of the
Equifax dataset accounted for by a given zip code or county. Because our
method of pulling Equifax data intentionally over sampled geographic areas
with lower populations, we weight each geography’s debt by the number of
households it encompasses.13 Next, we assign each geography a portion of
the “Total Household and Nonprofit Liabilities” from the Federal Flow of
Funds equal to that fraction.
In addition to the types of debt that MRS13 tracks, we also include a
measure of credit card debt at the zip code and county levels. Here, we take
the mean credit card debt by household in our Equifax sample and multiply
that by the number of households in each geography.
With net wealth thus defined, we are in a place to calculate the change in
net wealth over the Great Recession. MRS13 calculated this with geography
index i as
i
i
i
i
∆N W06−09
= ∆06−09 log(pS )∗S06
+∆06−09 log(pB )∗B06
+∆06−09 log(pH,i )∗H06
11
Specifically, we consider stocks to be corporate equities, both directly and indirectly
held. Then, bonds are given by Total Financial Assets for households and nonprofits less
stocks.
12
To avoid double counting F W , this requires that something be done about zip codes
that span multiple counties. We elected to assign all of a zip code’s F W into the county
that most people in that zip code inhabit.
13
Data on the number of households in each zip code and county come from the Census
and was interpolated linearly from 2000 until 2010. More information on the Equifax
sampling procedure is provided in appendix section A.1.1.
46
where pS is given by the S&P500 index, pB is given by the Vanguard Bond
Index, and pH,i is the Core Logic house price index.14 They then refer to
i
∆06−09 log(pH,i ) ∗ H06
i
N W06
as the housing net worth shock, and we will analogously refer to
i
i
∆06−09 log(pS ) ∗ S06
+ ∆06−09 log(pB ) ∗ B06
i
N W06
as the financial net worth shock.
A.1.3
Consumption
We use data from R.L. Polk by IHS Markit to find the quantity of new
automobiles registered in each year by residents of each county. As noted by
MRS13, these data are advantageous relative to other sources of consumption
data because they record where the car buyer lives rather than the point
of sale, but disadvantageous in that they do not include the price of each
vehicle purchased. To resolve this issue, we follow after MRS13 in allocating
an annual share of the national Census Retail Trade amounts for “Auto,
Other Motor Vehicle” to each county equal to the share of new autos that
county purchased in the Polk data. By construction, then, the aggregate auto
expenditures in our sample will accurately reflect the national difference from
2006 to 2009, but measurement error will be present at the county level to the
extent that auto prices did not evolve in the same way across counties from
2006 to 2009. If the price of pickup trucks dropped more than other types
of cars, for example, and a particular rural county purchases mainly pickup
trucks, then our data will underestimate the decrease in car consumption for
that county just as MRS13 did.
A.1.4
Financial Distress
Several different metrics of FD are used to test the robustness of our conclusions. As defined in Section 2.1, DQ30 gave the percentage of primary
14
The Core Logic house price index is available at both the county and zip code levels,
and so we calculate the home price changes at each level directly rather than deal with
the possible errors that could arise from aggregating zip-code-level shocks to the county
level.
47
borrowers in the Equifax dataset who are at least 30 days delinquent on a
credit card payment during some quarter of the year. CL80 was similarly
defined for primary borrowers as the percentage of people who have reached
at least 80% of their credit limit during some quarter of the year.
With these two definitions in place, the remaining metrics combine the
two in different ways. “DQ30 and CL80 (current year)” calculates for each
individual the portion of quarters in a year that they spent with either a
credit card payment 30 days delinquent or having reached 80% of their credit
limit15 and then averages that percentage across the geography.
“DQ30 and CL80 (last 6 years)” does the same over the last six years,
calculating the portion of those quarters that an individual spent with either
a credit card payment at least 30 days delinquent or having reached 80% of
their available credit, and averaging this portion across all individuals in the
sample from a given geography. In order to avoid bias in this metric, we
require that an individual be in the sample for the entirety of those six years
in order to be counted.
Given that our sampling method over samples the smallest zip codes, we
weight the aggregation of these four financial distress statistics to the county
level by the number of households in each zip code.
