Household Liquidity and Macroeconomic Stabilization: Evidence from Mortgage Forbearance (Working Paper 23-12)

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Federal Reserve Bank of Boston working paper No. 23-12, version of September 2023, by Sean Chanwook Lee and Omeed Maghzian, estimating the effect of household liquidity on macroeconomic stabilization using the 2020 CARES Act mortgage forbearance program. The abstract says that following statewide business reopenings, a 1 percentage point increase in the share of mortgages in forbearance leads to a 30 basis point increase in monthly employment growth in nontradable industries. The introduction says approximately 5 percent of all conforming mortgages were in forbearance by June 2020, with suspended monthly payments of about $900 on average. The paper states that its views are the authors' and do not indicate concurrence by the Federal Reserve Bank of Boston.

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                                                                                                    No. 23-12

Household Liquidity and Macroeconomic Stabilization:
       Evidence from Mortgage Forbearance
                     Sean Chanwook Lee and Omeed Maghzian
Abstract:
We estimate the impact of household liquidity provision on macroeconomic stabilization using
the 2020 CARES Act mortgage forbearance program. We leverage intermediation frictions in
forbearance induced by mortgage servicers to identify the effect of reducing short-term
payments with little change in long-term debt obligations on local labor market outcomes.
Following statewide business reopenings, a 1 percentage point increase in the share of
mortgages in forbearance leads to a 30 basis point increase in monthly employment growth in
nontradable industries. In a model incorporating geographical heterogeneity in intermediation
frictions, these responses imply a household-level marginal propensity to consume out of
increased liquidity that aligns with existing estimates for direct fiscal transfers. The implied
debt-financed fiscal multiplier effects of forbearance are sizable but depend on the repayment
terms of deferred payments and the monetary policy stance.

JEL Classifications: G21, G23, G28, G51
Keywords: mortgage forbearance, liquidity, debt relief, CARES Act, employment, labor
market

Sean Chanwook Lee (seanclee@g.harvard.edu) was a graduate research fellow in the Federal Reserve Bank of Boston
Research Department when he completed this version of this paper. He is a PhD student in economics at Harvard
University. Omeed Maghzian is also a PhD student in economics at Harvard University. This paper was formerly
titled “Macroeconomic Effects of Mortgage Forbearance: Evidence from the CARES Act.” An online appendix is
available from Lee.

The authors thank Michael Blank, John Campbell, Gabriel Chodorow-Reich, Marco Di Maggio, Daniel Green, Samuel
Hanson, David Laibson, Peter Maxted, Andrei Shleifer, Jeremy Stein, Ludwig Straub, Adi Sunderam, Winnie van
Dijk, James Vickery, PaulWillen, and various seminar participants for insightful discussion and comments. Lee
acknowledges support from the John Meyer Dissertation Fellowship from the Harvard Joint Center for Housing
Studies. Maghzian acknowledges support from the National Science Foundation Graduate Research Fellowship and
the Stone Program in Wealth Distribution, Inequality, and Social Policy.

This paper presents preliminary analysis and results intended to stimulate discussion and critical comment.

The views expressed herein are those of the authors and do not indicate concurrence by the Federal Reserve Bank of
Boston, the principals of the Board of Governors, or the Federal Reserve System.

This paper, which may be revised, is available on the website of the Federal Reserve Bank of Boston at
https://www.bostonfed.org/publications/research-department-working-paper.aspx.

This version: September 2023                                            https://doi.org/10.29412/res.wp.2023.12
1     Introduction
Limited household liquidity can depress aggregate demand during economic downturns. For in-
stance, during the Great Recession, the wave of defaults following the housing crisis had desta-
bilizing effects on both local and aggregate economic activity, which persisted for several years.
Since then, policymakers and academics have actively discussed how to best prevent defaults and
stimulate consumption among distressed borrowers as a means to promote macroeconomic stabil-
ity. While the discussion has primarily revolved around understanding the stabilizing properties of
various state-dependent mortgage modifications (e.g., Eberly and Krishnamurthy, 2014; Seru and
Piskorski, 2018; Campbell et al., 2021), a common underlying theme emphasizes the importance
of ensuring household liquidity during times of crises.
    In recognition of households’ countercyclical liquidity needs, the U.S. federal government en-
acted a large-scale discretionary debt relief in response to the COVID-19 crisis. As part of the
Coronavirus Aid, Relief, and Economic Security (CARES) Act, all federally backed mortgage
borrowers with pandemic-related financial hardships became eligible to request forbearance with-
out the need for documentary evidence. Borrowers were permitted to temporarily halt their pay-
ments without facing any fees or penalties and could remain in forbearance for a period of up to
18 months. The scale of liquidity provided through forbearance was substantial. As depicted in
Figure 1, approximately 5 percent of all conforming mortgages were in forbearance by June 2020,
resulting in suspended monthly payments of about $900 on average. Upon exiting forbearance,
borrowers were typically given the option to defer repayment of their missed payments until the
end of their mortgage term as a second-lien loan. Hence, the primary role of the CARES Act for-
bearance was to reduce short-term payments while preserving long-term debt obligations, making
it an ideal setting to analyze the effects of enhancing household liquidity on economic stabiliza-
tion.1
    In this paper, we estimate the stabilizing effects of mortgage forbearance implemented under
the CARES Act during the pandemic recession. Our empirical analysis examines the labor market
recovery of U.S. regions that varied in the amount of liquidity provided through mortgage forbear-
ance. Our findings suggest that mortgage forbearance played a significant role in boosting local
    1 See Ganong and Noel (2020) for an insightful discussion on the importance of distinguishing between liquidity

effects and wealth effects.


                                                        2
Figure 1: Mortgage Forbearance Rates in the GSE Mortgage Market. This figure shows the
share of GSE mortgages in forbearance (red curve) along with the entry and exit rates (black and
gray bars) at each month. We use vertical dotted lines to mark the date the CARES Act passed and
the two subsequent dates when the mortgage forbearance program was extended. Data sources:
Fannie Mae and Freddie Mac.


demand during the economic recovery. To provide a micro-foundation for this macro-stabilization
effect, we then develop a stylized heterogeneous-area New Keynesian model that relates local la-
bor market outcomes to household-level consumption responses. Interpreted through the lens of
this model, our empirical estimates imply an annual household-level marginal propensity to spend
(MPX) of 67 cents and a marginal propensity to consume (MPC) of 43 cents per dollar of liquid-
ity provided through forbearance. The implied cross-sectional multiplier of mortgage forbearance
suggests that household liquidity provision through debt forbearance can be a cost-effective fiscal
stabilization tool during economic downturns.
   Two distinct features of the mortgage forbearance program enable us to identify the impact
of liquidity provision on regional employment outcomes. First, despite the broad eligibility cri-
teria, enrollment in mortgage forbearance was not automatic; households in need had to request
forbearance. As a result, U.S. regions varied considerably in the uptake of forbearance. However,
the voluntary nature of program enrollment introduces a potential issue of reverse causality, as the
local forbearance rate is endogenous to the region’s economic exposure to the recession.
   The second feature of the forbearance program helps us address this endogeneity concern.



                                                 3
In contrast to other forms of fiscal policy, the implementation of the program was carried out
by mortgage servicers, financial intermediaries in the mortgage market responsible for collecting
monthly payments and facilitating transactions with mortgage-backed securities (MBS) investors.
We uncover the striking fact that different mortgage servicers exhibit significant variation in their
propensity to provide forbearance that cannot be explained by observable loan and borrower char-
acteristics. Using loan-level data for Government-Sponsored Enterprise (GSE) mortgages, we
document that servicers can differ by as much as 7 percentage points in forbearance provision
to observably similar borrowers. Reassigning a borrower from a servicer at the 25th percentile
to one at the 75th percentile of the weighted propensity distribution results in an increase in the
probability of take-up that is equivalent to 24 percent of the mean forbearance rate.
    Our empirical strategy exploits these intermediation frictions in the supply of forbearance to
identify the impact of liquidity provision on regional employment outcomes. Specifically, we em-
ploy the regional average of the estimated servicer propensity, weighted by local servicer market
shares, as an instrument for the regional forbearance outcome. Consistent with our loan-level
analysis, we demonstrate that this shift-share measure has substantial explanatory power for the
forbearance rates of regions defined by three-digit Zip codes. This instrument is valid under the
assumption of conditional exogeneity of servicers’ forbearance propensities. That is, conditional
on our baseline controls, regions with high and low take-up frictions as indicated by our instru-
ment do not differ in other ways that could affect their economic recovery (Borusyak et al., 2022).2
We provide supporting evidence for this identifying assumption based on the absence of differ-
ential pre-trends in employment outcomes. Additionally, to ensure that the regional variation in
servicer propensity is not driven by local economic conditions, we estimate the servicer propensity
separately for each state, using only loans outside of that state.
    Our empirical specification incorporates a set of baseline controls to account for the varying
exposure of each region to the pandemic recession. In addition to average loan characteristics and
demographic and socioeconomic factors that reflect regional differences in demand for debt relief,
    2 Two institutional details support the plausibility of this condition. First, despite the program’s broad eligibility,

servicers exercised some discretion in determining what constituted an application to the program. Instances of public
complaints reported to the Consumer Financial Protection Bureau (CFPB) indicate that certain companies wrongfully
demanded documentation or were difficult to reach, while others granted forbearance simply upon receiving inquiries
about the program. Second, the mortgage servicing market displays significant concentration, with the top 20 firms
servicing 66 percent of all conforming mortgages as of February 2020. This wide coverage by large servicers implies
that the program implementation may not be tailored to the specific distress levels of individual regions.


                                                            4
we control for employment growth predicted by local industry shares to account for differences
in sectoral compositions. Moreover, we include a measure of local labor market slack induced
by the initial economic shock to account for any potential path dependence in the labor market
recovery. Lastly, we incorporate state fixed effects to account for any state-level differences in
policy responses, such as unemployment insurance benefits or lockdown policies.
   Even though our instrument helps mitigate the endogeneity issue between forbearance out-
comes and regional economic exposure to the crisis, estimating the impact of household liquidity
provision at the regional level is complicated by the initial negative supply shocks caused by stay-
at-home orders and business closures during the economic lockdowns at the onset of the COVID-
19 pandemic. The demand-based stabilization resulting from liquidity provision may have been
suppressed, as households may have diverted their spending away from the local economy during
these lockdowns. To address this concern, we estimate the employment effects starting from the
date when each state relaxed its initial lockdown policy. Since we include state fixed effects in
our regressions, our identification strategy relies on cross-sectional differences across areas within
each state that all reopened about the same time.
   Using our servicer-based instrument, we estimate that a 1 percentage point increase in the for-
bearance rate leads to an approximately 30 basis point increase in monthly employment growth in
nontradable sectors during the 18 months following statewide business reopenings. The interquar-
tile range in our instrument corresponds to a regional difference in nontradable employment growth
equivalent to 7 percent of the mean growth rate (or 16 percent of the standard deviation) during
our sample period. In contrast, we find no significant effect for employment in tradable industries
and a positive but smaller effect for total employment, as predicted by the theory (Mian and Sufi,
2014). Overall, our main empirical results suggest that (1) frictions in the implementation of mort-
gage forbearance by financial intermediaries produced economic spillovers, and that (2) effective
liquidity provision through forbearance helped stabilize local employment during the recession.
   We conduct several tests to evaluate the validity of our empirical design. First, since our in-
strument relies on the geographic distribution of financial intermediaries, one potential threat is
that it may capture the general functioning of local financial institutions involved in intermediating
various forms of economic stimulus, not just mortgage forbearance. To address this concern, we
show that our instrument does not predict other relief measures intermediated through financial


                                                  5
institutions such as the Paycheck Protection Program (PPP), mortgage refinancing, and personal
bankruptcy filings. Second, our baseline results are robust to several confounding factors including
the COVID-19–infection rate, death rate, population density, and other measures of fiscal stimulus.
Lastly, we construct alternative estimates of servicer propensity that condition on mortgages that
became past due during the pandemic. We find that this alternative propensity estimate exhibits
a strong positive correlation with our main estimate, and our baseline regression results remain
robust when using this alternative servicer effect as an instrument.
    We next turn to our theoretical analysis to compare our regional estimates with existing evi-
dence on household-level consumption responses. Building on Chodorow-Reich et al. (2021), we
develop a regional macroeconomic model that incorporates a housing sector and accounts for geo-
graphical heterogeneity in intermediation frictions. We derive a separation result that decomposes
the regional estimate on nontradable wage bill into the product of four terms: the local Keynesian
multiplier, the labor share of income in nontradable sectors, the expenditure share of nontradable
goods, and the household-level MPC for homeowners with mortgage debt. Under a standard cal-
ibration of parameters, we find that the implied annual MPX out of a dollar of liquidity provided
is 0.67, which is equivalent to the annual MPC of about 0.43 (Laibson et al., 2022). Our estimates
are broadly consistent with the range of existing estimates for household-level spending responses
(e.g., Parker et al., 2013; Kueng, 2018; Baker et al., 2023).3
    Finally, we provide a mapping of our estimates into a cross-sectional debt-financed fiscal mul-
tiplier to facilitate comparison with existing multiplier estimates for other government policies.
Under our preferred assumptions regarding the repayment behavior of deferred mortgage pay-
ments and the prevailing interest rate, our results indicate a cross-sectional forbearance multiplier
of 2.25. The large returns to forbearance-based fiscal stimulus stem from its cost-effectiveness as
a means of temporary liquidity provision, which obligates borrowers to ultimately repay the de-
ferred payments in the future. As a result, the direct outlay needed to implement the policy is small
compared with the benefit. This feature stands in stark contrast to other forms of fiscal stimulus
that often rely on direct fiscal transfers. Overall, our findings suggest that mortgage forbearance
is an effective stabilization tool, particularly when coupled with accommodative monetary policy
   3 The empirical literature typically reports quarterly MPXs in the range of 0.5 to 0.9 and nondurable MPXs in

the range of 0.2 to 0.3 (Havranek and Sokolova, 2020). Our implied estimates may be somewhat larger than these
quarterly estimates since they represent households’ annual spending responses.


