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Loan Delinquency Projections
for COVID-19
WP 20-02
Grey Gordon
Federal Reserve Bank of Richmond
John Bailey Jones
Federal Reserve Bank of Richmond
Loan Delinquency Projections for COVID-19∗
Grey Gordon
John Bailey Jones
Federal Reserve Bank of Richmond
Federal Reserve Bank of Richmond
April 15, 2020
Abstract
We forecast the effects of the COVID-19 pandemic on loan delinquency rates
under three scenarios for unemployment and house price movements.
In the
baseline scenario, our model predicts that loan delinquency rises from 2.3% in 2019 to
a peak of 3.9% in 2025 with a total of $580B in write-offs. In 2021, absent policy
intervention, the model predicts that delinquency
would
be
3.1%.
However,
mortgage forbearance, student loan forbearance, and fiscal transfers keep delinquency
from increasing in 2021. The greatest reductions in delinquency are achieved through
mortgage forbearance and student loan forbearance, with fiscal transfers playing a
smaller role. In our adverse (favorable) scenario, loan delinquency peaks at 8.1%
(2.8%) and write-offs total $1.1T ($420B).
∗
For helpful comments and suggestions, we are grateful to Tom Barkin, Huberto Ennis and Alex Wolman.
Luna Shen and Emma Yeager provided outstanding research assistance. The views expressed are not necessarily
those of the Federal Reserve Bank of Richmond or the Board of Governors.
1
1
Introduction and main findings
In the text below, we describe a series of exercises that use data from the 2016 Survey of
Consumer Finances (SCF) to project the incidence of loan delinquency or default in the near
future. To make these projections, we assume that delinquency or default occurs when either
of two financial ratios—the debt-service to income (DSY) ratio and the loan to value (LTV)
ratio—exceed certain thresholds. We determine how many people will be above these thresholds by simulating DSY and LTV ratios for each SCF household under different unemployment
and house price scenarios. Using this methodology, we also assess how well various policy
proposals—fiscal transfers, student loan forbearance, and mortgage forbearance—mitigate the
increases in delinquency and default (D-D). While these calculations cannot substitute for a
complete economic model, they should provide reasonable first-pass estimates.
We consider three scenarios for the unemployment and house price shocks: a favorable
case, a severe case, and an intermediate case. In the absence of policy interventions, we find the
following:
1. When both shocks follow their intermediate trajectories, the D-D rate—measured as the
fraction of debt 90+ days delinquent—rises from 2.3% in 2019 to 3.1% in 2021 and
subsequently peaks at 3.9% in 2025. The delayed peak is due to persistence in house
price decline. Total write-offs, absent policy intervention, end up being $580B.
2. When both shocks follow their worst-case trajectories, the D-D rate rises to 3.5% in 2021
and peaks at 8.1% in late 2025. Total write-offs end up being $1.1T.
3. When both shocks follow their most favorable trajectories, the D-D rate rises to 2.6% in
2021 and peaks at 2.8% in 2022. Total write-offs end up being $420B.
As model validation, we consider a “Great Recession” scenario where unemployment increases by 10 percentage points (our favorable case) and housing prices decline by 25% (our
severe case). There we project an increase in D-D of 5.5 percentage points (pp). This matches
fairly closely the 6.5pp increase found in the data, even though in our scenario unemployment
peaks well before home prices bottom out, lowering the model’s peak D-D rate.
The three policy interventions we analyze begin in the second quarter of 2020 and last for
at most three years. Among the three policies we consider, the greatest reduction in the D-D
rate is achieved by mortgage forbearance, then by student loan forbearance, and lastly by fiscal
transfers. With all three policies in place, as they currently are under the Coronavirus Aid,
Relief, and Economic Security (CARES) act, D-D rates and write-offs fall below their 2019
2
levels in the near term. It is important to note that, since we do not have a complete model, we
cannot determine the true costs and benefits of these interventions.
2
Methodology
2.1
Overview
Our methodology is:
1. Use the 2016 SCF to calculate DSY and home LTV ratios for each household.
2. Assuming that delinquency or default occurs when these ratios exceed threshold values,
find the thresholds that replicate the thresholds observed in the final quarter of 2019.
