Homelessness Reading Group

March 30, 2023

Homeless Programs and Social Insurance

Igor Popov

A Presentation of

THe problem

  • Each year, over 1.5 million Americans rely on homeless programs for overnight shelter
  • Over 200,000 on any given night are without any shelter at all

On the one hand, greater generosity helps smooth consumption in face of adverse events. On the other, program expansions incur costs by distorting households’ incentives

Contribution

Estimates the causal effect of homeless assistance funding on

  • Size
  • Composition
  • Behavior

of homeless populations

HUD Funding of Continuums of Care

Exploit funding eligibility formula

HMIS

PIT count

Results

  • Federal funding reduces unsheltered homelessness
\$100,000 \implies \downarrow \ 46 \ \textrm{unsheltered}
  • Locally, federal funding increase the size of the local homeless family population as it encourages homeless families to migrate (2/3) and families to substitute away from social support networks (1/3)
\$100,000 \implies \uparrow \ 73 \ \textrm{homeless family population}
  • Federal funding has no effect on the individual homeless population

data sources

HMIS

- Demographics, sources of income, living situation prior to program entry, destination upon program exit, government benefit receippt

- Survey Individuals use make use of Gov Funded homeless programs

- Can track individuals over time

- Standardized across the US

- Locally managed by each Continuum of Care

data sources

Point in Time Count

- Counts Unsheltered homeless residents in the last week of January

- Every other year

- Locally managed by each Continuum of Care

Data

Why don't we see a chronically homeless count in AHAR?

Funding

  • Federal Grants  administered by HUD: "McKinney-Vento" grants
  • Continuum of Care Program Grant (2 Billion annually)
  • Emergency Solutions Grant (250 Million annually)
  • All organizations within a Continuum of Care’s boundaries collectively apply for CoC funding as a “collaborative applicant.”
  • The mean (median) CoC receives $3.2 milllion ($1.6 million) in federal homeless assistance funding

Continuums of Care

  • Distributes funding to each service provider and local government entity that requested funds as a part of the continuum
  • Coordinate services and decide on community goals and priorities for homeless services.
  • Maintain data on its local homeless populations
n(x, \theta) = l_s(x, \theta) + l_u(x, \theta) + h(x, \theta)

Unsheltered Homeless

Sheltered Homeless

Housed

\theta

Community Characteristics: 

x

Grant Funding Allocation:

Population

x, \theta \longmapsto n(x, \theta)

Conceptual Framework

Conceptual Framework

l(x, \theta) = l_s(x, \theta) + l_u(x, \theta)

Homeless:

\partial_xl_s(x, \theta) = \partial_x l(x, \theta) -\partial l_u(x, \theta)

Estimand

"Spillover Effect"

"Targeted Effect"

"Local Substitution"

"Migration"

\partial_xl(x, \theta) = \partial_x n(x, \theta) -\partial h(x, \theta)

Spillover Effect:

Determination of Funding

Empirical Framework

  • Appropriations bill determines the level of funding for homeless assistance grants
  • Formula allots share of budget to each "entitlement community"
  • CoC can apply for the total amount summed across the entitlement communities within its boundry

Cities and certain counties

Community Development Block Grant formula

Empirical Framework

A = 0.25\textrm{PopShare} + 0.5\textrm{PovertyShare} + 0.25\textrm{OvercrowdedShare}
B = 0.2\textrm{GrowthLagshare} + 0.3\textrm{PovertyShare} + 0.5\textrm{Pre1940HousingShare}
\textrm{Funding Share} = k \ \textrm{max}(A,B)

Empirical Framework

y_c = \beta_0 + \beta_1\textrm{HomelessAssistance}_c + X_c\beta_2 + \varepsilon_c
\textrm{HomelessAssistance}_c = \delta_0 + \delta_1\textrm{Pre1940}\textrm{HousingShare}_c + X_c \delta_2 + v_c

Total, Unsheltered, Migrating

Results

Additional Clarity

  • Specifically, communities that receive more generous funding allocations offer more space in emergency shelters and permanent supportive housing units for chronically homeless individuals. Potentially unsheltered individuals and families both respond by entering programs

How would they learn about these increases?

Additional Clarity

  • Homeless individuals do not migrate to areas with greater homeless program funding, but homeless families do.

Why?

The Model

Individual

  • Choose the probability of being homeless
  • Choose housing/consumption in each state of the world

Social Planner

  • Choose the the amount of per-capita benefit to offer

The Model

\Big(\Omega, \mathcal{F}, \mathbb{P}\Big)

Probability Space

e = \mathbb{P}(\textrm{Housing})

Probability of Shelter

\Omega = \{\textrm{housing}, \textrm{Sheltered homesless}, \textrm{Unsheltered homeless}\}

Sample Space

The Model

Individual

Housing

\textrm{Utility} : \mathcal{R}_+ \times \mathcal{R}_+ \to \mathcal{R}_+
c, a \longmapsto u(c, a)

Consumption

\textrm{Policy} :\mathcal{R}_+ \times \Omega \to \mathcal{R}_+ \times \mathcal{R}_+
b, \omega \longmapsto c^*(\omega), a^*(\omega) = \underset{c, a \in F_{w,p,b}(\omega)}{\textrm{argmax}} \ u(c, a)

Constraint Function

The Model

Optimal Effort

e^*(b) = \underset{e \in (0,1)}{\textrm{argmax}} \ V_b(e)
V_b(e) := \mathbb{E}_{\mathbb{P}_e}\big[U(c_b^*, a_b^*)] - \psi(e)

Optimal Benefit

\underset{b}{\textrm{argmax}}\ V_b(e^*(b))

The Model

Planner

\tau : \mathcal{R}_+ \to \mathcal{R}_+

Tax

\textrm{Expenditure}: \Omega \times \mathcal{R}_+ \to \mathcal{R}_+
b, \omega \longmapsto R(b, \omega) = \begin{cases} 0 & \text{if } \omega = \textrm{Homeless} \\ \tau(b) & \text{if } x = \textrm{Housed} \end{cases}
\textrm{Revenue}: \Omega \times \mathcal{R}_+ \to \mathcal{R}_+
b, \omega \longmapsto Q(b, \omega) = \begin{cases} b & \text{if } \omega = \textrm{Homeless} \\ 0 & \text{if } \omega = \textrm{Housed} \end{cases}

Homelessness Reading Group

By Patrick Power

Homelessness Reading Group

Presentation of Igor Popov's paper: Homeless Programs and Social Insurance

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