                                                       6
that enables low-cost deficit financing.
   After reviewing the literature and our contribution below, the paper is structured as follows.
Section 2 provides background on the CARES Act mortgage forbearance. Section 3 describes our
data sources, and Section 4 details our procedure for estimating the servicer forbearance propen-
sities and constructing the shift-share instrument. Section 5 discusses our research design and
presents the empirical results. Section 6 describes our model, followed by a discussion of the
implied household-level consumption responses and the debt-financed fiscal multiplier effect in
Section 7. Section 8 concludes.


Related literature.   An expansive literature examines the economic effects of the COVID-19 cri-
sis and the policy responses implemented during the pandemic (e.g., Chetty et al., 2020; Coibion et
al., 2020; Guerrieri et al., 2022; Granja et al., 2022; Pence, 2022). Within this literature, our work
is closely related to those focused on forbearance programs. Cherry et al. (2021) provide a com-
prehensive overview of the CARES Act forbearance across various categories of household debt
that include mortgages, student loans, and auto loans. Zhao et al. (2020) analyze income and liquid
asset trends for homeowners in relation to their employment and mortgage forbearance statuses,
while An et al. (2022) show that mortgage forbearance has contributed to reducing inequality. In
comparison to the existing work, we are the first in the literature to analyze the stabilizing effects
of mortgage forbearance on regional economic outcomes.
   Our analysis emphasizes the role of financial intermediaries in the mortgage market (e.g.,
Cordell et al., 2008; Agarwal et al., 2011; Kim et al., 2018; Kruger, 2018; Jiang et al., 2020;
Kermani and Wong, 2021; Fuster et al., 2021; Aiello, 2022). Agarwal et al. (2017) examine the
effect of intermediary-specific factors in the implementation of the Home Affordable Modifica-
tion Program (HAMP) in the aftermath of the Great Recession. Agarwal et al. (2011) and Kruger
(2018) document that intermediaries were more inclined to modify their portfolio loans compared
with those for which they provide only external servicing. During the COVID-19 crisis, Cherry
et al. (2021) document that shadow banks offered forbearance at lower rates compared with tra-
ditional depository institutions. While this study focuses on the difference between banks and
shadow banks, we document more generally that there is vast heterogeneity in forbearance out-
comes across different mortgage servicers even among these two broad categories of financial


                                                  7
intermediaries.
    Our paper is most closely related to a contemporary work by Kim et al. (2022), who also
examine the role of mortgage servicers in forbearance outcomes and find that servicers widely vary
in the propensity to enter mortgages into forbearance for observably similar borrowers.4 While
Kim et al. (2022) focus on the microeconomic implications of mortgage forbearance by examining
its effect on individual-level outcomes in credit bureau data, such as credit card balances and
auto loans, we instead focus on understanding its macro-stabilizing effects by analyzing regional
economic outcomes. Our results are consistent with their findings that liquidity from deferred
payments served to support both nondurable consumption and precautionary savings.
    The positive impact of mortgage forbearance reflects the importance of household balance
sheets in the transmission of economic shocks (e.g., Mian and Sufi, 2014; Hurst et al., 2016;
Di Maggio et al., 2017; Beraja et al., 2019; Berger et al., 2021) and stabilization policies (e.g.,
Agarwal et al., 2017; Ganong and Noel, 2019; Auclert et al., 2019; Defusco and Mondragon, 2020).
Ganong and Noel (2020) compare principal reductions and maturity extensions in a mortgage
modification program and find that borrowers’ liquidity needs drive defaults and consumption
decisions. Consistent with their results, we find that injecting liquidity into household balance
sheets through mortgage forbearance dramatically reduced mortgage defaults and enhanced local
demand during the recovery from the pandemic recession. We also contribute to the literature on
cross-sectional fiscal multipliers (e.g., Chodorow-Reich, 2019; Nakamura and Steinsson, 2014;
Auclert and Mitman, 2018) and provide the first estimate for mortgage forbearance.
    Lastly, we connect to the literature on optimal mortgage design (e.g., Eberly and Krishna-
murthy, 2014; Piskorski and Tchistyi, 2010; Seru and Piskorski, 2018; Guren et al., 2021). In
particular, our work is closely related to Campbell et al. (2021), who examine mortgage design
features that enable borrowers to make interest-only payments and extend the maturity of their
mortgages during recessions to promote macroeconomic stability. Given the notable similari-
ties between mortgage forbearance under the CARES Act and the state-dependent modification
features proposed in that study, our work provides empirical evidence supporting the stabilizing
effects of mortgage payment suspension during economic downturns.
   4 While Kim et al. (2022) focus on GNMA mortgages guaranteed by various government agencies, we focus

on mortgages securitized by the GSEs. Despite the difference in our specific focus, our findings are similar and
complementary to each other.


                                                       8
2     Mortgage Forbearance under the CARES Act
The Coronavirus Aid, Relief, and Economic Security (CARES) Act, enacted into law on March
27, 2020, included a broad mandate allowing households to request forbearance on all federally
backed mortgage loans. Mortgages eligible for forbearance include those purchased or securitized
by the government-sponsored enterprises (GSEs) (Fannie Mae and Freddie Mac) as well as those
guaranteed by Ginnie Mae (GNMA), which are insured by various government agencies including
the Federal Housing Administration (FHA) and the U.S. Department of Veterans Affairs (VA).5
Forbearance under the CARES Act is granted upon the borrower’s attestation to financial hardship
caused by the pandemic and does not require documentation or formal proof.6 This practice lies
in sharp contrast to standard mortgage modification or disaster relief programs, which generally
require extensive proof of hardship or income documentation.
    Mortgage borrowers in forbearance are given an option to postpone monthly payments for a
fixed duration without incurring additional fees or penalties.7 To insulate borrowers’ credit scores,
the CARES Act also requires that intermediaries must not report any missed payments of loans
in forbearance to credit reporting agencies. Despite the wide eligibility and generous terms, for-
bearance enrollment is not automatic: Borrowers must request both the initial forbearance and any
extensions from their mortgage servicer.
    The original CARES Act specified a six-month forbearance that could be extended up to 12
months, but regulators later allowed for an additional six-month extension.8 At its inception, there
was a lack of clarity on how payments would be structured upon forbearance exit, but the FHA
released statements in April 2020 clarifying that deferred payments would not be due in lump sum
at the end of the forbearance period. In particular, when mortgage borrowers exit forbearance, they
    5 The private sector also extended forbearance to borrowers of non-agency mortgages that were not eligible for the

CARES Act (Cherry et al., 2021).
     6 In particular, Section 4022 of the CARES Act states, “During the covered period, a borrower with a federally

backed mortgage loan experiencing a financial hardship due, directly or indirectly, to the COVID-19 emergency may
request forbearance on the federally backed mortgage loan, regardless of delinquency status, by (A) submitting a
request to the borrower’s servicer and (B) affirming that the borrower is experiencing a financial hardship during the
COVID-19 emergency.”
     7 One notable downside is that borrowers are unable to refinance their mortgage while in forbearance. Once they

exit forbearance, they are required to make payments for three months to regain eligibility to refinance.
     8 For GSE loans, borrowers can request up to six months of additional forbearance if their initial forbearance began

on February 28, 2021, or earlier. For FHA/VA loans, borrowers can request up to six months of additional forbearance
if their initial forbearance began on June 30, 2020, or earlier.



                                                           9
Figure 2: Evolution of Mortgage Payments in Forbearance. This figure shows the trend in
monthly payments before and after entering forbearance. The estimates are conditional on a sample
of GSE mortgage borrowers who were not delinquent before entering forbearance and who remain
forborne as of each month after entering forbearance. Data sources: Fannie Mae and Freddie Mac.


are typically granted the option to defer repayment of their missed payments to the end of their
mortgage term as a second-lien loan that does not accrue interest, which effectively constitutes a
free loan for the missed payments.9


2.1     Forbearance Rates and Trends

At the national level, forbearance take-up closely tracked the economic fallout precipitated by the
COVID-19 pandemic. Figure 1 shows the monthly fraction of GSE loans in forbearance, which
sharply increased after March 2020 following the passage of the CARES Act. The forbearance
rate peaked at about 5 percent in May 2020 and gradually declined to 2 percent by June 2021.
Following the initial spike, new loans continued to enter forbearance at a steady rate from June
2020 until the end of the program. Forbearance exits were highest in the three to six months
following the CARES Act passage and continued at a rate higher than program entry thereafter.
The same qualitative pattern holds among GNMA mortgages, albeit with a quantitatively larger
magnitude (see Appendix Figure B1).
   9 Due to this feature, the CARES Act mortgage forbearance does involve a small wealth transfer in case borrowers

choose this exit option. Nevertheless, the magnitude of this wealth effect is likely negligible.



                                                           10
Figure 3: Distribution of Forbearance Rates across Zip3 Areas. This figure shows the geo-
graphic distribution of forbearance rates across Zip3 areas as of June 2020. The legend shows the
color coding of forbearance rates in percentages. Data sources: Fannie Mae and Freddie Mac.


   Entering forbearance had a substantial impact on the monthly payments made by mortgage
borrowers. Figure 2 shows the trend in monthly payments for forborne borrowers with a GSE-
securitized mortgage. Before borrowers enter forbearance, the average monthly payment amount
is $1,324. Upon their entering, the monthly payment subsequently falls to $444, resulting in sus-
pended monthly payments of $880 on average. The fact that the average payment is still positive
reflects an intriguing pattern that approximately one third of the borrowers continued to make
payments while in forbearance. Conditional on remaining in forbearance, the average deferred
payment does not vary with the duration of forbearance.
   When borrowers exit forbearance, they are typically granted generous repayment options rather
than having to pay back their missed payments in lump sum. Appendix Figure A1 shows the com-
position of forbearance exits among GSE mortgages. Approximately 25 percent of borrowers who
exited forbearance did not have any missed payments during the forbearance period, which aligns
with the payment pattern of forborne borrowers described above. Among the 67 percent of bor-
rowers who had some missed payments, payment deferral (42 percent)—which let borrowers defer
repayment of the missed amounts to the end of their mortgage maturity—was the largest category,
followed by loan modifications (10 percent) which altered the terms of the original mortgage to fa-
cilitate smooth repayment. Interestingly, 7 percent of exiting borrowers repaid the missed amounts
in lump sum even though they were most likely not required to, and 8 percent exited forbearance
by selling their house and fully paying back their mortgage.

                                                11
    Lastly, Figure 3 shows the geographic distribution of forbearance rates across three-digit Zip
code (Zip3) areas as of June 2020. While approximately 5 percent of GSE mortgages were in
forbearance at the national level, the aggregate rate masks significant heterogeneity across regions
whose forbearance rates range from near 0 percent to more than 10 percent. Moreover, forbearance
outcomes widely vary across areas within each state.10


2.2     Intermediation Frictions in Mortgage Forbearance

Despite the broad eligibility and the minimal requirements for the program, not all borrowers took
advantage of the program. One indication of frictions in take-up is the fraction of borrowers with
mortgages past due who did not enter forbearance. This is because the non-take-up of forbearance
while being delinquent is a clear financial mistake for borrowers, as there is no penalty or cost
associated with the CARES Act forbearance. Figure A2 shows the share of GSE mortgages past
due and the fraction of these delinquent loans that are not in forbearance. About 30 to 40 percent
of delinquent borrowers failed to take up forbearance.11 Panel (b) of Appendix Figure B1 shows
the equivalent statistics for GNMA mortgages that exhibit a similar non-take-up rate.
    What explains this lack of participation among delinquent borrowers, despite the clear benefits
and limited documentation needed for forbearance? One possible reason is that differences in the
implementation of the program by servicers prevented some borrowers from taking advantage of
the program. Differences in the organizational practices of mortgage servicers resulted in varia-
tions in the accommodation of forbearance requests and their communication with households.12
This delegation of program implementation to mortgage servicers stands in contrast to other forms
of debt relief under the CARES Act. For instance, individuals with public student loans were
automatically placed in forbearance.
    Consumer complaints submitted to the Consumer Financial Protection Bureau (CFPB) corrob-
orate the supposition that there were large differences in the organizational practices of mortgage
  10 Since we control for state fixed effects in our regressions to account for state-level differences in policy responses,

we rely on these within-state variations in forbearance outcomes for identification.
   11 Among mortgages that are past due for 60 days or more, about 20 to 30 percent did not take up forbearance.
   12 As discussed by Kim et al. (2022), cash flow risk, regulatory oversight, and organizational structure can affect the

incentives of servicers to engage in accommodating forbearance practices. These incentives come into play due to the
ambiguity in the CARES Act about the specific practices that intermediaries should take in setting up the forbearance
program.



                                                           12
servicers in implementing the forbearance program. Appendix Table A1 categorizes the CFPB
complaints and provides an example for each category. Some servicers wrongfully requested doc-
umentation of financial hardship or, in some cases, outright denied requests to enroll in or extend
mortgage forbearance. In other cases, servicers placed mortgage borrowers in forbearance if they
had merely called to obtain more information about the federal program or even automatically en-
tered distressed mortgage borrowers into forbearance without their consent.13 There is also some
indication that servicers miscommunicated how they would treat forbearance exits, which may
have impacted households’ desire to enter the program, especially at the onset of the crisis.14 Mo-
tivated by the evidence discussed above, in Section 4, we quantify the servicer-induced frictions in
take-up by formally estimating different mortgage servicers’ propensities to provide forbearance
to an observably similar borrower.



