# Feedback Dynamics of the Low-Income Rental Housing Market: Exploring Policy
Responses to COVID-19

Katherine Marcal
School of Social Work Greenspun College of Urban Affairs
University of Nevada Las Vegas
Las Vegas, NV 89154
<EMAIL_ADDRESS>&Patrick J. Fowler
Brown School of Social Work, Public Health, and Social Policy
Division of Computational and Data Sciences
Washington University in St. Louis<EMAIL_ADDRESS>&Peter S. Hovmand
Center for Community Health Integration
School of Medicine
Case Western Reserve University School of Coumputing and Information
<EMAIL_ADDRESS>

###### Abstract

The COVID-19 recession threatens mass housing insecurity that undermines
economic recovery. Unprecedented federal policy responses halt court-ordered
evictions, but questions remain whether policies adequately account for
dynamics that drive landlord-tenant interactions including accumulations of
rental and mortgage arrears, rental unit availability, and low-income housing
options. A system dynamics model probes complex feedback dynamics driving
tenant and landlord decision-making in the low-income rental housing market
pre- and post-pandemic protections. Feedback loops highlight tradeoffs
considered by low-income tenants and landlords in the context of scarcity and
uncertainty. Simulations suggest the eviction moratorium reduced evictions by
51% before its expiration in late 2021, but rental arrears, overcrowding, and
homelessness remained high. Federal emergency rental assistance further
contributed to keeping evictions low, but showed only modest effects on
housing insecurity and homelessness. More rapid allocation of funds would
substantially increase impact. Failure to address underlying financial
hardship and limited affordable housing undermine COVID recovery.

Keywords: homelessness, affordable housing, housing assistance, COVID,
simulation model

##  1 Introduction

The financial fallout from the COVID-19 pandemic that hit the United States in
early 2020 encountered a low-income rental market already marked by
instability and scarcity. Housing insecurity and homelessness have long
persisted among low-income households in the United States; prior to the
pandemic, millions of households were precariously housed, navigating tight
low-income rental markets with scarce resources. Extensive shutdowns to
mitigate spread of the virus led to an immediate spike in unemployment that
impeded low-income families’ abilities to meet basic needs. A federal eviction
moratorium passed in spring 2020 aimed to keep people housed during the public
health crisis, but did not contain measures to address unpaid arrears that
would accumulate in the meantime – thus introducing complex trade-offs and
incentives for tenants and landlords. The federal government has since
allocated $50 billion in rental assistance for low-income renters, but complex
eligibility requirements and technological limitations have impeded efficient
disbursement of funds. In this economic and political context, low-income
households have been forced to make difficult tradeoffs about housing costs
and quality while landlords navigate unpaid rent, shifting rental market
conditions, and frequent policy changes. The complex dynamics driving
decision-making among low-income renters and landlords are poorly understood,
impeding efficient solutions to persistent housing insecurity. The present
study applied system dynamics to examine the feedback mechanisms underlying
tenant-landlord decision-making that drive rental market trends. Findings
inform understanding of the often-hidden low-income rental housing market,
links between eviction and homelessness, and implications for mitigating
impacts of the pandemic.

###  1.1 Background

The COVID-19 pandemic triggered widespread financial hardship in a low-income
housing market already plagued by insecurity and strain. In 2019, half of
households earning up to $30,000 per year were experiencing severe housing
cost burden – defined as paying more than 50% of household income toward rent
– and were thus vulnerable to any economic disruption [1]. The economic shock
of COVID-related shutdowns that began in March 2020 most profoundly impacted
low-wage earners in service industries, immediately hindering their ability to
pay monthly housing costs. Among households earning up to $35,000 per year,
over half reported a job loss and one in three had missed a rent payment by
May [2]. By the end of 2020, half of low-income households reported they were
likely to be evicted within two months. Loss of income necessary to make
monthly rent payments thus devastated the already precarious housing security
of low-income families.

Job losses and COVID-related shutdowns did not correspond to an immediate,
dramatic spike in evictions and homelessness, due in part to the federal
eviction moratorium that halted processing of most evictions due to nonpayment
of rent through summer 2021 [3]. However, the moratorium allowed unprecedented
accumulation of arrears expected to drive a tidal wave of evictions if not
paid or forgiven [2]. In the post-COVID landscape, households have been forced
to weigh ongoing financial strain by accumulating arrears in unaffordable
housing, moving in with others to alleviate cost burden while increasing
crowding and household conflict, or finding cheaper, poor-quality
accommodations. The impact of COVID-19 on the low-income rental market was
thus not immediately apparent due to the complex, compensatory processes
contributing to highly visible outcomes such as eviction filings and
executions, foreclosures, and literal homelessness.

###  1.2 Addressing Complexity in the Low-Income Rental Housing Market

Complex feedback dynamics drive trends in the affordable housing market that
are not fully documented. Few studies have investigated patterns of housing
supply and demand, needs, and service use among inadequately housed
populations [4, 5, 6], and complex decision-making may lead to unintuitive
outcomes that are poorly understood. For example, only a portion of evictions
lead to literal homelessness, but the impact on frequent moves, doubling up,
or other forms of housing insecurity remain largely unseen [7, 8].
Furthermore, informal evictions – resulting from landlord pressure to vacate
without going through court proceedings – are not captured by traditional data
systems, and thus their impact is difficult to assess [9]. Prior computational
modeling suggests capacity constraints in the homeless services system shape
housing and service-seeking behavior [4], indicating that solely tracking
homeless service entries and literal homeless counts will overlook households
struggling to navigate the low-income rental market. Additional potential
feedback mechanisms that have yet to be investigated include landlord
tolerance for late rent given rental market conditions [10], tenant tradeoffs
between unaffordability and overcrowding [7], and bottlenecks in eviction
processing, service receipt, and filling vacant units [4]. The complexity of
feedback dynamics in the low-income rental market impede efficient targeting
of assistance and development of sustainable strategies to stabilize families.