A.2
Correlation between FD and the Housing Wealth
Shock
The motivating correlation between CL80 and the housing wealth shock of
2006-09 is robust to alternative definitions of financial distress, as can be
seen in Figure 13. “DQ120 between 2000 and 2006” refers to the percent of
people in a zip code who were 120 days or more delinquent on credit card
payments at least once between 2000 and 2006. “CL80 and Housing Debt”
gives the percentage of people in a zip code with both credit card debt at
least 80% of their credit limit and debt indicative of owning a house, be that
15
To give a clarifying example, say that there was an individual who in quarter 1 of 2006
was both at least 30 days delinquent on a credit card payment and had used over 80%
of their available credit card credit. Then, in quarter 2, they remained over 80% of their
credit card limit but did not have any credit card payments over 30 days delinquent. The
rest of the year occurred without any credit incident. On our metric, this individual would
have spent 50% of the year in financial distress. Similar calculations would be made for
all other individuals in our sample from his or her geography, and those numbers would
be averaged to reach the final result.
48
a mortgage or home equity line of credit. The levels of FD change depending
on the definition, but the corresponding pattern in the housing net worth
shock is immediately apparent in every case.
Figure 13: Correlation between the Housing Wealth Shock and FD under
Alternate definitions of FD.
Notes: “FD” quintile means are weighted by the number of households in each zip code
as of 2006, and “housing net worth shock” quintile means are weighted by 2006 net
wealth.
A.3
Regression
The first-stage OLS regression for Table 8 is provided in Table 10. As explained previously, Saiz’s measure of the elasticity of housing supply is used
as an instrument to identify exogenous variation in home value. For robustness, Table 11 presents an OLS regression using the same functional form
as Table 10. We have also computed the two-stage least squares regression
49
using the Lutz and Sand [2017](LS) update of Saiz’s housing price elasticity
measure. This provided for more observations, 1074, and did not change the
results.
It may be worried that there is another variable correlated with our measures of FD that better summarizes a households’ financial condition. However, our measures of FD seem to do as well or better in this respect than
other likely candidates. Iteratively controlling for the interaction between
the change in home values and the homeownership percentage, age, education, the unemployment rate, or average household leverage leaves our results
unchanged. The housing leverage ratio in particular is frequently suggested
as a possible source of error, so Figure 12 directly compares our baseline to
the results controlling for leverage, and Table 12 shows the corresponding
regression output.
Our results are also robust to varying methods for calculating the financial
wealth and housing shocks. MRS13 note that their method of calculating the
change in financial wealth assumes that every household holds the market
index of stocks and bonds. This assumption had to be made in their case
because the IRS SOI data had not been released from 2009 at the time
that their paper was written. Now, however, those data have been released,
and we can calculate the change in F W directly for each geography i as
i
i
F W09
− F W06
. Doing so does not change our results.
Similarly, in our baseline results we follow MRS13 to calculate the change
in home prices using the Core Logic price index defined at the zip code and
county level. Instead calculating the price change as the difference between
the Zillow median price in 2009 and 2006 does not alter our results.
B
B.1
Simulated Shocks
Quantifying the Covariance and Timing Channels
In Section 4.1, we compare the consumption effects of housing shocks and
income shocks in isolation with consumption in an economy where a housing
shock occurred the period before an income shock. The goal is to identify
what we have called a “timing effect,” the additional consumption losses
occurring because of the interaction of shocks across time. It is not immediately obvious how to make this comparison, however, and so here we make
our method for doing so clear.