3      Data
Our primary analysis is based on loan-level data on mortgage characteristics and performance,
combined with region-level data on employment statistics and demographic information. We de-
scribe the data used for our analysis below.


GSE Single-Family Loan Performance Data.                     We focus our analysis on conforming loans that
are purchased or securitized by Fannie Mae and Freddie Mac, which constitute approximately
70 percent of the U.S. agency mortgage market (Inside Mortgage Finance, 2023).15 We measure
forbearance from the loan-level data on GSE single-family mortgages. This is a monthly panel
dataset that provides a rich set of information on loan characteristics (for example, interest rates,
principal balance, payment history), borrower characteristics at origination (for example, credit
score, debt-to-income ratio), and property characteristics (for example, property type and location).
    13 This practice was alleged in a class action lawsuit against Wells Fargo, which admitted that the company had au-

tomatically placed certain types of loans in forbearance (for example, those in active Chapter 13 bankruptcy repayment
plans).
   14 In response to the widespread miscommunication of information by mortgage servicers, regulatory agencies

launched campaigns targeting households to inform them about debt relief programs (CFPB, 2021).
   15 While the loan-level data for GNMA mortgages are available for public use, they contain only state-level in-

formation about the location of the mortgaged property and thus are not suitable for our local labor market analysis.
Although we exclude GNMA mortgages from our main analysis, Appendix B describes the key features of the GNMA
microdata and discusses forbearance rates and trends in the GNMA mortgage market.


                                                          13
We identify the date when loans entered forbearance based on a flag that indicates the type of
assistance plan in which the borrower is enrolled at a given month. We define regions at the level
of the three-digit Zip code, which is the most detailed location information available in the GSE
data. We restrict our sample to fixed-rate mortgages that are active at any point after January 2020.
    We define the lender as the financial institution that initially sold the mortgage to one of the
GSEs and the servicer as the institution with servicing rights for that loan.16 In Section 4, we use
this information to estimate the average forbearance propensity of each mortgage servicer (con-
ditional on loan and borrower characteristics) and subsequently construct a shift-share instrument
for regional forbearance outcomes by combining the estimated forbearance propensities with the
servicers’ local market shares computed at the Zip3 level.


Quarterly Census of Employment and Wages. We use monthly employment from the Bureau
of Labor Statistics (BLS) Quarterly Census of Wages and Employment (QCEW) to construct our
main regional outcome measures.17 The QCEW is derived from quarterly reports filed by employ-
ers whose workers are covered by unemployment insurance laws, which constitute approximately
95 percent of the total private employment in the United States. We start with county-level sectoral
employment at the two-digit NAICS industry classification and seasonally adjust the data by taking
the change in employment relative to the corresponding month in 2019.18 We then cross-walk the
county-level employment to the Zip3-level using the 2019 population shares.
    Following Mian and Sufi (2014), we define nontradable industries as consisting of retail trade
(NAICS codes 44 and 45) and accommodation and food services (72), and tradable industries as
consisting of manufacturing (31 through 33), agriculture, forestry, fishing, and hunting (11), and
mining, quarry, and oil and gas extraction (21).19 In our main analysis, we use employment in
nontradable industries as a proxy for local demand.
  16 The GSE data disclose only the identity of the financial institutions that have at least 1 percent of market share

within a given acquisition or reporting quarter. We omit small-share servicers in our loan-level analysis but retain them
when calculating the local mortgage market shares.
   17 We primarily focus on employment instead of wages, as the QCEW data only contain quarterly wages.
   18 In our robustness check, we also seasonally adjust the data using a linear model with monthly indicator vari-

ables, along with an interaction between the monthly indicators and the period following March 2020. Standard
seasonal-adjustment algorithms that rely on moving-average adjustments (for example, Census Bureau X-11) artifi-
cially propagate the COVID-19 employment shock to preceding years.
   19 Following Chodorow-Reich et al. (2021), we use a two-digit classification of tradable and nontradable industries

to avoid the increased suppression of employment counts at industry-county cells in finer classifications.



                                                          14
American Community Survey. We use the U.S. Census Bureau’s American Community Survey
(ACS) 2015–2019 estimates archived by the National Historic Geographic Information System
(NHGIS) to obtain our measures of regional controls (Manson et al., 2021). In particular, we use
the average demographic characteristics (for example, age, race) and socioeconomic characteristics
(for example, income, unemployment rate, homeownership rate) at the Zip3 level. To account for
differential mortgage ownership across regions, we also compute the fraction with mortgages in
each Zip3 area and include it as a baseline control (Di Maggio et al., 2017).


Economic Tracker.          The Opportunity Insights Economic Tracker uses anonymized data from
private companies to provide economic indicators at both national and regional levels since the
beginning of the pandemic (Chetty et al., 2020). The data include real-time information on em-
ployment rates, business activities, and mobility. We use the number of COVID-19 cases and
mortality provided by the Tracker, which are collected by the New York Times from local public
agencies. We also use state-level policy milestones available through the Economic Tracker that
provide information on the duration of stay-at-home orders as well as nonessential business closure
and reopening dates.



4      Heterogeneity in Forbearance Propensities across Servicers
In this section, we first document that there is substantial heterogeneity in forbearance propensity
across different mortgage servicers. We then use this heterogeneity to motivate our instrument for
the local forbearance outcome. Our approach makes use of the fact that financial intermediaries
provide a source of idiosyncratic variation in the supply or availability of forbearance, conditional
on demand-based determinants of the program.20


4.1      Loan-level Analysis of Forbearance Outcome

We examine the extent to which a borrower’s mortgage servicer predicts forbearance utilization.
We consider a linear probability model that relates a mortgage borrower’s forbearance outcome to
    20 We draw from related work using intermediary-level variation to study regional and aggregate outcomes (e.g.,

Greenstone et al., 2020; Amiti and Weinstein, 2018).



                                                        15
borrower characteristics, local economic conditions, and the servicer identity:21


                                      1{Fi t } = βX i t + αz(i )t + αs(i ) + ϵi t ,                           (1)


where 1{Fi t } is an indicator variable equal to 1 if a loan i is in forbearance during month t , z(i )
is the three-digit Zip code of the property, and s(i ) is the servicer of the loan. The object of our
interest is the servicer’s contribution to forbearance take-up, αs(i ) . To account for differences in
the composition of borrowers serviced and their underlying need for mortgage relief, we control
for a vector of loan characteristics X i t that reflects borrower demand and the Zip3-by-month fixed
effects αz(i )t that capture local economic conditions. Loan characteristics include current interest
rates, remaining principal balance, credit score at origination, loan-to-value ratio at origination,
debt-to-income ratio at origination, and an indicator variable for first-time homeowner. We esti-
mate Equation (1) during the 12-month period following the passage of the CARES Act.
    Figure A3 presents the estimated servicer fixed effects for the 58 mortgage servicers that have
greater than 1 percent market share in our sample. Panel (a) plots the distribution of the ser-
vicer fixed effects, whereas panel (b) depicts the fixed effects for the top and the bottom mortgage
servicers. The range of estimated servicer propensities is approximately 7 percent. Given the
mean forbearance rate of 3.36 percent in our estimation sample, this difference is sizable and eco-
nomically meaningful. Moving a borrower from the 25th percentile to the 75th percentile of the
weighted servicer propensity distribution leads to an increase in the probability of take-up that is
equivalent to 24 percent of the mean forbearance rate.
    The servicers’ heterogeneity in forbearance propensity is robust to alternative specifications.
In particular, following Kim et al. (2022), we restrict our estimation sample to the set of borrowers
that were current prior to the onset of the pandemic but missed at least one payment during our
sample period, and we estimate a cross-sectional model in which the dependent variable is an
indicator for whether a mortgage ever entered forbearance during our sample period. We find
that this alternative approach also produces a wide dispersion in the estimated servicer effects and
that these alternative estimates are strongly positively correlated with our main estimates. The
robustness of our findings under this alternative design shows that servicer heterogeneity plays an
  21 In Online Appendix D, we motivate our estimating equation by deriving the relationship of forbearance take-up

to servicer and borrower characteristics in a simple household model of forbearance.


                                                          16
important role in driving forbearance outcomes.


4.2    Instrument for Regional Forbearance Outcome

Assessing the stabilizing effect of forbearance is challenging due to the fact that the take-up of
forbearance is endogenous to the severity of the economic shock induced by the pandemic as well
as other confounding factors that affected the subsequent recovery. To overcome this challenge,
we use our estimated servicer propensities to construct a shift-share measure at the regional level
that captures disparities in program availability stemming from idiosyncratic differences among
servicers. We then employ this measure as an instrument for the regional forbearance rate under
the assumption that regions with varying servicer propensities do not exhibit systematic differences
in other characteristics that would affect local employment growth, conditional on a set of controls
described below (Borusyak et al., 2022).
    We first describe the construction of the instrument. Denote S as the set of mortgage servicers.
Let ℓz,t ,s be the dollar amount of mortgages serviced by servicer s in Zip3 region z at month t , and
let ℓz,t =       s∈S ℓz,t ,s be the total amount of outstanding mortgage debt in region z at month t . The
             P

local market share of the servicer s is then w z,t ,s = ℓz,t ,s /ℓz,t . The shift-share measure of servicer
effects for region z is defined as:
                                                            w z,t0 −1,s αs ,
                                                      X
                                             SS z =                                                          (2)
                                                      s∈S

where t 0 denotes the beginning of the pandemic recession, and αs is the servicer fixed effects from
the loan-level regression in Equation (1). We use the pre-pandemic market share as of February
2020 to account for the potential endogeneity of servicer market shares during the pandemic.22 To
ensure that the estimated servicer effects do not reflect local economic conditions, we use the state-
level, leave-one-out (LOO) estimates of the servicer effects when constructing the shift-share. That
is, for each state, we estimate the servicer effects separately by restricting the estimation sample to
loans outside of that state.
    In Appendix Figure A4, we show the geographic distribution of our shift-share measure across
Zip3 areas. Similar to the geographic distribution of the forbearance rates, there is significant
geographic dispersion in our shift-share measure both across and within each state.
  22 In practice, the market shares of servicers do not change in a meaningful way over our sample period.




                                                            17
Figure 4: Forbearance Rates by Shift-share Quartiles. This figure plots the forbearance rates
for Zip3 areas that are at the top (solid black curve) and bottom (dashed gray curve) quartiles of the
shift-share distribution. The red vertical line marks the passage of the CARES Act. Data sources:
Fannie Mae and Freddie Mac.


Instrument Relevance. Figure 4 plots the mortgage forbearance rates in Zip3 areas that are at
the top and bottom quartiles of our shift-share measure. On average, during our sample period,
there is approximately 1 percentage point difference in the forbearance rates between these two
groups of regions. Although monthly differences shrink over time, the magnitude of the observed
differences, on average, is sizable and economically meaningful.
    The differences in forbearance rates across regions, however, could also be a result of the se-
lection of servicers into regions with different characteristics that impact forbearance demand.23
Appendix Table A2 shows various observable characteristics of regions that are above and below
the median of the shift-share instrument. As anticipated, there are some statistically distinguishable
differences across the two groups of regions, including average loan characteristics (for example,
principal balance) and demographic and socioeconomic characteristics (for example, racial com-
position, education, average income). To account for these observable differences, we control for
average loan characteristics as well as demographic and socioeconomic characteristics as baseline
controls in our regressions.
    We next assess the conditional relevance of our shift-share instrument on regional forbearance
  23 When estimating servicer effects from our loan-level regression, we can only control for loan characteristics

and a limited set of borrower characteristics available in the GSE data, which may not fully capture demand-based
determinants of forbearance.


                                                       18
outcomes in a simple panel regression. In column (1) of Appendix Table A3, we first include
state-by-month fixed effects to account for any time-varying, state-level differences. A one stan-
dard deviation increase in the shift-share measure leads to a 0.47 percentage point increase in the
forbearance rate. In column (2), when we additionally control for average loan characteristics and
demographic and socioeconomic characteristics at the Zip3 level, this coefficient drops to 0.22 but
remains both statistically and economically significant.24
    Lastly, we present some evidence that our shift-share measure is not predictive of other mea-
sures of fiscal stimulus and debt relief during the COVID-19 recession. One potential confounding
factor to our shift-share measure is the Paycheck Protection Program (PPP), another large-scale fis-
cal stimulus under the CARES Act that provided support to small and medium businesses. Since
the disbursement of PPP funds was mediated through financial intermediaries (Granja et al., 2022),
our shift-share measure exploiting the geographical distribution of financial intermediaries could
be predictive of the regional distribution of the PPP funds. In column (3) of Appendix Table A3,
we test for this possibility and find that our shift-share measure is not predictive of the regional
distribution of the PPP funds. Similarly, in columns (4) and (5), we verify that our shift-share
measure is not predictive of the mortgage refinancing rate as well as the bankruptcy filing rate.



5     Empirical Design and Results
We present our baseline empirical design and main results. We discuss the identification conditions
required for a causal interpretation of our findings. We also show robustness of our findings along
a number of dimensions.


5.1    Empirical Design

We estimate the impact of mortgage forbearance on Zip3-level economic outcomes. To account
for the endogeneity of forbearance take-up to local economic conditions, we rely on plausibly ex-
ogenous variation in forbearance captured by our shift-share measure of servicer frictions. Our
baseline structural equation relates a change in region-level outcome, Y z,t , to the average forbear-
  24 Appendix Figure A5 shows the binscatter of the regional forbearance rate and our shift-share instrument, with

and without including Zip3 controls.