Tenant and landlord decision-making occurs in the context of limited
affordable housing supply and widespread economic hardship, and traditional
data systems fail to capture underlying feedback processes [6]. Low-income
households struggle to maintain stable housing in the absence of widely
available affordable options. Housing cost burden forces households to live
paycheck-to-paycheck, relying on monthly income to afford rent with little to
no savings for emergencies [11, 12]. Disruptions to regular paychecks can
quickly delay rent payments, risking eviction. Unpaid rent likewise strains
landlords in the low-income rental market, who are primarily small “mom and
pop” operations with one or two rental properties [13] Rent payments generate
landlord income, which is then used to pay mortgages. Late rent can thus
increase foreclosure risk over time, although the foreclosure process moves
more slowly and offers more opportunities for borrowers to resolve cases [14].
Foreclosures have immediate implications for landlords, who lose income from
rental units; foreclosures also impact tenants residing in foreclosed units,
who are displaced. Finally, foreclosures impact the market more broadly by
removing available affordable rental units, constraining supply.

The complex dynamics of the low-income rental market impede effective,
efficient policy solutions to evictions, scarce affordable housing, and
homelessness. Tracking rates of evictions, foreclosures, and homelessness
alone overlook the complex decision-making processes that drive outcomes.
Actors alter their behavior in response to others’ behaviors as well as market
conditions. Reinforcing processes represent vicious or virtuous cycles that
compound system outcomes over time; in contrast, stressors to the system
trigger compensatory processes that undermine runaway growth. The economic
shock triggered by the pandemic illuminates these dynamics by disrupting
business as usual, thus providing a crucial opportunity to understand the low-
income rental market and develop effective, sustainable solutions to housing
insecurity and homelessness.

Prior research applying system dynamics modeling shows promise for
illuminating the complex feedback processes driving behavior. Studies
investigating the Dutch [15] and Egyptian [6] housing markets highlight the
roles of construction, zoning policies, and broader economic context in
shaping housing options, which are most limited for low-income populations
[16]. Policy barriers that impede increasing the affordable housing supply
contribute to ongoing instability for low-income households. System dynamics
has further been applied to investigate the needs and service use patterns of
homeless households [4, 5]. Failure to account for difficult tradeoffs made in
the face of scarce resources risks exacerbating housing insecurity that goes
largely unseen and unaddressed.

The following paper uses system dynamics simulation modeling to address the
following research questions: (1) What are the main tenant and landlord
feedback dynamics driving trends of evictions, foreclosures, and homelessness
in the low-income rental housing market? (2) What are the projected effects of
the COVID-triggered economic fallout and federal eviction moratorium on these
dynamics? Simulation modeling addresses data limitations and dynamic
complexity in relationships between tenants and landlords, evictions and
foreclosures, and housing insecurity and homelessness. Findings will improve
understanding of the complex dynamics driving tenant and landlord decision-
making as well as long-term insights into addressing housing insecurity for
low-income households.

##  2 Model Structure

A stock-and-flow structure models the low-income rental housing market. The
structure draws upon prior empirical research, theory, and consultation with
housing and homelessness experts. The model is formulated and simulated
according to a series of integral equations to track the dynamics of rent and
mortgage payments, eviction, turnover, and homelessness among low-income
renters, landlords, and rental units. The model includes four primary
substructures: tenant rent payments, landlord mortgage payments, rental units,
and tenant households. Given focus on eviction and homelessness risk, the
model population is limited to low-income, housing insecure renters – defined
as those who earn less than 130% of the Federal Poverty Level and cannot
maintain housing without risk of experiencing housing cost-burden, doubling
up, or eviction. Rental units are limited to those that are low-cost and
occupied by or available to low-income renters. When tenants experience income
increases that substantially alter their ability to afford housing, they are
considered to stabilize and thus transition outside of the model boundary.

###  2.1 Rent Payments

Rent payments become due each month (Rd) according to the average monthly rent
per unit [dollars/rental unit/month] multiplied by total occupied rental units
in the system (Figure A1). Total rent due is calculated as an accumulation of
rent becoming due each month given payments (Equation 1), and accumulates
until it is paid off (RP; Figure 1). The outflow RP depends on the average
time for residents of a rental unit to pay rent (Equation 1.1).

Equation 1:

$\begin{split}R=\int_{0}^{t}(R_{d}-R_{p})dt+R_{0}\\\
WhereR=Totalrentdue[dollars]\\\ R_{d}=Monthlyrentbecomingdue[dollars/month]\\\
R_{p}=Rentpayments[dollars/month]\\\ \end{split}$ (1)

Equation 1.1:

$\displaystyle R_{p}=\frac{R}{AT_{r}}$ (2) $\displaystyle Where:$
$\displaystyle AT_{r}=Averagetimefortenantstopayrent$ (3)

Figure 1: Rent payments accumulating due to housing cost burden

AT_r increases (delaying rent payments) as the ratio of rent due to household
income exceeds 0.30 – a standard threshold above which households are
considered “cost-burdened” by housing (Equation 2). This delay occurs through
an effect (E_r) fit according to an asymptotic curve (Figure 2). Thus if we
assume the initial average time to pay monthly rent is one month, the actual
average time is one month multiplied by an effect that begins to increase
asymptotically when rent due exceeds 30% of income per rental unit, with E_R =
1 indicating no effect. A MAX function prevented the value of the equation
from going below 1, indicating lack of problematic household economic stress
and thus no effect on time to pay rent. Given the model included only low-
income, housing insecure households typically experiencing high housing cost
burden, it was assumed that tenants would not pay ahead on their rent [1, 17].
This mechanism may function differently for higher-income households. Rent due
(R) accumulates unless paid by the tenant or forgiven. A reinforcing loop (R1)
describes how inability to afford rent each month leads to persistent late
payments and accumulating arrears.

Figure 2: Graphical function linking housing cost burden to time to pay rent

Household economic stress reflects the strain on household finances given
housing costs; as the accumulated arrears per household increase relative to
new monthly rent due, stress increases asymptotically, driving household
decisions to move or double up in order to avoid eviction or homelessness
(Figure 3). Household economic stress acts as a multiplier on the baseline
turnover rate with E_es = 1 indicating no effect (Equation 3). We assume
exceeding the rent burden threshold quickly impacts ability to pay rent as
basic and thus use an asymptotic curve to represent the effect. Values do not
fall below (1,1) as it is assumed tenants live on the edge of affordability
and do not pay “ahead” on rent.

