11footnotetext: School of Economics, The University of
Queensland22footnotetext: Corresponding author:
<EMAIL_ADDRESS>Centre for the Business and
Economics of Health, The University of Queensland

###### Abstract

Housing expenditure tends to be sticky and costly to adjust, and makes up a
large proportion of household expenditure. Additionally, the loss of housing
can have catastrophic consequences. These specific features of housing
expenditure imply that housing stress could cause negative mental health
impacts. This research investigates the effects of housing stress on mental
health, contributing to the literature by nesting housing stress within a
measure of financial hardship, thus improving robustness to omitted variables
and creating a natural comparison group for matching. Fixed effects (FE)
regressions and a difference-in-differences (DID) methodology are estimated
utilising data from the Household Income and Labour Dynamics in Australia
(HILDA) Survey. The results show that renters who are in housing stress have a
significant decline in self-reported mental health, with those in prior
financial hardship being more severely affected. In contrast, there is little
to no evidence of housing stress impacting on owners with a mortgage. The
results also suggest that the mental health impact of housing stress is more
important than some, but not all, aspects of financial hardship.

##  1 Introduction

A frequent research finding is that lower socioeconomic status is associated
with higher rates of common mental health disorders, suggesting prima facie
that living and working in lower socioeconomic environments can lead to poor
mental health outcomes (Dohrenwend et al., 1992; Lorant et al., 2003). A
prominent explanation is that disadvantaged environmental circumstances can
cause chronic arousal of stress pathways, with physiological disregulation
increasing the risk of developing mental illness (Tafet & Bernardini, 2003;
Fisher & Baum, 2010). Although a number of socioeconomic factors, such as
poverty, low eduction, unemployment, and housing circumstances, are associated
with poor mental health, the highly correlated nature of socioeconomic
variables makes causal pathways hard to identify (Fuchs, 2004). This research
investigates the effects of housing stress on mental health. It contributes to
the literature by nesting housing stress within a measure of financial
hardship, allowing for a natural comparison group, and therefore increasing
robustness to omitted variables and reverse causality.

Housing is a commonly investigated social determinant of health, with some
researchers hypothesising that the experience of housing stress, where housing
costs become overly burdensome on individual finances, can lead to declines in
mental health, contributing towards the observed socioeconomic gradient in
mental health (Bentley et al., 2011; Reeves et al., 2016). The economic
features of housing expenditure means it has a particularly strong influence
on personal finances, especially for those with limited resources. Housing
costs make up a large proportion of total expenditure for most lower income
individuals, and actions taken to reduce this expenditure can involve large
adjustment costs. Additionally, housing is a necessity and, thus, the loss of
housing can have catastrophic consequences.

Previous research investigating the effect of housing stress on mental health
has tended to find that unaffordable housing leads to small but significant
declines in mental health (Mason et al., 2013; Bentley et al., 2011). However
the challenges of reverse causality and omitted variables suggest there are
limitations to these results. Reverse causation is a concern as it is highly
plausible that individuals with declining mental health are more prone to
financial difficulties, including housing stress. This could occur, for
example, if mental health declines are associated with more erratic or
impulsive behaviour, which in turn increases the probability of experiencing
housing stress. Omitted variables are a challenge for any observational
setting and especially when investigating housing stress, as many
socioeconomic variables are highly correlated (Fuchs, 2004). One concern is
that the literature on housing stress tends to omit financial hardship from
the analyses, despite financial hardship and mental health having strong
associations (Fryers et al., 2003; Butterworth et al., 2009). If results are
based on a fixed effects (FE) regressions alone, the predominant methodology
used in this research area, then they could be prone to bias in the presence
of omitted variables and reverse causality.