                                                       19
ance rate during a fixed time period:


                 ∆ log Y z,t0 →T = β0 + β1 Forbz,t0 →T + β2 X z,t0 −1 + β3 P z,t0 →T + βstate + e z ,     (3)


where ·z,t0 →T denotes the monthly average of a variable in region z from month t 0 to T . Our
coefficient of interest is β1 , which captures the impact of forbearance, conditional on pre-pandemic
observable characteristics X z,t0 −1 , time-varying regional controls P z,t , and state fixed effects βstate .
In our baseline specification, Y z,t is the employment in nontradable sectors.
    We estimate Equation (3) with two-stage least squares (2SLS), using our shift-share measure
of servicer effects as an instrument for the average forbearance rate in the following specification
of the first-stage:


                   Forbz,t0 →T = γ0 + γ1 SS z,t0 →T + γ2 X z,t0 −1 + γ3 P z,t0 →T + γstate + ϵz ,         (4)


where SS z,t is the instrumental variable described in Equation (2). As in the second-stage specifi-
cation, we control for pre-pandemic regional characteristics X z,t0 −1 , time-varying regional controls
P z,t , and state fixed effects γstate .


Identifying Assumption.           The key identifying assumption of our approach is that conditional
on our baseline controls, other aggregate factors that are correlated with servicers’ forbearance
propensities impact areas with high and low exposure to the servicer effects uniformly. The exo-
geneity of our instrument is motivated by the treatment of servicer propensities as "shocks" from
the perspective of regional economies (Borusyak et al., 2022). The sorting of leniant servicers
to regions with generally greater forms of fiscal stimulus would be one example of a violation of
this condition. Because we estimate forbearance in the cross-section of U.S. regions, we assume
asymptotic behavior in the number of regions. We interpret our 2SLS as capturing the local aver-
age treatment effect (LATE) under the monotonicity assumption of servicer propensities on local
forbearance take-up, which is plausible in our setting.
    Our identifying assumption is conditional on a set of baseline controls that are meant to address
the fact that locations with higher values of SS z may differ on observable dimensions that impact
their recovery during the pandemic recession. For example, part of the observed differences in

                                                         20
outcomes across locations may not only reflect greater mortgage forbearance but also differences
in borrower profiles or demographics. To account for these differences, we include a range of pre-
pandemic controls such as average loan characteristics (principal balance, interest rate, credit score
and LTV/DTI ratios at origination, first-time homebuyer) and demographic and socioeconomic
characteristics of the population (age, education, race, income, pre-pandemic unemployment rate,
fraction with mortgage). Additionally, we address the fact that Zip3 areas may have differential
exposure to the pandemic based on local industry compositions by including the predicted change
in local employment based on NAICS3 industry shares (Chodorow-Reich and Wieland, 2020).25
Lastly, because our state fixed effects account for any statewide differences in economic outcomes,
our estimate is derived from variations across within-state Zip3 areas.


Sample Period and Regression Window. One complication in examining the change in regional
demand in response to mortgage forbearance activity is that local economies experienced concur-
rent “supply shocks” from state-ordered economic lockdowns or consumer hesitation in visiting
local stores. The first stay-at-home order was issued by California in March 2020, with many states
following suit. The beginning of the recession poses a challenge to our empirical design because
economic lockdowns can limit the propagation of local demand effects stemming from deferred
mortgage payments. To overcome this challenge, our specification examines changes in local em-
ployment during an 18-month window following the first reopening month of each state (t 0 ).26
Our estimates of regional employment effects can therefore be interpreted as capturing differences
in the speed of recovery following the initial lockdown.
    Our regression-window adjustment suggests two points that are worth addressing. First, since
different regions have different reopening dates, the economic recovery can be affected by the
timing of reopening. Our state fixed effects help account for this possibility by comparing within-
state Zip3 areas that all reopened in the same month, though local governments may deviate from
the state’s lockdown guidance. Second, to the extent that different regions were economically
impacted by the pandemic differentially (for example, due to more severe lockdowns or limitations
  25 In particular, we construct a shift-share industry employment measure for each region using pre-pandemic indus-

try shares and the national employment growth in each NAICS3 industry.
   26 States varied in their announced reopening date, but the vast majority of permitted businesses reopened between

the start of May and the end of July in 2020.



                                                         21
                                   First-stage                  Reduced-form                  2SLS
                                 (1)          (2)              (3)        (4)           (5)           (6)
                                    ∗∗∗
 Shift-share (in SD)          0.389        0.189∗∗∗         0.102 ∗∗∗
                                                                       0.055∗∗∗
                               (0.057)      (0.057)          (0.016)    (0.013)
 Forbearance rate (%)                                                                0.291∗∗∗      0.294∗∗
                                                                                      (0.063)      (0.111)
 State FE                        Y              Y              Y           Y             Y            Y
 Zip3 controls                   N              Y              N           Y             N            Y
 R-squared                      0.28           0.46           0.62        0.78            -            -
 N                              841            841            841         841           841          841
 Outcome mean (%)               2.04           2.04           1.13        1.13          1.13         1.13
 Outcome SD (%)                 1.40           1.40           0.52        0.52          0.52         0.52
 Standard errors in parentheses; ∗ p < 0.05, ∗∗ p < 0.01, ∗∗∗ p < 0.001

Table 1: Baseline Results on Nontradable Employment. This table shows the regression results
of our baseline specification for nontradable employment growth. Columns (1)-(2), (3)-(4), and
(5)-(6) respectively show the results for first-stage, reduced-form, and 2SLS regressions, with and
without including Zip3-level controls. The shift-share variable is expressed in SD units. All out-
come variables are expressed in percentages. Data sources: GSEs, QCEW, and ACS.


in remote work based on local industries), some regions may have had more slack in their labor
markets, which could have affected the speed of their employment recovery. We account for this
possibility by controlling for each region’s initial drop in total employment as a proxy measure of
local labor market slack in our baseline specification.27


5.2    Main Results

Nontradable Employment Growth.                  Table 1 presents our main results. Column (1) shows the
results from the first-stage regression without regional controls. In column (2), we include regional
controls, which corresponds to our preferred specification described by Equation (4). Conditional
on regional characteristics, a one standard deviation increase in the shift-share instrument leads
to a 0.19 percentage point rise in the regional forbearance rate. This increase corresponds to
approximately 9.2 percent of the average forbearance rate during our sample period, which is 2.04
percent. The F-statistic of our first-stage is 11.9, which reflects strong relevance of our servicer-
based instrument for regional forbearance outcome.
  27 We measure the initial drop in total employment in each region as the log difference between pre-pandemic

employment (as of February 2020) and the lowest level of employment observed during the lockdown period.



                                                         22
   Columns (3) and (4) present the reduced-form estimates of regressing monthly employment
growth on our shift-share instrument without and with regional controls, respectively. In our pre-
ferred specification in column (4), a one standard deviation increase in the shift-share measure
leads to a 5.5 basis point increase in the average monthly growth of nontradable employment. Ac-
cordingly, the implied 2SLS estimate in column (6) suggests that a 1 percentage point increase in
the share of mortgages in forbearance leads to a 29 basis point increase in the monthly nontradable
employment growth. Given that the mean and the standard deviation of the nontradable employ-
ment growth are 1.13 and 0.52 percent in our sample period, our estimate is sizable and significant
both statistically and economically. For example, moving a region from the 25th percentile to the
75th percentile of our shift-share distribution would lead to an increase in nontradable employment
growth equivalent to 7.4 percent of the mean growth rate (or 16.1 percent of the standard deviation)
during our sample period.
   While we focus on nontradable employment as our primary outcome, we show in Appendix
Table A4 that the results are almost identical when we instead use nontradable payroll as the
outcome variable. Appendix Table A5 displays the results weighted by Zip3 population, which
are also similar to the baseline results. Lastly, Appendix Table A6 displays the OLS estimates
for comparability. The OLS estimates are considerably smaller or close to zero in magnitude,
which likely reflects the endogeneity of forbearance outcomes to local economic conditions that
can lead to reverse causality. This finding highlights the importance of separating supply-side
frictions, conditional on demand-based factors, for identifying the economic impact of forbearance,
as discussed in Sections 4 and 5.1.


5.3   Robustness

We interpret our baseline specification as providing evidence of the local demand effects associ-
ated with the greater liquidity provided by mortgage forbearance. We now examine alternative
specifications and additional outcome variables that corroborate this interpretation of our baseline
estimates. We also assess the robustness of our main results to including a variety of potential
confounding factors.




                                                23
                                   Non-Tradable                      Tradable                     Total
                                  (1)         (2)                (3)          (4)            (5)          (6)
                                     ∗∗∗
 Forbearance rate (%)         0.291        0.294∗∗             0.017        -0.129       0.136  ∗∗∗
                                                                                                        0.105∗
                               (0.063)     (0.111)            (0.049)      (0.114)        (0.035)       (0.049)
 State FE                          Y           Y                  Y            Y              Y            Y
 Zip3 controls                     N           Y                  N            Y              N            Y
 N                               841         841                835          835            841           841
 Outcome mean (%)                1.13        1.13               0.38         0.38           0.62         0.62
 Outcome SD (%)                  0.52        0.52               0.48         0.48           0.28         0.28
 Standard errors in parentheses; ∗ p < 0.05, ∗∗ p < 0.01, ∗∗∗ p < 0.001}

Table 2: Tradable and Total Employment. This table shows the 2SLS estimates for different
employment sectors. Columns (1) and (2), (3) and (4), and (5) and (6), respectively, show the
results for nontradable, tradable, and total employment, with and without including Zip3-level
controls. The shift-share variable is expressed in SD units. All outcome variables are expressed in
percentages. Data sources: GSEs, QCEW, and ACS.


Pre-Pandemic Placebo Effects.             To test whether our estimates are driven by differences in the
secular growth rates in different regions, we estimate Equation (3) using the 12-month, pre-pandemic
employment growth as the outcome variable. Appendix Table A7 displays the results. We find that
our shift-share measure does not predict forbearance outcome in the period preceding the CARES
Act, as shown by the precisely estimated null effects in the first stage reported in columns (1) and
(2).28 More importantly, the shift-share measure does not predict employment growth during the
pre-pandemic period, as evidenced by the small and insignificant reduced-form estimates reported
in columns (3) and (4). The lack of pre-trends in employment growth is also confirmed in Figure
5, which plots the local-projection estimates of our shift-share instrument on employment growth
(discussed further below). Hence, differences in the trajectory of Zip3 areas before the pandemic
do not explain our results on employment growth during the recovery period.


Tradable Employment and Total Employment. While we have so far focused on nontradable
employment growth as a proxy for local demand effects, we follow Mian and Sufi (2014) in as-
sessing whether our instrumented measure of forbearance predicts regional employment in tradable
sectors and total employment, which are less influenced by local aggregate demand. Columns (3)
and (4) of Table 2 present the 2SLS estimates of mortgage forbearance on monthly employment
  28 This result is mechanical in large part, as typically only a small number of distressed borrowers are under for-

bearance.


                                                         24
growth in the tradable sectors. The coefficient estimates are not statistically distinguishable from
zero, confirming that mortgage forbearance had little impact on tradable employment. Columns (5)
and (6) report the results using total employment growth as the outcome variable. A 1 percentage
point increase in the forbearance rate leads to an 11 basis point increase in the monthly growth in
total employment, which is smaller in magnitude compared with the increase for nontradable sec-
tors. Overall, these results support the interpretation that the increased liquidity provided through
mortgage forbearance had an impact on regional employment through local aggregate demand
effects.


Robustness to Confounding Factors.              To explore the sensitivity of our empirical design, Table 3
presents the 2SLS estimates from alternative specifications that include additional covariates. Col-
umn (1) reproduces the result from our baseline specification in column (6) of Table 1. Column (2)
includes the COVID-19–infection and mortality rates to account for labor supply effects associated
with greater exposure to the pandemic. In column (3), we consider systematic differences between
rural and urban areas (for example, COVID-19 exposure, viability of social-distancing measures,
and the distribution of mortgage servicers) by controlling for population density.29 Including these
additional controls does not materially change our estimate.
    Next, we assess the robustness of our results to controlling for other measures of economic
stimulus during the pandemic that can impact local employment recovery.30 In columns (4) and
(5), we control for the share of refinanced mortgages and the per capita PPP amount, respectively.
In column (6), we control for the personal bankruptcy filing rate in 2020 and also for the equiva-
lent rate in 2019 to account for the fact that some financial intermediaries automatically enrolled
their distressed mortgage borrowers into forbearance (for example, those associated with an active
Chapter 13 bankruptcy repayment plan). Including these additional controls does not significantly
change our estimate, which is consistent with our previous analysis in Section 4.2 that our shift-
share measure does not predict other economic stimulus measures.
    Lastly, column (7) includes all additional controls from columns (2)-(6) and shows that the
  29 Alternatively, controlling for the RUCA (Rural-Urban Commuting Area) classifications of the U.S. Department

of Agriculture Economic Research Service yields similar results.
   30 State-level differences in fiscal stimulus, such as unemployment insurance (UI) generosity or broadened Supple-

mental Nutrition Assistance Program (SNAP) eligibility, are already absorbed by state fixed effects in our baseline
specification.