50
Table 10: First-Stage OLS Regression
(1)
b/se
26.324∗∗∗
(2.96)
14.040∗∗∗
(3.22)
-13.967
(14.35)
Saiz Elasticity
∆06−09 Income
∆06−09 Income × DQ30 (current year)
∆06−09 Income × CL80 (current year)
(2)
(3)
∆06−09 Home Value
b/se
b/se
26.343∗∗∗
26.341∗∗∗
(2.96)
(2.96)
14.593∗∗∗
15.641∗∗∗
(4.15)
(3.92)
(4)
b/se
26.304∗∗∗
(2.96)
13.899∗∗∗
(3.99)
-12.948
(14.17)
∆06−09 Income × CL80 and DQ30 (current year)
-19.814
(16.28)
∆06−09 Income × CL80 and DQ30 (last 6 years)
∆06−09 Financial Wealth
-0.790
(0.70)
2.245
(3.70)
∆06−09 Financial Wealth × DQ30 (current year)
∆06−09 Financial Wealth × CL80 (current year)
-1.059
(0.93)
-1.088
(0.86)
-14.739
(21.33)
-0.514
(0.86)
3.475
(3.32)
∆06−09 Financial Wealth × CL80 and DQ30 (current year)
3.833
(3.97)
∆06−09 Financial Wealth × CL80 and DQ30 (last 6 years)
-0.000∗∗∗
(0.00)
0.000∗∗∗
(0.00)
0.000∗∗∗
(0.00)
-0.000∗∗∗
(0.00)
106.420∗∗
(32.29)
216.400
(181.27)
dYxY
dFWxY
dYxFW
dFWxFW
Percent of Households that Own Homes, 2006
DQ30
CL80
-0.000∗∗∗
(0.00)
0.000∗∗∗
(0.00)
0.000∗∗∗
(0.00)
-0.000∗∗∗
(0.00)
80.435∗
(31.75)
-0.000∗∗∗
(0.00)
0.000∗∗∗
(0.00)
0.000∗∗∗
(0.00)
-0.000∗∗∗
(0.00)
94.546∗∗
(31.93)
0.450
(4.82)
-0.000∗∗∗
(0.00)
0.000∗∗∗
(0.00)
0.000∗∗∗
(0.00)
-0.000∗∗∗
(0.00)
98.560∗∗
(31.18)
19.566
(170.17)
CL80 and DQ30 (current year)
174.526
(201.20)
CL80 and DQ30 (last 6 years)
-194.177∗∗∗
(41.91)
623
23.47
Constant
Observations
F
51
-138.684∗∗
(53.57)
623
23.53
-181.803∗∗∗
(49.99)
623
23.32
205.513
(235.41)
-190.110∗∗∗
(47.99)
623
23.51
Table 11: Auto Spending, County-Level
∆06−09 Home Value
∆06−09 Home Value × DQ30 (current year)
∆06−09 Home Value × CL80 (current year)
∆06−09 Home Value × DQ30 and CL80 (current year)
∆06−09 Home Value × DQ30 and CL80 (last 6 years)
∆06−09 Income
∆06−09 Income × DQ30 (current year)
∆06−09 Income × CL80 (current year)
∆06−09 Income × DQ30 and CL80 (current year)
∆06−09 Income × DQ30 and CL80 (last 6 years)
∆06−09 Financial Wealth
∆06−09 Financial Wealth × DQ30 (current year)
∆06−09 Financial Wealth × CL80 (current year)
∆06−09 Financial Wealth × DQ30 and CL80 (current year)
∆06−09 Financial Wealth × DQ30 and CL80 (last 6 years)
Percent of Households that Own Homes, 2006
DQ30
CL80
DQ30 and CL80 (current year)
DQ30 and CL80 (last 6 years)
Constant
Observations
Dependent Variable: ∆06−09 Auto Spending $000
(1)
(2)
(3)
(4)
b/se
b/se
b/se
b/se
-0.097∗∗
-0.120∗∗
-0.112∗
-0.120∗∗
(0.04)
(0.04)
(0.04)
(0.04)
0.855∗∗∗
(0.17)
0.616∗∗∗
(0.14)
0.786∗∗∗
(0.17)
1.020∗∗∗
(0.20)
-0.728∗
-1.404∗∗∗
-1.053∗∗
-0.990∗∗
(0.32)
(0.38)
(0.36)
(0.37)
5.429∗∗∗
(1.45)
6.435∗∗∗
(1.35)
6.295∗∗∗
(1.53)
7.645∗∗∗
(2.04)
0.334∗∗∗
0.417∗∗∗
0.345∗∗∗
0.280∗∗
(0.08)
(0.10)
(0.10)
(0.10)
-1.908∗∗∗
(0.40)
-1.597∗∗∗
(0.35)
-1.655∗∗∗
(0.43)
-1.691∗∗
(0.52)
7.406∗
8.694∗∗
8.186∗
10.383∗∗
(3.29)
(3.26)
(3.28)
(3.22)
-73.860∗∗∗
(18.56)
-69.113∗∗∗
(17.23)
-71.589∗∗∗
(20.54)
-70.408∗∗
(24.29)
5.881
10.182
7.410
3.571
(4.37)
(5.45)
(5.17)
(5.06)
1083
1083
1083
1083
Note: Regressions are weighted by the number of owner-occupied housing units in each County in 2006.