A further complication encountered in this line of research is how housing
stress should be measured. Although there is no general consensus on this
issue, many researchers opt to use threshold based indicators to identify if
an individual or household is under housing stress (Nepal et al., 2010). For
example, a common approach is to define housing stress as a household or an
individual spending more than 30 percent of their income on housing (Baker et
al., 2020; Mason et al., 2013; Bentley et al., 2011). This definition may or
may not be combined with another threshold that limits housing stress to
households or individuals in the lower part of the income distribution,
commonly the bottom 40 percent. These threshold type measures are useful
policy variables for describing the prevalence of housing stress, and may be
easily understood in public debate. However, using these definitions for
empirical research at the individual level can be problematic. This is because
small changes around the thresholds could have an undue influence on the
results, especially when within variation alone is used to identify the effect
of housing stress. If we consider housing stress to be a latent variable,
missing housing payments are likely to be a strong signal of circumstances
where housing costs are overly burdensome on personal finances. This seldomly
utilised measure is a more direct signal of housing stress than threshold
based financial indicators.

This research classifies individuals that are unable to make rental or
mortgage payments on time due to a shortage of money as being in housing
stress. That is, housing stress is considered as a specific form of financial
hardship. Accordingly, in the empirical analysis, we can differentiate between
individuals experiencing other forms of financial hardship without housing
stress, and those experiencing financial hardship with housing stress. As the
former is more comparable to the latter than, say, those not experiencing any
financial hardship, it provides a natural comparison group. This lends itself
to a DID framework where those experiencing housing related and non-housing
related financial hardship are the treatment group, and those experiencing
non-housing related financial hardship only are the control group.
Additionally, this research conducts FE regressions that account for both
housing stress and financial hardship, a potential omitted variable in other
papers.

This research is performed using longitudinal data from Australia, where
modest government housing assistance payments, a limited supply of public
housing options, and a relatively high exposure to private rental markets may
increase the mental health impacts of housing stress (Bentley et al., 2016).
In Australia, the price-to-income ratio of housing has increased 78 percent
between 1980 to 2015, and over the past two decades housing ownership rates
have decreased from 70 percent to 66 percent of households (Hall & Thomas,
2016). Over the same period, the proportion of households living in public
housing has reduced from just under 6 percent to around 3 percent, and the
households renting in the private rental market has increased from 20 percent
to 27 percent (ABS, 2019). Housing is now the largest item of household
expenditure, with lower-income households most affected.111Lower-income
households are defined as the 38 percent between the $3^{rd}$ and $40^{th}$
percentiles of equivalised disposable households income. For these lower
income households, 57 percent of private renters and 41 percent of owners with
a mortgage allocate more than 30 percent of their gross income to housing
expenditure (ABS, 2019).

Using longitudinal data from the Household Income and Labour Dynamics in
Australia (HILDA) Survey, this research finds that renters in prolonged
financial hardship are most impacted by housing stress. Using FE regressions,
renters are found to have a $0.18$ standard deviation decline in self reported
mental health when in housing stress, compared to having financial hardship
without housing stress. The DID estimates reveal that renters in two previous
periods of financial hardship that are exposed to housing stress have a 0.2
standard deviation decline in their mental health score, compared to similar
individuals not exposed to housing stress. The results differ by tenure, with
little or no effect found on mental health for mortgagors in housing stress,
consistent with other research findings (Mason et al., 2013). The results also
suggest that the mental health impact of housing stress is more important than
some, but not all, aspects of financial hardship.

##  2 Economic Aspects of Housing Expenditure

Housing makes up the largest proportion of household expenditure, which tends
to be sticky and costly to adjust. These characteristics help explain why
housing stress could impact on mental health. The ABS Household Expenditure
Survey 2015-16 shows that housing makes up an average of 20 percent of
household spending, more than any other category (ABS, 2017).222Housing costs
consist of rent, interest payments on mortgages, rates, home and content
insurance, repairs and maintenance. This proportion is even larger for
households in the lower income or wealth quintiles. For individuals that enter
into financial hardship, reducing the largest aspect of expenditure would be a
logical course of action, however this can be complicated by high adjustment
costs, making it hard to reduce housing expenditure at the margin.

The high adjustment costs associated with housing expenditure can be
exacerbated by the nature of housing products as relatively indivisible and
subject to long-term contracts. Housing is commonly subject to long-term
contracts, either mortgages or leases, that lock in expenditure commitments
into the future, either reducing the opportunities to move to cheaper
alternatives, or increasing the cost of doing so. Additionally, housing is a
relatively indivisible, or discrete product, that tends to be purchased as a
whole by household units, further limiting expenditure adjustment
opportunities, especially in the short-run. Sub-letting or sharing
accommodation can reduce housing expenditures, however these too have their
own adjustment and ongoing costs.

