The full text on this page is automatically extracted from the file linked above and may contain errors and inconsistencies.
Household Financial Distress and the
Burden of 'Aggregate' Shocks
WP 20-12
Kartik Athreya
Federal Reserve Bank of Richmond
Ryan Mather
Federal Reserve Bank of St. Louis
Jose Mustre-del-Rio
Federal Reserve Bank of Kansas City
Juan M. Sanchez
Federal Reserve Bank of St. Louis
Household Financial Distress and the Burden of
“Aggregate” Shocks∗
Kartik Athreya† Ryan Mather‡
José Mustre-del-Rı́o§ Juan M. Sánchez¶
September 15, 2020
Abstract
The goal of this paper is to show that household-level financial distress
(FD) varies greatly, meaning there is unequal exposure to macroeconomic
risk, and that FD can increase macroeconomic vulnerability. To do this, we
first establish three facts: (i) regions in the U.S. vary significantly in their
“FD-intensity,” measured either by how much additional credit households
therein can access, or in how delinquent they typically are on debts, (ii)
shocks that are typically viewed as “aggregate” in nature hit geographic
areas quite differently, and (iii) FD is an economic “pre-existing condition”:
the share of an aggregate shock borne by a region is positively correlated
with the level of FD present at the time of the shock. Using an empirically
disciplined and institutionally rich model of consumer debt and default,
we show that in the shocks dealt by the Great Recession and in the initial months in the COVID-19 pandemic, FD mattered. Our model implies
that the uneven distribution of FD creates widely varying consumption
responses to shocks. This is true even when subjecting regions (with differing levels of FD) to the same shocks, which highlights the importance
of FD independently of its correlation with shocks.
Keywords: Geography, Consumption, Credit Card Debt, Recession,
Bankruptcy, Foreclosure, Mortgage, Delinquency, Financial Distress.
JEL Classification: D31, D58, E21, E44, G11, G12, G21.
∗
We thank seminar participants at the St. Louis Fed and Kansas City Fed, 2018 A. Stockman
Conference, SED conference, and Atlanta Fed “Joint Central Bankers Conference.” The views
expressed herein are those of the authors and should not be attributed to the Federal Reserve
Banks of Kansas City, Richmond or 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
Introduction
The primary goal of this paper is use data and quantitative theory to measure the
presence—and inequality of—financial distress (FD) across households and assess
the role it plays in how households respond to macroeconomic shocks. We will
also, in turn, assess how the aggregate state of financial distress in the economy
matters for macroeconomic outcomes.
Our paper has both an empirical and a structural component. Starting with
the data, we establish three main facts regarding financial distress in U.S. macroeconomic data. First, using proprietary data, we show that the prevalence of
household balance sheets with FD—as measured either by proximity to exhaustion of available credit commitments from lenders, or as having delinquent debt—
varies across regions. Second, we establish from the data that the “localized”
impact of an event associated with a major aggregate disruption, such as the
Great Recession or the COVID-19-induced downturn, also varies greatly. Third,
we show that the size of these localized shocks is positively correlated with the
level of FD present at the time of the shock. In other words, the most financially distressed households are also, apparently, the least fortunate in terms of
exposure to recessions.
To understand what these facts imply for households and the macroecononomy, we develop a sophisticated model of household consumption, debt, and
default decisions. We use the model, once disciplined by the facts, to measure
the impact of an empirically positive correlation between the aggregate shocks
hitting a region and that region’s level of FD at the time of the shock–hereafter
noted as it’s prior FD. Specifically, we examine how local responses and macroeconomic conditions are affected by the demonstrated positive correlation of a zip
code’s prior FD with (i) asset price declines (using measured declines in house
prices at the onset of the Great Recession) and (ii) income losses (using data
from the first months of the COVID-19 pandemic). Hereafter, we refer to these
episodes as “aggregate” shocks, using quotation marks to remind the reader of the
uneven distribution of these shocks over households with varying degrees of FD.
Based on our findings, we assert that more FD means more consumer fragility,
and—at least in the case of the collapse of house prices—greater macroeconomic
1
vulnerability.
More specifically, we develop a model that collects all the (zip-coded) geographies that fall in a given quintile of incidence of FD. The result is five artificial
economies made up of the zip codes experiencing the relevant quintile of FD.
Within each economy, our model of consumption is rich enough to encompass heterogeneity in income risk, life-cycle consumption needs, housing, debt repayment,
and, importantly, non-repayment (delinquency) and formal default (bankruptcy).
To ensure that we carefully incorporate heterogeneity present in each of the “regions”, we estimate the model separately for each of the five categories of zipcode-level FD. We then use this battery of estimated models to demonstrate the
channels at work and show—via region-specific counterfactuals—that these channels are relevant for the localized, and then aggregate, consumption response to
“aggregate” shocks.
Our analysis delivers two conclusions. First, the impact of “aggregate” shocks
on regional spending is very unequal, where regions with higher prior FD are
prone to suffer a more significant decline. But the difference is not just because
“aggregate” shocks are unevenly distributed. It is also because these regions react differently even after receiving the same shock. Our counterfactuals show,
for example, remarkably different consumption responses by region when we hit
each region with a baseline 9 percent decline in house prices—to mirror data
from Great Recession. In the areas with the lowest FD, consumption increases
by almost 4 percent, as some households can buy houses at the now-lower prevailing prices, and then allocate the savings to more non-durable consumption. In
contrast, in the regions with the highest incidence of FD, the same shock delivers
the more familiar pattern of a sharp 1.1 percent consumption decline.1
Our model suggests that, through these same mechanisms, the current macro
shock to income arising from the COVID-19 crisis will also generate unequal
responses of consumption across regions with different levels of FD. To evaluate
this, we construct a counterfactual exercise where each region suffers an 8 percent
decline in income (as opposed to the house price declines that were dominant in
the Great Recession but do not characterize the more recent shock). We find
that consumption declines across all “geographies”, including by 2.8 percent in
1
We corroborate this pattern with Mian et al. [2013]-style regressions in the appendix.
2
the region with the lowest FD, but declines far more—by 4.2 percent—in the
region with the highest FD at the onset of the shock. In this clear sense, the
presence of FD amplifies the consumption response to shocks that may hit any
region.
What if we had ignored FD in our analysis? To address this, we consider two
counterfactual economies that do not allow for unsecured debt repudiation, and
hence do not feature anything like the persistent high-credit-cost state of FD. The
results show that the economy’s response to the decline in house prices during the
Great Recession would have been an increase in aggregate consumption, instead
of the small overall decline we find in our benchmark economy with FD (which
in turn varied across FD quintiles). Similarly, excluding FD from the model, the
aggregate marginal propensity to consume declines by almost one-third—from
0.41 to 0.33—for the income shock meant to represent the COVID-19 shock. Our
findings demonstrate, we believe for the first time, that FD may be a relevant
aspect of the data to capture in analysis of the localized consumption response
to “aggregate” shocks.
1.1
Financial Distress
Two formal definitions of FD are developed in Athreya et al. [2019] and are
the same as used here: a significant fraction of available credit card credit is
exhausted, as measured by the percentage of remaining credit, or there is delinquent debt.2 In that work, both these measures of FD are shown to be relatively
common (i.e., high incidences) and 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
by distress for many, with some facing much more frequent difficulties.
On one level, FD resembles conventional measures of liquidity constraints.
One definition defines FD this way: a household is in FD if it has exhausted more
than 80 percent of its credit limit. Measures of indebtedness are also plausibly
natural contributors to FD: given any fixed borrowing capacity, more debt means
2
These two definitions are formalized for their use in this paper at the beginning of Section
2.
3
less ability to handle the next shock that arrives. However, in reality, credit
limits vary significantly across households, so our measure is better because it
uses both debt and credit limits. Similarly, leverage could be an alternative
to FD. Nevertheless, FD is broader primarily because it is defined to include
information encoded in past debt repayment decisions, something done neither
by current debt nor leverage. In that sense, FD may help identify households’
characteristics such as attitudes toward debt and repayment, which are crucial
to determine the consumption response to shocks.
Defined as we have done, FD offers an encompassing, easily measured, and
timely way to gauge households’ and the broader economy’s vulnerability to
shocks. It is encompassing because, unlike other measures, it does not require
knowledge of the items on households’ balance sheets or prices 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-to-view sources (e.g., family or business assets
that can be liquidated). Similarly, individuals with low levels of observable net
worth may not be constrained.3
By contrast, seeing an individual become significantly delinquent, or utilizing
most if not all unsecured credit, is 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 influences the marginal propensity
to consume (MPC), and the latter is central to accounts of macroeconomic susceptibility to shocks, FD is a window into both the individual and the aggregate
MPC. As for ease of measurement and timeliness, our measures of FD are built
on rich and frequently updated credit bureau data at the individual level.
3
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.
4
1.2
Literature review
Our work connects with several strands of the literature. At the most general
level, our findings suggest that the inclusion of FD into macro models is important to capture the real options available to households seeking to avoid debt
repayment and bankruptcy. Its inclusion allows our model to capture—when
calibrated—rich available data that help the baseline model get closer into replicating realistic consumption responses to shocks. In this sense, our work is related
to the contributions of Kaplan et al. [2014] and Carroll et al. [2017]. While our
focus is only on consumption, that interest is driven by the standard (old- and
new-Keynesian) views that at high frequencies, what happens to consumption
is vital for the determination of income. Thus, our findings also connect with
emerging literature of heterogeneous-agent models with market incompleteness
and new Keynesian features [Kaplan et al., 2018].
The most closely related papers in terms of the empirics we uncover are ones
that also document the relationship between shocks during recessions and prior
conditions. Guvenen et al. [2014] display the entire distribution of income losses
across many recessions. Especially relevant to our work is their finding that income losses during a recession generally tend to be larger the lower a person’s
pre-recession income. Our work also focuses on the link between prior conditions and recession outcomes in housing markets. Here, Piazzesi and Schneider
[2016] similarly show that cheaper houses during the 2000s experienced a more
significant boom-bust cycle than more expensive ones, using city-level data from
Zillow. Finally, Patterson [2018] shows that regions with higher MPC faced more
significant employment fluctuations during the Great Recession.
Our work complements and extends these papers. It complements the literature by explicitly showing the covariance between shocks during the Great
Recession and the COVID-19 pandemic with households’ ex-ante FD. It extends
the literature by assessing how this fact matters through the lens of a rich model
that incorporates FD as a choice. In particular, it studies the necessary counterfactuals.
There is, of course, a larger set of related papers that emphasize the role of
delinquency or bankruptcy for macroeconomic fluctuations. The main difference
5
between previous work and ours is that while we focus on FD before the shock
arrives, those analyses study how allowing for skipping debt payments shapes the
responses of macro variables. In particular, 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 aggregate demands externalities).
A more empirical group of papers 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 home ownership. Aladangady
[2017] and Aruoba et al. [2018] obtain empirical results in line with our finding
that greater FD is associated with higher MPC. 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
life-cycle model to compute counterfactual exercises that help us understand the
aggregate implications of shocks and FD.
The work of Mian et al. [2013], replicated and extended by Kaplan et al. [2016],
is essential to acknowledge here because that paper is the central reference when
it comes to examining the response of consumption to the decline in home prices
across zip codes. Since Mian et al. [2013] also analyze how MPC varies with
leverage, in our empirics we make clear that our results on the role of FD is not
merely repackaging leverage.4
Our model is closer to the model of mortgage default developed by Hatchondo
et al. [2015]. However, it incorporates (i) default on secured and unsecured debt
as in Mitman [2016], (ii) formal and informal default as in Athreya et al. [2017],5
and (iii) five regions, each represented by an heterogeneous-agent model as in
Dupor et al. [2018].
Several other papers are related to our work because they use heterogeneousagent models to analyze the decline in consumption after house price shocks or,
4
We establish the difference between the two in Figure A3 of appendix Section A.3, and
Table 1. Note also that in appendix Section 6, which includes a few regressions to test whether
our model’s conclusions are sensible in the data, we control directly for housing leverage. Our
results remain unchanged when we do so.
5
See also Athreya et al. [2015] and Athreya et al. [2019].
6
more generally, during the Great Recession. Berger et al. [2018] was the first
paper to study how prices affect consumption in a heterogeneous-agent model
with incomplete markets. They show how consumption responses depend on
factors such as the level and distribution of debt, the size and history of house
price shocks, and the credit supply level. Kaplan et al. [2019] build a quantitative model with long-term mortgages and default. Their key new component is
the change in expected house price growth, which help accounting for the joint
evolution of house prices and consumption during the Great Recession. 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.