Additional controls not shown here include interactions between the levels and changes in housing
wealth, income, and financial wealth.
52
Table 12: Auto Spending at the County-Level Controlling for Leverage (IV)
(1)
b/se
-0.058
(0.11)
1.107∗
(0.44)
∆06−09 Home Value
∆06−09 Home Value × DQ30 (current year)
∆06−09 Auto Spending
(2)
(3)
b/se
b/se
-0.273∗
-0.152
(0.13)
(0.13)
(4)
b/se
-0.096
(0.13)
1.509∗∗∗
(0.39)
∆06−09 Home Value × CL80 (current year)
1.361∗∗
(0.49)
∆06−09 Home Value × CL80 and DQ30 (current year)
∆06−09 Home Value × CL80 and DQ30 (last 6 years)
∆06−09 Home Value × Housing Leverage Ratio
Housing Leverage Ratio, 2006
Hou. Leverage Ratio, 2006 × DQ30 (current year)
-0.241∗∗
(0.09)
19.940
(28.80)
-159.518
(137.46)
-0.203∗
(0.09)
72.274∗
(36.41)
-0.220∗
(0.09)
46.834
(35.80)
-318.021∗
(135.79)
Hou. Leverage Ratio, 2006 × CL80 (current year)
Hou. Leverage Ratio, 2006 × CL80 and DQ30 (current year)
-264.291
(161.99)
Hou. Leverage Ratio, 2006 × CL80 and DQ30 (last 6 years)
DQ30 (current year)
1.268∗
(0.58)
-0.238∗∗
(0.09)
28.291
(36.95)
-171.738
(194.17)
-23.770
(87.90)
CL80 (current year)
57.944
(79.66)
CL80 and DQ30 (current year)
14.773
(97.78)
CL80 and DQ30 (last 6 years)
Percent of Households that Own Homes, 2006
-2.699
(6.88)
7.445
(21.27)
623
Constant
Observations
-2.272
(5.96)
-9.676
(22.75)
623
-2.569
(6.31)
0.315
(23.82)
623
-11.671
(119.99)
0.036
(6.34)
0.240
(25.25)
623
Notes: regressions are weighted by the number of owner-occupied housing units in each county in 2006.
Additional controls not shown here include the change in income, the change in financial wealth, and
interactions between changes and levels for income, financial wealth, and housing wealth. The changes in
income and financial wealth are also interacted with leverage.
53
Figure 14: Decomposition of a Housing Shock Covarying with β followed by
an Income Shock
Figure 14 plots the log difference in aggregate consumption relative to the
steady state under varying shock possibilities. The average percentage change
in consumption for a covarying housing shock followed by an income shock
is given by (F +G+H)/3. To compare this with the two shocks in isolation, we
take their average percentage changes in consumption over the same three
periods and add them together: (A+B+C)/3 + (D+E)/3. Through the timing
effect, (F +G+H)/3 > (A+B+C+D+E)/3, as shown in the last panel of the figure.
An analogous calculation is made to find the timing effects behind a uniform
housing shock followed by an income shock.