High adjustment costs can be seen as either direct or indirect. The direct
costs are related to the actual event of moving. Besides the direct monetary
costs, such as hiring a vehicle for moving furniture, there are also numerous
time costs involved, such as searching for accommodation or packing
possessions. These direct costs are higher for owners, who normally pay
additional taxes, legal and agent fees. The indirect costs related to a move
can be ongoing. For example, moving could require new employment with no
guarantee of the same wage, or increased transportation costs if moving
further away from a workplace. Welfare costs can also be high when moving if
an individual has strong local connections to friends, family, educational
institutions or other organisations in the community.

Large housing expenditures combined with high adjustment costs are likely to
make housing particularly salient for individuals in financial hardship.
Additionally, the loss of housing can have catastrophic consequences. Not
being able to meet housing expenditure commitments can be particularly serious
when combined with other risk factors for homelessness, such as thin social
support networks, limited earning capacity, exposure to domestic violence, or
pre-existing mental or substance abuse disorders (Morrell-Bellai et al.,
2000). These features of housing expenditure imply that housing stress could
have significant negative impacts on mental health.

##  3 Literature Review

Regression has been the most frequently employed technique to investigate the
effect of housing stress on mental health. However, the potential for omitted
variable bias and reverse causality lead to caution interpreting some results.
Reeves et al. (2016) is an exception in the literature, utilising a quasi-
experimental methodology that is able to address these concerns. The study
uses a policy change in the U.K. that reduced the housing benefit paid to low
income private renters, as an exogenous shock to investigate the impact of
less affordable housing on depressive symptoms. The housing benefit
expenditure is the second largest welfare payment in the U.K., and the 2011
policy change was a sizeable reduction of £1,220 per year.333This benefit
reduction made up the largest individual contribution to budgetary savings
amidst a range of austerity measures. Using a repeated cross section from the
Annual Population Survey and a DID methodology, the effect of the policy
change was a 1.8 percentage point increase in the probability of self-reported
depressive symptoms by the benefit recipients, compared to individuals not
receiving the benefit.444These results were robust to modelling choices, with
similar results found using interrupted time-series analysis, and matching
methods.

The more common approach in the literature is to combine longitudinal data
with a FE methodology. This reduces omitted variable bias by removing time-
invariant factors. Bentley et al. (2011) uses FE regressions to investigate
the effect of unaffordable housing on mental health using data from the HILDA
Survey. This finds that unaffordable housing causes small but significant
decreases in self-reported mental health for individuals in the lower part of
the income distribution when they transition into unaffordable
housing.555Variables controlled for were age, equivalised disposable household
income, and moving from one house to another. This mental health decline was
not seen for individuals in higher income households. Mason et al. (2013) also
uses a FE framework to investigate how the relationship between housing stress
and mental health differs by tenure. Their results show that renters are more
exposed than owners to the effects of unaffordable housing. Bentley et al.
(2016) uses FE regressions to investigate if the effect of housing stress on
mental health differs based on the housing context across nations. Using
longitudinal data from the U.K. and Australia, they find evidence that in the
U.K. renters are offered some protection against the effects of unaffordable
housing. The research of Baker et al. (2020) uses both within and between
variation to allow for inclusion of initial mental health status when
considering the effect of prolonged exposure to unaffordable housing.
Prolonged exposure is found to be significant, with the effect size larger in
magnitude compared to intermittent exposure.