3. Develop several scenarios for how household income and home prices might respond to
the coronavirus pandemic.
4. Under each scenario, recalculate the financial ratios and find the revised D-D rates.
2.2
Debt and Delinquency
Suppose that at date t, SCF household i has dki,t dollars of type-k debt. We will consider
three classes of debt: credit card balances (CC), student loans (SL), and home mortgages (HM).
The service cost associated with any sort of debt is the sum of the interest charges and principal
repayments due at that time. To project debt service costs at any future date t, si,t , we hold the
quantities of debt fixed at their 2019 value, but allow service rates to vary over time (due to
policy changes):
SL SL
HM HM
si,t = RtCC dCC
di,2019Q4 ,
i,2019Q4 + Rt di,2019Q4 + Rt
where Rtk denotes the debt service rate for debt type k at date t.1
To calculate the DSY ratio, we divide the last four quarters of debt service payments by the
last four quarters of income. Letting yi,t be quarterly income from the SCF,2 the debt-service to
income ratio, dsyi,t , is
si,t + si,t−1 + si,t−2 + si,t−3
.
dsyit =
yi,t + yi,t−1 + yi,t−2 + yi,t−3
1
2
We assume the debt-service rate is identical across households.
The SCF reports annual income, which divide by 4 to produce a quarterly measure.
3
We assume that a household goes delinquent or defaults on their credit card and/or student
loan debt whenever its DSY ratio exceeds the cutoff value α. Letting bi,t be a 0-1 indicator of
D-D on CC and SL debt, we have
1, if dsy > α,
it
bi,t =
0, otherwise.
For home mortgage debt (HM), we assume D-D occurs whenever households are significantly underwater on their mortgages. Let PtHM aHM
i,2019Q4 denote the home’s value as of date t.
HM
Here ai,2019Q4 is the value of household i’s home in 2019Q4, and PtHM is the price of a home at
date t relative to its price in 2019Q4. A household’s loan-to-value ratio, ltvi,t , is
ltvi,t =
dHM
i,2019
,
PtHM aHM
i,2019
We assume that mortgage D-D occurs whenever ltvi,t exceeds the cutoff value β and mortgage
debt service is positive—a household cannot be delinquent if it does not need to service its debt.3
Letting fi,t be a 0-1 indicator of HM default, we have
fi,t
2.3
1, if ltv > β and RHM > 0,
i,t
t
=
0, otherwise.
Simulation Dynamics
Our simulations start in the fourth quarter of 2019 and run through the second quarter of
2030. The dynamics in our simulations come from three sets of variables: the debt service
charges RtCC , RtSL and RtHM ; (relative) house prices PtHM ; and individual incomes, yi,t .
The dynamics of the debt service charges are simple. In the absence of loan forbearance,
the charges equal their 2019 values, which we describe below; when there is loan forbearance,
the charges for the affected loans are set to zero. The trajectories of relative house prices under
our three scenarios, shown in the top panel of Figure 1, are somewhat more involved, but in all
cases prices reach their lowest values in the fourth quarter of 2025. Prices fall by 5%, 15%, and
25% in the favorable, baseline, and severe scenarios; roughly, these are the declines from a mild
recession, a bad recession, and the Great Recession.
3
When a household is not underwater (ltvi,t < 1), it makes little sense (ignoring closing costs) for it to default:
the house can be sold, the mortgage paid off, and the equity kept. This is true even if debt-service costs are high,
which is why we assume HM default occurs only in response to a high LTV ratio.
4
The dynamics of income are the most complicated. Each period a fraction of households are
hit with unemployment shocks. Households hit by the shocks have their income fall by the proportion (1 − θ). The “replacement rate” θ measures the extent to which unemployment benefits
and other programs offset income losses in unemployment, and we set it to 50% based on recent
estimates. In line with the recently passed CARES act, we also allow for the possibility that
households receive transfers under a fiscal stimulus plan. We use Tte and Ttu to denote transfers made to the employed and unemployed, respectively. Letting ui,t be a 0-1 unemployment
indicator, income is given by
(
yi,t =
yi,2019Q4 + Tte ,
θyi,2019Q4 + Ttu ,
if ui,t = 0,
if ui,t = 1.