B.2
Income Shocks
In Table 6, it was shown that being in FD increases an agent’s responsiveness
to changes in housing wealth. This also holds true during income shocks, as
54
Table 13: Heterogenous Response to Income Shock
%
Av. %
share share
FD Group Change
FD Shock
Change pop
low beta
C Year of
Full Economy
Total
-2.47
-2.45 100.00
32.00
13.81
Homeowners in Year of Shock
Total
-2.75
-2.64 78.15
26.00
9.26
High FD
-2.81
-2.94
5.74
93.89
26.27
Low FD
-3.08
-2.99 18.66
74.86
27.16
No FD
-2.57
-2.42 53.75
1.78
1.23
Nonhomeowners in Year of Shock
Total
0.12
-0.69 21.85
53.04
30.09
High FD
-2.37
-2.51 10.51
99.57
56.06
Low FD
-1.96
-1.81
1.80
61.21
37.10
No FD
5.11
2.84
9.53
0.14
0.10
Notes: The “No FD” group includes individuals that have not been in FD for the last
six time periods. Among those with some FD over the last six time periods, the 50th
percentile of time spent in FD was found, and agents were divided into “high” and “low”
FD based upon that threshold. Note that because this grouping is done based on the last
six time periods, agents who have been in the model for fewer than six periods are omitted
we now show in the analogous Table 13. Cho et al. [2019] find something
similar empirically, namely, that the consumption responses of households to
income shocks are increasing in household debt. They provide the intuition
that interest payments on debt form “consumption commitments” that are
costly to adjust, and so households respond by cutting consumption that
is not committed in this way more than would otherwise be expected. In
our model, being already in FD when a shock hits further limits households’
ability to alter such consumption commitments and amplifies the effect of
the shock on consumption that is not committed.
What is more, just as Section 4.1 showed that a housing shock can amplify
the effect of a subsequent income shock, an income shock can amplify the
effect of a subsequent housing shock. Figure 15 shows that the effect of a
uniform housing shock on consumption in the year that it occurs is over 10
times as pronounced when coming after an income shock.
55
Figure 15: Income Shocks Amplify the Effect of Subsequent Housing Shocks
Note: This graph plots the aggregate consumption changes under a variety of shock
combinations. An initial income shock is applied at year zero. Then, in the “Income
then Housing” line, a uniform housing shock is applied to the economy in year 1.
56
C
C.1
Recursive formulation of model
Nonhomeowner
If the household of type j does not own a house, it must decide whether or
not to default on its financial asset/debt holdings a and whether to stay as
a renter R or buy a house B. Given these two decisions, we can write the
lifetime utility of a household in this situation as:
(
Nj,n (a, z, ) =
)
Irent Rj,n (a, z, ) + (1 − Irent )Bj,n (a + en (z, ), z) . (6)
max
Irent ∈{0,1}
where earnings are en (z, ) = exp(f + ln + z + ). Here Irent equals one when
the household choose to rent, R is the lifetime value of renting, and B is the
lifetime value of buying a house. These value functions take the form of:
(
)
DQ
P
BK
Rj,n
(a, z, ), Rj,n
(a, z, ), Rj,n
(a, z, )
Rj,n (a, z, ) = max
,
(7)
and
P
Bj,n (a, z, ) = Bj,n
(a, z, ).
(8)
Notice that households that purchase a house are not allowed to default
(in any form) on credit card debt, so the last equality is only for expositional clarity. The super scripts in each value function represent whether the
household is defaulting or not on financial assets. We describe these problems
next.
Renter and no financial asset default. A household that is a renter
and decides not to default on financial assets can only choose next period’s
financial assets a0 :
P
Rj,n
(a, z, ) = max
0
a
s.t.
h
i
u(c, hR ) + βj E Nj,n−1 (a0 , z 0 , 0 )|z
a
c + qj,n
(hR , 0, a0 , z)a0 = e + a,
e = exp(f + ln + z + ).
57
(9)
Here q a is the price of borrowing financial assets, which depends on housing,
income states, and discount factor type j.
Renter and bankruptcy. A household that is a renter and decides to
formally default on financial assets a solves the following trivial problem:
BK
(a, z, )
Rj,n
h
i
0 0
= u(c, hR ) + βj E Nj,n−1 (0, z , )|z
s.t.
(10)
c = e − (filing fee),
e = exp(f + ln + z + ).
Here, filing fee is the bankruptcy filing fee.