Besides the use of panel regression methods, Bentley et al. (2011), Mason et
al. (2013) and Baker et al. (2020) also employ a threshold approach to
measuring housing stress, where individuals are considered to be in housing
stress if they spend more than 30 percent of their income on
housing.666Commonly gross income used, however there is no agreed income
measure for this threshold. This housing expenditure threshold is usually
combined with an income threshold to reflect that spending a high proportion
of income on housing is likely to create a greater burden for lower income
earners. For example, Bentley et al. (2011) uses a 30 percent threshold for
housing costs and tests for heterogeneity based on income thresholds. Mason et
al. (2013) also employs a 30 percent threshold, and only analyses individuals
in the lower 40 percent of the income distribution. The approach used by Mason
et al. (2013) is known as the 30/40 rule definition of housing stress (Nepal
et al., 2010). Although this rule is commonly used for policy discussion on
housing affordability, especially in Australia, its arbitrary thresholds
create limitations when used in research. This is especially the case when
using FE models, where small variations around a threshold over time can make
a disproportionately large contribution to parameter estimates. One solution
is offered by Taylor et al. (2007), which uses survey responses regarding
problems with making mortgage or rental payments, and being more than two
months behind on payments, as proxies for unsustainable housing commitments.

Bentley et al. (2011), Mason et al. (2013) and Baker et al. (2020) all aim to
isolate the effect of housing stress on mental health after controlling for
household income, however do not control for financial hardship. If financial
hardship also causes mental health declines, and if it is positively
correlated with housing stress, then it too should be included, or the effect
of housing stress will be overstated.

A separate stream of the literature has found that financial hardship is
associated with mental health declines. Fryers et al. (2003) conducts a review
of this literature and finds that material circumstances are a marker of
increased rates of common mental disorders. The researchers consider a number
of indicators of common mental health disorders using a meta-analysis and find
that material circumstances, along with education and employment, are the
strongest markers. Butterworth et al. (2009) looks directly at financial
hardship indicators using the Personality and Total Health (PATH) Through Life
Study. Using logistic regression of the second wave of the survey, and
controlling for demographics, socioeconomic status, and prior depressive
symptoms, the research finds a strong association between financial hardship
and depression. Kahn & Pearlin (2006) also considers the effect of financial
hardship on health, both physical and mental. Considering a sample of adults
aged over 65 years and relying on recall of life experiences, they find that
past financial hardship significantly determines a number of health outcomes,
including depression, with persistence of hardship found to be particularly
important. Kiely et al. (2015) considers the effects of financial hardship on
self-reported mental health, utilising the financial hardship indicators in
the HILDA Survey. Its results from a series of logistic regressions are
consistent with deprivation related hardship increasing the risk of mental
health problems, with less predictive power associated with income poverty.

The economics literature is well known for employing natural experiments and
other causal approaches to address issues of endogeneity, and while there are
contributions to investigating the effects of housing and location on mental
health, housing stress has not specifically been addressed. Cattaneo et al.
(2009) provides evidence that housing quality improvements affect physical and
mental health outcomes. The research analyses a government program in Mexico
that replaced dirt with cement floors, taking advantage of variation in the
timing of the program roll-out for identification. They find housing quality
interventions improved the mental health of adults. In the Moving to
Opportunity study, Kling et al. (2007) considers how neighbourhood effects can
impact on mental health. Endogenous neighbourhood selection is overcome by
using data from a randomised experiment where families in high-poverty U.S.
housing projects are offered vouchers to move to lower-poverty neighbourhoods,
with the results finding mental health benefits for adults, but mixed results
for youth.

To summarise, research investigating the effects of housing stress on mental
health commonly omits financial hardship and employs threshold based financial
indicators to measure housing stress. This research focus on these potential
limitations and employs commonly used econometric techniques to address
robustness concerns. These techniques are outlined in the next section.

##  4 Identification

The following section outlines the identification strategy for estimating the
effect of housing stress on mental health, compared to non-housing related
financial hardship alone, with the key concept being a nesting of the housing
stress measure within the financial hardship measures. Previous research
commonly tries to find the effect of housing stress independent of financial
circumstances, using income to control for financial circumstances (for
example, Bentley et al. (2011)). However, in contrast to income, financial
hardship indicators directly assess the impact of financial resources on life
events, and have been found to be associated with mental health (Butterworth
et al., 2009). Excluding financial hardship from the mental health equation
could upwardly bias the magnitude of the housing stress parameter, given
financial hardship is positively correlated with housing stress, and
negatively correlated with mental health.777This assumes that larger values
indicate better mental health.

This research considers several types of financial hardship, with housing
stress being one of them. Therefore, if an individual is in housing stress, by
construction they must also be in financial hardship. This set-up is more
robust against omitted variable bias, as it both accounts for financial
hardship as an independent variable, and provides a natural comparison group,
where individuals in housing stress are compared to those in financial
hardship without housing stress.