Finally, our paper is related to a rapidly emerging COVID-19 literature. Using
a very different data source, Chetty et al. [2020] show that early during the
pandemic, spending patterns declined sharply in sectors that require physical
interaction, because of layoffs, particularly of low-income employees. Also related,
Kaplan et al. [2020] document that individuals in vulnerable occupations have
lower labor incomes and lower liquid wealth. Lastly, Glover et al. [2020] emphasize
the different economic effects of the pandemic on young and old individuals.
Overall, this emerging literature is in line with our interpretation of the
COVID-19 crisis as a shock to employment and earnings that disproportionately
affect areas with higher FD. Of course, our analysis of the COVID-19 crisis is
only complementary to the Great Recession analysis because this is an ongoing
event, and the availability of information is rapidly growing.
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. and the
way that this variation is correlated with housing wealth losses during the Great
Recession and projected income losses during the COVID-19 pandemic. With
those facts established, we turn in Section 3 to our model, which as stated above,
is capable of incorporating the desired margins of adjustment—and the costs
associated with making them. Section 4 presents the parameterization. Section
5 contains the results, and Section 6 offers concluding remarks.
7
2
Financial Distress and “Aggregate” Shocks:
Three Facts
The empirics we develop below will make use of two main definitions of FD
developed by Athreya et al. [2019]. The first of these, labeled DQ30, is the the
percentage of individuals with a credit card account at least 30 days delinquent at
some point during the year. The second measure, labeled CL80, is the percentage
of individuals within a zip code who have reached at least 80 percent of their credit
limit over the same time interval.6 Using these definitions, we demonstrate that
(i) the incidence of FD varied substantially across geographies at the onset of the
Great Recession, (ii) the size of the shocks that occurred during both the Great
Recession and the COVID-19 pandemic varied substantially across geographies,
and (iii) the incidence of FD prior to both the Great Recession and COVID19 pandemic and the size of shocks experienced in an area were significantly
positively correlated.
Fact 1: household financial distress is unevenly distributed
across zip codes
FD, as we have defined it, provides a useful and timely indicator of the financial
health of a zip code and is easily accessible (in our case, via Equifax data). Figure
1 shows that both of our measures of zip-code-level FD convey the same message:
the incidence of FD varied widely in 2002, which we take to be early enough to
describe FD conditions before the Great Recession.7 Indeed, no state can be
characterized as having entirely high or low FD, though FD does seem to be
highest in the Southeast and Deep South.
These national pictures mask a high degree of dispersion within individual
cities. Take, for example, two contiguous zip codes in St. Louis, Missouri: 63110
to the north and 63105 to the south. In 2006, 6.8 percent of households in the
the southern zip code were in FD (DQ30), while more than twice that portion,
6
Any other metrics for FD used within this paper as robustness checks are defined and
discussed in appendix Section A.3.
7
The wide variance in FD shown here is not unique to 2002; similar maps from other years
up to the present day reveal the same.
8
(a) DQ30
(b) CL80
Figure 1: National Maps of FD Dispersion in 2002
Source: FRBNY Consumer Credit Panel/Equifax.
9
15.5 percent, were in FD in the northern zip code. When housing prices started
to collapse in, the loss in home value as a percentage of net wealth varied substantially as well:8 the southern zip code lost 0.5 percent, while the northern zip
code lost twice as much, 1.0 percent.
The starkly different experiences of these two adjacent zip codes in terms of
FD and wealth loss is not an anomaly. In our sample, the standard deviation of
FD using DQ30 across Metropolitan Statistical Areas (MSAs) is 0.024, but the
average standard deviation of zip codes within a given MSA is nearly twice that,
0.045. Similarly, while the standard deviation of CL80 is 0.026 across MSAs, it is
0.053—again, roughly double that on average—across zip codes within MSAs. In
sum, differences in financial distress within MSAs are larger than between MSAs.
Intuitively, this spatial concentration appears entirely consistent with the more
general spatial stratification by economic condition exhibited in most, if not all,
U.S. cities.
Aside from purely geographic heterogeneity, the variation—and inequality—
in FD can also be seen in the distribution of the quantity of debt in delinquency.
Figure 2 presents the Lorenz curve for the distribution of (at least 30-day) delinquent debt. We see that the top quintile of debt holders hold more than half
of this debt. This is true both for credit card debt and for total debt. Conversely, the bottom 40 percent of debt holders account for less than 20 percent
of delinquent debt.
While the data displayed so far are cross-sectional, this snapshot of dispersion
is indicative of long-term characteristics. Athreya et al. [2019] use data at the
individual level to show 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 than the average person. FD
is similarly persistent at a community level, and even more so than would be
expected if individual-level FD persistence were the only factor at play.9
8
The method that we use to assign home values and net wealth to zip codes is described in
appendix Section A.2.
9
This is documented in appendix Section A.3.1.
10
Figure 2: Distribution of Delinquent Debt across Zip codes, 2002
Source: FRBNY/Equifax CCP.
Fact 2: “Aggregate” shocks are unevenly distributed across
zip codes
The Great Recession and the COVID-19 pandemic are both clearly macroeconomic, or “aggregate”, events. Nevertheless, they did not effect all households
and geographies uniformly, but landed on each with greater or lesser severity. We
now describe how we represent each event within our model.
Great Recession: In terms of the “initial” shock experienced by households
during the Great Recession, it is clear that there was a massive decline in house
prices that began before the recession and continued well after. This drop in prices
substantially damaged household balance sheets on average; but in keeping with
the theme of this paper, it did not do so with any sort of uniformity across the
country. Indeed, in a non-neglible portion of zip codes, the median home value
rose, as shown in Figure 3. More familiar, of course, is the action on the other
tail of the distribution: in a non-negligible share of zip codes, the median home
value fell more than 50 percent.
11
Figure 3: Distribution of Home Price Losses, 2006-2012
Source: Zillow.
COVID-19 Pandemic: Unlike a decline in wealth from a decline in house
prices, as in the Great Recession, the current pandemic essentially placed a substantial “tax” on certain forms of consumption (e.g, restaurants), as well as on
some types of production (e.g., meatpacking). This impulse then translated very
quickly into a change in labor demand, and hence changes in employment and
wages. Moreover, as people pursued social distancing to mitigate the spread of
COVID-19, employment in specific industries was (far) more negatively impacted
than in others. In particular, industries such as “Accommodation”, “Food Services and Drinking Places,” and “Arts, Entertainment and Recreation” experienced catastrophic losses, as their usual business models require public interaction considered dangerous during a pandemic. Conversely, other sectors were far
less affected, with some even experiencing increases in activity, e.g., the home
improvement and grocery sectors.
Figure 4 plots the data on employment for the leisure and hospitality subsectors. There were large declines during April, amounting to more than 40 percent for the subsectors combined. There has been some recovery afterword, but
prolonged social distancing measures have prevented these sectors from attaining
12
a sort of “V-shaped” recovery. Significantly, during July, many states reinstated
their lockdown measures, due to large increases in COVID-19 infections.
Figure 4: Change in Employment in the Leisure and Hospitality Sector
Note: Seasonally adjusted data from the BLS.
This uneven effect across sectors and workers translates into an uneven effect
across the zip codes in which those workers live. Using Longitudinal EmployerHousehold Dynamics (LEHD) Origin-Destination Employment Statistics (LODES)
data,10 we calculate the share of workers at the zip-code level whose primary job
is in “leisure and hospitality.”11 The resulting variation is very clear, as seen in
Figure 5. A substantial share of zip codes feature employment that is much more
concentrated than the national average, while a substantial portion of zip codes
exhibit the reverse pattern. The absolute variation is also large by any meaningful metric: 1-2 percent of zip codes have at least 30 percent of their employment
in this extremely hard hit sector.
10
We use data from 2017, which is the most recent year of data available.
We identify workers in leisure and hospitality as those whose primary job is in either “Accommodation and Food Services” (NAICS sector 72) or “Arts, Entertainment, and Recreation”
(NAICS sector 71). Importantly, we present the share of workers living in each zip code whose
primary job is in one of the sectors, as opposed to the share of workers within one of these
subsectors employed by businesses in a given zip code.
11
13
Figure 5: Distribution of Employment Shares across the Leisure and Hospitality
sector
Source: Census LODES. The vertical dotted line correspond to household-weighted national
means.
Fact 3: Ex-ante FD and the share of the “aggregate” shock
hitting a region are positively correlated
Thus far we have established (i) that FD—at the zip-code level—varies widely in
the U.S. and (ii) that plausibly exogenous shocks (house price shocks in the Great
Recession and work cessation in the COVID-19 pandemic) have caused uneven
consequences across areas. We now establish our third fact: FD is a relevant
pre-existing economic condition. In other words, we show that the presence of
FD prior to shocks that are clearly “aggregate” in their effect on national-level
outcomes contains “news” about the severity of the shock when it does finally
arrive. And the news is not good: in both the Great Recession and in the ongoing
COVID-19 pandemic, the most financially distressed households (again, at the
zip-code-incidence level) were hit the hardest.
Great Recession: Starting with the Great Recession, Figure 6 shows that
home values during this event declined the most in more financially distressed
14
communities. By 2012, regardless of FD, median home prices declined on average
by around 15 percent relative to their 2006 levels. However, home price declines
in zip codes with higher FD were in many cases twice that, or worse.
Figure 6: Regional Changes in House Prices by Financial Distress
Note: FD is measured with DQ30, which is the share of individuals who are at least 30 days
delinquent on a credit card at some point in a given year. For ease of viewing, the data have
been divided into 40 bins with respect to DQ30, and each dot represents the mean of that bin
weighted by the housing wealth in each zip code as of 2006.
Perhaps worst of all, households hardest hit were not diversified. Specifically,
we find that households with high financial distress also tended to hold a larger
share of their net wealth in their homes. This implies that when losses are
measured as a percentage of 2006 net wealth, home value losses are even more
strongly correlated with FD. In other words, the skewed distribution of home price
losses generated an even more heavily skewed distribution of net wealth losses for
regions with higher FD. Appendix Section A.3.3 illustrates this relationship.
COVID-19 Pandemic Similarly, in the COVID-19 pandemic, the declines
in hours worked and employment were systematically larger in more financially
distressed communities. As shown in Figure 7, there is a strong and consistent
positive relationship between FD incidence at the zip-code level (measured by
15
the incidence of DQ30 in 2018) and the share of those area’s workers employed
in “Leisure and Hospitality.” We also include the “Retail and Trade” sector to
show that another most-affected sector also displays a similar pattern.12
Figure 7: Share of COVID-19 “Affected” Employment by Financial Distress
Sources: Census LODES and FRBNY Consumer Credit Panel/Equifax. Each dot represents
the mean of a DQ30 bin weighted by the number of households in each zip code.
A natural conjecture, then, is that income losses among high-FD areas will be
more significant in percentage terms than those of low-FD areas. To investigate
this, we complement this information with the Household Pulse Survey. There,
the Census asked households if they experienced income losses. To estimate the
relationship between the share of households not affected (with no income loss)
and the incidence of FD, we leverage data from the 10th wave. That is, we use
the Pulse Survey to calculate the state-level shares of individuals who report
“no earnings losses since March 13, 2020 (for self or household member).” We
merge these state-level responses with our preferred Equifax FD measure (DQ30).
Figure 8 shows that states with a higher incidence of FD tend have a lower share
of households that escape the COVID-19 shock altogether—i.e., who have no
labor earnings losses since March 13.
12
According to BLS data, retail trade employment fell by 15 percent in April and recovered
to a year-over-year decline of 8 percent in June.
16
Figure 8: Share of COVID-19 “No earnings losses” by Financial Distress
Sources: Census Pulse Survey Wave 10 and FRBNY Consumer Credit Panel/Equifax. Each
dot represents the average state-level response of “% reporting no earnings losses since March
13.” Dashed line represents line of best fit, weighting each state by population.
Overall, the facts presented in this section suggest areas with higher FD may
be more severely affected by the ongoing COVID-19 pandemic and the efforts to
contain it.13
We turn now to the development of a model aimed at delivering an understanding the role of FD in macroeconomic vulnerability. As will become clear,
the model is a rich one: it takes household consumption seriously, including housing and the contractual arrangements—renting or buying—used to obtain it, and
features secured and unsecured debt and debt default.
13
In a pair of graphs frequently updated, we additionally document that communities with
high FD seem also to have higher numbers of COVID-19 cases and deaths per capita. Falling
ill can come with a host of repercussions including medical bills, lost time at work, and stringent quarantine instructions. To the extent that the severity of community responses is positively correlated with the local severity of the pandemic, this may also point to additional
consequences including lengthened stay-at-home orders, strained public health resources, and
stronger local preferences against engaging publicly with local businesses. We will not explicitly
model any of these consequences. If we did, however, the result would be an income shock more
strongly correlated with FD, magnifying the results that we do present.