The dynamics of unemployment are as follows. Each unemployed household remains unemployed in the subsequent quarter with probability ρ and returns to work with probability 1−ρ.
We assume that ρ is constant over time. Households employed at date t transition into unemployment at date t + 1 at the rate δt , which varies over time in accordance with the aggregate
unemployment rate Ut .
The bottom panel of Figure 1 shows the trajectory of the aggregate unemployment rate under
our three scenarios. Unemployment peaks at 10%, 20% and 30% in the favorable, baseline, and
severe scenarios, respectively.
3
Model Inputs
In this section we document how we set the inputs for the model. Readers uninterested in
these details should skip to the results in section 4.
3.1
Household data
The household data come from the 2016 wave of the Survey of Consumer Finances. We
include families in the sample if their income was at least $10,000 and their debts (credit card,
student loans, mortgages) totaled at least $1,000. Households older than 65 are dropped, as they
do not have much debt and are unlikely to be affected by changes in the aggregate unemployment rates. With these restrictions, our initial sample of 31,240 families drops to 15,009.
5
1
House price index, assumed path
0.95
0.9
0.85
0.8
Baseline
Severe
Favorable
"Great Recession"
0.75
2019:1 2020:2 2021:3 2022:4 2024:1 2025:2 2026:3 2027:4 2029:1 2030:2
0.3
Unemployment rate, assumed path
Baseline
Severe
Favorable
"Great Recession"
0.25
0.2
0.15
0.1
0.05
0
2019:1 2020:2 2021:3 2022:4 2024:1 2025:2 2026:3 2027:4 2029:1 2030:2
Figure 1: Unemployment rates and house prices by scenario
6
3.2
Debt service and delinquency
The debt service charges in the pre-COVID baseline are set as follows:
Debt class
Service costs
k
R2019Q4
Explanation
Student loans
.0335
Mortgage
.0183
Credit card
.04
Other debts
0
3.4% interest with 10% paid off annually. This is a .134
debt service rate annually, .0335 quarterly.
4% interest with 3.33% paid off annually. This is a .0733
debt service rate annually, .0183 quarterly.
16% interest with 0% paid off annually. This is a .04
quarterly rate.
Other debts omitted.
Table 1: Debt service charges
We set the delinquency cutoff for the DSY ratio, α, so that the fraction of CC and SL debt
that is delinquent (the debt-weighted average of bi,2019Q4 ) is 10.0%, which is the 90+-days-late
delinquency rate for combined CC and SL balances.4 This yields α = 0.495.
We set the default cutoff for the LTV ratio, β, so that the fraction of HM debt in default (the
debt-weighted average of fi,2019Q4 ) is 1.07%, the 90+-days-late delinquency rate for mortgage
balances reported for that date.5 This yields β = 1.26. This implies households must be
significantly underwater in order to default, which is due at least in part to the high transaction
costs of selling a home (typically around 7%).
3.3
Aggregate unemployment dynamics
Recall that the probability that an unemployed household remains unemployed is ρ, while
the transition rate from employment to unemployment is given by a separation rate / job destruction rate of δt . Given these transition rates for individuals, we have the following laws of
motion for unemployment Ut and employment Et :
Ut+1 = δt Et + ρUt ,
Et+1 = (1 − δt )Et + (1 − ρ)Ut ,
As shown in the top panel of Table 2, ρ is chosen to match either a 20-, 30-, or 40-week average
duration of unemployment, depending on the scenario. Then given a path for unemployment,
4
Authors’ calculations using data from the Federal Reserve Bank of New York’s Quarterly Report on Household
Debt and Credit, available here, with the underlying data available here.
5
See Figure 12, “Percent of Balance 90+ Days Delinquent by Loan Type”, of the report available here.
7
{Ut }, we infer the separation rate as
δt =
Ut+1 − ρUt
.
Et
For aggregate unemployment, we assume that 2020Q2 unemployment reaches a peak of
Umax , stays there for τ U periods, and subsequently reverts to its long-run average at a rate φU .