The two models outlined below are estimated separately for owners with a
mortgage and private renters, informed by previous research that has found
differences based on tenure (Mason et al., 2013). The baseline FE
specification is first discussed, followed by the dynamic DID estimator.

###  4.1 Baseline Model

Consider the following equation that models mental health, $MH_{it}$, for each
individual $i$ in time period $t$, as a function of housing stress:

$\displaystyle
MH_{it}=\alpha_{i}+\lambda_{t}+\tau\cdot\mbox{HousingStress}_{it}+X_{it}^{\prime}\beta+\epsilon_{it}\;,$
(1)

where $\mbox{HousingStress}_{it}$ is an indicator equal to one if $i$ is in
housing stress at time $t$; $\alpha_{i}$ is an individual specific FE;
$\lambda_{t}$ is a time specific FE; $X_{it}$ is a vector of control variables
that consists of equivalised disposable household income, the employment
status (full-time, part-time, or otherwise888This category is defined as
unemployed or not in the labour force.), a measure of physical health (the
SF-36 Physical Component Summary (PCS) lagged one period), and dummy variables
indicating the quintile of disadvantage of the neighbourhood where the
individual lives; $\epsilon_{it}$ is a random error term.

Equation (1) assumes that mental health is directly impacted by housing
stress, with the impact of financial resources fully accounted for by income.
However, as discussed earlier, if financial hardship has a direct impact on
mental health after accounting for income, then $\tau$ could be bias.
Financial hardship is therefore added to equation 1, incorporating the nested
structure of housing stress within financial hardship:

$\displaystyle
MH_{it}=\alpha_{i}+\lambda_{t}+\theta\cdot\mbox{Hardship}_{it}+\tau\cdot\mbox{HousingStress}_{it}+X_{it}^{\prime}\beta+\epsilon_{it}\;.$
(2)

$\mbox{Hardship}_{it}$ is an indicator variable equal to one if $i$ is in
financial hardship at $t$ and zero otherwise, and $\mbox{HousingStress}_{it}$
is now equivalent to the interaction term
$(\mbox{Hardship}_{it}\times\mbox{HousingStress}_{it})$. These are equivalent
because if $\mbox{HousingStress}_{it}=1$, this implies that
$\mbox{Hardship}_{it}=1$.

Equation (2) is a two-way FE model that can be estimated from panel data with
$N$ individuals and $T$ time periods using standard methods. The estimation of
coefficients using within variation alone allows for individual specific,
time-invariant omitted variables to be correlated with the dependent
variables. The null hypothesis of $\tau=0$ tests if housing stress has
additional effects compared to non-housing related financial hardship alone,
and can be tested with a t-test using cluster robust standard errors,
clustering on the individual. For consistent estimation of the housing stress
coefficient $\tau$, strict exogeneity is required. This could be seen as
reasonable, as equation (2) accounts for financial hardship, a number of
control variables, and time-invariant factors, although the assumption would
not hold if there was reverse causality from mental health to housing stress.

The uncertainty of the strict exogeneity assumption required for consistent FE
estimates motivates a complementary DID methodology. This framework has the
advantages of incorporating explicit matching based on treatment and pre-
treatment periods, and allowing for the key identification assumption to be
testable. Additionally, it allows us to explore heterogeneous effects from
housing stress, based on prior financial hardship experience.

###  4.2 Matched Difference-in-differences

To assess the additional effect of housing stress on mental health, compared
to non-housing related financial hardship alone, the ideal experiment would
randomly assign individuals in non-housing related financial hardship to
receive either housing stress (the treatment group) or no housing stress (the
control group). Given data from treatment and control groups in the pre- and
post-treatment periods, the average treatment effect (ATE) of housing stress,
compared to non-housing related financial hardship alone, could be estimate
using a number of methods, including a standard DID equation.999A number of
methods are appropriate due to the random allocation of the treatment.