Figure 3: Graphic function linking arrears with household economic stress

Equation 3:

$\begin{split}E_{e}s=y_{f}+(y_{0}-y_{f})*exp(-exp(alpha)*t)\\\
Where:y_{f}=asymptote=3.0\\\ y_{0}=y-intercept=-108.2\\\
\alpha=growthrate=1.4\\\ \end{split}$ (4)

Graphical functions were shaped according to the theoretical assumption that
late payments have the largest impact early on, as households transition from
being tenants in good standing to officially delinquent and thus at risk of
losing housing, with this impact tapering off with increasing debt. We assume
no additional fees or secondary borrowing associated with late rent. Equations
were fit to the points generated by graphs.

###  2.2 Mortgage Payments

Like rent, mortgage payments come due each month (M_d; Figure 4). It is
assumed that landlords rely on income generated from tenant rent payments
(R_p) to make mortgage payments (M_P); when unpaid rent accumulates, landlord
income decreases and mortgage likewise accumulates (Equation 4).

Figure 4: Mortgage payments delayed due to reduced landlord income from rent
payments

In a process analogous to tenant income impacting ability to pay rent,
decreased landlord income due to missed rent payments (R_p) delays mortgage
payments (M_P). When mortgage due (M) exceeds income per rental unit generated
for landlords (I_L), mortgage payments are delayed by a multiplicative effect
(E_m; Equation 5) generated by an S-shaped curve with E_m=1 indicating no
effect (Figure 5). Thus, mortgage due (M) accumulates unless paid by
landlords. The S-shaped effect reflected the assumption that landlords would
have more resources than tenants, and thus experience strain from overdue
payments more slowly than would low-income tenants.

Figure 5: Graphical function linking mortgage due to time to pay mortgage

Equation 5:

$\begin{split}E_{m}=Y_{(}Em,max)+\frac{(Y_{(}Em,min)-Y_{(}Em,max))}{(1+(\frac{r_{E}m}{e_{E}m})^{(}b_{E}m))}\\\
Where:Y_{(}Em,max)=upperasymptote=3.0\\\ Y_{(}Em,min)=lowerasymptote1.0\\\
e_{E}m=inflectionpoint=1.5\\\ b_{E}m=slope=10.0\\\
r_{E}m=M/I_{L}=ratioofmortgageduetolandlordincomeperrentalunit\\\ \end{split}$
(5)

###  2.3 Rental Units

A third stock-and-flow structure captures low-cost rental units that may
transition through four states: occupied, pending eviction, unoccupied, and
foreclosed (Figure 6). Equations 6-6.3 describe values of each state over
time. Occupied rental units are occupied by tenants in good standing and up-
to-date on rent payments. Rental units pending eviction are occupied by
tenants against which an eviction has been filed but not yet processed.
Unoccupied rental units are those available for rent but currently unoccupied.
Foreclosed units are rental units that have been removed from the rental
market with occupants removed as a result of foreclosure.

Figure 6: Rental units becoming unoccupied due to evictions and mobility;
foreclosures reducing affordable housing stock

Equation 6:

$\displaystyle
U_{o}cc=\int_{0}^{t}(t_{n}+e_{r}-t_{m}-f_{o}-e_{f})dt+U_{(}occ,0)$ (6)

Equation 6.1:

$\displaystyle U_{p}end=\int_{0}^{t}(e_{f}-e_{p}-fS_{r})dt+U_{(}pend,0)$ (7)

Equation 6.2:

$\displaystyle
U_{u}nocc=\int_{0}^{t}(e_{p}+t_{m}+f_{s}-t_{n}-f_{u}o-s_{d})dt+U_{(}unocc,0)$
(8)

Equation 6.3:

$\begin{split}U_{f}ore=\int_{0}^{t}(f_{o}+f_{u}o-f_{s})dt+U_{(}fore,0)\\\
Where:U_{o}cc=Occupiedrentalunits[rentalunits]\\\
U_{p}end=Rentalunitspendingeviction[rentalunits]\\\
U_{u}nocc=Unoccupiedrentalunits[rentalunits]\\\
U_{f}ore=Foreclosedrentalunits[rentalunits]\\\
e_{f}=Evictionfilings[rentalunits/month]\\\
e_{r}=Evictionfilingsresolving[rentalunits/month]\\\
e_{p}=Evictionsbeingprocessed[rentalunits/month]\\\
t_{m}=Tenantsmovingout[rentalunits/month]\\\
fo=Foreclosuresofoccupiedunits[rentalunits/month]\\\
fuo=Foreclosuresofunoccupiedunits[rentalunits/month]\\\
f_{s}=Salesofforeclosedunits[rentalunits/month]\\\
t_{n}=Newtenantsmovingin[rentalunits/month]\\\ rs_{d}=Declininglow-
costrentalstock\\\ \end{split}$ (9)

Accumulated unpaid rent triggers eviction filings (e_f) through an effect E_or
(Equation 6.4). A minimum constraint on E_or is set to 1 such that when
accumulated unpaid rent exceeds monthly rent owed, risk for eviction filing
increases; when accumulated unpaid rent is less than rent owed, E_or=1
indicating no effect. Eviction risk similarly increases when landlords feel
financial pressure, as they rely on rent income to make mortgage payments;
landlords are more likely to file evictions when they fall behind on mortgage
payments. Finally, eviction risk is also driven by household conflict
(discussed in the following section); overcrowded housing can increase charges
of excessive noise and nuisance that lead to eviction filings.

Equation 6.4:

$\begin{split}E_{o}r=\frac{R_{u}}{L_{t}ol}\\\
Where:R_{u}=Accumulatedunpaidrentperunit[dollars/unit]\\\
L_{t}ol=Landlordtoleranceforoverduerent[dollars/unit]\end{split}$ (10)

Once filed, evictions must be processed. The processing rate is a function of
housing court capacity; prior to the pandemic, courts processed approximately
38% of eviction filings per month. Courts experience strain and slowed
processing when a surge in eviction filings occurs. COVID-19 social distancing
policies (sd) have further slowed court proceedings. Thus, the proportion of
evictions processed is reduced by strain on the courts as well as social
distancing policies; the number of evictions processed per month e_p) is equal
to the proportion of evictions processed divided by the average time to
process one eviction (Equation 6.5).