Renter and delinquency. A household that is a renter and decides
to skip payments (i.e., become delinquent) on financial assets a solves the
following trivial problem:
DQ
Rj,n
(a, z, )
s.t.
h
i
= u(c, hR ) + βj E γNj,n−1 (0, z , ) + (1 − γ)Nj,n−1 (a(1 + r ), z , (11)
)|z
0
0
R
0
0
c = e,
e = exp(f + ln + z + ).
Here, γ is the probability of discharging delinquent debt, and rR is the rollover interest rate on delinquent debt.
Homebuyer. A household of type j that is buying a house and has cash
in hand a must choose next period’s financial assets a0 , the size of their house
h0 , and the amount to borrow in the mortgage for the house m0 .
To simplify the problem later, consider a individual choosing to buy a
house of size h0 ∈ {h1 ....., hm },
h
i
0
0
0
0 0 0 0
B̂j,n (a, z; h ) = max
u(c, h ) + βj E Hj,n−1 (h , m , a , z , )|z
(12)
0
0
a ,m
a
s.t. c + qj,n
(h0 , m0 , a0 , z)a0 =
m
(h0 , m0 , a0 , z)m0 − Im0 >0 ξM − (1 + ξB )ph0 ,
a + qj,n
m
qj,n
(h0 , m0 , a0 , z)m0 ≤ λph0 .
58
Here, q m is the price of borrowing m0 for a house, which depends on house
size, income states, and discount factor type j. The other constraints reflect
a loan-to-value constraint and that houses must come in discrete sizes. With
this notation, the problem of a homebuyer is simply
Bj,n (a, z) =
max
h0 ∈{h1 .....,hH }
B̂j,n (a, z; h0 ).
(13)
Notice that in the case of the renter the cash on hand is simply financial assets
plus earnings. Below, we will use the same value function B for individuals
in different situations (e.g., moving from one house to another).
C.2
Homeowner
The homeowner’s problem is more complex. On the financial asset dimension,
homeowners must decide to default or repay their financial assets. On the
housing dimension, homeowners can : (i) pay their current mortgage (if any),
(ii) refinance their mortgage (or ask for a mortgage if their don’t have one),
(iii) default on their mortgage, (iv) sell their house and buy another one, or
(v) become a renter. The value function H is given by the maximum of:
(
)
B
R
Hj,n (h, m, a, z, ) = max Pj,n (·), Fj,n (·), Dj,n (·), Sj,n
(·), Sj,n
(·)
(14)
where:
(
)
DQ
P
BK
Pj,n (h, m, a, z, ) = max Pj,n
(·), Pj,n
(·), Pj,n
(·) ,
(15)
P
Fj,n (h, m, a, z, ) = Fj,n
(·),
(16)
(
Dj,n (h, m, a, z, ) = max
B
Sj,n
(h, m, a, z, ) = SnB,P (·),
59
)
DQ
P
BK
Dj,n
(·), Dj,n
(·), Dj,n
(·)
,
(17)
(18)
R
Sj,n
(h, m, a, z, ) = SnR,P (·).
(19)
Notice that households that choose to refinance their mortgage cannot
default on financial assets in any way. Additionally, sellers must also pay
their financial assets.
Mortgage payer and no financial asset default. Households that
decide to pay their mortgage and their financial assets have the following
problem:
h
i
P
0
0 0 0
Pj,n
(h, m, a, z, ) = max
u(c,
h)
+
β
E
H
(h
,
m(1
−
δ),
a
,
z
,
)|z
(20)
j
j,n−1
0
a
s.t.
a
c + qj,n
(h, m(1 − δ), a0 , z)a0 = e + a − m,
e = exp(f + ln + z + ).
Mortgage payer and bankruptcy. Households that decide to pay their
mortgage but formally default on their financial assets have the following
(trivial) problem:
h
i
BK
Pj,n
(h, b, a, z, ) = u(c, h) + βj E Hj,n−1 (h0 , m(1 − δ), 0, z 0 , 0 )|z (21)
s.t.
c = e − filing fee − m,
e = exp(f + ln + z + ).