To replicate this ideal experiment as closely as possible, this research
proceeds by using a matching method. Individuals observed over three
consecutive periods, with housing stress and non-housing related financial
hardship in the third period, are considered as candidates for the treatment
group. Similarly, individuals observed over three consecutive periods, with
non-housing related financial hardship in the third period but no housing
stress, are considered as candidates for the control group. The last of the
three periods is referred to as the event (in reference to the event-studies
literature), and an event time $t$ is constructed such that the event occurs
at $t=0$. The two periods prior to the event, occurring at $t=-1$ and $t=-2$,
are referred to as the pre-treatment time periods (consistent with DID
terminology).

Based on financial hardship in the pre-treatment periods, candidate
individuals are allocated into matched subgroups. Specifically, the Low
financial hardship group has no financial hardship in the pre-treatment
periods, $t=-2$ and $t=-1$; the Moderate financial hardship group has non-
housing related financial hardship at $t=-1$, but not at $t=-2$; and the High
financial hardship group has two periods of non-housing related financial
hardship in the pre-treatment periods, $t=-1$ and $t=-2$.

Within the same subgroup, some individuals have multiple candidates. When this
is the case, only one set of three observations are kept based on two rules.
First, if the individual is a candidate for both treatment and control groups,
they are allocated to the treatment group only. Second, if the individual has
multiple sets of three observations, only the first set of three observations
(i.e. earliest based on calendar year) is selected.

This matching method is valid under the assumption that individuals in housing
stress and non-housing related financial hardship are similar to individuals
in non-housing related financial hardship alone, given the same prior
financial hardship experience. If this assumption is valid, the control group
can be used to form counterfactuals for the treatment group, and the
additional effect of housing stress can be estimated. These effects can be
heterogeneous based on prior financial hardship experience (i.e. based on the
subgroup) and estimated using a dynamic DID estimator, with a test for
parallel trends equivalent to testing the validity of the matching procedure.

More formally, for individual $i$ in (time invariant) group
$g\in\\{\mbox{Treat},\mbox{Control}\\}$, at event time $t$, unconfoundedness
is assumed in the following form:

$\displaystyle\mathbb{E}[MH_{igt}(0)|\alpha_{g},\boldsymbol{D_{g}},\boldsymbol{X_{i}},\mbox{Hardship}^{\prime}=h]=\mathbb{E}[MH_{igt}(0)|\alpha_{g},\boldsymbol{X_{i}},\mbox{Hardship}^{\prime}=h]$
$\displaystyle\mathbb{E}[MH_{igt}(1)|\alpha_{g},\boldsymbol{D_{g}},\boldsymbol{X_{i}},\mbox{Hardship}^{\prime}=h]=\mathbb{E}[MH_{igt}(1)|\alpha_{g},\boldsymbol{X_{i}},\mbox{Hardship}^{\prime}=h]$

where $MH_{igt}^{(h)}(0)$ and $MH_{igt}^{(h)}(1)$ are the potential outcomes
under the control and treatment event respectively; $\boldsymbol{D_{g}}$
represents the history of housing stress such that
$\boldsymbol{D_{g}}=\\{D_{g,-2},D_{g,-1},D_{g,0}\\}$, where $D_{g,t}$ is equal
to one if individual $i$ with $g=\mbox{Treat}$ is in $t=0$, and zero otherwise
(this amounts to $D_{Treat}=\\{0,0,1\\}$ and $D_{Control}=\\{0,0,0\\}$); the
vector $\boldsymbol{X_{i}}$ represents the history of control variables such
that $\boldsymbol{X_{i}}=\\{X_{i,-2},X_{i,-1},X_{i,0}\\}$, and $\alpha_{g}$ is
a group specific FE that captures time-invariant differences between treatment
and control groups. The variable $\mbox{Hardship}^{\prime}$ represents the
history of financial hardship that the entire subsample is conditioned on,
such that $h\in\\{\\{0,0,1\\},\\{0,1,1\\},\\{1,1,1\\}\\}$. The remaining
notation suppresses the conditioning on $h$, instead using a superscript $(h)$
to indicate dependence on the subsample.