17
3
A Life-Cycle Model of Housing and FD
The question we are interested in is straightforward: How does (an area’s) household financial health, as measured by FD, matter for the transmission of housing
and income shocks to consumption? Given that FD is partially endogenous, however, answering this question meaningfully requires a model of debt acquisition,
debt repayment, and consumption decisions. We now lay out such a model. In
subsequent sections, we deploy it to measure, via specific counterfactuals, the role
of FD in the response of consumption to housing and income shocks, including
a quantification of the importance of the positive correlation between initial FD
and these shocks.
3.1
Agents, Markets, and Debt Default
There is a continuum of finitely lived individuals who are risk averse and discount
the future exponentially. All individuals face risk of death in each period and
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 . Critically,
all agents are subject to risk in their income y (specified below). Lastly, agents
will be allowed to differ in the rate at which 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 .14
With respect to markets, households have (limited) access to credit and each
period choose non-durable consumption c, housing h, mortgages m0 , and financial
assets (or debt) a0 . Households may choose to obtain housing services through
homeownership or by renting. These options are an important form of heterogeneity to incorporate ex-ante, given the differences observed in homeownership
rates across income categories in U.S. data.
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 (owner-occupied) houses,
14
Heterogeneity in the discount factor is common in macroeconomics at least since Krusell
and Smith [2003]. However, the modeling and the calibration of β heterogeneity here follows
closely Athreya et al. [2019].
18
agents borrow using mortgages m0 . Importantly, borrowing capacity in the mortgage market is endogenously given by a zero-profit condition on lenders due to
the limited commitment of agents to repay mortgages.15
If agents choose to save in the financial asset a > 0, they receive a risk-free rate
r. However, when agents borrow (a < 0), the discount price of their unsecured
debt (q) depends on how much the borrow because debt may be repudiated. Debt
repudiation can occur in one of two ways. First, the agent may cease payment.
This option is known as delinquency (DQ) or informal default. Importantly,
because with delinquency a household’s debt is not necessarily forgiven, we allow
for a probabilistic elimination of debts, with an i.i.d. probability η. This tractably
captures not only the absence of a formal elimination of the debt but also the
empirical reality that creditors periodically give up on collections efforts.
With probability 1 − η, then, a household’s rolled-over debt is not discharged.
In this case, the household pays a “penalty” rate, rR , of interest higher than
the average rate paid by borrowers.16 Moreover, in any period of delinquency,
we prohibit saving, and since the agent did not borrow but failed to repay as
promised, their consumption equals income. Second, as in standard 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.
3.2
Nonhomeowners
The options faced by a nonhomeowner with assets a and income y are represented
in Figure 9. First, they can choose to either rent or to buy a house and become
a homebuyer. If renting is chosen, the nonhomeowner must decide between the
three options described below. There is a letter associated with each position in
the tree, representing the notation we use for the value function associated with
each choice. For example, the value function for a nonhomeowner with state
15
Housing choices, mortgages, and foreclosures are modeled as in Hatchondo et al. [2015].
Athreya et al. [2017] analyze facts about informal default and introduced it to
heterogeneous-agent models. Athreya et al. [2015] use this model to study the effect of the
Bankruptcy Abuse Prevention and Consumer Protection Act of 2005.
16
19
variable a and y is N . For the sake of brevity, our formal description of this
recursive problems is presented in Appendix B.
Figure 9: 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
3.2.1
Renting a house
P P , pay/save assets a
BK , default on a
P , payincome
m
A renter of discount factor type j with
y who decides toPpay
unsecured
DQ , becomeassets
debt (or has positive financial assets) chooses the next period’sPfinancial
delinquent on a
0
a . Hence, the agent’s budget constraint reads
F , refinance
a
0
0
c + qj,n
(hR , 0,
m afor, y)a
m0 = y + a.
Pay/save assets a
Here, y denotes income and q a denotes the price (i.e., discount) applied to finanDP , pay/save a
cial assets. As noted above, the fact that agents can repudiate debt means that
H, homeowner
D, default on
DBK , default on a
its price will with
reflect
incentives,
which
(a, y,default
h, m)
m and rent
hR depend on the agent’s state vector
and hence on housing, income, and their discount factor type. DDQ , become delinquent on a
Instead, if that renter decides to formally default on unsecured debt a, she
faces the following trivial budget constraint:
c = y −(filing fee), where the “filing
SR , sell h
Pay/save a
fee” is the bankruptcy filing fee. and rent hR
Finally, if that renter decides to skip payments (i.e., become delinquent) on
unsecured debt a, they consume c = y and will have financial assets tomorrow
equal to
SB , sell h
Choose h0 and m0 ; pay/save a
0,
with prob. γ,
a0 =
(1 + rR )a,
with prob. 1 − γ.
20
1
Here, γ is the probability of discharging delinquent debt, and rR is the roll-over
interest rate on delinquent debt.
3.2.2
Buying a house
An agent buying a house must choose next period’s financial assets a0 , the size of
the house h0 , and the amount to borrow for the house m0 . This 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 λ of the value of the house.
3.3
Homeowners
The choices available to an existing homeowner are presented in Figure 10. A
homeowner’s problem is more complex. On the financial asset dimension, homeowners must decide to default or repay their unsecured debt. On the housing
dimension, homeowners can (i) pay their current mortgage, (ii) refinance their
mortgage, (iii) default on their mortgage, (iv) sell their house and buy another
one, or (v) become a renter. Each option and the associated budget constraint
are discussed below.
3.4
Making the mortgage payment
Agents repaying their mortgage who also decide to pay their unsecured debt face
the following budget constraint:
a
c + qj,n
(h, m(1 − δ), a0 , y)a0 = y + a − m.
21
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 10: 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
Notice that the bond prices these agents face depend on house size 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 mort1
gage payments decay, which may happen for example because there is inflation
and payments are fixed in nominal terms.
Agents who pay their mortgage but formally default on unsecured debt have
the following budget constraint, c = y − (filing fee) − m, where “filing fee” is the
bankruptcy filing fee and m is the current mortgage payment.
Similarly, households who decide to pay their mortgage but informally default
on their unsecured debt consume c = y − m and have financial assets tomorrow
22
equal to
a0 =
3.4.1
0,
with prob. γ,
(1 + rR )a,
with prob. 1 − γ.
Refinancing the mortgage
An agent who refinances cannot default on unsecured debt 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:
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
qj,n
(h0 , m0 , a0 , y)m0 ≤ λph0 .
Here, qn∗ m is the value of prepaying a mortgage of size m with n remaining periods
worth of payments, which is:
1−
qn∗
3.4.2
=
1−δ
1+r
1−
n+1
, for n ≥ 1.
1−δ
1+r
Foreclosing on the mortgage
An agent who defaults on her mortgage and chooses to pay her unsecured debt 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 pays
a
her financial assets: c + qj,n
(hR , 0, a0 , y)a0 = y + a.
Using the same reasoning as above, we can write the problem of a mortgage
defaulter who chooses bankruptcy on unsecured debt as the problem of renter who
files for bankruptcy. Thus, the budget constraint is simply c = y − f iling f ee.
Lastly, we can write the problem of a mortgage defaulter who chooses delinquency as the problem of renter who is also delinquent on existing debt. This
means that consumption is given by c = y and financial assets tomorrow are
23
equal to
a0 =
3.4.3
0,
with prob. γ,
(1 + rR )a,
with prob. 1 − γ.
Selling the house
A home seller who decides to rent cannot default on financial assets. Hence, their
optimization problem collapses to that of a renter with financial assets equal to
a plus the gains from selling their current house. The agent’s budget constraint
in this case reads:
a
c + qj,n
(hR , 0, a0 , y)a0 = y + a + ph(1 − ξS ) − qn∗ m.
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.
If instead the seller decides to buy another house, she must also pay her
financial obligations. Therefore, this agent’s problem is just a special case of a
homebuyer with cash on hand equal to 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 .
3.5
Debt prices
The price of debt, or the interest rate, is determined by risk-neutral lenders that
make zero expected discounted profits. In this section, we present the three main
components of debt prices. The full specification of each of these (three) prices
is in Appendix B.
m
The price of a mortgage, qj,n
, for an agent of type j, with income y, and
0
financial wealth a for the next period and that promises a payment of m0 is
24
given by:
qnm (h0 , m0 , a0 , y)
m
m
m
+ qdef
+ qprepay,j,n
qpay,j,n
ault,j,n
,
=
1+r
where r is the risk-free interest rate. 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 financial debt payment, default, or delinquency. We don’t
restrict agent choices at all in this regard, which makes our setting very flexible.
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, and
as is consistent with our overall approach, mortgage default can occur alongside
financial debt payment, default, or delinquency. Notice that under this formulation, mortgage prices fully internalize how financial asset positions today and
tomorrow affect the probability of mortgage default.
We can express unsecured debt prices similarly. When an agent of type j,
income y, house size h0 , and mortgage size m0 issues debt and promises to pay a0
a
(h0 , m0 , a0 , y), where:
next period, the amount they borrow is given by a0 qj,n
a
qj,n
(h0 , b0 , a0 , y)
a
a
+ qDQ,j,n
qpay,j,n
.
=
1+r
a
. Conditional on being
First, consider the price of a payment tomorrow, qpay,j
a nonhomeowner, this occurs in two scenarios: the agent is a renter with no
unsecured debt default or a homebuyer. Conditional on being a homeowner,
payment occurs if the homeowner: (i) is a mortgage payer with no unsecured
debt default, (ii) is refinancing the mortgage, (iii) is a mortgage defaulter with
no unsecured debt default, (iv) is selling the house to become renter, and (v) is
selling the house to buy another house. Regardless of homeownership status, in
these cases, creditors get paid the same amount per unit of debt issued by the
household.
a
Next, consider the price given delinquency tomorrow, qDQ,j
. Conditional on
being a nonhomeowner, this occurs only when renters choose delinquency. Mean-
25
while, conditional on being a homeowner, this value occurs in two cases: when
mortgage payers choose delinquency and when mortgage defaulters choose delinquency. In all of these cases, debt gets rolled over at a rate of (1 + rR ) with probability (1 − γ). Importantly, though, tomorrow’s price of this “rolled-over” debt
will depend on the agent’s 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.
4
Estimation of the model to capture five FD
“regions”
In order to most closely tie our empirical and quantitative work together, we
need to take a stance on what a geographical region means in the model and
data. A crucial feature is that even inside a zip code, we would need a force to
deliver heterogeneous outcomes across agents to capture the fact that in any zip
code, only a fraction of households are in FD. Defining a region as a zip-code,
county, or even state would be computational prohibitive, as it would require a
large number of estimations of our baseline model.
Thus, as a balance between expanding the reach of the model into more
granular data and preserving practicality, we proceed as follows. First, we order
the zip-codes in our sample by their incidence of FD and split the data into
quintiles (5 groups, each with the same population size). Next, we construct five
“regions” that combine all zip codes that fall within each given quintile of FD.
We then treat these as “economies” or “geographies”, calculate several statistics
(e.g., FD, income, wealth, and homeownership rate) for each region, and use
these moments as targets for five different estimations of our baseline model.
The statistics obtained are shown in Table 1.
By construction, FD is increasing across quintiles, and in terms of the absolute
levels of FD (as defined by DQ30), we see that it increases from 8.6 percent of
households in quintile 1 (Q1) to nearly triple that (23.5 percent) in quintile 5
(Q5). This is a first, and clear, indication that people in different quintiles tend
to be differently positioned when it comes to their balance sheets.
26
Table 1: Descriptive Statistics by Quintile of DQ30 in 2002
1
Quintiles of DQ30 in 2002
2
3
4
5
Wealth
53.51
164.5
154.6
95.00
179.9
Income Per Household (HH) $000
Net Wealth Per HH. $000, ages 25-55
Fin. Wealth Per HH $000, ages 25-55
Net Fin. Wealth Per HH $000, ages 25-55
Median Home Value $000
91.75
358.5
321.9
224.0
297.0
65.26
216.0
201.4
128.1
219.0
46.22
127.1
123.4
72.71
154.8
39.86
88.12
83.00
42.13
128.6
Less Than High School
High School
College
Age
7.659
19.70
72.64
44.27
Human Capital
11.95 16.69 19.63
24.78 26.82 27.99
63.27 56.49 52.37
43.61 43.27 42.84
23.73
29.23
47.04
42.64
Percent of HHs that Own a Home
Percent of HHs with Housing Debt
Housing Debt per Home Owner $000
CC Debt Per Household $000
Housing Leverage
76.30
49.77
135.0
5.238
44.11
71.93
44.67
102.3
4.803
47.98
Debt
68.76
39.83
83.91
4.407
44.57
61.69
31.84
58.95
3.806
43.36
64.25
36.27
73.38
4.171
46.04
Delinquency
HHs with housing debt and in FD / HHs (in %) 5.910 8.555 10.82 13.32 19.46
HHs with housing debt / HHs in FD (in %)
33.31 30.72 28.37 26.90 25.99
Foreclosure Rate
1.520 1.812 2.239 2.579 3.335
Bankruptcy Rate
0.392 0.553 0.631 0.648 0.639
DQ30
8.566 12.11 14.92 17.83 23.54
Note: Here, housing debt refers to a mortgage or home equity line of credit. Housing leverage
is measured as housing debt divided by the total housing wealth in each geography. The
number of households weights all means, except housing debt per homeowner, which is
naturally weighted by homeowners. “ages 25-55” signifies that for the corresponding rows, we
used financial wealth aggregates from the SCF for individual from 25 to 55 years old. This is
done because elderly populations hold a large share of financial wealth, and our model
economy is calibrated for individuals 25 to 55 years old.