Equation 6.5:

$\begin{split}e_{p}=\frac{e_{p}rop}{AT_{p}roc}*sd\\\
Where:e_{p}rop=Initialproportionevictionsprocessedpermonth[dimensionless]\\\
AT_{p}roc=Averagetimetoprocessoneeviction[months]\end{split}$ (11)

###  2.4 Households

The model tracks low-income households at risk for eviction and homelessness
(Figure 7). “Housing Insecure Households” includes renter households earning
up to 150% of the federal poverty level who are cost-burdened by housing
(paying at least 30% of income toward rent; Equation 7). “Literally Homeless
Households” encompasses households living in shelters, on the streets, in
abandoned buildings, in vehicles, or anywhere else not meant for human
habitation (Equation 7.1)

Figure 7: Households transitioning between housing insecure and literally
homeless

Households may enter either setting for the first time (“New Housing
Insecurity” (I_new) and “New Homelessness” (H_new) or stabilize from either
setting (I_stbl and H_stbl). A proportion of evictions and foreclosures will
result in homelessness; however, the majority will lead to families moving
into cheaper housing or doubling up, thus remaining in the stock “Housing
Insecure Households.” It is assumed that when households are evicted, move to
alternate housing, double up, or enter homeless, they do not carry any
remaining rent debt with them.

Equation 7:

$\displaystyle H_{h}i=\int_{0}^{t}(I_{n}ew+H_{e}xit+H_{d}u-H_{e}nt-
I_{s}tbl)dt+H_{(}hi,0)$ (12)

Equation 7.1:

$\begin{split}H_{l}h=\int_{0}^{t}(H_{n}ew+H_{e}nt-H_{e}xit-
H_{d}u-H_{s}tbl)dt+H_{(}lh,0)\\\
Where:H_{h}i=Housinginsecurehouseholds[households]\\\
I_{n}ew=Newhousinginsecurity[households/months]\\\
I_{s}tbl=Stabilizingfromhousinginsecurity[households/months]\\\
H_{l}h=Literallyhomelesshouseholds[households]\\\
H_{e}nt=Enteringhomelessness[households/months]\\\
H_{e}xit=Exitinghomelessness[households/months]\\\
H_{d}u=Doublingupafterhomelessness[households/months]\\\
H_{n}ew=Newhomelessness[households/months]\\\
H_{s}tbl=Stabilizingfromhomelessness[households/months]\\\ \end{split}$ (13)

Crowding (c) results as more households move into a finite number of rental
units, thus increasing the number of units housing doubled up households
(defined as >1 household per rental unit; Figure 8; Equation 8). Increased
crowding drives household conflict via an effect E_cr (Equation 8.1). When the
average number of households reaches 1 or fewer, there is assumed to be no
“crowding” effect.

Equation 8:

$\displaystyle c=\frac{[\frac{H_{hi}}{(U_{occ}+U_{pend})}]}{c_{ref}}$ (14)

Equation 8.1:

$\begin{split}E_{cr}=Y_{Ecr,max}+\frac{Y_{Ecr,min}-Y_{Ecr,max}}{1+(\frac{r_{Ecr}{e_{Ecr}}}{)}^{b}_{Ecr}}\\\
Where:Y_{(}Ecr,max)=upperasymptote=2.0\\\ Y_{Ecr,min}=lowerasymptote=1.0\\\
e_{Ecr}=inflectionpoint=1.5\\\ b_{Ecr}=slope=5\\\
r_{Ecr}=ratioofactualhouseholdsperrentalunittoreferencevalue(1householdperunit)\end{split}$
(15)

Thus, crowding increases as the number of households per total occupied rental
units exceeds the crowding reference value (1 household/rental unit).
Household conflict was calculated as the product of crowding and turnover
effects.

Figure 8: Graphical function linking households per rental unit with crowding
effect

###  2.5 Key Feedback Mechanisms

The structures described above are linked by key feedback mechanisms driving
tenant and landlord behavior in the low-income rental housing market. Three
primary feedback loops describe tenant behavior in response to economic
disruption (Figure 9). Timely payments depend upon household income remaining
at a level adequate to cover rent payments given other basic needs [10]. If
household incomes decrease, rent payments are delayen the wake of the COVID-
related shutdowns, households face financial strain as they struggle to afford
monthly expenses given a period of reduced income. This strain delays rent
payments as families must make tradeoffs about which bills to pay first [18,
19] thus slowing the outflow of overdue rent and contributing to the
accumulation of arrears. Accumulating debt further strains families in a
vicious cycle (R1).

Figure 9: Feedback loops describing accumulation of unpaid rent (R1), tenant
tradeoffs in the wake of household financial strain (B1), and consequences of
doubling up to alleviate housing cost burden (R2)

A balancing loop describes the tradeoffs tenants face in the wake of household
economic distress (B1). Disrupted or inadequate income creates household
financial strain as families struggle to afford basic needs. Without action,
families continue to accumulate arrears and risk eviction by landlords;
conversely, families may choose to leave their current housing knowing arrears
can never be paid, and either move somewhere cheaper or double up with friends
or family. Leaving unaffordable housing can alleviate financial strain and
prevent families from facing formal evictions.

Third, a reinforcing loop from moving triggers exposure to other stressors
such as poor quality, overcrowded conditions and household conflict. Thus,
consequences of alleviating financial strain through moving emerge via
increased household conflict, which can trigger eviction filings for nuisance-
related reasons; abrupt loss of housing can thus drive further need for
doubling up as families struggle to find stable, affordable housing in the
wake of eviction (R2).

A second set of major feedback loops model landlord decision-making in
response to delayed rent payments and market conditions (Figure 10). Most
landlords in the low-income rental market are small “mom-and-pop” operations
with just one or two units who rely on income from tenant rent payments to
afford their mortgages [13, 20]. In the wake of major disruption to tenant
incomes such as the pandemic-relation shutdowns, a reinforcing loop increases
evictions due to landlords’ own financial hardship (R3) while a balancing
process slows mass evictions even in the absence of widespread policy
protections (Figure 10).

Figure 10: Feedback loops describing fluctuating landlord income as a result
in changing rental unit occupancy through evictions (R3) as well as strain on
the housing court system slowing evictions as a result of surges (B2)

The reinforcing loop (R3) details the mechanism by which landlords’ own
financial pressures drive eviction decisions. When landlords fall behind on
mortgage payments, they are more likely to initiate eviction proceedings –
either as an attempt to displace a non-paying tenant or pressure tenants into
catching up [9]. Eviction filings increase processed evictions, which reduce
rental unit occupancy and thus landlord income, further delaying mortgage
payments. A balancing loop (B2) describes how the volume of eviction filings
might impact processing time, thus keeping units occupied. An increase in
eviction filings in a period of economic downturn strains court capacity to
process cases, thus slowing evictions. This in turn keeps rental units
occupied and contributing to landlord income; this delay allows tenants more
opportunity to resolve eviction filings by catching up on payments, working
out payment plans, or seeking rental assistance. Failure to pay would lead to
repeated eviction filings or landlord pressure to vacate voluntarily.