                                                         25
                               (1)     (2)     (3)     (4)     (5)      (6)    (7)
 Forbearance rate (%)        0.294∗∗ 0.304∗ 0.289∗ 0.295∗∗ 0.289∗∗ 0.283∗∗ 0.287∗
                             (0.111) (0.125) (0.113) (0.112) (0.102) (0.108) (0.112)
 COVID rate (%)                      -0.027                                  -0.034
                                     (0.072)                                 (0.069)
 Death rate (%)                      -11.55                                  -10.83
                                     (12.03)                                 (11.80)
 Population density                           0.016                           0.017
                                             (0.026)                         (0.026)
 Refinancing rate (%)                                 0.026                   0.031
                                                     (0.056)                 (0.058)
 PPP amount (per capita)                                     -0.001          -0.000
                                                             (0.002)         (0.002)
 2019 Bankruptcy filings (%)                                          1.23∗   1.24∗
                                                                      (0.60) (0.61)
 2020 Bankruptcy filings (%)                                           -1.31  -1.34
                                                                      (0.69) (0.70)
 State FE                       Y       Y       Y       Y       Y        Y      Y
 Zip3 controls                  Y       Y       Y       Y       Y        Y      Y
 N                             841     841     841     841     841      841    841
 Standard errors in parentheses; ∗ p < 0.05, ∗∗ p < 0.01, ∗∗∗ p < 0.001

Table 3: Robustness to Confounding Factors. This table shows the robustness of 2SLS estimates
to potential confounding factors. Column (1) repeats our baseline estimate. Columns (2) through
(6) additionally control for COVID-19 exposure, population density, mortgage refinancing rate,
PPP amount, and bankruptcy filing rate, respectively. Column (7) includes all controls. The shift-
share variable is expressed in SD units. The outcome variable is expressed in percentages. Data
sources: GSEs, QCEW, ACS, Economic Tracker, Small Business Administration (SBA), and U.S.
Courts.


resulting estimate is similar to our baseline estimate. Overall, our empirical design is robust to
controlling for potential confounding factors considered above.


Dynamic Effects of Forbearance. While our baseline specification focuses on the average change
in outcome during a fixed, 18-month window, we consider a possibility that the effect of mortgage
forbearance is time-varying over our sample period. For example, since mortgage forbearance
primarily serves as a short-term liquidity injection to households, mortgage forbearance may have
a stronger impact on short-horizon outcomes. To investigate these dynamic effects, we run a lo-
cal projection analysis by regressing our shift-share instrument on the cumulative change in the
regional forbearance rate and the nontradable employment at each month, conditional on our base-

                                                         26
       (a) Cumulative Forbearance Differential             (b) nontradable Employment Growth

Figure 5: Local Projection: First-Stage and Reduced-Form. This figure plots the local-
projection estimates of our shift-share instrument (black curve) along with their 95 percent confi-
dence intervals (dashed gray curve). Panel (a) shows the cumulative effect on forbearance. Panel
(b) shows the effect on nontradable employment. The shift-share measure is expressed in SD units.
Data sources: GSEs, QCEW, and ACS.


line controls described above.
    In Figure 5, panel (a) displays the local-projection estimates of our shift-share instrument on
the cumulative forbearance rate along with their 95 percent confidence intervals. A one standard
deviation increase in our shift-share measure leads to a sharp accumulation of forbearance differ-
ential of roughly 2 percentage points in the first 12 months followed by a steady but slower increase
in the following period. This pattern is consistent with our previous analysis in Figure 4 that for-
bearance rates across regions in the shift-share quartiles exhibited a greater divergence during the
initial year.
    Panel (b) plots local-projection estimates for nontradable employment growth. The pre-reopening
estimates confirm the absence of differential trends, which complements our earlier analysis of the
pre-pandemic placebo effects. After statewide reopenings, a one standard deviation increase in our
shift-share measure results in a significant surge in nontradable employment of approximately 50
basis points within the first six months. Notably, this rapid initial recovery is followed by a partial
reversion of effects in the subsequent six months, which is then followed by a rebound. Although
the exact reason for this pattern remains unclear, one hypothesis suggests that the swift initial re-
covery might have triggered a more severe outbreak of the second wave of COVID-19 in late 2020,


                                                  27
prompting stronger policy responses from local government authorities, which, in turn, could have
affected the labor market recovery.31


Alternative Servicer Effects. We explore the sensitivity of our results to using the servicer for-
bearance propensities estimated from an alternative specification described in Section 4.1. Specif-
ically, following Kim et al. (2022), we restrict our estimation sample to loans that missed at least
one payment during the pandemic and estimate a cross-sectional model that has an indicator vari-
able for entering forbearance at any point during our sample period as the outcome variable. Since
delinquent borrowers would undoubtedly benefit from forbearance, this alternative specification
more explicitly controls for forbearance demand. We then construct a shift-share measure based
on these alternative servicer effects and re-estimate our baseline specification.
     Appendix Table A8 shows that the results are broadly similar to our baseline results. For
example, the preferred specification in column (6) suggests that a 1 percentage point increase in
the forbearance rate leads to a 32 basis point increase in monthly nontradable employment growth,
which is comparable to our baseline estimate of a 29 basis point increase.



6      Theoretical Model
Our empirical analysis suggests that mortgage forbearance played an important role in fostering
local employment during the recovery phase of the pandemic recession. In this section, we develop
a stylized heterogeneous-area New Keynesian model that relates local labor market outcomes to
household-level consumption responses. In Section 7, we interpret our results through the lens
of this stylized model and directly map our empirical estimates to the household-level MPC. Our
setup relies heavily on the framework used by Chodorow-Reich et al. (2021) but differs in ways
specific to our setting. In particular, we enrich the household block by introducing homeownership
and mortgage ownership statuses and incorporate geographical heterogeneity in intermediation
frictions to align the model with our empirical setting. We describe the key features of the model
in the main text and present additional details in Online Appendix E.
    31 In response to the second wave of COVID-19, many state governments implemented a second lockdown that

included statewide business closures (Chetty et al., 2020).




                                                          28
6.1     Model Environment

We consider a continuum of areas (a ) where firms produce nontradable (N ) or tradable (T ) goods
using capital (K ) and labor (L ) as factors of production. Time is discrete and denoted by t ∈
{0, 1, . . .}. We model t = 0 as the “short-run,” whereby labor is initially immobile and the economy
is subject to a negative aggregate shock. We allow for capital to be mobile in all periods. We
assume that monetary policy stabilizes aggregate demand by targeting the average nominal wage.
However, wage stickiness, combined with cross-sectional heterogeneity across areas, implies that
local labor market outcomes are determined by local demand in the short run. We model t ≥ 1 as
the “long-run,” whereby labor is fully mobile across areas. Under average nominal wage targeting,
production and employment in each area are determined solely by productivity in the long run.
    Each area is populated by infinitely lived households that consume one unit of housing every
period. There are three types of households denoted by superscript i ∈ {r, c, m} with their respec-
tive share given by θ i . The type-r households are “renters” who live hand-to-mouth and spend
their income every period after paying a constant rent D . The type-c households are unconstrained
“capitalists” who hold a uniform portfolio of capital distributed across all areas. They own a
house without mortgage debt and make endogenous consumption-saving decisions. The type-m
households are “mortgagors” who own a house with infinite-maturity mortgage debt M on which
they make a constant payment r m M every period. Among mortgage owners, a fraction µ lives
hand-to-mouth, similar to renters, and spends their income net of mortgage payments every pe-
riod. The remaining fraction 1 − µ is unconstrained, similar to capitalists, and makes endogenous
consumption-saving decisions. The liquidity constraint for the hand-to-mouth mortgage owners is
the key source of the consumption effects generated from mortgage forbearance, as we detail be-
low. Lastly, we assume that renters supply labor endogenously, whereas capitalists and mortgagors
provide labor exogenously.32


Mortgage Forbearance Policy.             Since our main objective is to examine how regional differences
in mortgage forbearance translate into differences in local employment, we introduce a stylized
version of the mortgage forbearance program in our model. Specifically, we model mortgage
  32 As in Chodorow-Reich et al. (2021), these assumptions help us isolate the wealth effects on consumption from

those on labor supply while generating empirically sensible Keynesian multiplier effects and changes in labor.



                                                         29
forbearance as the option for mortgage owners to skip their mortgage payment in period 0 in
exchange for increasing their mortgage debt from M to M ′ for all subsequent periods. We analyze
the setting where M ′ is set such that the present discounted value of the increase in future payments
is equal to the value of the missed payment in period 0.33 Hence, mortgage forbearance provides
liquidity to constrained homeowners without affecting their overall debt obligations.


Geographic Heterogeneity in Intermediation Frictions. To align the model with our empirical
setting, forbearance in each area is intermediated by a local mortgage servicer that is subject to
some level of operational frictions. Consequently, only a fraction Ψa ∈ [0, 1] of mortgage owners in
area a actually get to participate in the program. The variation in the availability of the forbearance
program serves as the source of geographical heterogeneity in our model. We assume that areas
are identical otherwise.34


6.2     Households
                                                                                        i
At each period t , households of type i residing in area a allocate their consumption C a,t between
nontradable and tradable goods to maximize the consumption aggregator,

                                        i
                                      C a,t      i ,N
                                            = (C a,t  /η)η (C a,t
                                                              i ,T
                                                                   /(1 − η))1−η ,                               (5)


where η is the share of nontradables in consumption. Since the household problem depends on the
type of agents considered, we discuss each type in turn.


Renters. Since renters live hand-to-mouth, they do not hold any form of assets and therefore
spend all of their net-of-rent labor income each period. To introduce local aggregate demand ef-
fects, we assume renters supply labor endogenously subject to partially sticky wages and disutility
of labor. The aggregate labor of renters is specialized across a continuum of types ν ∈ [0, 1], where
a worker of type ν supplies L ra,t (ν) with an elasticity of substitution ϵw between different types of
labor. A fraction 1 − λw of labor types supply labor according to the nominal wage W targeted by
  33 More formally, we assume M ′ is set such that r m M = P∞     r m (M ′ −M )
                                                              n=1 Πn R f        .
                                                                     k=1 t +k
   34 In particular, as a simplifying assumption, we do not model regional differences in forbearance demand and

instead focus on the supply-side frictions, which are the source of identifying variation in our empirical analyses.


                                                         30
the monetary policy. The remaining fraction λw set wages to maximize:

                                                                                          r
                                     Wa,t (ν)L ra,t (ν) − D                (L ra,t (ν))1+φ
                                                                    −χ                        ,                   (6)
                                              P a,t                            1 + φr

where φr is the inverse Frisch elasticity of labor supply. Importantly, linear disutility of labor
excludes wealth effects arising from labor supply (Greenwood et al., 1988).


Mortgagors. Representative mortgage owners can be subdivided into those who are constrained
(i = mc ) and those who are unconstrained (i = mu ). Mortgagors of each type supply a fixed
amount of labor L and choose consumption to maximize:

                      t     i
         Σ∞
          t =0 (1 − ρ) logC a,t                                                                                   (7)

          subject to
                                           A ia,t +1
                 i
         P a,t C a,t + r m M (1 − Ψa ) +      f
                                                           = Wa,t L + A ia,t ,                          t = 0,    (8)
                                             Rt
                                                               A ia,t +1
                 i
                     +rm       M (1 − Ψa ) + Ψa M +    ′
                                                                           = Wa,t L + A ia,t ,
                           ¡                               ¢
         P a,t C a,t                                              f
                                                                                                        t ≥ 1,    (9)
                                                                 Rt

         A ia,t = 0,                                                                              i = mc, ∀t ,   (10)


where 1−ρ is the discount factor common to all households, A ia,t is the household’s asset holdings,
Wa,t is the wage, and P a,t is the local price index of the consumption aggregator.
   Mortgage owners who are hand-to-mouth (i = mc ) are constrained to have zero liquid assets,
and thus their consumption expenditure each period is equal to their labor income net of mortgage
payments. Consequently, the MPC for this household type is always equal to 1. When the negative
aggregate shock occurs in period 0, mortgage forbearance provides liquidity to these households
by permitting them to defer their current payment in exchange for higher payment amounts in
all future periods. However, due to intermediation frictions, only a fraction Ψa is able to take
advantage of this policy.
   Unconstrained mortgage owners (i = mu ), on the other hand, are not liquidity-constrained and




                                                                 31
their consumption is determined by the level of their permanent income,
                                                  Ã                                  !
                                                      ∞ W             m
                                                          a,t +n L − r M
                                    mu
                                        =ρ                                     + A mu
                                                      X
                            P a,t C a,t                        f      f            a,t .       (11)
                                                   n≥0       R t ...R t +n−1

The MPC of these households is equal to ρ . Since forbearance preserves overall debt obligations
and does not change the lifetime wealth of these households, unconstrained mortgage owners do
not benefit from forbearance and hence are indifferent to the policy. For simplicity, we assume that
these households do not participate in the program.
     Aggregating the two types of mortgage owners, the representative mortgage owner’s consump-
tion is given by
                                         m        mc             mu
                                       C a,t = µC a,t + (1 − µ)C a,t ,                         (12)

where µ denotes the share of constrained mortgagors. The MPC of the representative mortgagor is
equal to µ + (1 − µ)ρ .


Capitalists. Capitalists behave similarly to unconstrained mortgage owners, except that they do
not make mortgage payments and earn capital income in each period. Accordingly, their MPC out
of income is equal to ρ .