Naturally, FD is inversely related to various other measures of economic
health, wealth, and human capital. Areas with high FD tended in 2002 to have
lower incomes, net wealth, and home values. Lower wealth in high FD areas prevents these areas from sustaining higher levels of debt, both in terms of housing
debt and, perhaps more surprisingly, credit card debt. This lower credit card
27
debt arises because despite zip codes with high FD using a higher proportion of
their available credit, they 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
a high credit limit and having used a lower portion of that limit. Thus, 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 lowest FD quintile.
Since we intend to look at the interaction between FD and housing shocks,
and since those in high-FD zip codes are somewhat less likely to own homes, it
would be problematic if the differences in FD across zip codes are driven mainly
by people who do not own homes. To examine this, we need to identify at the
individual level homeownership and FD, something we cannot do with Equifax.
We proxy for homeownership within the Equifax data by using natural objects
that we can observe: whether an individual has either a mortgage or a home
equity line of credit (housing debt).17 The bottom panel of the table shows that
when we consider the fraction of people identified to both own a home and be
in FD, the resulting differences between quintiles are similar in magnitude to
those of FD considered directly. Taken as a whole, this is important, as it clearly
suggests that it is highly unlikely that the dispersion in FD is being driven by
people who do not own homes.
In assigning parameters to each region, we proceed in two steps. First, we
directly set values for a subset of the most “standard” parameters and impose
that these are common to households across our notion of regions. Second, given
these first-stage values, we estimate the remaining parameters so that the modelsimulated data match the statistics mentioned above for each of the five regions.
4.1
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 percent. In addition, we
17
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 percent with housing debt usually
underestimates the percentage of households that own the home they live in by about a third.
28
externally calibrate the parameters governing the income process, bankruptcy
filing costs, retirement, and mortality. The initial distribution of net financial
wealth-to-earnings are set to match the distribution of net financial wealth to
earnings of 25 year olds in the Survey of Consumer Finances between 1998 and
2016.
Turning to preferences, we make two data-disciplined changes to an otherwise
standard formulation. First, as previously mentioned, we follow Athreya et al.
[2019] and assume agents can either discount the future relatively little (i.e., be
“patient”) and have discount factor βH , or discount it more significantly (i.e., be
“impatient”) and use discount factor βL ≤ βH . Let sL denote the share of the
population of type L. This allows the model to capture well the joint distribution
of net financial wealth, delinquency (incidence and persistence), and bankruptcy.
Second, it matters that our model match as well as possible the joint distribution of homeownership and FD. Here, we find that a simple allowance for the
“specialness” of owner-occupied housing (presumably capturing a variety of benefits that ownership confers) relative to renting helps reconcile theory and data.
This is represented in a simple manner: 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:
((1 − θ)c1−1/α + θ(1 + θiR Irenting )h1−1/α )(1−γ)/(1−1/α)
,
u(c, h) =
1−γ
where γ denotes the risk aversion parameter, α governs the degree of intratemporal substitutability between housing and non-durable consumption goods,
and θ determines the expenditure share for housing. The parameter θiR Irenting
captures the type-specific ( i ∈ {L, H}) disutility from renting relative to owning a house. Following Hatchondo et al. [2015], we set γ to 2, α to 0.5, and θ
to 0.11. Since we ultimately calibrate the rental house size hR to match each
region’s homeownership rate, we normalize the value of the disutility of renting
for individuals with a low discount factor, θLR = 0. Thus, what remains to be
R
determined is the region-specific value of θH
.
Following Livshits et al. [2007], the penalty rate for delinquent debt is set at
20 percent annually and the bankruptcy filing costs are at 2.8 percent of average
29
income, or roughly $1,000.
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 ,
where: l(n) denotes the life-cycle component, in,t is a transitory component, and
i
zn,t
is a persistent component as 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.
In retirement, the household receives a fraction of the last realization of the
persistent component of its working-age income using the replacement ratio fori
mula: 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 percent to 14 percent, with an average replacement rate
of 47 percent. The age-specific survival probabilities follow Kaplan and Violante
[2010].
4.2
Estimating the remaining parameters
The remaining parameters to be determined are (i) the discount factors of impatient types βL , (ii) the discount factors of patient types βH , (iii) the share
of impatient types in the population sL , (iv) the probability of delinquent debt
being fully discharged η, (v) the house price per unit p, (vi) the rental house
size hR , and (vii) the disutility that type-H agents receive from renting versus
R
owning a house θH
. We estimate these seven parameters so that model-simulated
data replicates some critical features of the data about homeownership, financial
wealth, and FD for each of the five regions we construct.
Table 3 presents the model’s fit for each of the quintile-specific moments.
30
Table 2: Externally set parameters
Parameter
l
W
ρn
a0
σ2
σe2
r
γ
α
θ
ξB
ξS
ξ̄S
ξM
δ
A0
A1
A2
λ
f
rR
Value
—
65
—
—
0.063
0.0166
0.03
2
0.5
0.11
0.03
0.03
0.22
0.15
0.02
0.7156
0.04
0.14
0.9
0.028
0.2
Definition
Life-cycle component of income
Retirement age
Mortality age profile
Initial net financial asset distribution
Variance of
Variance of e
Risk-free rate
Risk aversion
Elasticity of substitution
Consumption weight of housing
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 et al. [2015]
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 et al. [2007]
Livshits et al. [2007]
The model does an excellent of matching differences in financial wealth across
the five regions. Additionally, it replicates the fact that homeownership declines
as regional FD rises and does a good job of matching the share of individuals in
FD that have housing debt. Because most individuals in FD who own a home will
tend to have mortgages or home equity lines of credit (HELOCs), this measure
can be thought of as a good proxy for the homeownership rate conditional on
being in FD. One shortcoming of the model is that it struggles to precisely match
the ratio of median home values to mean income. While in the data there is no
systematic pattern of this ratio with FD, the model suggests the ratio declines
slightly as FD rises.
The rest of the table focuses on FD and shows that the model does a good
job of matching the overall regional patterns as well. Indeed, the model nearly
exactly matches the fact that average delinquency rates rise with each quintile of
FD, and so do bankruptcy rates. Additionally, the model matches the fact that
the persistence of FD actually falls as the quintile number increases.
Table 4 shows the resulting parameter estimates and reveals some systematic
differences across the quintiles of FD. Most notably, the share of impatient people
systematically rises across the quintiles. For example, in Q1, less than a quarter
31
Table 3: Regional Calibrations
Moment
Wealth / Income
Homeownership rate
Home value / Income
DQ rate (in %)
BK rate (in %)
Persistence of FD
With housing debt
/ In FD (in %)
Data
2.49
76.9
3.23
8.6
0.37
5.45
33.6
Q1
Model
2.46
80.6
3.37
8.3
0.38
5.23
31.3
Data
2.01
72.7
3.30
12.1
0.54
4.74
31.3
Q2
Model
1.97
75.0
3.11
11.0
0.54
4.41
30.9
Data
1.79
68.9
3.42
14.9
0.62
4.06
28.6
Q3
Model
1.78
70.3
3.13
13.8
0.58
3.84
27.0
Data
1.62
65.3
3.33
18.9
0.64
3.55
27.2
Q4
Model
1.56
68.1
3.07
17.3
0.67
3.61
26.7
Data
1.09
61.6
3.23
23.6
0.64
2.88
26.0
Q5
Model
1.09
61.0
3.08
23.3
0.64
2.76
25.5
Note: “Wealth/Income” represents mean net financial wealth divided by mean income; “Home value/Income”
is the median home value divided by mean income, and “With housing debt / In FD” is the percent of the
population with housing debt, conditional on being in FD.
of the population discounts the future relatively more. In contrast, in the fifth
quintile, over half of the population is impatient. In terms of the values for the
discount factors, the model requires only modest differences across quintiles but
large differences across types. For example, the high discount factor is essentially identical across the quintiles of FD, and the low discount factor βL is only
significantly lower in the Q5 of FD compared to the other four.
Lastly, the data—filtered through our framework—imply significant differR
, regardless of the
ences in the utility of rental house sizes between types, θH
R
is that rental houses are
quintile of FD. One way to interpret the parameter θH
perceived to be of different sizes by agents of different types. For example, in
Q3, the coefficient of 4.38 implies that βH -type households perceive rental houses
as about 20 percent of the size perceived by βL -type households. This difference
allows the model to match the low homeownership rate among households in FD
(mostly βL types)—approximated by the percent of households with housing debt
among those in FD—together with a high overall ownership rate.18
18
Indeed, with a single parameter governing the size of rental houses, the model-implied
ownership rate is biased away from the data value and has the wrong FD composition. The
comparatively high ownership rate of low-FD individuals dictates a small rental house size, but
with a single parameter, even high-FD individuals own houses and so the overall ownership rate
is too high. Conversely, the comparatively low ownership rate of high-FD individuals dictates
a large rental house size, but with a single parameter even low-FD individuals choose to rent,
making their overall ownership rate counterfactually low. Allowing for differences in rental
house size by β type resolves this tension.
32
Table 4: Regional Parameter Estimates
Parameter
Low discount factor βL
High discount factor βH
Share pop. w/ low discount factor sL
Rental house size hR
R
Utility of renting versus owning for H-type θH
Owner-occupied house price p
Discharge prob. of DQ debt γ
LTV λ
Average earnings (relative to Q3)
5
Q1
Q2
Q3
Q4
Q5
0.64
1.04
0.24
4.02
7.28
3.63
0.87
0.9
1.41
0.65
1.03
0.30
3.81
5.63
2.74
0.75
0.9
1.17
0.62
1.03
0.35
3.58
4.38
2.36
0.70
0.9
1.0
0.56
1.03
0.39
2.92
4.12
2.45
0.68
0.9
0.89
0.51
1.02
0.50
2.50
14.2
2.51
0.67
0.9
0.76
Quantitative Exercises
We now use the model to understand the relationship between financial distress,
shocks (to housing wealth, then income), and the response of consumption during the two macroeconomic events we consider. This analysis requires, first of
all, that we generate within the model a stylized Great Recession and then an
episode that captures some key aspects of the COVID-19-induced lockdown. In
our quantitative analysis, both shocks will be exogenous. Of course, house prices
and labor income have endogenous components (see, e.g., Garriga and Hedlund
[2017] for a rich analysis of the former, and of course countless business analyses
of the latter). Our goal is not provide an account of these price movements,
but rather to understand how shocks are unequally distributed and unequally
transmitted into consumption.
We then use the model to uncover the micro-level mechanisms at work in an
aggregate shock.19 We stress that our work is not an attempt to analyze the
economic impact of the COVID-19 pandemic per se. Indeed, any macroeconomic
shock for which we had relatively granular measures of idiosyncratic incidence
would do; the two shocks we utilize are both recent and sizeable and between
them cover two kinds of economic stress (net worth and labor income) that are
empirically relevant. An additional impetus for using the ongoing pandemic in
particular is that as a major macroeconomic event, it is relatively clean in its
19
A validation of the primary mechanism is presented in the last part of the paper.
33
(extremely) exogenous nature, at least at the outset.
As just noted, the Great Recession and the COVID-19 pandemic attacked
different parts of a household’s financial well-being. In the case of the Great
Recession, household net worth was destroyed, while in the pandemic, incomegeneration effectively became impossible for a subset of households, certainly in
the short-run. Thus, by studying both, we expand the reach of our analysis of
how FD matters for macroeconomic outcomes.
5.1
A first aggregate shock: A collapse in asset valuations
A central aspect of the Great Recession was a large drop in home prices. We
therefore replicate this event in our model by subjecting each of our calibrated
“regions” to exogenous changes in house prices. Again, we remind the reader
that our approach is to treat those in a category (specifically, quintile) of FD,
gauge their response to a shock, and then compare this response to those of the
other quintiles of FD. One aspect of our representation of the shocks is that they
respect the data we presented in Section 2. Namely, that the shocks landed most
heavily on areas that exhibited greater financial distress at the outset.
A key finding from these experiments is that our model implies very different
consumption responses across “regions.” We find also that much of these differences remain even when we subject the regions to the same shock. Differences
in initial FD alone appear to drive very disparate regional outcomes for a given
shock. That is, FD matters.