###  2.6 Economic Impact of COVID-19

The COVID-19 pandemic was modeled using a positive step function representing
the overnight exogenous financial shock, while a smoothed negative step
function represented a prolonged economic recovery (Equation 14). The
magnitude of the spike was calibrated to results of the U.S. Census Bureau’s
Pulse Survey launched in April 2020 on household impacts of the pandemic (U.S.
Census Bureau, 2021) while the shape of the effect was calibrated to the U.S.
unemployment rate (Federal Reserve Bank of St. Louis, 2021).

Equation 11.

$\begin{split}STEP(M_{e},TS_{e})-SMTH(STEP(M_{e},TS_{e}),D_{e})\\\
WhereM_{e}=Magnitudeofeconomicimpact\\\ TS_{e}=Starttimeofeconomicimpact\\\
D_{e}=Durationofeconomicrecovery\end{split}$ (16)

Figure 11: Graphical function representing the economic impact of COVID-19 on
low-income households

The economic impact of COVID-19 was included as an exogenous effect at five
points throughout the model structure. The effect acted to reduce average
household income, increase the rates of new housing insecurity and
homelessness, and reduce the rates of stabilization from housing insecurity
and homelessness (Equations 11.1-11.5). Additionally, the COVID-19 effect
reduced housing court capacity as a result of social distancing guidelines
(Equation 14.6), reducing the number of cases that could be processed during
the height on the pandemic and acting as a balance on evictions.

Equation 11.1.

$\begin{split}AverageHouseholdIncome=\\\
INITAverageHouseholdIncome*(1-COVID-19EconomicImpact)\end{split}$ (17)

Equation 11.2.

$\begin{split}RateofNewHousingInsecurity=\\\
INITRateofNewHousingInsecurity*(1+COVID-19EconomicImpact)\end{split}$ (18)

Equation 11.3.

$\begin{split}RateofNewHomelessness=\\\
INITRateofNewHomelessness*(1+COVID-19EconomicImpact)\end{split}$ (19)

Equation 11.4.

$\begin{split}FRStabilizingfromHousingInsecurity=\\\
INITFRStabilizingfromHousingInsecurity=\\\
*(1-COVID-19EconomicImpact)\end{split}$ (20)

Equation 11.5.

$\begin{split}FRStabilizingfromHomelessness=\\\
INITFRStabilizingfromHomelessness=\\\ *(1-COVID-19EconomicImpact)\end{split}$
(21)

Equation 11.6.

$\begin{split}ProportionofEvictionFilingsProcessed=INITProportionofEvictionsProcessed\\\
*ReducedCourtCapacityDuetoSocialDistancing*EvictionMoratorium\\\
Where:ReducedCourtCapacityDuetoSocialDistancing=\\\ 1\textendash
COVID-19EconomicImpact\end{split}$ (22)

Reduced court capacity to process evictions acts as a balancing force on the
number of evictions following a surge in filings, which strains courts and
increases processing time.

###  2.7 Policy Interventions

Two additional structures testing impacts of COVID relief policies for
renters. First, the federal eviction moratorium enacted in late March 2020
halted most evictions due to nonpayment of rent, which comprise the majority
of evictions in the U.S. each year. The moratorium was extended several times
before expiring in most places by Fall 2021 [21, 3]. A switch turned the
moratorium on in the third week of March 2020, reducing the proportion of
evictions processed by 90% for 18 months (Equation 12). An additional effect
likewise reduced eviction filings, reflecting nationwide data suggesting
landlords were slow to resume filings during and after the moratorium
(Equation 12.1).

Equation 12.

$\begin{split}EvictionMoratorium=-STEP(INIT_{P}roportion_{o}f_{E}victions_{P}rocessed\\\
*ES_{E}M*Eviction_{M}oratorium_{O}N,TS_{E}M)\\\
+STEP(INIT_{P}roportion_{o}f_{E}victions_{P}rocessed*ES_{E}M*\\\
Eviction_{M}oratorium_{O}N,ET_{E}M)\end{split}$ (23)

Equation 12.1.

$\begin{split}1-STEP(Eviction_{M}oratorium_{O}N*\\\
Magnitude_{R}eduction_{i}n_{F}ilings_{D}uring_{M}oratorium,TS_{E}M-.5)\\\
+SMTH1(STEP(Eviction_{M}oratorium_{O}N*\\\
Magnitude_{R}eduction_{i}n_{F}ilings_{D}uring_{M}oratorium,TS_{E}M+Duration_{E}M+3),36\\\
Where:ES_{E}M=Effectsizeofevictionmoratorium\\\
TS_{E}M=Starttimeofevictionmoratorium\\\
ET_{E}M=Endtimeofmoratorium\end{split}$ (24)

Second, the Consolidated Appropriations Act of 2021 and the American Rescue
Plan together allocated nearly $50 billion in emergency rental assistance
(ERA) for low-income renters impacted by the pandemic. A stock-and-flow
structure reflecting the initial available ERA funds and estimated rate of
disbursement by the U.S. Treasury [22] was linked to rent payments to reflect
assistance filling in gaps for delinquent tenants (Figure 12).

Figure 12: Emergency rental assistance structure

###  2.8 Model Calibration and Validation

The model was calibrated using data from a range of sources. Estimates of
literal homelessness came from the 2018-2020 Annual Homeless Assessment
Reports (AHAR), which include point-in-time counts every January of sheltered
and unsheltered homelessness [23, 1, 24], and the National Low-Income Housing
Coalition [25, 26]. Estimates of eviction filings and evictions came from
Eviction Lab [27, 28]. Finally, the impact of COVID-19 on low-income rental
housing market was calibrated based on unemployment rates and self-reported
economic hardship [29, 2]. When available, historical data were plotted to
create reference modes; model parameters were adjusted with empirical and
theoretical justification so that simulations were able to replicate reference
modes.