The treatment effect is assumed to be additive such that

$\displaystyle\mathbb{E}[MH_{igt}^{(h)}(1)|\alpha_{g},\boldsymbol{X_{i}}]=\mathbb{E}[MH_{igt}^{(h)}(0)|\alpha_{g},\boldsymbol{X_{i}}]+\tau_{t=0}^{(h)}$

where $\tau_{t=0}^{(h)}$ is the heterogeneous treatment effect equal to a
constant $\tau^{(h)}$ at event time $t=0$, and zero otherwise.101010In the
additive treatment effect equation, conditioning on treatment status is not
required because unconfoundedness is assumed.

Fundamental to the potential outcomes framework is that both potential
outcomes cannot be observed, only $MH^{(h)}_{igt}=(1-D_{gt})\times
MH^{(h)}_{igt}(0)+D_{gt}\times MH^{(h)}_{igt}(1)$. Then

$\displaystyle\mathbb{E}[MH_{igt}^{(h)}|\alpha_{g},\boldsymbol{D_{g}},\boldsymbol{X_{i}}]=\mathbb{E}[MH_{igt}^{(h)}(0)|\alpha_{g},\boldsymbol{X_{i}}]+\tau^{(h)}D_{igt}.$

Making the following functional form assumption

$\displaystyle\mathbb{E}[MH_{igt}^{(h)}(0)|\alpha_{g},\boldsymbol{X_{i}}]=\alpha_{g}^{(h)}+\lambda_{t}^{(h)}+X_{it}^{\prime}\beta^{(h)},$

the conditional expectations function can be written as

$\displaystyle\mathbb{E}[MH_{igt}^{(h)}|\alpha_{g},\boldsymbol{D_{g}},\boldsymbol{X_{i}}]=\alpha_{g}^{(h)}+\lambda_{t}^{(h)}+X_{it}^{\prime}\beta^{(h)}+\tau^{(h)}D_{igt}\,.$
(3)

Equation (3) assumes a common trend is followed by all individuals,
represented by $\lambda^{(h)}_{t}$. This follows directly from the
unconfoundedness assumption and is equivalent to the parallel trends
assumption in a DID framework. Equation (3) can be modified to include
separate trends for the treatment and control groups to assess parallel trends
via visual inspection and hypothesis testing. Thus, estimation of equation (3)
is given by the dynamic DID model

$\displaystyle\begin{split}MH_{it}^{(h)}=\,&\alpha_{1}^{(h)}\,+\alpha_{2}^{(h)}\cdot\mbox{Treat}_{i}\,+\,\gamma_{1}^{(h)}\cdot\mathbbm{1}[t=-1]\,+\,\gamma_{2}^{(h)}\cdot\mathbbm{1}[t=-1]\cdot\mbox{Treat}_{i}\\\
&+\,\delta^{(h)}\cdot\mathbbm{1}[t=0]\,+\,\tau^{(h)}\cdot\mathbbm{1}[t=0]\cdot\mbox{Treat}_{i}\,+\,X^{\prime}_{it}\beta^{(h)}\,+\,\epsilon_{it}\;,\end{split}$
(4)

where $\mbox{Treat}_{i}$ is an indicator variable equal to one if individual
$i$ is in the treatment group, and zero if in the control group; and
$\mathbbm{1}[t=s],\,s\in\\{-2,-1\\}$ is a time dummy equal to one when $t=s$
and zero otherwise. To account for any time effects from the calendar year
when the event occurs, event time FEs are added as additional control
variables to $X_{it}$.

As all individuals in the control group experience financial hardship at
$t=0$, this effect is fully captured by $\delta^{(h)}$. The parameter
$\tau^{(h)}$ represents the additional effect of housing stress, compared to
individuals that have only non-housing related financial hardship. Equation
(4) can be estimated using least squares with cluster robust standard errors,
clustering on the individual.

The parallel trends assumption can be inspected visually, and tested
explicitly with a t-test under the null hypothesis $\gamma_{2}^{(h)}=0$;
evidence of a non-zero coefficient corresponds to a rejection of the parallel
trends assumption.