Turning to details, we proceed in this part of the analysis by subjecting the
stationary distribution of each region to an exogenous and unanticipated (but
permanent) house price decline. Importantly, we allow for region-specific house
prices shocks that mimic the previously documented house-price declines across
different FD regions. To use the data presented in Section 2, we summarize the
information into the five “regions” created. Because the model is yearly, we need
a yearly change in house prices for each region. We selected the change between
2007 and 2008.20
20
It is useful to note that we obtain very similar results using the average yearly change
34
The first row of Table 5 shows the shocks hitting the economy. The baseline
decline in house prices is significantly uneven across FD “regions”: it is only 7
percent for Q1, but reaches 11.5 percent for Q5. The implied aggregate implications are presented in the sixth column. Note that the aggregate decline in house
prices is 9.1 percent. The last column shows a counterfactual aggregate economy
in which each region has a decline in house prices of 9.1 percent.
The rest of Table 5 shows the implications of the decline in house prices. Because the house price shocks are modeled as permanent changes, all the values
presented are measured as percentage change relative to old steady-state averaged over three periods as in Dupor et al. [2019].21 The aggregate decline in
consumption is only 0.03 percent. In terms of a MPC out of a change in house
prices, this change implies that consumption declines less than 1 cent per dollar decline in house prices. To put this in context, Mian et al. [2013] estimate
an MPC for nondurable spending of 1.6 cents per dollar and essentially zero for
grocery spending.
Given our aim to understand the manner in which FD affects the ability
of households (and by extension the macroeconomy) to withstand shocks, it is
essential to focus on the change in consumption across regions. The contrast
across quintiles is very striking: consumption increases by 0.42 percent in Q1
but decreases 1.32 percent in Q5. The changes in other variables offer clues
about the mechanism. Note, for example, that household financial assets decline
across quintiles after the shocks. Perhaps the most important is the change in
unsecured debt, which declines by 14.5 percent for Q5 but only by 2.1 percent
for Q1.
These differences across “regions” are relevant because they show that the
response to “aggregate” shocks may be very different. However, they are also
meaningful because they have aggregate implications. Comparing the aggregate
results presented in the last two columns, we can see that aggregate consumption
declines only slightly (0.03 percent) with the actual distribution of shocks and
increases significantly (0.88 percent) with the shocks distributed uniformly.
between 2006 and 2009 as well.
21
For example, if the change measured relative to the steady state is 2 percent and is preceded
by a path of 2 percent in the first period, 3 percent in the second, and 4 percent in the third
one, the change presented in the table would be 3 percent.
35
Table 5: House Price Shock Experiments
% chg in
House prices
Consumption
Fin. assets
Unsec. debt
Home equity
Ownership
Unequal shocks
FD “Regions” or Quintiles
Q1
Q2
Q3
Q4
Q5
-6.99 -8.60 -10.0 -10.9 -11.5
0.42
0.04 0.10 -0.37 -1.32
-1.63 -1.39 -1.73 -1.53 -1.50
-2.11 8.27 -4.47 -11.6 -14.5
-6.71 -9.39 -11.0 -12.6 -14.5
0.38 -1.62 -1.55 0.44 0.09
Aggregate
-9.10
-0.03
-1.42
-8.50
-10.1
-0.53
Equal shocks
Aggregate
-9.10
0.88
-1.41
26.3
-10.1
-0.53
Note: All values are measured as percentage change relative to the old steady state, averaged
over three periods during the transition to new steady state.
In what we have reported so far, we have used the data directly, inclusive of
the covariance structure summarized in “Fact 3” above. However, it is important to provide some isolation of how the distribution of the shocks across FD
“regions”, purely on its own, works to alter the transmission of a shock. We
therefore examine next the case with shocks identical across all “regions.” We see
that total spending (consumption), i.e., spending aggregated across FD quintiles,
increases by almost 1 percentage point. To understand where that difference in
the aggregate numbers is coming from, Figure 11 presents the implied regional
consumption responses from both experiments. In the case with equal shocks
among “regions,” the differences between the most and least distressed regions
are even more stark. In this case, we see that the least financially distressed region
sees consumption increase by nearly 4.0 percentage points. This is the basis for
our claim that relatively microeconomic, i.e., zip-code level, FD matters for who
bears the burden of macroeconomic risk, and to some extent for macroeconomic
vulnerability itself.
While the previous analysis helps illuminate the importance of accounting
for regional heterogeneity in FD and the role of uneven shocks, it does not fully
delineate the importance of modeling FD. To address this, we now conduct two
more exercises. First, we consider what happens in a setting with no possibility
of informal default or bankruptcy (referred to as “no FD”). This case is, in one
sense, the standard case studied in most models of consumption, where neither
formal nor informal default are typically allowed. This baseline case of course
36
Figure 11: Consumption Responses to House Price Shocks by Quintile of FD and
Experiment Type
Notes: All consumption changes are relative to old steady states and are averages over three
periods during the transition to new steady state. Dashed line represents economy-wide
average of corresponding variable under benchmark case. Dotted line represents
economy-wide average of corresponding variable under same shock case.
cannot make any contact with empirical notions of FD and also (really, hence)
implies that all financial debt is risk-less because it is always repaid. Following
that, we address the importance of modeling FD in a second counterfactual where
we disallow unsecured borrowing altogether—think of this case as adding a zero
borrowing constraint. We refer to this as the “no borrowing” case. Figure 12
presents the results of these two counterfactual scenarios.
Across the economies, the availability (or lack thereof ) of FD matters substantially for the response of consumption to house price shocks. In general, across all
economies, removing the possibility of FD shrinks the drop in consumption (or
increases the jump). Focusing on the most distressed quintile/region/economy
(Q5), the economy without FD has a minimal consumption drop instead of the
-1.3 percent decline in the benchmark economy. In the economy with no unsecured borrowing, the difference relative to the benchmark is even more striking,
with consumption in Q5 increasing by half a percentage point due to the decline
in house prices.
37
The horizontal lines in Figure 12 represent the aggregate changes. The aggregate numbers reflect what happens in each “region”: removing FD reduces
the drop in consumption (or increases the jump). In both counterfactual cases,
the aggregate change in consumption would be positive instead of slightly negative. Again, this highlights the role of FD for the response of the economy to
“aggregate” shocks.
The key mechanism behind the differential consumption response of the nonFD economy to the baseline reflects a well-known feature of models of defaultable
debt: unsecured borrowing is risk-less, and consumers can borrow much more
to smooth consumption. In the no-borrowing economy, precisely to deal with
the inability to borrow, agents generally have higher asset positions to smooth
housing shocks. Additionally, the richness of our model allows us to capture a
more subtle effect running from wealth to consumption: better asset positions
reinforce the income and substitution effects of lower house prices for “soon to
be owners”, who can raise their non-housing consumption.
38
Figure 12: Consumption Responses by Quintile of Financial Distress and Debt
Arrangement
Notes: All consumption changes are relative to old steady states and are averages over three
periods during the transition to new steady state. The horizontal lines represent the
economy-wide average consumption drop in each case.
5.2
A second aggregate shock: Income Loss
The economic downturn generated by the COVID-19 pandemic has (aside from its
direct health effects) affected households differently than did the asset-price collapse that was the first manifestation of the Great Recession. Section 2 showed
that areas with greater FD also tend to have larger employment shares in industries that were more affected by the social distancing that accompanied the
COVID-19 pandemic. It also showed that areas with more FD had fewer households that were not affected by this crisis. In this section, we map these numbers
into the five quintiles, or “regions,” for use in our calibrated model. We then
present a simulation exercise in which agents are subject to earnings shocks that
are obtained from the information in Section 2 and from professional forecasts for
income losses over the rest of the year. Much like the results from the previous
section, we find that the dispersion in income shocks results in significant dispersion in consumption responses across the FD distribution. Additionally, and
39
again in line with the previous section, we find that even if income shocks are
uniformly distributed across the FD distribution, there remain notable differences
in consumption responses across the quintiles of FD.
There are three steps in our calibration of the COVID-19 shock. First, we
compute the share of workers in “leisure and hospitality” for each quintile. These
are the most affected workers, as they have a decline in yearly earnings of 30
percent. The decline in income for this group was calibrated to be in line with
the data presented in Figure 4.22 The findings are presented in the first column in
Table 6. It shows the share of households in the “leisure and hospitality” sector
increases across FD quintiles, ranging from 9.17 percent in Q1 to 12.1 percent in
Q5. This fact naturally replicates the correlation of FD and the share of workers
in this sector at the zip-code level shown in Figure 7.
The second step in our calibration of the COVID-19 shock is to identify
workers who are not affected by the lockdown, perhaps because they can work
remotely. Figure 8 already showed that the share of households that are not
affected is decreasing in the incidence of FD at the state level, according to data
from the Census Pulse Survey. We use that relationship to obtain the predicted
share that is not affected for each of our “regions” and present the results in the
second column of Table 6. While 52.2% of households in Q1 did not have income
losses over the first 4 months of the lock-down, this share is only 38.4% for Q5.
Table 6: Distribution of COVID-19 related earnings losses by FD.
FD
Quintile
1
2
3
4
5
∆ Sectoral Income, %
Implied Aggregate % ∆
Share of workers by Sectors:
Most affected Not affected somewhat affected
9.17
52.2
38.7
10.0
48.9
41.0
10.6
46.4
43.0
11.1
43.7
45.2
12.1
38.4
49.5
-30.0
0.00
-9.08
-3.12
0.00
-3.88
Average
∆ Income
-6.26
-6.74
-7.09
-7.43
-8.13
-7.00
The third and last step is to derive how affected households are that belong
22
This provides a conservative estimate for the rest of the year given that the loosening of
the lock-down during June generated a new wave of cases.
40
neither to the most-affected nor to the unaffected sectors. We set this number
such that the aggregate decline in income for our 2020 simulation matches the
predicted decline of 7 percent by the consulting firm Macroeconomic Advisers.
Given that the predicted aggregate decline is so severe, and that about 40 percent
of households will be unaffected, we need a decline in income for the “somewhat
affected” households of 9.1 percent to finalize our calibration.
The last column in Table 6 summarizes the shock presenting the decline of
average income by quintile. In the “region” with the lowest incidence of FD
(Q1), the decline in income averages 6.26 percent, while the decline in average
income for the region with the highest incidence of FD (Q5) is 8.13 percent.
Next, we hit each of our five calibrated “regions” with income shocks following the
distributions displayed in Table 6. These shocks are modeled as unanticipated and
transitory. For instance, in Q1, we randomly select 9.17 and 38.7 percent of the
households and reduce their incomes by 30 percent and 9.08 percent, respectively.
Table 7 shows the results. The first row repeats the information about the
change in income for each “region.” Across quintiles it is clear that there are
differences in how much consumption responds to income shocks. While individuals in Q1 decrease their consumption on average by just under 2 percent,
individuals in Q5 decrease their consumption by more than 4 percent. These
striking differences show that without any policy interventions, households were
expected to respond very differently to the COVID-19 shock. As the sixth column shows, aggregate consumption would decline by 2.79 percent. Given the size
of the shock, this implies a MPC equal to 0.33, which is comparable to MPCs
out of transitory income shocks reported in Table 1 of Carroll et al. [2017] when
looking at horizons of one year. Additionally, it is worth highlighting that since
we distinguish between financial wealth and housing wealth when calibrating our
economies, our model-based MPCs will in general be higher, as shown in Carroll
et al. [2017].
Table 7 also presents information about other statistics that are useful to
understand the differences across quintiles. One fact to highlight is the increase
in bankruptcies, which is much higher for Q5 than Q1.
The last column in Table 7 shows how the aggregate change would look if the
share of households in each group were the same for all quintiles. The results
41
Table 7: COVID Income Shock Experiments
% chg in
Income
Consumption
Fin. Assets
Fin. debt
Home equity
DQ incidence
BK incidence
Ownership
Unequal shocks
FD “Regions” or Quintiles
Q1
Q2
Q3
Q4
Q5
-6.26 -6.74 -7.09 -7.43 -8.13
-1.99 -2.35 -2.90 -3.20 -4.20
-1.45 -1.81 -1.88 -1.97 -2.33
7.56 9.34 9.59 7.20 5.54
-0.48 -0.67 -0.69 -0.77 -1.08
11.87 11.48 9.18 7.37 7.33
4.07 10.35 12.72 13.75 14.33
-0.69 -0.97 -1.23 -1.56 -2.08
Equal shocks
Aggregate
Aggregate
-7.00
-2.79
-1.76
7.42
-0.67
8.88
11.68
-1.26
-7.00
-2.75
-1.78
7.17
-0.67
8.70
11.01
-1.23
Notes: Income shocks are transitory. All values are measured as percentage change relative to
old steady state. Change in income and consumption are measured in period of shock.