Uncertainty underlay the model structure and reference modes given imperfect
existing data and the sensitive nature of housing decisions among very low-
income households. Thus a range of prior studies contributed empirical and
theoretical knowledge to the model-building process [15, 4, 5, 6].
Furthermore, several measures built confidence in model structure and
simulation results. Model simulated trends were compared to historical data
using Theil’s U, an indicator of bias and variation in prediction (Appendix
III). Parameter sensitivity analyses simulated the model across +/- 15% of all
initial values to test robustness of the model structure to initial
conditions. Inputting extreme parameters assessed model behavior under
unrealistic [30, 31]. Shapes of graphical functions were first built according
to prior theoretical and empirical research; algebraic equations underlying
functions were used to generate parameters for sensitivity analyses in R
Version 4.0.3 [32]. Key housing policy experts consulted on model structure
and outputs in an iterative fashion as an additional validity check. All model
building and simulations were conducted in Stella Architect Version 2.1.

Once the model was calibrated, simulations reflected alternate scenarios for
policy evaluation and planning. Run 1 reflected pre-pandemic dynamics in the
low-income rental market and assess the accuracy of model outputs relative to
real-world data. Run 2 included the economic impact of COVID-19 on the low-
income rental housing market with no policy interventions. Run 3 tested the
impact of COVID-19 with the federal eviction moratorium in place for 18 months
[21, 3]. Run 4 added the federal Emergency Rental Assistance (ERA) program,
which allocated $46.5 billion to keep tenants housed.

The total time horizon for simulations was 50 months (January 2018 through
February 2022). This included a 24-month “burn-in” period such that Month 1
represented January 2020 and the analytical time horizon was 26 months –
through February 2022. The model was simulated using the Euler integration
method with a delta time of 0.25 months.

###  2.9 Simulation Results

Simulations estimate the economic fallout from COVID-19 severely impedes low-
income households’ ability to afford housing without intervention in Figure 13
and Figure 14. Tenants accumulate $20.4 billion in unpaid rent over 36 months,
which leads to 1.5 million excess evictions across the follow-up – an increase
of over 25% compared to pre-pandemic rates. Unpaid rent also drives crowding
and homelessness, which increase 45% and 120% respectively.

The federal eviction moratorium enacted in March 2020 dramatically reduces
tenant displacements through September 2021 compared with no federal
intervention. The moratorium removes incentives for tenants to double up to
avoid housing cost burden and eviction, however; with the moratorium in place,
arrears remain at nearly $20 billion by the end of the simulation period.
Eviction filings lagged in the wake of the moratorium’s expiration [28],
keeping eviction rates below pre-pandemic rates through the follow-up period
despite signs of an initial rebound. The moratorium reduces total evictions by
51% across the 26-month follow-up compared to no intervention. Pausing
evictions allows some households time to pay off debts, double up, or move
before facing formal displacement.

Federal emergency rental assistance further aids households in retaining
housing in spite of the COVID-19 economic fallout. Initial roll-out was
delayed, with states slow to disburse funds due to complicated eligibility
criteria and application processes for both tenants and landlords. As of
February 2022, only 42% of funds allocated by the federal government had been
paid out to tenants. Simulation results show that with this rate of
disbursement, arrears, crowding, and homelessness remain high despite $27
billion in assistance remaining unused. An additional simulation (Run 4a)
builds on this finding to tests an alternate scenario wherein ERA funds are
disbursed more rapidly from the start; under these conditions, arrears,
crowding, and homelessness plummet quickly. Although funds run out sooner,
each dollar goes further by stabilizing cost-burdened and homeless households
more efficiently. Increasing speed of disbursement burns through funds more
quickly but heads off additional accumulation of arrears that feed enduring
housing insecurity, crowding, and homelessness.

Figure 13: Results of simulations testing the impact of COVID-19, the federal
eviction moratorium (EM), and federal emergency rental assistance (ERA) on
accumulated arrears (top) and monthly evictions (bottom) Figure 14: Results of
simulations testing the impact of COVID-19, the federal eviction moratorium
(EM), and federal emergency rental assistance (ERA) on average crowding (top)
and literal homelessness (bottom)

##  3 Discussion

The low-income rental housing market is marked by instability, scarcity, and
difficult tradeoffs. In the present study, a system dynamics model highlights
the complex dynamics driving tenant and landlord behaviors in the context of
limited affordable housing and precarious incomes. Prior to COVID-19, vicious
cycles of household economic stress and interpersonal conflict hinder tenants’
abilities to secure and maintain stable housing; compensatory processes lead
landlords to calibrate to market conditions in order to keep units occupied
and avoid foreclosures. These feedback mechanisms underlie persistent rates of
housing insecurity and homelessness over time. The economic fallout from the
pandemic exacerbates low-income rental market vulnerabilities. Pervasive
economic hardship in the absence of widely available supports fuels the low-
income population with high barriers to housing. Post-COVID evictions displace
tenants, exposing households to overcrowded or unsafe conditions as well as
literal homelessness. Low-income landlords continuously consider how to pay
their mortgages and make a profit. Eviction decisions depend on tenant
delinquency as well as landlords’ own financial hardship. The COVID-19
recession and the policy responses introduce volatility into a low-income
housing system driven by complex decision-making processes.

Simulations suggest trends in evictions and literal homelessness only
partially reflect instability and hardship that characterize the low-income
rental market. Widespread financial strain as households accumulate arrears
triggers decisions aimed at avoiding eviction and homelessness – two of the
most visible, easily tracked outcomes. Doubling up allows more families to
avoid homelessness, but contributes to conflict that may erode living
conditions over time. The federal eviction moratorium implemented in response
to COVID-19 paused formal evictions while household economic strain persisted;
projections suggest this translated to increased crowding and homelessness
with delays. While tenants aim to avoid evictions, landlords rely on evictions
to minimize lost income. Future efforts to stabilize housing and reduce
homelessness for low-income households must consider decision-making in the
context of these conflicting goals. The eviction moratorium may have had
additional benefits beyond the scope of the present study. While the lowest-
income renters typically face the highest risk for eviction and thus were most
likely to benefit from the eviction moratorium, the moratorium applied equally
to all renters and thus likely kept some higher-earning tenants in housing and
out of the model population. In general, the eviction moratorium would have
allowed renters regardless of income level to remain in their current housing.
Findings show lasting benefits of the moratorium for evictions, but arrears,
crowding, and homelessness do not improve without significant government
financial investment for the most vulnerable renters.