Mortgage payer and delinquency. Households that decide to pay
their mortgage but informally default on their financial assets have the following (trivial) problem:
DQ
Pj,n
(h, m, a, z, )
h
= u(c, h) + βj E γHj,n−1 (h0 , m(1 − δ), 0, z 0 , 0 )
+(1 − γ)Hj,n−1 (h0 , m(1 − δ), a(1 + rR ), z 0 , 0 )|z
s.t.
c = e − m,
e = exp(f + ln + z + ).
60
(22)
i
Mortgage refinancer. A household that is a house refinancer cannot
default on financial assets a and must prepay its current mortgage, choose
next period’s financial assets a0 , and choose the amount to borrow m0 with
their new mortgage:
P
Fj,n
(h, m, a, z, ) = B̂j,n (a + ph(1 + ξB ) − qn∗ m + en (z, ), z; h)
(23)
Note, this problem is just a special case of a homebuyer who is “rebuying”
their current home of size h, but now has cash-on-hand equal to earnings plus
financial assets minus fees from prepaying the previous mortgage m. Also
note that ph(1+ξB ) is simply an adjustment so the household doesn’t actually
pay adjustment costs of “rebuying” their current home.
Mortgage defaulter and no financial asset default. A household
that defaults on its mortgage and chooses not to default on its financial assets a immediately becomes a renter and must choose next period’s financial
assets a0 . Importantly, since we assume the cost of defaulting on your mortgage is a utility cost Φ, we can easily write this problem as the problem of a
renter minus the utility cost of mortgage default:
P
P
Dj,n
(h, m, a, z, ) = Rj,n
(a, z, ) − Φ.
(24)
Mortgage defaulter and bankruptcy. Using the same trick as above,
we can write the problem as a mortgage defaulter who chooses bankruptcy
(on financial assets) as the problem of a renter who files for bankruptcy:
BK
BK
Dj,n
(h, m, a, z, ) = Rj,n
(a, z, ) − Φ.
(25)
Mortgage defaulter and delinquency. Lastly, we can write the problem as a mortgage defaulter who chooses delinquency (on financial assets) as
the problem of a renter who is delinquent on existing debt:
DQ
DQ
Dj,n
(h, m, a, z, ) = Rj,n
(a, z, ) − Φ.
(26)
Seller to renter. Note that a seller who decides to rent (and not default
on financial assets) is simply a renter with financial assets equal to a plus
the gains/losses from selling their current house.
R,P
P
Sj,n
(h, m, a, z, ) = Rj,n
(a + ph(1 − ξS ) − qn∗ m, z, )
61
(27)
Seller to other house. This problem is just a special case of a homebuyer with cash on hand equal to earnings plus current financial assets plus
gains/losses from selling the previous house.
P,B
Sj,n
(h, m, a, z, ) = Bj,n (a + ph(1 − ξS ) − qn∗ m + en (z, ), z).
C.3
(28)
Mortgage prices
When a household asks for a mortgage that promises to pay m0 next period,
the amount it borrows is given by m0 qnm (h0 , m0 , a0 , z), where:
m
qj,n
(h0 , m0 , a0 , z) =
m
m
m
qpay,j,n
+ qprepay,j,n
+ qdef
ault,j,n
.
1+r
(29)
First, consider the price of payment tomorrow, qpay
m
qpay,j,n
(h0 , b0 , a0 , z) =
(30)
i
ρn E mort pay, no def + mort pay, BK + mort pay, DQ z ,
h
with:
h
i
m
0
00 00
0
P
mort pay, no def = IPj,n−1
1
+
(1
−
δ)q
(h
,
m
,
a
,
z
)
(31)
,
0
0
0
0
0
(h ,m ,a ,z , )
j,n−1
a
00
0
0 0 0 0
= âP,P
j,n−1 (h , m , a , z , ),
h
BK (h0 ,m0 ,a0 ,z 0 ,0 ) 1 + (1 −
mort pay, BK = IPj,n−1
i
m
δ)qn−1
(h0 , m00 , 0, z 0 )
, (32)
and
h
mort pay, DQ = IP DQ (h0 ,m0 ,a0 ,z0 ,0 ) 1 + (1 − δ) ×
(33)
j,n−1
i
m
m
γqj,n−1
(h0 , m00 , 0, z 0 ) + (1 − γ)qj,n−1
(h0 , m00 , a00 , z 0 ) ,
with:
a00 = (1 + rR )a0 and m00 = m0 (1 − δ).