Changes in all other variables are measured in period after shock.
indicate that the effect would be less severe, but changes in all the variables are
small. For instance, the decline in consumption is now 2.75 percent versus a
decline of 2.79 percent in the benchmark. Similarly, debt increases by more in
the benchmark, but the difference is 7.42 percent vs. 7.17 percent.
However, the preceding finding does not mean that differences in the incidence
of FD does not matter. Just as we did in the case of the shock representing
the Great Recession, Figure 13 answers the question of what the consumption
responses would look like if all quintiles were subject to the same distribution of
income shocks. As can be seen, most of the behavior remains the same as in the
benchmark. In both cases, there are significant differences in consumption across
regions/FD quintiles. With the same shocks, the decline in spending by the least
financially distressed is 2.2 percent, while it is about one-and-half times as large
as that amongst the most financially distressed (3.6 percent). Another way to
think about this finding is the following: If the entire United State were to look
like our regions with the highest FD, the aggregate decline in consumption would
be 3.6 percent instead of 2.8 percent, or roughly $200 billion greater on impact.
Lastly, to uncover the role of FD as a mechanism in dealing with this aggregate shock to income, as opposed to asset valuation, we proceed as before
and conduct the same pair of counterfactual exercises. To remind the reader,
42
Figure 13: Consumption Responses to COVID Income Shocks by Quintile of FD
and Experiment Type
Notes: All changes are measured in period of shock. Dashed line represents economy-wide
average of corresponding variable under benchmark case. Dotted line represents
economy-wide average of corresponding variable under same shock case.
these counterfactual scenarios are (i) an economy where borrowing is allowed but
default (and hence FD) is not, and (ii) an economy where debt is disallowed
altogether. Figure 14 presents the results.
We see from the figure that both removing the FD option and removing the
option to borrow are associated with significantly smaller aggregate consumption
declines. In particular, note that aggregate consumption declines 2.3 percent
instead of 2.79 percent.
6
Empirical validation
Our model suggests that FD matters: microeconomic distress is related to greater
sensitivity to macroeconomic shocks. This was seen throughout the results of
sections 5.1 and 5.2 where at an aggregate level, higher FD was associated with
larger consumption declines in response to shocks. In our model, at the individual level, agents cut their consumption more drastically not just because FD
prevents them from having access to credit, but also because other characteris43
Figure 14: Consumption Responses by Quintile of FD and Debt Arrangement
Notes: All changes are measured in period of shock. The dashed line represents the
economy-wide average consumption drop under the benchmark model. The dotted line
represents the economy-wide average consumption drop when no FD is allowed. The
dash-dotted line represents the economy-wide average consumption drop when no borrowing
is allowed.
tics correlated with FD. Using the case of homeowners as an example, those in
FD mostly turn out to be those with higher discount factors (the “impatient”
types) who in turn often have long histories of facing high borrowing costs in
the unsecured credit market. As a result, their consumption is mainly financed
through other means such as mortgage refinancing. When housing and income
shocks arrive, these means vanish and they respond by aggressively cutting consumption. To what extent can additional evidence be brought to bear to validate
this mechanism?
While we lack sufficiently detailed data at the individual level to corroborate this mechanism directly, in the case of the house price shock, we can test
this result by asking what happens at a more aggregate level. That is, we can
ask 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 now estimate the MPC out of housing shocks following the
seminal work of Mian et al. [2013]. In particular, we want to determine whether
44
MPCs vary in a significant fashion by FD holding constant other regional features
such as income, wealth, etc. Formally, we estimate regressions of the form:
∆Cti = α + β1 ∆HVti + β2 F Dti + β3 (∆HVti × F Dti ) + β4 Xti + it .
(1)
Here, ∆Cti is the dollar change in consumption in geographic region i between t
and t+1; ∆HVti is the change in home value; F Dti is the level of FD in region i at
time t; Xti is a vector of other regional covariates that can be both in levels and
changes; and it is the error term.23 The coefficient of central interest is β3 , the
interaction between FD and housing shocks. 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 (except for FD which is measured in 2002), while all
changes are measured between 2006 and 2009.
Table 8 reports the results of estimating equation (1). All columns reveal
statistically significant coefficients at the 0.001 level for house price shocks (i.e.,
the change in home value between 2006 and 2009) and the interaction of these
shocks with FD. Comparing across columns suggests that our estimated coefficients are robust to the definition of FD we use. Importantly, the interaction
term is positive: higher FD in 2002 is associated with larger consumption drops
between 2006 and 2009.
It is easiest to interpret the interaction term coefficients with some examples.
Figure 15 shows how the coefficients in Column (2) of Table 8 translate into
differing MPCs by level of FD. 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
horizontal line represents the MPC estimated by Mian et al. [2013]. In general,
our estimates are slightly smaller.24 More importantly, the MPC increases with
23
One minor difference against the regressions of Mian et al. [2013] is that, where they
calculate ∆HVti and the change in financial wealth ∆F Wti by multiplying the initial value in
each by the percentage change in corresponding market indices, we take the direct difference
in zip-code level home values and financial wealth between 2006 and 2009. This affords us
broader coverage, and is possible because we now have access to home value and IRS SOI data
for 2009 that they did not. The full construction of these variables is described in Appendix A
and particularly subsection A.2.
24
Related, Dupor et al. [2019] estimate that the MPC is 0.9 cents, which is smaller than the
MPC estimated by Mian et al. [2013] but also in the range of our estimates.
45
Table 8: Auto spending at the zip-code level
FD Measurement taken in 2002:
∆06−09 Home Value
FD
∆06−09 Home Value × FD
Observations
(DQ30)
-0.005
(0.00)
-5.283***
(1.15)
0.099***
(0.02)
14136
∆06−09 Auto Spending
(CL80)
(CL80 and DQ30)
-0.008
-0.009*
(0.00)
(0.00)
-5.203***
-5.525***
(1.02)
(1.19)
0.070***
0.097***
(0.02)
(0.02)
14136
14136
(ADQ30)
-0.006
(0.00)
-3.670***
(0.74)
0.070***
(0.01)
14136
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 zip code as of 2006. Standard errors appear in parentheses.
the incidence of FD from less than 1 cent to more than 2 cents.
Figure 15: Marginal Propensity to Consume out of a Dollar change in home prices
by Quintile of DQ30 in 2002.
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 at the
zip-code level by Mian et al. [2013] in their fifth column of Table 5.
46
7
Concluding Remarks
The main findings of this paper are that household-level FD is very unequally
distributed, that FD affects consumer vulnerability to macroeconomic shocks,
and that in some cases, FD and its dispersion matter for the aggregate consumer spending response to an economywide shock. Our paper proceeds by first
establishing three facts: (i) regions in the U.S. vary significantly in their “FDintensity,” measured either by how much additional credit households therein
can access or in how delinquent they typically are on debts, (ii) shocks that are
typically viewed as “aggregate” in nature hit geographic areas quite differently,
and (iii) FD is an economic “pre-existing condition”: the share of an aggregate
shock borne by a region is positively correlated with the level of FD present prior
to the shock. Using an empirically disciplined and institutionally rich model of
consumer debt and default, we show that in both the Great Recession and in the
initial outcomes in the COVID-19 pandemic, FD mattered. Our model implies
that the uneven distribution of FD implied uneven consumption responses. We
find that this remains true even when breaking the positive correlation between
initial FD and the incidence of an “aggregate” shock on each region.
In identifying FD as an amplifier of shocks—starting with household-level
spending—our findings reinforce the message first discovered and conveyed by
Mian et al. [2013] and Mian and Sufi [2010]. Those authors were the first to show
decisively that macroeconomic outcomes run through household balance sheets
and credit health.
Our work suggests also that the state of households vis-à-vis their creditors,
which we capture through FD, is also likely to be important in governing macroeconomic fragility in terms of aggregate consumer spending and provides information in addition to that encoded in leverage or net worth.
A conjecture for future work that emerges from our paper is that macroprudential policy may benefit from tracking either or both of the measures of
FD we have provided. FD can be observed at a fairly granular level and hence
may well be relevant to forecasting not only the severity of damage to local or
regional consumption from macroeconomic shocks, but also the amplification of
the shocks themselves.
47
References
Aditya Aladangady.
Housing wealth and consumption: Evidence from
geographically-linked microdata. American Economic Review, 107(11):3415–
46, 2017.
Boragan Aruoba, Ronel Elul, and Sebnem Kalemli-Ozcan. How big is the wealth
effect? Decomposing the response of consumption to house prices. 2018.
Kartik Athreya, Juan M. Sánchez, Xuan S. Tam, and Eric R. Young. Labor
market upheaval, default regulations, and consumer debt. Review of Economic
Dynamics, 18(1):32–52, January 2015.
Kartik Athreya, Juan M. Sánchez, Xuan S. Tam, and Eric R. Young. Bankruptcy
and delinquency in a model of unsecured debt. International Economic Review,
59(2):593–623, 2017.
Kartik Athreya, José Mustre-del Rı́o, and Juan M. Sánchez. The persistence of
financial distress. The Review of Financial Studies, 32(10):3851–3883, 2019.
Adrien Auclert and Kurt Mitman. Consumer bankruptcy as aggregate demand
management. 2019.
David Berger, Veronica Guerrieri, Guido Lorenzoni, and Joseph Vavra. House
Prices and Consumer Spending. Review of Economic Studies, 85(3):1502–1542,
2018.
J. Y. Campbell and J. F. Cocco. How Do House Prices Affect Consumption?
Evidence from Micro Data. Journal of Monetary Economics, 53(3):591621,
2007.
Christopher Carroll, Jiri Slacalek, Kiichi Tokuoka, and Matthew N. White. The
distribution of wealth and the marginal propensity to consume. Quantitative
Economics, 8(3):977–1020, November 2017.
Raj Chetty, John N. Friedman, Nathaniel Hendren, and Michael Stepner. How
did covid-19 and stabilization policies affect spending and employment? a new
real-time economic tracker based on private sector data, June 2020.
48
Bill Dupor, Marios Karabarbounis, Marianna Kudlyak, and M. Saif Mehkari. Regional Consumption Responses and the Aggregate Fiscal Multiplier. Working
Paper Series 2018-4, Federal Reserve Bank of San Francisco, February 2018.
Bill Dupor, M. Saif Mehkari, Rong Li, and Yi-Chan Tsai. The 2008 US Auto
Market Collapse. Technical report, 2019.
Carlos Garriga and Aaron Hedlund. Mortgage Debt, Consumption, and Illiquid
Housing Markets in the Great Recession. October 2017.
Andrew Glover, Jonathan Heathcote, Dirk Krueger, and Jose-Victor Rios Rull.
Controlling a pandemic. April 2020.
Joseph Gruber and Robert Martin. Precautionary savings and the wealth distribution with illiquid durables. 2003.
Fatih Guvenen, Serdar Ozkan, and Jae Song. The nature of countercyclical
income risk. Journal of Political Economy, 122(3):621–660, June 2014.
Juan Carlos Hatchondo, Leonardo Martinez, and Juan M. Sánchez. Mortgage
defaults. Journal of Monetary Economics, 76:173–190, November 2015.
Kyle F. Herkenhoff. The role of default (not bankruptcy) as unemployment
insurance: New facts and theory. Working Paper, January 2013.
Kyle F. Herkenhoff and Lee E. Ohanian. Foreclosure delay and u.s. unemployment. Working Paper, March 2012.
Greg Kaplan and Giovanni L. Violante. How Much Consumption Insurance beyond Self-Insurance? American Economic Journal: Macroeconomics, 2(4):
53–87, October 2010.
Greg Kaplan, Giovanni L. Violante, and Justin Weidner. The Wealthy Hand-toMouth. Brookings Papers on Economic Activity, 45(1 (Spring):77–153, 2014.
Greg Kaplan, Kurt Mitman, and Giovanni L. Violante. Non-durable Consumption and Housing Net Worth in the Great Recession: Evidence from Easily
Accessible Data. NBER Working Papers 22232, National Bureau of Economic
Research, Inc, May 2016.
49
Greg Kaplan, Benjamin Moll, and Giovanni L. Violante. Monetary Policy According to HANK. American Economic Review, 108(3):697–743, March 2018.
Greg Kaplan, Kurt Mitman, and Giovanni L. Violante. The housing boom and
bust: Model meets evidence. 2019.
Greg Kaplan, Ben Moll, and Gianluca Violante. Pandemics according to hank.
May 2020.
P. Krusell and A Smith. Consumption-savings decisions with quasi-geometric
discounting. Econometrica, 71(1):365–375, 2003.
Moritz Kuhn and José-Victor Rı́os-Rull. 2013 update on the u.s. earnings, income,
and wealth distributional facts: A view from macroeconomics. Federal Reserve
Bank of Minneapolis Quarterly Review, 37(1):1–73, April 2016.