Specifically, after the peak we assume ln(Ut ) = (1 − φU )µU + φU ln(Ut−1 ). In our severe
scenario, we take Umax = 30%, τ U = 6 (i.e., six quarters), and use the estimated mean and
persistence (µU , φU ) = (1.627, 0.973). While 30% would indeed be severe, St. Louis Fed President James Bullard notably mentioned the possibility.6 In our baseline, we assume maximum
unemployment of 20% lasting for four quarters, and we allow for a faster recovery by using
φU = 0.94. The favorable case has an even smaller and shorter-lived dip, Umax = 10%, τ U = 2,
with an even faster recovery of φU = 0.9. The scenarios are summarized in Table 2.
Scenario
Inputs
Description
Unemployment
Baseline
Umax = 0.20, φU = 0.94, τ U = 4,
ρ = 0.5833
Favorable
Umax = 0.10, φU = 0.9, τ U = 2,
ρ = 0.3750
Severe
Umax = 0.30, φU = 0.973, τ U = 6,
ρ = 0.6875
Housing
Baseline
Favorable
Severe
HM = 0.85, φHM = 0.98, τ HM =
Pmin
22
HM = 0.95, φHM = 0.95, τ HM =
Pmin
22
HM = 0.75, φHM = 0.99, τ HM =
Pmin
22
Peak unemployment 20% lasting 4 quarters,
medium recovery, average individual unemployment duration 30 weeks
Peak unemployment 10% lasting 2 quarters,
fast recovery, average individual unemployment duration 20 weeks
Peak unemployment 30% (Bullard estimate)
lasting 6 quarters, slow recovery, average individual unemployment duration 40 weeks
Half-life recovery time from peak-to-trough
in Great Recession
Small dip, fast recovery
AR(1) estimated on log real house price index
is 0.998 (even more persistent)
Table 2: Unemployment and housing scenarios
6
See https://www.bloomberg.com/news/articles/2020-03-22/fed-s-bullard-says-u-s-jobless-rate-may-soar-to30-in-2q.
8
3.4
House price dynamics
To model house price dynamics, we turn to the last recession to get realistic measures of
HM
HM
peak-to-trough movements and recovery rates. We begin by setting P2020Q2
= P2020Q1
=
HM
P2019Q4
= 1. From that point, home prices fall linearly for the next τ HM quarters, reaching
HM
the trough value of Pmin
. After reaching the trough, we assume the price reverts to the 2019Q4
value at the gross rate φHM . Formally,
PtHM
1,
t − 2020Q2 HM
1+
(Pmin − 1),
=
τ HM
(P HM )φHM ,
t−1
if t ≤ 2020Q2,
if t ∈ {2020Q2, . . . , 2020Q2 + τ HM },
if t > 2020Q2 + τ HM .
HM
The bottom panel of Table 2 describes (Pmin
, φHM , τ HM ) for each of our scenarios.
3.5
Policy interventions
Recall that income follows
(
yi,t =
yi,2019Q4 + Tte ,
θyi,2019Q4 + Ttu ,
if ui,t = 0,
if ui,t = 1,
where θ is the replacement rate for households with an unemployed member, and Tte and Ttu
are government transfers. We set θ to 0.5, based on a recent micro-simulation analysis by the
Urban Institute.7 Table 3 summarizes the policy interventions.
Abbreviation
Policy
Parameters
NP
FP
No additional policy intervention
Fiscal stimulus
SLP
MP
Student loan forbearance
Mortgage forbearance
θ = 0.5, Tte = 0, Ttu = 0
e
u
θ = 0.5, T2020Q2
= 1200, T2020Q2
=
9600 + 1200
SL
R2020Q2:2023Q2
=0
HP
R2020Q2:2023Q2 = 0
Table 3: Policy experiments
7
The study is available at www.urban.org/sites/default/files/publication/25461/412580-What-Happens-toFamilies-Income-and-Poverty-after-Unemployment-.PDF.
9
4
4.1
Projections
Baseline projections with policy outcomes
Figure 2 shows how the aggregate delinquency rate—measured as the fraction of total debt
that is delinquent—evolves over time in the baseline scenario, where both unemployment and
housing prices follow their intermediate trajectories. In the absence of any countervailing policies, delinquency rates peak at about 3.9% at the end of 2025, and write-offs reach $580 billion.