6.3       Production and Equilibrium

Nontradable goods are produced using a Cobb-Douglas technology with labor L N
                                                                            a,t and capital
  N
K a,t ,
                                               ¢αN ¡ N               ¢1−αN
                               N
                                           /αN      L a,t /(1 − αN )
                                    ¡ N
                             Y a,t = K a,t                                 ,                   (13)

where αN denotes the capital share in the nontradable sector. The tradable good is produced with
tradable inputs from each area that similarly combine labor L Ta,t and capital K a,t
                                                                                 T
                                                                                     using a Cobb-
Douglas technology,

                                       µZ                    ¶ ϵ
                                                              ϵ−1
                                                   T ϵ−1
                              Y tT =            (Y a,t ) ϵ          ,                          (14)
                                            a
                                T
                                     ¡ T        ¢αT ¡ T              ¢1−αT
                              Y a,t = K a,t /αT      L a,t /(1 − αT )      ,                   (15)



                                                             32
where ϵ is the elasticity of substitution between tradable inputs produced in each area, and αT
denotes the capital share in the tradable sector.
                                                    f
   Monetary policy sets the risk-free rate R t such that the average nominal wage is equal to the
target level at every time period:
                                           Z
                                                   Wa,t d a = W ,                                 (16)
                                               a

where W is exogenously determined. In the absence of cross-sectional heterogeneity, monetary
policy would stabilize the labor supply in each area at its frictionless level (that is, the level that
would obtain without nominal rigidities). However, heterogeneity due to regional asymmetries
in intermediation frictions can induce local aggregate demand effects when labor is immobile in
the short run, because the policy would only stabilize the average labor supply across areas. We
assume that risk-free assets are in zero net supply.
   Given the distribution of the intermediation frictions {Ψa }a , an equilibrium of the economy
is characterized by a set of prices for input factors, consumption goods, the capital asset, and
the interest rate such that (1) firms choose output according to their production technologies; (2)
consumption, labor, and assets are determined by the maximization problem of households; (3)
monetary policy targets the nominal wage W ; and (4) the markets for goods, input factors, and
the risk-free asset all clear. Online Appendix E provides a more complete characterization of the
equilibrium.


6.4    Linearization around a Common-Friction Benchmark

We first consider a common-friction benchmark where all areas are subject to the same level of
frictions in mortgage forbearance take-up, Ψ. Due to the assumption on nominal wage targeting
and the perfect symmetry across regions in this case, the short-run wage is equal to the preset-level,
W0 = W . Labor supply is the same as that of the frictionless benchmark, which we calibrate to be
equal to the level exogenously supplied by mortgage owners, L 0 = L .
   Next, to investigate the implications of heterogeneous frictions across areas, we log-linearize
the equations that characterize the equilibrium around this common-friction benchmark (see Online
Appendix E for derivations). Denoting the log-deviation of a variable Y for each area as ∆y (e.g.,




                                                        33
∆ψa ≡ Ψa − Ψ), we can derive the following conditions:

                                             ∆ ψa θ m r m M                             1 − αT 1 − η ¡
                                              ¡ ¢
                 N                    N                                                                          T
     ∆ w a,0 + l a,0       = M (1 − α )ηµ                                                           ∆
       ¡               ¢                                                                                             ¢
                                                                        + (M − 1)                      w a,0 + l a,0   ,   (17)
                                                      W L 0N                            1 − αN η
                 T
     ∆ w a,0 + l a,0   = −(ϵ − 1)(1 − αT )∆w a,0 .
      ¡              ¢
                                                                                                                           (18)


    Equation (17) decomposes the change in nontradable wage bill (as a result of local deviation
in intermediation frictions) into components that reflect the direct and indirect effects of increased
forbearance take-up. The first term is the direct effect, where M is the local Keynesian multiplier
effect, 1−αN is the labor share of nontradable sectors, η is the spending share of nontradables, and
µ captures the MPC out of liquidity provided through forbearance.35 Intuitively, the direct effect
of forbearance is a function of the total amount of liquidity provided through forbearance, which
depends on the level of intermediation frictions (∆ ψa ) and the amount of mortgage payments
                                                                        ¡     ¢

(θ m r m M ).
    The second term highlights the indirect effects of forbearance through adjustments to tradable
wage bills, which result from the common price of labor across the two sectors. However, based
on the muted response of tradable employment to forbearance in our empirical analyses, we infer
that most of the observed effects stem from the direct liquidity effects of forbearance. Hence,
                                                                    ³                   ´
                                                                                  T
following Chodorow-Reich et al. (2021), we set ∆                        w a,0 + l a,0       = 0 by assuming a unit elasticity of
substitution between tradable inputs (ϵ = 1) in Equation (18).


Model Summary and Separation Result. Rearranging Equations (17) and (18) and focusing
on the special case with ϵ = 1, we derive a modified version of the separation result presented in
Chodorow-Reich et al. (2021) that is tailored to our specific setting:

                                       N
                           ∆ w a,0 + l a,0   W L 0N = M (1 − αN )ηµ ×                ∆ ψa θ m r m M
                             ¡             ¢                                           ¡ ¢
                                                                                                               .           (19)
                           |        {z            }                                  |     {z      }
                       Nontradable payroll increase                               Liquidity from forbearance

  35 While µ is formally defined as the share of constrained mortgage owners, we interpret this term as the portion

of the representative mortgagor’s MPC that can be attributed to the constrained mortgage owners in our model. As
discussed in Section 6.2, the total MPC of the representative mortgagor is µ+(1−µ)ρ , where the first and second terms
represent the components attributed to constrained and unconstrained types, respectively.




                                                               34
This expression shows that the dollar amount of the increase in nontradable payroll (due to liq-
uidity provision through forbearance) can be decomposed into the product of four terms: the local
Keynesian multiplier (M ), the labor share of income (1 − αN ), the spending share of nontradables
(η), and the household-level MPC for mortgage owners in forbearance (µ). In Section 7, we use
this decomposition to recover the household-level MPC implied by our empirical estimates under
standard calibrations of other parameters.



7     Discussion
In this section, we combine our empirical estimates from Section 5 with the theoretical results from
Section 6 to compute the implied household-level MPC as well as the cross-sectional multiplier
effects of mortgage forbearance. We compare our results to existing estimates in the literature for
alternative forms of liquidity provision and discuss the policy implications of our findings.


7.1   Implied Household-Level MPC

We use the separation result presented in Equation (19) to translate our empirical estimate on labor
market outcomes into household-level consumption responses. To align the units with our empir-
ical estimate, we consider a 1 percentage point increase in the share of mortgages in forbearance
(that is, ∆ψa = 1%). Because our empirical analysis covers a period of 18 months, we interpret the
length of period 0 in our model as one year and, accordingly, the parameter µ as the annual MPC
out of a dollar of liquidity provided through forbearance.
    We begin by converting our empirical estimate into monetary values. We first calculate the
amount of liquidity provided from a 1 percentage point increase in the forbearance rate as:


                            ∆(Liquidity from forbearance) = Ab × N 1% ,                         (20)


where Ab is the average amount of suspended mortgage payment among forborne borrowers (shown
in Figure 2). We use the estimate adjusted for the fact that approximately one-third of borrowers
continued to make payments while in forbearance. We then multiply the average suspended pay-



                                                 35
ment by N 1% , a quantity equivalent to 1 percent of the total mortgage market.36 Next, we compute
the increase in nontradable wage bill resulting from the liquidity provided through forbearance as:


                                ∆(Nontradable payroll) = β̂2SLS
                                                           1    × W0N L 0N ,                                (21)


where βb2SLS
        1    is our preferred estimate on nontradable payroll (reported in column (6) of Appendix
Table A4),37 and W0N L 0N is the total wage bill of nontradable sectors from QCEW at the beginning
of our sample period. Appendix Table A9 summarizes the calibration of parameters and statistics.
    Substituting Equations (20) and (21) into Equation (19) and rearranging, we obtain

                                                ∆(Nontradable payroll)
                        M (1 − αN )ηµ =                                         = 0.35.                     (22)
                                            ∆(Liquidity from forbearance)

To recover µ, we externally calibrate three additional parameters. We set the local Keynesian
multiplier to a commonly used value in the literature, M = 1.8, and also assign a standard value to
the labor share of income, (1−αN ) = 2/3. We compute the ratio of the total wage bill in nontradable
and tradable sectors from QCEW to approximate the relative consumption shares, and set η = 0.44.
Substituting these terms yields
                                                bMPX = 0.67.
                                                µ                                                           (23)

    It is important to note that our empirical estimate on the local labor market reflects households’
spending responses for all expenditures, which encompass both durable and non-durable consump-
tion. However, because our model assumes a notional consumption flow that does not differentiate
between these two types, we follow the approach of Laibson et al. (2022) to map the MPX estimate
in Equation (23), which is derived from our empirical results, into a notional MPC estimate that is
  36 Since our empirical analysis covers only the GSE mortgage market, we adjust the number of GSE mortgages by

a factor of 2.15 to account for the presence of a roughly equivalent number of GNMA mortgages in forbearance. See
Appendix C for details.
   37 Alternatively, following Chodorow-Reich (2019), we can convert our baseline estimate on nontradable employ-

ment (reported in Table 1) into a wage bill using the average wage, which yields nearly identical results.




                                                       36
the object of interest in our model:38
                                                    bMPC = 0.43.
                                                    µ                                                               (24)

Hence, our estimate suggests that a dollar of liquidity provided through mortgage forbearance
increases a household’s annual expenditure by 67 cents and its consumption by 43 cents.


Comparison with Existing Estimates. The magnitudes of the implied household-level MPX
and MPC are in line with existing estimates from the literature. For example, estimates of the MPX
for total expenditure typically range from 0.5-0.9, whereas estimates for nondurable expenditure
range from 0.15-0.25 (e.g., Johnson et al., 2006; Agarwal and Qian, 2014; Kueng, 2018). The
notional MPC, in theory, lies between the MPX for nondurables and the total MPX (Laibson et al.,
2022). It is worth noting that empirical estimates typically measure quarterly spending responses,
whereas our implied MPX and MPC estimates are more likely to reflect annual spending responses.
Hence, our implied estimates may be somewhat larger than the quarterly estimates reported in the
literature.


7.2     Multiplier Effects of Mortgage Forbearance

We next approximate the implied multiplier effects of mortgage forbearance by comparing the
costs and benefits associated with the CARES Act forbearance program. We provide a back-
of-the-envelope calculation that translates our main empirical estimate into a multiplier effect.
Our multiplier estimate is likely to be conservative since we only focus on nontradable sectors
and do not consider any spillover effects on other industries. Furthermore, we only consider the
effect of forbearance on local employment and do not include other potential general-equilibrium
channels of stabilization, such as boosting house prices (e.g., Anenberg and Scharlemann, 2021)
and preventing defaults and foreclosures (e.g., Campbell et al., 2011; Gupta, 2019).
  38 Laibson et al. (2022) provide a simple mapping of notional MPCs into MPXs:


                                                        s 1
                                                     µ      ¶
                                               MP X = 1+ ×    M PC ,
                                                        δ τ

with durable share s , real interest rate r , durable depreciation rate δ, and time horizon τ. The main difference between
the two measures arises from spending on durable goods, which involves upfront expenditures that are gradually
converted into notional consumption over time.




                                                           37
    We approximate the cross-sectional fiscal multiplier by comparing the dollar value of our em-
ployment effect and the cost of providing mortgage forbearance as follows:

                                                  ∆(Nontradable labor bill)
                                       MC X ≈                               .                                        (25)
                                                  ∆(Government spending)

Since the numerator can be obtained using the same calculation shown in Equation (21), we fo-
cus on analyzing the denominator, which represents the fiscal costs associated with providing the
liquidity of the amount specified in Equation (20).39
    We make several assumptions to approximate the fiscal expense to the federal government.
First, since the fiscal cost of the program depends on the repayment terms of deferred mortgage
payments, we assume a simplified repayment structure in which all mortgage borrowers exiting
forbearance are allowed to defer their missed payments to the end of their mortgage maturity as
an interest-free, second-lien loan. While a few different types of repayment plans were adopted
in practice, payment deferral has been the most popular option for a majority of borrowers exiting
forbearance in our data (see Appendix Figure A1).
    Second, we assume that the federal government finances the expense by issuing a long-term
bond in the amount equal to the deferred mortgage payments in Equation (20). We further assume
that the long-term bond has a maturity of 11.8 years, which is the average effective remaining
maturity of all forborne loans in the data, at an interest rate of 1.46 percent, which was the 30-year
Treasury rate at the onset of the CARES Act in March 2020.40 , 41
    Under these assumptions, the fiscal cost of the program primarily consists of the waived interest
payments on these interest-free loans since the principal balance of the loan amount is repaid by
  39 We assume that the direct costs associated with the CARES Act forbearance program are borne entirely by the

federal government. Implementation of the forbearance policy may have also resulted in costs by servicers who may
have had to adapt organizational practices to comply with the CARES Act. We implicitly assume that these costs are
negligible compared with the direct fiscal costs when assessing the cross-sectional fiscal multiplier.
   40 We compute the effective remaining maturity of a mortgage using the benchmark prepayment model developed

by the Public Securities Association (PSA). In our baseline, we use the PSA-100 model, which is a very conservative
choice that assumes no volatility in the interest rate. If we instead assume a moderate level of volatility in the interest
rate (for example, PSA-200 model), the effective maturity becomes shorter at seven years and the cross-sectional
multiplier estimate becomes even larger at 3.68 (see Row 1 of Appendix Table A10).
   41 Since the interest-free loan from payment deferral after forbearance can induce a behavioral response that damp-

ens borrowers’ prepayment behavior, we conduct a sensitivity check applying a stricter assumption on the conditional
prepayment rates (for example, PSA-75 model) in computing the effective maturity of a mortgage (see row [3] of
Appendix Table A10). Although the effective maturity becomes longer at 13.9 years, the cross-sectional multiplier
estimate remains sizable at 1.95.



                                                           38
the borrowers at the end of their mortgage maturity. Our back-of-the-envelope calculation suggests
a cross-sectional multiplier estimate of


                                             MˆC X = 2.25.