Igor Livshits, James MacGee, and Michèle Tertilt. Consumer bankruptcy: A
fresh start. American Economic Review, 97(1):402–18, March 2007.
Atif Mian and Amir Sufi. The great recession: Lessons from microeconomic data.
American Economic Review, 100(2):51–56, 2010.
Atif Mian, Kamalesh Rao, and Amir Sufi. Household Balance Sheets, Consumption, and the Economic Slump. The Quarterly Journal of Economics, 128(4):
1687–1726, 2013.
Kurt Mitman. Macroeconomic Effects of Bankruptcy and Foreclosure Policies.
American Economic Review, 106(8):2219–2255, August 2016.
Christina Patterson. The matching multiplier and the amplification of recessions.
2018.
Anthony Pennington-Cross. The duration of foreclosures in the subprime mortgage market: A competing risks model with mixing. Working Paper 027A,
Federal Reserve Bank of St. Louis, 2006.
Monika Piazzesi and Martin Schneider. Housing and macroeconomics. In John B.
Taylor and Harald Uhlig, editors, Handbook of Macroeconomics, volume 2,
pages 1547–1640. North-Holland Press, 2016.
50
Albert Saiz. The Determinants of Housing Supply. The Quarterly Journal of
Economics, 125(3):1253–1296, 2010.
A
Empirical Analysis
In the following subsections, we present detailed information about each variable
and how it was constructed, as well as various empirical results to supplement
what is shown in the paper. Table A1 shows some initial summary statistics for
the entire data set.
Table A1: Descriptive Statistics Across Zip codes
Housing Net Worth Shock, 2006-9
Change in home value $000, 2006-9
Net Worth per Household $000, 2006
Income Per Households, $000, 2006
No. Hou. per zip code (ths), 2006
Housing Leverage Ratio, 2006
∆06−09 auto spending per hou. $000
Fraction in DQ30, 2006
Fraction in CL80, 2006
Count
Mean
S.D.
p25
p50
p75
14230
14230
14230
14230
14230
14230
14230
14230
14230
-0.098
-38.905
487.854
72.861
11.390
0.453
-2.108
0.142
0.228
1.035
64.130
934.963
53.508
6.399
0.173
6.447
0.048
0.054
-0.109
-62.833
159.956
45.125
6.703
0.347
-2.525
0.108
0.192
-0.030
-13.200
269.338
58.838
10.968
0.433
-1.517
0.138
0.228
0.005
2.300
496.700
82.823
15.305
0.536
-0.835
0.172
0.264
Note: All statistics are weighted by the number of households in the first quarter of 2006 for each zip code. p25, p50, and p75
respectively give the 25th, 50th, and 75th percentiles.
Sources: IRS SOI, FRBNY Consumer Credit Panel/Equifax, Census Bureau, Zillow, SCF.
A.1
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, 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 oversample areas with lower
population.
51
Specifically, we pull a 100 percent sample of individual Equifax records from
the smallest zip codes by population and decrease that percentage linearly until
pulling a 50 percent sample of Equifax records for the largest zip codes.25 In order
to remain in our sample for a given quarter, individuals must be between 25 and
65 years old, inclusive.26 Then, we correct for oversampling by reweighting using
population data from the 2000 and 2010 Census.
A.2
Constructing measures of wealth and consumption
The household wealth portion of our dataset was constructed at the zip code and
county levels using a method almost identical to that of Mian et al. [2013]. Net
wealth is defined as the sum of housing wealth H and financial wealth F W less
debt D. 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.27 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 credit28 recorded in Equifax, in each geography multiplied by the number of
households in that geography, taken from the Census.
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 financial
wealth recorded in the Survey of Consumer Finances (SCF) corresponding to
25
Zip-code level data on CL80 and DQ30 are available at this link for the years 2006 and
2018.
26
Age is calculated using an individual’s recorded birth year, and so any records not including
a birth year are also excluded.
27
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. Mian et al. [2013] 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.
28
This includes both the home equity installment balance and the home equity revolving
balance.
52
that fraction.29 F W at the county level is simply calculated as the sum of F W
in its component zip codes.30 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 in the Census. Next, we assign each geography a portion of the total debt
from the SCF equal to that fraction.
In addition to the types of debt that Mian et al. [2013] 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.
As a measurement of 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
zip-code and county. As noted by Mian et al. [2013], 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
Mian et al. [2013] in allocating an annual share of the national Census Retail
Trade amounts for “Auto, Other Motor Vehicle” to each zip code and county
equal to the share of new autos that residents of each geography 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 local level to the extent that auto prices did not
evolve in the same way across zip codes and counties from 2006 to 2009. If
29
Mian et al. [2013] used the Federal Flow of Funds for this purpose, but we use the Survey of
Consumer Finances because it allows us to limit our financial wealth totals to those of a certain
age range. Specifically, our model is calibrated to match dynamics among people who are 25
to 55 years old, and so we likewise restrict the data to that age range when setting calibration
targets. As shown in Kuhn and Rı́os-Rull [2016], the SCF and Federal Flow of Funds match
up quite nicely in terms of aggregates. The SCF is not avaliable in every year, and so wherever
necessary we interpolate linearly between avaliable years.
30
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.
53
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 Mian et al.
[2013] did.
A.3
Financial Distress
Several measures of FD are used in this paper. As defined in Section 2, DQ30
gives the percentage of primary 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 percent of their credit limit during some quarter of
the year.
With these two definitions in place, the remaining metrics used in the regression tables elsewhere make slight modifications to serve as robustness checks.
“DQ30 and CL80” 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 percent of their credit limit31 and then averages that percentage across
the geography. “ADQ30” is defined much like DQ30, but gives the percentage
of people in a zip code who are at least 30 days delinquent on any kind of debt
recorded by the Federal Reserve Bank of New York/Equifax CCP.
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.
31
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 percent
of their available credit card limit. Then, in quarter 2, they remained over 80 percent 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 percent of the year in financial distress. Similar calculations would be made for all
other individuals in our sample from their geography, and those numbers would be averaged to
reach the final result.
54
A.3.1
The persistence of “pre-existing” regional FD
FD defined in this way is highly persistent over time at an individual level, as
shown in Athreya et al. [2019]. Thinking of a zip code as a collection of individuals, it follows that there should be some persistence in FD characteristics at a
community level as well, although limited by the way that individuals sometimes
move. In fact, however, FD at the zip-code level is more persistent than would
be expected if individual-level persistence were the only factor at play. Figure A1
illustrates this point. Conditional on a zip code having been in the worst quintile
of FD in 2000, there is a 55 percent chance that it was still in the worst quintile
18 years later. This is over twice as likely as random chance would predict, and
occurs despite the fact that some or all of the original households that inhabited
each zip code in 2000 could have moved out.
Figure A1: Persistence of Financial Distress at the Zip-code Level
Note: This graph is weighted in each year by the number of households in each zip code.
“Random Chance, Quintile 5” presents what the probability of being in quintile 5 would be in
each year if FD occurred randomly across zip codes.
Indeed, given from 2007 ACS data that the average person in the United
55
States will move about 12 times in their lifetime, and assuming those moves are
distributed randomly over a 80-year lifetime, a back of the envelope calculation
suggests that the average person in our sample moved 2.6 times in the years 20012017. If FD were only persistent at the individual level, then, and people had no
tendency to sort themselves into zip codes with similar FD patterns, we would
again expect the odds that a zip code in the worst quintile of FD in 2000 remains
there in 2018 to be near random. Given that it is not, this shows evidence for
additional mechanisms driving the persistence of zip-code level FD than simple
persistence at the individual level. Zip codes that did leave the worst quintile did
not move far. 24 percent had moved to quintile 4 by 2018, and only 4 percent
had moved to the least-distressed quintile.
The persistence of regional FD helps us to disentangle the underlying preexisting conditions of FD at the onset of an economic shock from an FD response
endogenously made due to the shock. In the case of the Great Recession, as
shown in Figure A2, the share of debt in delinquency rose in tandem with the
fall in home prices as people sought to smooth consumption by missing debt payments. Communities already in greater FD had less ability to use this channel
for smoothing consumption. For each shock we consider, distinguishing zip codes
that temporarily entered FD from those that were already in FD requires measuring FD somehow separately from this endogenous response. Because FD is so
persistent, this can be done by measuring it for each zip code before the shock
occurred. We specifically use FD measurements taken in 2002 for the Housing
shock modelling the Great Recession and measurements taken in 2018 for the
income shock modelling the COVID-19 pandemic.
A.3.2
Differences between FD and leverage
It is important to note that FD is not merely housing leverage repackaged, as may
be wondered given some analogous findings of Mian et al. [2013]. Indeed, as shown
in Figure A3, there does not appear to be a clear relationship between the two
contemporaneously in 2002. Considering the 2006 housing leverage ratio against
FD in 2002, there appears to be if anything a negative relationship between the
two; i.e., more regions with more financial distress have lower leverage!
56
Figure A2: Evolution of Aggregate House Prices and Financial Distress
Note: The shaded area represents the Great Recession.
Housing Leverage Ratio, 2002
.4
.45
.5
.55
.6
Figure A3: Correlation of Housing Leverage with FD (DQ30) in 2002
.1
.15
.2
DQ30 in 2002
.25
.3
.05
.1
.15
.2
DQ30 in 2002
.25
.3
Housing Leverage Ratio, 2006
.35
.4
.45
.5
.05
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 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.
A.3.3
Correlation between FD and the Housing Wealth Shock
In considering the implications of this drop in house prices for household balance
sheets, it is useful to convey lost housing wealth as a fraction of net wealth. We
follow Mian et al. [2013] in defining net wealth N W as the sum of housing wealth
57
H and financial wealth F W less debt D. In their framework, the housing net
worth shock for a zip code i is then defined as the change in housing wealth
i
∆Hi,06−09 divided by the initial net wealth N W06
.
Figure A4 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 2002 was associated with larger
declines in housing wealth shocks in the Great Recession.
Figure A4: Housing Wealth Shocks (2006-09) and FD (DQ30) in 2002
Sources: IRS SOI, Zillow, FRBNY Consumer Credit Panel/Equifax, Census Bureau, SCF.
Each dot represents the mean of that bin weighted by 2006 net wealth of bins with respect to
DQ30.
Notice that the housing-net-wealth shock decomposes into two contributing
effects—the change in home prices and the share of wealth that was held in
housing in 2006—as follows:
∆Hi,06−09
=
i
N W06
∆H
|
}
i,06−09
i
H06
{z
Hi
06
.
i
N W06
| {z }
% chg. in house prices share of wealth in housing
In terms of the change in home prices, Figure 6 shows that regions with more FD
experienced greater percentage losses. These regions also tend to hold a larger
share of their net wealth in their homes,32 so that they experienced a more severe
32
This can be seen, for example, in table 1. The difference between “Net Wealth Per HH”
and “Net Fin. Wealth Per HH” is the housing wealth per household. Dividing this by the net
wealth per household shows that housing wealth as a percentage of net wealth is monotonically
increasing in FD: Quintiles 1,2,3,4, and 5 have housing shares of net wealth respectively equal
to 37.5 percent, 40.7, 42.2, 42.8, and 52.2 percent.
58
housing net wealth shock along the second channel as well.
In other words, even if every zip code had experienced the same percentage
decline in home prices, those with high FD would have tended to experience larger
net wealth shocks. Similarly, this relationship would have held even if the share
of wealth in housing had been held constant and only the home prices had been
allowed to vary. As it is, the correlation at the zip code level between FD and
the local housing net worth shock is highly robust because both of these effects
are present and working in the same direction.
For example, the correlation is robust to alternative definitions of FD, as can
be seen in Figure A6a. 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. As would be expected from the regional persistence of
FD discussed in appendix Section A.3.1, these results are also not dependent upon
measuring FD in a particular year. Figure A6b shows that the same relationship
holds when measuring FD just before the recession started in 2006.
A.3.4
Amplification
Changes in house prices are amplified differently into housing net worth shocks
because of differences in leverage. A net worth shock is defined as in Mian et al.
[2013] by
∆log(pH,i )H i
i
∆log(pH,i
06−09
06−09 )H06
06
=
i
i
N W06
H06
|
{z
}
chg. in house prices
Hi
06
.
i
N W06
| {z }
share of wealth in housing
Thus, the amplification is driven by two underlying components of the housing
net worth shock, both of which themselves correlated with FD: the change in
home prices and the share of wealth that was held in housing in 2006. Setting
each component in turn constant to isolate variation in the other, it is possible
to uncover the relative importance of each component to the overall housing
net worth shock. Figure A7 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
59
Figure A5: Robustness of the correlation between housing wealth shocks and FD
(a)
Note: “120 day Delinquency sometime 2000-06” gives 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, 2002” gives the percentage of people in a zip code both in
FD under the CL80 definition and having debt indicative of owning a house (i.e., a mortgage
or home equity line of credit). “DQ30 and Housing Debt, 2002” is similar.