Parameter sensitivity analyses tested the robustness of the model structure to
initial parameter values +/-15%. The ratio of total rental units to low-income
households emerges as an area of sensitivity; the low-income rental market
relies on a certain level of doubling up, such that combining incomes allows
more families to stay housed in the mechanism described by B1. When the number
of rental units increases relative to households such that doubling up
decreases, evictions and homelessness spike; this dynamic points to the
challenges of increasing affordable housing that may not actually be
affordable for very low-income households juggling multiple monthly expenses
that strain resources.

A number of policy implications arise from the present study. Housing policies
must offer opportunities to avoid eviction filings that benefit both landlords
as well as tenants. The eviction moratorium demonstrates that pausing or
delaying evictions of low-income households can lead to permanent declines as
tenants have more opportunities to catch up on payments or find alternate
living arrangements without experiencing formal eviction or entering
homelessness. Measures that slow the eviction process in the low-income rental
market incentivize landlords to work with tenants on payment plans rather than
turning to the courts. Although a need exists for broader economic and housing
policies that make housing more affordable, slowing evictions stabilize
severely housing-burdened households without triggering unintended
consequences, including raised rents and gentrification [33].

A number of feasible options exist for slowing evictions. One potential
longer-term solution would be to reform the eviction policies to mirror the
foreclosure process. Currently, landlords are protected by federal law that
prohibits lenders from initiating foreclosures in most cases until the
borrower is over 120 days delinquent (12 C.F.R. § 1024.41). In contrast,
evictions occur quickly; a recent study found that the average debt owed by
tenants in eviction hearings was $1,200 [34] or just over one months’ rent at
the U.S. median level [23]. Nationally, 60% of eviction judgements are decided
in the plaintiff’s favor [27]. A slower eviction process makes filing
evictions a less attractive option for landlords, who may increase their
tolerance for overdue rent and be more willing to accommodate payment plans.
Second, removing evictions from tenant records after a period of time may
mitigate the effect of evictions on future housing stability, allowing tenants
to more easily find housing and landlords to more easily fill vacant units.
Imposing time limits on the impact of eviction histories can prevent erosion
of renter applicant quality and more quickly enable households to exit
homelessness. Finally, rapid, widespread dispersion of rental assistance
allocated as part of the federal COVID response can address the outstanding
arrears that contribute to ongoing financial strain despite the eviction
moratorium. Despite billions of dollars allocated to states for rental
assistance, technological limitations and complex eligibility criteria have
hindered efficient distribution of funds to households in need. More rapid
payments can keep low-income families housed and mitigate housing insecurity
as the eviction moratorium lifts.

###  3.1 Limitations

Findings from modeling must be considered in light of study limitations.
First, the model is calibrated at a national level using the best available
data; results thus provide an aggregate view of the U.S. low-income rental
market, but do not capture geographic variation in rental markets due to
differing costs of living, affordable housing availability, and labor markets.
Future modeling should consider local variation to estimate trends in specific
metropolitan areas or geographic regions. Second, results reflect assumptions
about sustained economic and public health recovery from the COVID-19
pandemic; future surges driven by variants or stalled vaccination rates may
drive future mitigation efforts that prolong or alter the economic recovery.

The model also does not track cumulative harm to households from experiencing
eviction, homelessness, and crowding. In most states, eviction histories
impact credit scores for years, impeding the ability to secure new housing.
Exposure to literal homelessness is associated with enduring stigma and
adverse consequences for physical and mental health. Prolonged experiences of
inadequate housing, eviction, and homelessness may also drive households to
accrue additional late fees or seek emergency loans through payday lenders,
further impacting financial hardship over time. Future modeling should
consider the potential long-term, cumulative effects of housing insecurity on
tenant behaviors and outcomes.

Finally, the pandemic-triggered economic impact and recovery are modeled as
exogenous variables unaffected by trends in the low-income rental market and
policy responses to the affordable housing crisis. Examination of the
interactions between the affordable housing market and broader economic
recovery is an important area of future research.

###  3.2 Implications for Future Research

Despite limitations, the present study highlights important insights into the
dynamics underlying the low-income rental market that can inform post-COVID
relief efforts. The model points to a number of important opportunities for
future inquiry. First, little is known about complex landlord decision-making
in response to market conditions. In slack markets, landlords may adjust
expectations for tenants and tolerate late rent for longer before initiating
eviction filings with the assumption that late rent is better than no rent
[10]; landlords may also respond differently to eviction histories when
evictions are widespread and it becomes difficult to find tenants with clean
records. The dynamics underlying landlord cost-benefit analyses should be
explored using participatory approaches and incorporated into future model
iterations. Second, low-income households make complex tradeoffs in household
budgeting to juggle unaffordable basic needs [19]. A thorough accounting of
how household expenses are managed when incomes are too low to pay all bills
each month may inform efforts to provide assistance during economic downturns.
Finally, delays in disbursing ERA funds have impeded efforts to stabilize the
low-income rental market; modeling efforts should examine barriers to rapid
implementation of assistance during times of crisis. Future research should
evaluate efforts to address widespread financial hardship that reduce emphasis
on individual eligibility criteria and focus on systemic interventions [33].

###  3.3 Conclusions

The expiration of the eviction moratorium and delayed rollout of emergency
rental assistance threatens a continuing crisis of housing insecurity and
homelessness in the wake of the COVID-19 pandemic. Understanding the tradeoffs
and conflicting interests of tenants and landlords in a context of scarcity
can help target interventions that keep families housed. Rapid assistance that
addresses accumulated arrears and reduces incentives for landlords to evict is
necessary for housing security and public health in vulnerable communities.