Appendix C describes our calculation in greater detail, and Appendix Table A10 presents the sen-
sitivity of our estimate to various assumptions.
    Our cross-sectional multiplier estimate is sizable and in line with estimates in the literature,
which typically range from 1 to 2.5 (Chodorow-Reich, 2019). This implies that mortgage for-
bearance is a highly effective fiscal m easure f or s tabilizing a ggregate d emand d uring t imes of
economic distress. The efficacy o f m ortgage f orbearance c an b e p rimarily a ttributed t o i ts low
cost. To see why, consider an alternative repayment structure that immediately forgives borrowers
of their missed payments during forbearance. Under this scenario, the fiscal cost for the program
is equal to the total amount of deferred mortgage payments, which implies a multiplier estimate
of 0.35 as shown in Equation (22). This suggests that the efficacy of mortgage forbearance arises
from its low cost as a measure of temporary liquidity injection, which lies in contrast to direct
fiscal transfers that typically involve larger c osts. Lastly, while our multiplier estimate is sensitive
to the interest rate assumption, it tends to be higher at lower interest rates (see Appendix Table
A10). For example, if the interest rate is 2 percent instead of 1.46 percent, our multiplier estimate
would become somewhat smaller at 1.70. This finding suggests that mortgage forbearance can be
especially effective in the low-interest-rate environment or when interacted with an expansionary
monetary policy during economic downturns.



8    Conclusion
In this paper, we estimate the macroeconomic effects of a large-scale mortgage forbearance pro-
gram introduced by the CARES Act. While the CARES Act made debt forbearance almost univer-
sally eligible for all federally backed mortgages, forbearance outcomes vary considerably across
different mortgage servicers for observably similar mortgage borrowers. We use heterogeneity in
regional exposure to this servicer effect to construct a shift-share measure that has significant ex-


                                                   39
planatory power for the regional forbearance rate and use it as an instrument to estimate the effect
of mortgage forbearance on local economic outcomes.
   Our findings suggest that mortgage forbearance boosts local demand during economic recovery
from a recession and thus can be a highly cost-effective fiscal measure of economic stabilization.
While policy discussions have emerged regarding the inclusion of state-dependent modification
features in mortgage contracts to promote macroeconomic stability during economic downturns
(e.g., Eberly and Krishnamurthy, 2014; Guren et al., 2021; Campbell et al., 2021), this paper pro-
vides empirical evidence substantiating the stabilizing effects of such features by demonstrating the
significant impact of the large-scale mortgage forbearance program on local labor market recovery.
   We conclude by discussing directions for future research. First, it is important to empirically
analyze household-level consumption responses out of mortgage forbearance. Since our results on
local labor markets hinge on the consumption effects of households, credible evidence on house-
holds’ spending responses can micro-found the macro-stabilization effects and confirm the channel
through which mortgage forbearance augments local demand during economic downturns. Second,
while this paper focuses on the consumption effects of mortgage forbearance, it would be inter-
esting to analyze other potential general-equilibrium consequences of forbearance in the housing
market, such as prevented foreclosures, spillovers to house prices, and new mortgage originations
(e.g., Campbell et al., 2011; Gupta, 2019; Anenberg and Scharlemann, 2021).




                                                 40
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                                            44
                                     APPENDIX

A    Additional Figures and Tables




Figure A1: Composition of Forbearance Exits. This figure shows the share of exit categories
among GSE mortgages. The sample includes all forborne mortgages that exit forbearance at some
point during the April 2020–March 2022 period. Data sources: Fannie Mae and Freddie Mac.




             (a) 30+ Days Past Due                          (b) 60+ Days Past Due

Figure A2: Delinquent GSE Mortgages Not in Forbearance. The left-hand panel shows the
share of delinquent mortgages that are past due by 30 days or more (navy curve) alongside the
fraction of such mortgages that are not in forbearance (gray bars). The right-hand panel shows
the equivalent information for delinquent mortgages that are past due by 60 days or more. Data
sources: Fannie Mae and Freddie Mac.


                                             45
     (a) Distribution of Servicer Fixed Effects        (b) Top and Bottom Servicer Fixed Effects

Figure A3: Servicer Forbearance Propensity. This figure shows the variation in the estimated
forbearance propensities for mortgage servicers. The left-hand panel shows the distribution of the
servicer fixed effects. The right-hand panel shows the forest plot of mortgage servicers with the
top and bottom forbearance propensities. Data sources: Fannie Mae and Freddie Mac.




Figure A4: Distribution of Shift-Share Measure across Zip3 Areas in June 2020. This figure
shows the geographic distribution of the shift-share measure that captures the average forbearance
propensity of mortgage servicers in each Zip3 area. The legend is expressed in terms of SD units.
Data sources: Fannie Mae and Freddie Mac.




                                                  46
              (a) State Fixed Effects                    (b) State Fixed Effects + Zip3 Controls

Figure A5: Instrument Relevance. This figure shows the binscatter of regional forbearance rates
and our shift-share instrument. The left-hand panel plots the variables residualized with respect to
state fixed effects. The right-hand panel plots the variables residualized with respect to state fixed
effects and Zip3-level controls. Data sources: GSEs and ACS.




                                                 47
   Category     Subcategory                          Consumer Complaint Narrative
                                 “I am looking for loan forbearance under the covid-19 assistance from XXX. I
                Unable to        have spent over 36 hours on hold only to be cut off. I try to fill out the form on
 Difficulty
                reach servicer   their website and it does not recognize my loan number. I can not find a means
 with
                                 to email them.”
 enrollment
                                 “I have been seriously affected by COVID, my husband passed away and the
                Denial of        bank refuses to assist me with any of the government backed programs, like
                request          mortgage forbearance .... I have called several times, went to the branch and all
                                 I get is the round around excuses.”
                                 “I requested forbearance .... I have been affirming that I am experiencing finan-
                Request of
                                 cial hardship during the COVID-19 ... Unfortunately XXX informed me that I
                documentation
                                 have to submit various documents to prove that I am having a financial crisis.”
                                 “XXX is making it difficult to extend the required mortgage forbearance. When
                Unable to        I attempted to select “extend forbearance” it said I was not eligible. I am con-
 Difficulty
                reach servicer   cerned that XXX is not following the intent of the relief package, and making it
 with
                                 unreasonably difficult to get the extension.”
 extension
                                 “I was in the mortgage forbearance program .... requested an additional 180 day
                Request of       extension ... denied the extension by my loan servicer who is requesting addi-
                documentation    tional financial information .... I would simply like to be granted the additional
                                 180 days as outlined in the Cares Act ....”
                                 “I am having problems working with my mortgage company, XXX. At the be-
                Denial of        ginning of the pandemic, I did receive my COVID forbearance for 3 months
                request          but after that period they haven’t allowed me to continue with forbearance even
                                 though I have been contacting them continuously.”
                                 “Tried calling XXX to see if they can help during the COVID-19 pandemic and
                                 they are only offering forbearance but you have to pay it back after the three
 Inaccurate     Exit options
                                 months in full. How can somebody pay back three months all at once if you’re
 information
                                 having troubles already ...”
                                 “With the Current COVID economic collapse, I called my mortgage holder,
                Credit health
                                 XXX, they informed me they can place my loan in forbearance, however, it
                and exit
                                 will ruin my credit and all payments will be due in 90 days, in full, no partial
                options
                                 payments or my loan will be foreclosed on.”
                                 “I reached out to XXX to inquire about borrowers assistance for covid 19 re-
                Enrollment       lated changes. They automatically enrolled me into a forbearance program and
 Unconsented
                upon inquiry     cancelled my bi-weekly automatic payments. ... I never agreed to or signed a
 enrollment
                                 forbearance agreement.”
                                 “XXX is a trash company who put my mortgage in forbearance when no one
                Automatic        asked. I’ve been paying my mortgage on time and in full every month and when I
                enrollment       try to refinance my mortgage away from that horrible company, the new company
                                 gets a message that my loan is currently in forbearance.”
                                 “I was on forbearance with XXX due to COVID. I requested to discontinue for-
                Delay in         bearance and began paying mortgage payments. After numerous, weekly phone
 Difficulty
                processing       calls and hours of time on hold, I have been promised ... It is now almost 6
 with
                                 months and is not complete.”
 unenrollment
                                 “I have a mortgage with XXX and went in to forbearance when covid hit. ...
                Automatic        We were ready to come out after the three months that was agreed upon but they
                extension        extended it without permission for another three months. I called and asked how
                                 to cancel the forbearance and the story changes every time I called.”

Table A1: CFPB Consumer Complaints. This table categorizes examples of consumer com-
plaints to the Consumer Financial Protection Bureau related to mortgage forbearance.


                                                48
                                         Without State FE               With State FE
                                      Difference    p-value        Difference     p-value
                                          (1)          (2)             (3)          (4)
 Average Loan Characteristics
   Principal Balance (in $K)           33.239          0.00         15.153          0.00
   Interest Rate                        0.017          0.19         -0.001          0.91
   Credit Score at Origination          1.893          0.00          0.589          0.28
   LTV Ratio at Origination            -1.239          0.00         -0.509          0.06
   DTI Ratio at Origination             0.953          0.00          0.366          0.00
   First Time Homebuyers                0.001          0.83          0.004          0.34

 Demographic and Socioeconomic Characteristics
  Age: 30-39                         0.007             0.00           0.004         0.00
  Age: 40-49                         0.004             0.00           0.003         0.00
  Age: 50-59                        -0.002             0.00           0.000         0.81
  Age: 60-69                        -0.006             0.00          -0.003         0.08
  Age: 70+                          -0.007             0.00          -0.006         0.00
  Education: 12 Years               -0.038             0.00          -0.023         0.00
  Education: 13-15 Years            -0.012             0.00          -0.007         0.00
  Education: 16 Years                0.027             0.00           0.020         0.00
  Education: 17+ Years               0.020             0.00           0.013         0.00
  White                             -0.073             0.00          -0.024         0.00
  Black                              0.042             0.00           0.016         0.00
  Asian                              0.014             0.00           0.005         0.06
  Hispanic                           0.051             0.00           0.015         0.00
  Population (in logs)               0.487             0.00           0.296         0.00
  Population Density (in logs)       0.665             0.00           0.466         0.00
  Average Income (in $K)             3.543             0.00           2.540         0.00
  Unemployment Rate, 2015-2019       0.001             0.18           0.000         0.59
  Homeownership Rate                -0.026             0.00          -0.007         0.22
  Fraction with Mortgage             0.039             0.00           0.026         0.00

 Pandemic Controls
   COVID Rate (%)                        0.001         0.95          -0.009         0.51
   Death Rate (%)                        0.000         0.72           0.000         0.69
   PPP Amount (in $K per-capita)         0.167         0.20           0.195         0.00
   Refinancing Rate (%)                  2.364         0.00           0.788         0.07
   Bankruptcy Filing Rate (%)           -0.005         0.52           0.006         0.18

Table A2: Covariate Balance. This table displays the covariate balance between Zip3 areas that
are above and below the median of our shift-share instrument. Column (1) shows the average
difference between the two groups of regions. Column (3) shows the difference controlling for
state fixed effects. Columns (2) and (4) present the p-values obtained from a test of the null
hypothesis that the difference is zero. Data sources: GSEs, ACS, Economic Tracker, SBA, and
U.S. Courts.

                                             49
                          (1)                     (2)               (3)           (4)           (5)
                     Forbearance             Forbearance       PPP amount     Refinancing Bankruptcy
                       rate (%)                rate (%)        (per capita)    rate (%)   filing rate (%)
 Shift-Share (in SD)  0.465∗∗∗                 0.217∗∗            -2.480        -0.016         0.004
                       (0.085)                 (0.073)           (2.191)        (0.015)       (0.003)
 State x Time FE           Y                       Y                 Y             Y             Y
 Zip3 controls             N                       Y                 Y             Y             Y
 R-squared              0.402                   0.505              0.844         0.251         0.768
 N                      15138                   15138              8920          15138         15138
 Standard errors in parentheses; ∗ p < 0.05, ∗∗ p < 0.01, ∗∗∗ p < 0.001

Table A3: Predictability of Forbearance and Other Economic Stimulus Measures. This table
shows the results of a panel regression of forbearance rates and other economic stimulus measures
on our shift-share instrument, controlling for state-by-time fixed effects, average loan characteris-
tics, and demographic and socioeconomic characteristics. The shift-share variable is expressed in
SD units. Standard errors are two-way clustered by month and Zip3. Data sources: GSEs, ACS,
SBA, and U.S. Courts.




                                   First-stage                  Reduced-form                 2SLS
                                 (1)          (2)              (3)         (4)         (5)          (6)
                                    ∗∗∗
 Shift-share (in SD)          0.389        0.189∗∗∗         0.114 ∗∗∗
                                                                        0.056∗∗
                               (0.057)      (0.057)          (0.022)    (0.020)
 Forbearance rate (%)                                                               0.331∗∗∗     0.298∗
                                                                                     (0.080)     (0.136)
 State FE                        Y              Y              Y           Y            Y           Y
 Zip3 controls                   N              Y              N           Y            N           Y
 R-squared                      0.28           0.46           0.54        0.69           -          -
 N                              841            841            841         841          841         841
 Outcome mean (%)               2.04           2.04           1.63        1.63         1.63       1.63
 Outcome SD (%)                 1.40           1.40           0.66        0.66         0.66       0.66
 Standard errors in parentheses; ∗ p < 0.05, ∗∗ p < 0.01, ∗∗∗ p < 0.001

Table A4: Results on Nontradable Payroll. This table shows the regression results of our baseline
specification for nontradable payrolls. Columns (1) and (2), (3) and (4), and (5) and (6) respectively
show the results for first-stage, reduced-form, and 2SLS regressions, with and without including
Zip3-level controls. The shift-share variable is expressed in SD units. All outcome variables are
expressed in percentages. Data sources: GSEs, QCEW, and ACS.