62
Here, ρn is the age-specific survival probability, and I equals 1 whenever
the corresponding value function is the maximum of Pj,n−1 .
Next, consider the price of pre-payment tomorrow, qprepay . This occurs when
the household chooses to refinance their current house, or when they choose
to sell their current house. Importantly, in either case (and regardless of what
the household chooses to do immediately after selling their current house)
creditors receive value q ∗ :
m
qprepay,j,n
(h0 , m0 , a0 , z) =
(34)
E
h
IFj,n−1 (h0 ,m0 ,a0 ,z0 ,0 )
i
∗
R
B
q
z
.
+ISj,n−1
+
I
0
0
0
0
0
0
0
0
0
0
(h ,m ,a ,z , )
Sj,n−1 (h ,m ,a ,z , )
j,n−1
Finally, consider the price of defaulting on the mortgage tomorrow, qdef ault .
Creditors recover ph0 (1 − ξ¯S ). So, the price of default is simply:
m
0
0 0
qdef
ault,j,n (h , m , a , z) =
(35)
"
ρn E
C.4
#
IDj,n−1 (h0 ,m0 ,a0 ,z0 ,0 ) ph0 (1 − ξ¯S )
z .
m0
Bond prices
When a household issues debt and promises to pay a0 next period, the amount
it borrows is given by a0 qna (h0 , b0 , a0 , z), where:
a
qj,n
(h0 , m0 , a0 , z) =
a
a
qpay,j,n
+ qDQ,j,n
.
1+r
(36)
a
First, consider the price of payment tomorrow, qpay
. This occurs in the
following states: renter, no financial asset default; homebuyer, no financial
asset default; mortgage payer, no financial asset default; mortgage refinancer,
no financial asset default; mortgage defaulter, no financial asset default; seller
to renter; and seller to buyer. In all of these cases creditors get paid the same
amount per unit of debt issued by the household. Thus,
63
"
a
qpay,j,n
(h0 , m0 , a0 , z) = ρn E
P
IRj,n−1
(a0 ,z 0 ,0 ) + IBn−1 (a0 +en−1 (z 0 ,0 ),z 0 ,0 )
(37)
P
P
+IPj,n−1
(h0 ,m0 ,a0 ,z 0 ,0 ) + IFj,n−1
(h0 ,m0 ,a0 ,z 0 ,0 )
P
+IDj,n−1
(h0 ,m0 ,a0 ,z 0 ,0 )
#
+IS R,P
0
0 0 0 0
j,n−1 (h ,m ,a ,z , )
+ IS B,P
0
0 0 0 0
j,n−1 (h ,m ,a ,z , )
z .
Notice that the first two terms of the expectation can only occur if h0 =
hR , whereas the latter five only occur if h0 > hR . Additionally, the first
default term is unnecessary since mortgage default never occurs without the
depreciation shock when house prices are constant.
a
Next, consider the price given delinquency tomorrow, qDQ
. This occurs in
three states: renter, delinquency; mortgage payer, delinquency; and mortgage
defaulter, delinquency. In all of these cases debt gets rolled over at a rate
(1+rR ) with probability (1−γ). However, tomorrow’s price of this rolled-over
debt varies by state. Thus,
"
a
qDQ,j,n
(h0 , m0 , a0 , z) = (1 − γ)(1 + rR )ρn E IRDQ
0 0 0
j,n−1 (a ,z , )
+IDDQ
0
0 0 0 0
j,n−1 (h ,m ,a ,z , )
a
× qj,n−1
(hR , 0, a00 , z 0 )(38)
a
× qj,n−1
(hR , 0, a00 , z 0 )
#
a
+IP DQ (h0 ,b0 ,a0 ,z0 ,0 ) × qj,n−1
(h0 , m00 , a00 , z 0 )|z
n−1
with: a00 = (1 + rR )a0
and b00 = b0 (1 − δ).
Notice here too that the first term can only occur if h0 = hR , whereas the
latter two only occur if h0 > hR .
64
@FedFRASER