The peak in delinqency coincides with the trough of house prices; by this date, unemployment
has largely returned to its baseline value (see Figure 1). Even though housing prices have the
larger effect, in the nearer term unemployment raises delinquency as well. This can best be
seen in the delinquency rate for the sum of credit card and student loan debt in Table 4, which
rises from 10.0% to 13.2%. Because HM debt ($9.56T in 2019Q4) is about four times larger
than the sum of CC and SL debt ($2.44T), the overall delinquency rate most closely tracks the
delinquency rate for HM debt.
Figure 2 and Table 4 also show the effects of the policy interventions. As the policies we
evaluate all stop before 2025, the peak delinquency rates are invariant to policy. However, in the
nearer term, the policies lead to significantly lower delinquency rates. Mortgage forbearance
generates the largest decreases, but student loan forbearance has significant effects as well. Both
of these interventions push delinquency below its baseline rate, as they cover households that
would have been delinquent even in the absence of coronavirus-related shocks. The effects of
the fiscal stimulus are considerably smaller. It bears noting that in the absence of a complete
model, we cannot determine the true costs and benefits of these interventions. To give just one
example, policies that offset income losses or reduce delinquency may also dampen the fall in
house prices.
4.2
Severe and favorable projections with policy outcomes
Figure 3, along with the bottom two panels of Table 4, assesses two alternative scenarios.
Here we assume that the unemployment and house price trajectories are correlated: higher
rates of unemployment are accompanied by larger declines in house prices. The top panel
of Figure 3 illustrates the most severe scenario, where delinquency rates climb to 8.1% and
write-offs reach more than $1 trillion. The bottom panel shows the most favorable alternative,
where delinquency rates never reach 3% and write-offs reach a maximum of $420 billion. It
is worth noting that in every scenario, when all three policies are enacted—as they now have
been—write-offs drop to essentially zero in 2021. Hence, in the near term we do not expect
10
4
Debt delinquency over time, baseline with different policies
3.5
Percent of total debt
3
2.5
No policy
Fiscal
Stud. loan
Mortgage
All
2
1.5
1
0.5
0
2017:4
2020:2
2022:4
2025:2
2027:4
2030:2
Figure 2: Delinquency paths in the baseline scenario
Percentage of debt delinquent
Scenario
Unemp.
Housing
Baseline
Baseline
Baseline
Baseline
Baseline
Baseline
Baseline
Baseline
Baseline
Baseline
Severe
Severe
Severe
Severe
Severe
Severe
Severe
Severe
Severe
Severe
Favorable
Favorable
Favorable
Favorable
Favorable
Favorable
Favorable
Favorable
Favorable
Favorable
Policy intervention
FP
SLP
CC + SL
HM
All
CC + SL
HM
2021
Total
Yes
Yes
3.1
3.1
1.4
1.3
0.0
13.2
13.2
1.3
8.9
0.1
1.4
1.4
1.4
0.0
0.0
3.9
3.9
3.9
3.9
3.9
13.2
13.2
11.7
11.7
11.7
2.7
2.7
2.7
2.7
2.7
0.46
0.46
0.17
0.22
0.00
0.58
0.58
0.54
0.54
0.54
Yes
Yes
3.5
3.5
1.7
1.4
0.0
14.9
14.9
1.8
10.1
0.1
1.7
1.7
1.7
0.0
0.0
8.1
8.1
8.1
8.1
8.1
14.9
14.9
13.3
13.3
13.3
7.3
7.3
7.3
7.3
7.3
0.52
0.52
0.20
0.25
0.00
1.06
1.06
1.02
1.02
1.02
Yes
Yes
2.6
2.6
1.1
1.1
0.0
11.5
11.5
0.9
7.7
0.0
1.2
1.2
1.2
0.0
0.0
2.8
2.8
2.8
2.8
2.8
11.5
11.5
11.1
11.1
11.1
1.5
1.5
1.5
1.5
1.5
0.39
0.39
0.13
0.19
0.00
0.42
0.42
0.41
0.41
0.41
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
USD Trillions
All
Yes
Yes
Peak
MP
Yes
Yes
Average in 2021
Write-offs
Note: For the definitions of MP, SLP, and FP, see Table 3; “All” debt refers to HM + CC + SL.
Table 4: Projections by scenario and policy
11
delinquency rates to rise substantially, despite the large disruptions.