                                                         50
                                   First-stage                  Reduced-form                      2SLS
                                 (1)          (2)              (3)         (4)              (5)           (6)
 Shift-share (in SD)          0.370∗∗∗     0.157∗∗          0.099∗∗∗    0.047∗∗
                               (0.066)      (0.059)          (0.019)    (0.018)
 Forbearance rate (%)                                                                     0.366∗∗∗     0.293+
                                                                                           (0.106)     (0.150)
 State FE                          Y              Y             Y              Y              Y           Y
 Zip3 controls                     N              Y             N              Y              N           Y
 R-squared                       0.38           0.66           0.67           0.80             -          -
 N                               841            841            841            841            841         841
 Outcome mean (%)                2.04           2.04           1.13           1.13           1.13       1.13
 Outcome SD (%)                   1.4            1.4           0.52           0.52           0.52       0.52
 Standard errors in parentheses; + p < 0.10, ∗ p < 0.05, ∗∗ p < 0.01, ∗∗∗ p < 0.001

Table A5: Weighted Results on Nontradable Employment. This table shows the regression
results of our baseline specification for nontradable employment growth, weighted by Zip3 popu-
lations in 2019. Columns (1) and (2), (3) and (4), and (5) and (6) respectively show the results for
first-stage, reduced-form, and 2SLS regressions, with and without including Zip3-level controls.
The shift-share variable is expressed in SD units. All outcome variables are expressed in percent-
ages. Data sources: GSEs, QCEW, and ACS.




                                               OLS                                         OLS
                                     (1)                    (2)                    (3)                  (4)
 Forbearance rate (%)            0.034∗∗∗                 0.008                0.051∗∗∗               0.017
                                  (0.010)                (0.009)                (0.010)              (0.011)
 State FE                             Y                      Y                      Y                    Y
 Zip3 controls                        N                      Y                      N                    Y
 Weighted                             N                      N                      Y                    Y
 R-squared                          0.60                   0.73                   0.67                 0.80
 N                                  841                    841                    841                  841
 Outcome mean (%)                   1.13                   1.13                   1.13                 1.13
 Outcome SD (%)                     0.52                   0.52                   0.52                 0.52
 Standard errors in parentheses; ∗ p < 0.05, ∗∗ p < 0.01, ∗∗∗ p < 0.001

Table A6: OLS Results on Nontradable Employment. This table shows the regression results
of our baseline specification for nontradable employment growth, estimated using OLS. Columns
(1) and (2), (3) and (4), and (5) and (6) respectively show the results for first-stage, reduced-form,
and 2SLS regressions, with and without including Zip3-level controls. The shift-share variable is
expressed in SD units. All outcome variables are expressed in percentages. Data sources: GSEs,
QCEW, and ACS.



                                                         51
                                          First-stage                                 Reduced-form
                                  (1)                     (2)                     (3)                  (4)
 Shift-share (in SD)            -0.000                   0.001                  -0.005               -0.008
                                (0.003)                 (0.003)                (0.006)              (0.006)
 State FE                          Y                       Y                       Y                    Y
 Zip3 controls                     N                       Y                       N                    Y
 N                                841                     841                    841                  841
 Standard errors in parentheses; ∗ p < 0.05, ∗∗ p < 0.01, ∗∗∗ p < 0.001

Table A7: Pre-Pandemic Placebo Effects. This table shows the regression results for pre-
pandemic placebo effects. Columns (1) and (2) and (3) and (4) respectively show the results
for first-stage and reduced-form regressions, with and without including Zip3-level controls. The
shift-share variable is expressed in SD units. All outcome variables are expressed in percentages.
Data sources: GSEs, QCEW, and ACS.




                                   First-stage                  Reduced-form                     2SLS
                                 (1)          (2)              (3)         (4)             (5)           (6)
                                    ∗∗∗
 Shift-share (in SD)          0.384         0.127∗          0.083 ∗∗∗
                                                                        0.040∗∗
                               (0.058)      (0.060)          (0.016)    (0.014)
 Forbearance rate (%)                                                                    0.243∗∗∗      0.316+
                                                                                          (0.061)      (0.179)
 State FE                         Y              Y              Y              Y             Y            Y
 Zip3 controls                    N              Y              N              Y             N            Y
 R-squared                       0.28           0.45           0.61           0.78            -           -
 N                               841            841            841            841           841          841
 Outcome mean (%)                2.04           2.04           1.13           1.13          1.13        1.13
 Outcome SD (%)                  1.40           1.40           0.52           0.52          0.52        0.52
 Standard errors in parentheses; + p < 0.10, ∗ p < 0.05, ∗∗ p < 0.01, ∗∗∗ p < 0.001

Table A8: Alternative Servicer Effect Estimates. This table shows the regression results based on
alternative servicer effect estimates. Columns (1) and (2), (3) and (4), and (5) and (6) respectively
show the results of first-stage, reduced-form, and 2SLS regressions, with and without including
Zip3-level controls. The shift-share variable is expressed in SD units. All outcome variables are
expressed in percentages. Data sources: GSEs, QCEW, and ACS.




                                                         52
              Description                                         Value           Target / Source
 Theoretical Model Parameters
 M            Local Keynesian Multiplier                           1.8      Chodorow-Reich (2019)
 1 − αN       Non-Tradable Labor Share                             2/3    Chodorow-Reich et al. (2021)
 η            Non-Tradable Expenditure Share                      0.44             QCEW
  m
 r M (or A ) Mortgage Payment Amount
          b                                                       $900            Figure 2

 Labor and Mortgage Market Statistics
 N 1%        1% of Mortgage Market                            0.52M
    N GSE,1%    1% of GSE Market                              0.24M                  FRED
   F GNMA       Adjustment Factor for GNMA Mortgages           2.15             GSE / GNMA data
    N N
 W0 L 0      Monthly Non-Tradable Wage Bill                   $55.6B                 QCEW

 MPC-MPX Mapping
 s         Durable Share                                          0.125        Laibson et al. (2022)
 δ         Durable Depreciation Rate                               0.22        Laibson et al. (2022)
 r         Real Interest Rate                                        0         Laibson et al. (2022)

Table A9: Calibration of Parameters. This table presents the calibration of parameters that we
use in Section 7 to compute the implied household-level consumption responses and the cross-
sectional multiplier effects of forbearance.




                                                                        Interest Rate, i
                                                     T     1%       1.46% 2%           3%    4%
 1 Effective Maturity w/ PSA-200                     7.0   5.27      3.68     2.74    1.90   1.48
 2 Effective Maturity w/ PSA-100 (Baseline)         11.8   3.19      2.25     1.70    1.20   0.95
 3 Effective Maturity w/ PSA-75                     13.9   2.75      1.95     1.48    1.06   0.85
 4 Full Mortgage Maturity                           23.8   1.68      1.21     0.94    0.70   0.58

Table A10: Sensitivity of Forbearance Multiplier. This table shows the sensitivity of our cross-
sectional multiplier estimate of mortgage forbearance to underlying assumptions. i is the nominal
interest rate at which the federal government issues a long-term bond to finance the mortgage
forbearance expense. T is the maturity of the long-term bond. Effective maturity of a mortgage is
computed using the benchmark prepayment model developed by the Public Securities Association
(PSA) as described in Appendix C. Data sources: GSEs, FRED, and J.P. Morgan Markets.




                                               53
B     Comparison to GNMA Mortgage Market
Ginnie Mae Disclosure Data on MBS Portfolio Loans.             To supplement our analyses, we use
Ginnie Mae credit performance data on single-family mortgages. This is a loan-level monthly
panel data set that provides detailed information on loan and borrower characteristics. Since May
2020, Ginnie Mae has also published monthly supplemental data that contain loan-level forbear-
ance status. In contrast to the GSE data, however, the GNMA data disclose only state-level in-
formation on property location. Since our local labor market analysis requires more granular geo-
graphic information, the GNMA sample is excluded from our main analysis.


Forbearance Rates and Trends.        In panel (a) of Figure B1, the forbearance rate sharply in-
creased after March 2020, peaked at about 12 percent in June 2020, and gradually declined to 4
percent by June 2021. This pattern is qualitatively similar but quantitatively larger compared with
the pattern observed for GSE mortgages. The larger fraction of GNMA mortgages in forbearance
is consistent with the evidence that low-income households were more exposed to the recession.
The higher forbearance rate also implies that despite the lower market share of GNMA mortgages,
their contribution to the aggregate forbearance rate is comparable to GSE mortgages. In panel (b),
the non-take-up rate among delinquent mortgages is similar to the pattern for GSE mortgages.




            (a) Mortgage Forbearance Rates           (b) Delinquent Mortgages not in Forbearance

Figure B1: Forbearance Rates and Non-Take-Up in the GNMA Mortgage Market. The left-
hand panel shows the share of GNMA mortgages in forbearance along with the entry and exit rates
at each month. The right-hand panel shows the share of mortgages past due and the fraction of
these delinquent mortgages that are not in forbearance. Data source: Ginnie Mae.



                                                54
C     Multiplier Effect Calculation Details
We approximate the cross-sectional fiscal multiplier effects by comparing the dollar value of our
employment effects and the fiscal costs associated with providing mortgage forbearance as shown
in Equation (25):
                                          ∆(Nontradable payroll)
                                 MC X ≈                          .
                                          ∆(Government spending)

In this section, we provide a more detailed discussion of how we approximate the denominator,
which represents the fiscal costs associated with providing the liquidity of the amount calculated
in Equation (20).
    As noted in Section 7.2, we make a few assumptions. First, we assume that all mortgage bor-
rowers exiting forbearance choose to defer repayment of their missed payments to the end of their
mortgage maturity as an interest-free, second-lien, loan. In this case, the fiscal cost of the program
can be understood as the waived interest payments on these interest-free loans. Furthermore, since
we assume that the federal government finances this expense by issuing a long-term government
bond, the denominator of the above expression can be written as:

                                                                                 1 T
            ∆(Government spending) = ∆(Liquidity from forbearance) · [1 − (         ) ],         (26)
                                                                                1+i

where ∆(Liquidity from forbearance) is the dollar amount of liquidity provided through mortgage
forbearance, i is the interest rate on a long-term bond used to finance the fiscal expense, and T is
the average effective years remaining in mortgage maturity for all forborne loans. We discuss each
of these terms in turn.


Liquidity from Mortgage Forbearance.         We calculate the amount of liquidity provided through
mortgage forbearance using Equation (20):


                             ∆(Liquidity from forbearance) = Ab × N 1% ,


where Ab is the average amount of suspended mortgage payment among forborne borrowers. As
shown in Figure 2, approximately one third of the borrowers continued to make payments while
in forbearance. Hence, we use Ab = $880 to capture the actual amount of liquidity resulting from

                                                 55
forbearance.
    We then multiply this estimate by N 1% , a quantity equivalent to 1 percent of the total mortgage
market. Since our empirical analysis only covers the GSE segment of the agency mortgage market,
we adjust the number of GSE mortgages by a multiplicative factor to account for the presence of
a roughly equivalent number of GNMA mortgages in forbearance. Because the relative servicing
shares of the GSE and GNMA mortgages in the agency mortgage market are 0.7 and 0.3 (Inside
Mortgage Finance, 2023) and the average forbearance rates in these two segments of the market are
2.1 percent and 5.5 percent respectively in our sample period, we set the adjustment factor as 2.15
(= 0.7×2.1%+0.3×5.5%
        0.7×2.1%
                     ). We multiply the number of mortgages equivalent to 1 percent of the GSE
mortgage market, obtained from the Federal Reserve Economic Data (FRED), by this adjustment
factor.


Interest Rate (i ). In our baseline, we set the interest rate to i = 1.46%, the 30-year Treasury rate
at the onset of the CARES Act in March 2020.


Effect Maturity (T ). We compute the effective maturity of a mortgage using the benchmark
prepayment model developed by the Public Securities Association (PSA). The PSA-100 model
assumes that the conditional prepayment rate (CPR) is 0.2 percent in month 1, gradually increases
to 6 percent in month 30 (in increments of 0.2 percent), and stays at 6 percent for the rest of the
period. The PSA model scales linearly so that PSA of 200, for instance, would assume that CPRs
increase from 0.4 percent to 12 percent.
    In our baseline, we use the standard PSA-100 model and obtain the average effective remaining
maturity of all forborne loans of T = 11.8 years. This assumption is a conservative choice since
the PSA-100 model assumes no volatility in the interest rate and, accordingly, no prepayment due
to the interest rate change. In our analysis of PSAs using the JP Morgan Markets data, the PSA
maturity is near 100 only when there is a large positive gap between a mortgage’s coupon rate and
the prevailing market interest rate.42 However, the PSA maturity of a mortgage can be much higher
in general.43
  42 For instance, in September 2022, when the 30-year fixed rate mortgage rate was high at 6.11 percent, the PSA

maturity of a 4.5 percent GSE mortgage was 140.05, which is still above our baseline of 100. The average coupon rate
of all forborne mortgages in our data is 4.37 percent.
   43 In March 2020, for example, when the market rate was 3.45 percent, the PSA maturity of a 4.5 percent mortgage



                                                        56
Summary.       Substituting the terms described above, we approximate the denominator as:

                                                                        1
              ∆(Government spending) ≈ ($4.68 × 108 ) · [1 − (              )11.8 ] = $7.38 × 107 .
                                                                     1.0146

Finally, combining the numerator and the denominator, we obtain our multiplier estimate:

                                  ∆(Nontradable labor bill) $1.66 × 108
                        MC X ≈                             =            = 2.25.
                                  ∆(Government spending) $7.38 × 107

Appendix Table A9 presents our calibration of parameters. Appendix Table A10 displays the
sensitivity of our estimate to assumptions about the interest rate and the effective maturity.
was 770.95, which corresponds to CRPs that range from 1.5 percent to 46.3 percent.




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