(b)
Note: “30 day Delinquency of Any Type” gives the percentage of people in a zip code that are
30 or more days delinquent on any type of debt as recorded by the New York Federal Reserve
Bank/Equifax CCP. “% of CC debt 30 days Delinquent” gives the percentage of all credit
card debt in a zip code that is at least 30 days delinquent.
Sources: IRS SOI, Zillow, FRBNY Consumer Credit Panel/Equifax, Census Bureau, SCF.
Each dot represents the mean of that bin of FD weighted by 2006 net wealth.
60
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.
Figure A7: Decomposition of 2006-09 House Price Shock
Sources: IRS SOI, Zillow, FRBNY Consumer Credit Panel/Equifax, Census Bureau. Quintile
means of each object are weighted by that objects denominator in 2006; i.e., the “Housing Net
Worth Shock” and “Shock Holding the Change in Home Price Constant” are weighted by net
wealth, and the “Shock Holding the Share of Wealth in Housing Constant” is weighted by
housing wealth.
B
B.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, ) =
max
Irent ∈{0,1}
)
Irent Rj,n (a, z, ) + (1 − Irent )Bj,n (a + en (z, ), z) , (2)
61
where earnings are en (z, ) = exp(f + ln + z + ). Here Irent equals 1 when the
household chooses 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
BK
P
(a, z, ), Rj,n
(a, z, ) ,
(a, z, ), Rj,n
Rj,n (a, z, ) = max Rj,n
(3)
P
Bj,n (a, z, ) = Bj,n
(a, z, ).
(4)
and
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 superscripts in each value function represent whether the household is, or is
not, defaulting 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 has only to 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
(5)
a
c + qj,n
(hR , 0, a0 , z)a0 = e + a,
e = exp(f + ln + z + ).
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:
62
h
i
BK
Rj,n
(a, z, ) = u(c, hR ) + βj E Nj,n−1 (0, z 0 , 0 )|z
s.t.
(6)
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:
h
i
DQ
Rj,n
(a, z, ) = u(c, hR ) + βj E γNj,n−1 (0, z 0 , 0 ) + (1 − γ)Nj,n−1 (a(1 + rR ), z 0 , 0 )|z
(7)
s.t.
c = e,
e = exp(f + ln + z + ).
Here, γ is the probability of discharging delinquent debt and rR is the roll-over
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
63
of size h0 ∈ {h1 ....., hm },
B̂j,n (a, z; h0 ) = max
0
0
a ,m
h
i
u(c, h0 ) + βj E Hj,n−1 (h0 , m0 , a0 , z 0 , 0 )|z
(8)
a
s.t. c + qj,n
(h0 , m0 , a0 , z)a0 =
m
a + qj,n
(h0 , m0 , a0 , z)m0 − Im0 >0 ξM − (1 + ξB )ph0 ,
m
qj,n
(h0 , m0 , a0 , z)m0 ≤ λph0 .
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-tovalue 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 ).
(9)
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).
B.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 they 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
(·)
where:
64
(10)
(
)
DQ
P
BK
Pj,n
(·), Pj,n
(·), Pj,n
(·)
Pj,n (h, m, a, z, ) = max
,
P
Fj,n (h, m, a, z, ) = Fj,n
(·),
(
(11)
(12)
)
DQ
P
BK
Dj,n (h, m, a, z, ) = max Dj,n
(·), Dj,n
(·), Dj,n
(·) ,
(13)
B
Sj,n
(h, m, a, z, ) = SnB,P (·),
(14)
R
Sj,n
(h, m, a, z, ) = SnR,P (·).
(15)
Notice that households that choose to refinance their mortgage cannot default
on financial assets in any manner. Additionally, we model agents who elect to
sell as having to 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
(16)
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)
65
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
s.t.
(17)
c = e − filing fee − m,
e = exp(f + ln + z + ).
Mortgage payer and delinquency. Households that decide to pay their
mortgage but choose informal default on their financial assets have the following
(trivial) problem:
h
DQ
Pj,n
(h, m, a, z, ) = 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.
(18)
i
c = e − m,
e = exp(f + ln + z + ).
Mortgage refinancer. A household that refinances cannot default on financial assets a and must prepay their 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)
(19)
Note that 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
66
adjustment costs for 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 a 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
(a, z, ) − Φ.
(h, m, a, z, ) = Rj,n
Dj,n
(20)
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.
(21)
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.
(22)
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, ).
(23)
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,
67
P,B
Sj,n
(h, m, a, z, ) = Bj,n (a + ph(1 − ξS ) − qn∗ m + en (z, ), z).
B.3
(24)
Mortgage prices
When a household uses 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
+ qdef
+ qprepay,j,n
qpay,j,n
ault,j,n
.
1+r
(25)
First, consider the price of payment tomorrow, qpay ,
m
qpay,j,n
(h0 , b0 , a0 , z) =
(26)
i
ρn E mort pay, no def + mort pay, BK + mort pay, DQ z ,
h
with:
h
i
m
0
00 00
0
P
1
+
(1
−
δ)q
(h
,
m
,
a
,
z
)
,(27)
mort pay, no def = IPj,n−1
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
i
m
0
00
0
BK (h0 ,m0 ,a0 ,z 0 ,0 ) 1 + (1 − δ)q
mort pay, BK = IPj,n−1
(h
,
m
,
0,
z
)
,
n−1
68
(28)
and
h
mort pay, DQ = IP DQ (h0 ,m0 ,a0 ,z0 ,0 ) 1 + (1 − δ) ×
(29)
i
j,n−1
m
m
(h0 , m00 , a00 , z 0 ) ,
(h0 , m00 , 0, z 0 ) + (1 − γ)qj,n−1
γqj,n−1
with:
a00 = (1 + rR )a0 and m00 = m0 (1 − δ).
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 prepayment tomorrow, qprepay . This occurs when
the household chooses to refinance or 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) =
(30)
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:
0
0 0
m
qdef
ault,j,n (h , m , a , z) =
(31)
"
ρn E
B.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:
69
a
qj,n
(h0 , m0 , a0 , z)
a
a
qpay,j,n
+ qDQ,j,n
.
=
1+r
(32)
a
. This occurs in the followFirst, consider the price of payment tomorrow, qpay
ing 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,
"
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 )
(33)
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
. This occurs in
Next, consider the price given delinquency tomorrow, qDQ
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,
70
"
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
(hR , 0, a00 , z 0 )(34)
× qj,n−1
a
× qj,n−1
(hR , 0, a00 , z 0 )
#
a
(h0 , m00 , a00 , z 0 )|z
+IP DQ (h0 ,b0 ,a0 ,z0 ,0 ) × qj,n−1
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 .
C
COVID-19 related income losses
How do we pin-down COVID-19 related income losses? There are three steps in
our strategy. First, we compute the share of workers in “leisure and hospitality”
for each quintile. This share corresponds to the “most affected” workers. We
use the Census LEHD Origin-Destination Employment Statistics (LODES) data
described in Figure 5 together the classification of zip-codes to quintiles of FD
obtained from FRBNY Consumer Credit Panel/Equifax. Table A2 shows that
while the least distressed areas have a leisure and hospitality employment share
of around 9 percent, the most distressed areas have “most affected” employment
shares above 12 percent. Thus, the U.S. average masks substantial heterogeneity
by FD quintiles.
To obtain the decline in income for this group, we use the data in Figure 4.
During the months of April and May, the decline of this sector was more than
40 percent. By June, there was a recovery but the seasonally adjusted decline
was still larger than 30 percent. We use 30 percent as a conservative estimate for
the rest of the year, because starting in July there was a new wave of cases and
some states reinstated some restrictions, especially in the leisure and hospitality
sector.
The second step is to identify workers not affected by the lockdown. To
71
Table A2: Employment Shares in “leisure and hospitality”
Quintile of
FD
1
2
3
4
5
Employment share
Leisure and Hospitality
9.2
10.0
10.6
11.1
12.1
Source: Census LODES and FRBNY Consumer Credit Panel/Equifax.
calculate the share of workers not affected by quintile of FD, we leverage data
from the 10th wave of the Census Pulse Survey along with our FD measures from
Equifax (used in Figure 8). First, using the Pulse Survey, we calculate statelevel shares of individuals who report “no earnings losses since March 13, 2020
(for self or household member).” Second, we merge these state-level responses
to our preferred Equifax FD measure (DQ30). Third, we estimate a simple
linear regression relating state-level responses to state-level FD (weighted by state
population). Finally, we use the estimated coefficients of this regression to impute
quintile-specific shares of those not affected using each quintile’s average level of
FD. The results of the regression appear in Table A3, while the imputed share of
not affected workers by quintile of FD appear in the second column of Table 6.
Table A3: State-level percentage unaffected vs state-level FD
Variable
FD
constant
N
R2
Coefficient
-0.92
(0.42)
60.07
(4.93)
51
0.08
Note: Robust standard errors appear in parentheses.
The last step is to derive how affected households are that belong neither
to the most affected nor to the unaffected sectors. The reasoning here is very
simple. We want to select a decline in income such that the aggregate decline
in the economy is consistent with the predicted decline of 7.0 percent by the
72
consulting firm Macroeconomic Advisers. Notice that in this we need to take
into account differences in average income across quintiles. We need a decline
in income for the “somewhat affected” households of 9.1 percent to finalize our
calibration.
D
Regressions controlling by leverage
Next, we show how our main regression changes when controlling by leverage.
The crucial point is that the estimates of the interaction terms are very similar
to our benchmark results.
Table A4: Auto Spending at the Zip-code Level Controlling for Leverage
FD Measurement taken in 2002:
∆06−09 Home Value
FD
∆06−09 Home Value × FD
Housing Leverage Ratio06
∆06−09 Home Value × Housing Leverage Ratio06
Housing Leverage Ratio, 2006 × FD
Observations
(DQ30)
-0.012∗
(0.01)
-5.458
(3.13)
0.104∗∗∗
(0.02)
-0.228
(1.15)
0.018∗
(0.01)
-0.320
(6.69)
14136
∆06−09 Auto Spending
(CL80)
(DQ30 and CL80)
-0.013∗
-0.015∗
(0.01)
(0.01)
-7.239∗
-7.495∗
(2.89)
(3.32)
0.068∗∗∗
0.097∗∗∗
(0.02)
(0.02)
-1.216
-0.953
(1.69)
(1.48)
0.014
0.016∗
(0.01)
(0.01)
4.519
4.164
(6.16)
(7.11)
14136
14136
(ADQ30)
-0.013∗
(0.01)
-4.548∗
(2.02)
0.073∗∗∗
(0.01)
-0.677
(1.18)
0.019∗
(0.01)
1.637
(4.37)
14136
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.
E
County-Level IV regressions
To mitigate the risk that their results stem from an omitted variable correlated
with the decline in home prices, Mian et al. [2013] instrument for changes in home
value using housing supply elasticities from Saiz [2010]. Our results are robust
to these considerations as well, as shown in tables A5 and A6, where we present
the first and second stages of the regression as we do in Table 8 but instead at
the country level
73
Table A5: First-Stage Regression, County-level data
FD Measurement taken in 2002:
Saiz Elasticity
FD
Observations
F
(DQ30)
19.586∗∗∗
(1.80)
109.420∗
(52.50)
670
31.97
∆06−09 Home Value
(CL80)
(CL80 and DQ30)
19.900∗∗∗
19.705∗∗∗
(1.80)
(1.80)
43.793
91.864
(51.03)
(58.10)
670
670
31.47
31.47
(ADQ30)
18.762∗∗∗
(1.83)
91.533∗∗
(33.22)
670
32.45
Table A6: Second Stage regression, County-Level
FD Measurement taken in 2002:
∆06−09 Home Value
FD
∆06−09 Home Value × FD
Observations
(DQ30)
-0.273∗
(0.11)
-27.774
(19.83)
1.260∗
(0.53)
670
∆06−09 Auto Spending
(CL80)
(CL80 and DQ30)
-0.442∗∗
-0.367∗
(0.16)
(0.15)
-23.662
-29.674
(19.55)
(22.50)
1.304∗
1.407∗
(0.52)
(0.59)
670
670
(ADQ30)
-0.288∗
(0.12)
-17.526
(12.03)
0.887∗
(0.35)
670
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.
It may be worrisome that there is another variable correlated with our measures of FD that better summarizes a households’ financial condition. The housing leverage ratio in particular is frequently suggested as a possible source of
error, so Figure 15 directly compares our baseline to the results controlling for
leverage and Table A4 shows the corresponding regression output.
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.
74
@FedFRASER