4.3
Model validation: comparison with the Great Recession
A natural question to ask is how well our methodology would do at predicting outcomes in
the Great Recession, where unemployment rose to 10% and house prices fell by 25%. To assess
this in a simple way, we assume unemployment follows its favorable scenario and house prices
follow their severe scenario.
Figure 4 shows how D-D rates rise and fall during the Great Recession period, for both the
data and the model. Overall, the data and model D-D series show similar increases and similar
overall patterns. D-D rates rise sooner in the model than in the data. This is because in the
data, the unemployment peak and the house price trough were only two years apart,8 whereas
in the model we assume that unemployment peaks immediately while house prices reach their
minimum five years later. We think that this is a reasonable difference, given the swift onset of
the coronavirus shock, as opposed to the somewhat slower progression of the Great Recession.
Taking these considerations into account, we think the model performs very well.
4.4
Sensitivity analyses
While we have established that declining home prices lead to larger increases in delinquency,
and are for the most part responsible for its peak value, we have not fully disentangled their
effects from those of higher unemployment. Table 5 takes a step in this direction. The top
panel of the table shows the effects of each unemployment scenario, holding the home price
trajectory at its baseline. Moving from the baseline to the severe unemployment scenario raises
the total delinquency rate in 2021 by 0.2pp; moving to the favorable scenario lowers the rate
by 0.3pp. These effects are larger than the near-term (2021) effects of changing the house price
trajectory, as shown in the table’s bottom panel. Specifically, moving from the baseline to the
severe housing scenario raises the 2021 D-D rate by 0.1pp; moving to the favorable housing
scenario lowers the rate by 0.2pp.
Recall that, in the absence of loan forbearance, interest rates are held fixed throughout our
projections. We therefore do not account for the possibility that, say, interest rates will rise as
the economy recovers from the pandemic. Most home mortgages and student loans are fixedrate, implying that changes in interest rates affect service costs only for new borrowers. We
explored the consequences of raising the nominal credit card rate by 3pp annually at different
8
In the Great Recession, unemployment (FRED series UNRATE) peaked in late 2009 and house prices reached
their trough two years later (FRED series USSTHPI).
12
9
Debt delinquency over time, severe with different policies
8
Percent of total debt
7
6
5
4
3
No policy
Fiscal
Stud. loan
Mortgage
All
2
1
0
2017:4
3
2020:2
2022:4
2025:2
2027:4
2030:2
Debt delinquency over time, favorable with different policies
Percent of total debt
2.5
2
No policy
Fiscal
Stud. loan
Mortgage
All
1.5
1
0.5
0
2017:4
2020:2
2022:4
2025:2
2027:4
2030:2
Figure 3: Delinquency paths in the alternate scenarios
13
Debt delinquency in the Great Recession scenario
Comparison with data
Model (no policy)
Data
8
Percent of total debt
7
6
5
4
3
2
-20
-15
-10
-5
0
5
10
15
Quarters until peak
Figure 4: Comparison of model “Great Recession” scenario with the data
Percentage of debt delinquent
Scenario
Unemp.
Housing
Average in 2021
All
CC + SL
Write-offs
Peak
HM
USD Trillions
All
CC + SL
HM
2021
Total
3.9
4.2
3.8
13.2
14.9
11.5
2.7
2.7
2.7
0.46
0.50
0.42
0.58
0.62
0.54
3.9
7.8
3.0
13.2
13.2
13.2
2.7
7.3
1.5
0.46
0.48
0.43
0.58
1.02
0.47
Unemployment varies, housing fixed at baseline
Baseline
Severe
Favorable
Baseline
Baseline
Baseline
3.1
3.3
2.8
13.2
14.9
11.5
1.4
1.4
1.4
Housing varies, unemployment fixed at baseline
Baseline
Baseline
Baseline
Baseline
Severe
Favorable
3.1
3.2
2.9
13.2
13.2
13.2
1.4
1.7
1.2
Note: For the definitions of MP, SLP, and FP, see Table 3; “All” debt refers to HM + CC + SL.
Table 5: Projections by unemployment or housing scenario, holding the other fixed, and policy
14
points in the next few years. Because credit card debt is a small component of total debt, we
found extremely limited effects.
15
@FedFRASER