## References

  * [1] Joint Center for Housing Studies of Harvard University.  America’s Rental Housing 2020.  Technical report, Harvard University, Cambridge, MA, 2020.
  * [2] U.S. Census Bureau.  Household Pulse Survey Data Tables, 2021.
  * [3] National Low Income Housing Coalition.  National Eviction Moratorium.  Technical report, Washington, DC, 2021.
  * [4] Patrick J. Fowler, Peter S. Hovmand, Katherine E. Marcal, and Sanmay Das.  Solving Homelessness from a Complex Systems Perspective: Insights for Prevention Responses.  Annu. Rev. Public Health, 40(1):465–486, April 2019.  Publisher: Annual Reviews.
  * [5] Katherine E. Marçal, Patrick J Fowler, Peter S Hovmand, and Jessica Cohen.  Understanding Mechanisms Driving Family Homeless Shelter Use and Child Mental Health.  Journal of social service research, 47(4):473–485, 2021.  Publisher: Routledge.
  * [6] Mohamed Marzouk and Ismail Hosny.  Modeling housing supply and demand using system dynamics.  Housing, care and support., 19(2):64–80, 2016.  Place: United Kingdom : Publisher: Pavilion,.
  * [7] Matthew Desmond, Carl Gershenson, and Barbara Kiviat.  Forced Relocation and Residential Instability among Urban Renters.  The Social service review (Chicago), 89(2):227–262, 2015.  Place: CHICAGO Publisher: University of Chicago Press.
  * [8] Francisca García-Cobián Richter, Claudia Coulton, April Urban, and Stephen Steh.  An Integrated Data System Lens Into Evictions and Their Effects.  Housing Policy Debate, 31(3-5):762–784, 2021.  Publisher: Routledge _eprint: https://doi.org/10.1080/10511482.2021.1879201.
  * [9] Philip ME Garboden and Eva Rosen.  Serial Filing: How Landlords Use the Threat of Eviction.  City & community, 18(2):638–661, 2019.  Publisher: Wiley Subscription Services, Inc.
  * [10] John Balzarini and Melody L. Boyd.  Working With Them: Small-Scale Landlord Strategies for Avoiding Evictions.  null, 31(3-5):425–445, September 2021.  Publisher: Routledge.
  * [11] Marah A. Curtis, Hope Corman, Kelly Noonan, and Nancy E. Reichman.  Life Shocks and Homelessness.  Demography, 50(6):2227–2253, 2013.  Place: Boston Publisher: Boston: Springer.
  * [12] Brendan O’Flaherty.  What shocks precipitate homelessness?  Technical Report Discussion Paper No.: 0809-14, Columbia University, 2009\.
  * [13] Claudia Coulton, April Urban, Francisca Garcia-Cobian Richter, Michael Henderson, Michael Schramm, Jeesoo Jeon, and Robert Fischer.  Characteristics of rental properties and landlords in Cleveland: Implications for achieving lead safe rental housing.  Technical report, Center on Urban Poverty and Community Development, Cleveland, OH, 2020.
  * [14] Real Estate Settlement Procedures Act, 2017.
  * [15] Martijn Eskinasi, Etienne Rouwette, and Jac Vennix.  Houdini: A system dynamics model for housing market reforms.  Washington, DC, 2011.
  * [16] Jenny Schuetz.  To improve housing affordability, we need better alignment of zoning, taxes, and subsidies.  Technical report, Brookings Institute, Washington, DC, 2020.
  * [17] Susan K Urahn, Travis Plunkett, Erin Currier, Diana Elliott, Clinton Key, Sarah Sattelmeyer, Joanna Biernacka-Lievestro, Walter Lake, Sheida Elmi, and Sowmya Kypa.  Household Expenditures and Income: Balancing Family Finances in Today’s Economy.  Technical report, The Pew Charitable Trusts, Philadelphia, PA, 2016.
  * [18] Will Anderson, Vicki White, and Andrea Finney.  Coping with low incomes and cold homes.  Energy policy, 49:40–52, 2012.  Publisher: Elsevier Ltd.
  * [19] Timothy K. M Beatty, Laura Blow, and Thomas F Crossley.  Is there a ’heat-or-eat’ trade-off in the UK?  Journal of the Royal Statistical Society. Series A, Statistics in society, 177(1):281–294, 2014.  Publisher: Blackwell Publishing Ltd.
  * [20] Elora Lee Raymond, Richard Duckworth, Benjamin Miller, Michael Lucas, and Shiraj Pokharel.  From Foreclosure to Eviction.  Cityscape, 20(3):159–188, 2018.  Publisher: US Department of Housing and Urban Development.
  * [21] Maggie McCarty and Libby Perl.  Federal Eviction Moratoriums in Response to the COVID-19 Pandemic.  Technical report, Congressional Research Service, Washington, DC, 2021\.
  * [22] National Low Income Housing Coalition.  Treasury Emergency Rental Assistance (ERA) Dashboard.  Technical report, Washington, DC, 2022.
  * [23] U.S. Census Bureau.  American Community Survey, 2018.
  * [24] Joint Center for Housing Studies of Harvard University.  The State of the Nation’s Housing 2020.  Technical report, Cambridge, MA, 2020.
  * [25] National Low Income Housing Coalition.  Renters in Foreclosure: A Fresh Look at an Ongoing Problem.  Technical report, Washington, DC, 2012.
  * [26] National Low Income Housing Coalition.  The Gap: A Shortage of Affordable Homes.  Technical report, Washington, DC, 2021.
  * [27] Matthew Desmond, Ashley Gromis, Lavar Edmonds, James Hendrickson, Katie Krywokulski, Lillian Leung, and Adam Porton.  Eviction Lab National Database Version 1.0.  Technical report, Princeton University, Princeton, NJ, 2018.
  * [28] Eviction Lab.  Eviction Tracking.  Technical report, Princeton, NJ, 2022.
  * [29] Federal Reserve Bank of St. Louis.  Unemployment Rate, 2021.
  * [30] Mohamed Saleh, Rogelio Oliva, Christian Erik Kampmann, and Pål I. Davidsen.  A comprehensive analytical approach for policy analysis of system dynamics models.  European Journal of Operational Research, 203(3):673–683, June 2010\.
  * [31] Peter M Senge and Jay W Forrester.  Tests for building confidence in system dynamics models.  System Dynamics, TIMS Studies in Management Sciences, 14:209–228, 1980.
  * [32] Rogelio Oliva.  Model calibration as a testing strategy for system dynamics models.  European journal of operational research, 151(3):552–568, 2003\.  Publisher: Elsevier B.V.
  * [33] Ingrid Gould Ellen and Brendan O’Flaherty.  How to house the homeless.  New York : Russell Sage Foundation, New York, 2010.
  * [34] April Hirsch Urban, Aleksandra Tyler, Francisca Garcia-Cobian Richter, Claudia Coulton, and Tsui Chan.  The Cleveland Eviction Study: Observations in Eviction Court and the Stories of People Facing Eviction.  Technical report, Center on Urban Poverty and Community Development, Cleveland, OH, 2019.