##  5 Data

The longitudinal data used for the analysis is from the HILDA Survey, an
ongoing representative survey of Australian households that has been conducted
annually since 2001. The survey collects detailed information based around the
broad areas of income, labour and family dynamics, and includes information on
health status and housing. Table 1 provides summary statistics for the
variables used in this research. The summary statistics are for the years 2001
and 2019, the first and last cross sections of the panel, and includes all
responding adults in the sample.111111To maintain the representativeness of
the survey, a top-up sample was added in wave 11, accounting for the increased
number of observation in 2019 compared to 2001. Adults are considered aged 15
years and over. A responding adult is someone from a responding household that
completes an interview.

From Table 1, we see that in 2001 around 72 percent of sample respondents had
ownership of their place of residence (with or without a mortgage), while 26
percent were renters. Ownership rates in 2019 are lower, down to 66 percent,
while the proportion of renters increases to 31 percent. Furthermore, the
increasing proportion of renters is associated with increased participation in
the private rental market (that is, renting from a private landlord),
increasing from 20 percent in 2001 to 27 percent in 2019, while those renting
from a public housing authority decreased from 4 percent to 3 percent over the
same period. These patterns are consistent with that reported from Survey of
Income and Housing (SIH) conducted by the Australian Bureau of Statistics
(ABS, 2019).121212For example, the SIH shows, from 1997-8 to 2017-18, private
renters increased from 20 percent to 27 percent, and ownership fell from 70
percent to 66 percent, as discussed in Section 1.

The two mental health measures used as dependent variables for the analysis
are shown in Table 1: These are the Mental Component Summary and the Mental
Health Scale, both of which are derived from the Short Form-36 (SF-36) Survey.
The SF-36 is an internationally recognised tool for assessing an individual’s
functional health status and well-being. It has been found to produce valid
and reliable results at both clinical and population levels, and is collected
in each wave of the HILDA Survey (ABS, 1997). Aggregating responses from five
of the thirty-six questions related to mental health provides one of eight
aggregate scales, the Mental Health Scale131313The Mental Health Scale is
transformed to range from 0 - 100.. These eight aggregate scales can be
further summarised into two measures representing the physical and mental
dimensions of health, referred to as the Physical Component Summary (PCS) and
the Mental Component Summary (MCS). The MCS and PCS range from 0-100, have a
standard deviation of 10, and higher values represent better health (see
appendix 9.2 for further details). Due to the common usage, validity and
reliability of the MCS, it is chosen as the primary measure for mental health,
with the Mental Health Scale used for robustness checks.

Table 1: Full Sample Summary Statistics

Year | 2001 | 2019
---|---|---
Variable | N | Mean | SD | N | Mean | SD
Owner | 13969 | 0.72 | 0.45 | 17441 | 0.66 | 0.47
Owner with mortgage | 13969 | 0.31 | 0.46 | 17462 | 0.36 | 0.48
Monthly mortgage payments | 4394 | 1503 | 1160 | 6204 | 2096 | 1750
Renter | 13969 | 0.26 | 0.44 | 17441 | 0.31 | 0.46
Rents from private landlord | 13969 | 0.2 | 0.4 | 17455 | 0.27 | 0.45
Rents from public housing | 13969 | 0.04 | 0.2 | 17455 | 0.03 | 0.18
Monthly rental payments | 3573 | 1051 | 565 | 5495 | 1490 | 838
Financial hardship | 12484 | 0.35 | 0.48 | 15530 | 0.26 | 0.44
Missed housing payments | 12718 | 0.09 | 0.29 | 15707 | 0.06 | 0.23
Could not pay bills | 12848 | 0.19 | 0.39 | 15765 | 0.11 | 0.31
Sold or pawned something | 12772 | 0.07 | 0.25 | 15733 | 0.06 | 0.24
Went without meals | 12783 | 0.05 | 0.21 | 15744 | 0.05 | 0.21
Went without heating | 12762 | 0.04 | 0.19 | 15732 | 0.03 | 0.18
Sort help from friends or family | 12816 | 0.17 | 0.37 | 15767 | 0.13 | 0.33
Sort help from welfare or community organisation | 12787 | 0.05 | 0.23 | 15732 | 0.04 | 0.2
Unable to raise $2000 ($3000) for emergency | 12849 | 0.17 | 0.37 | 15832 | 0.12 | 0.33
Mental component summary | 12323 | 48.59 | 10.4 | 15698 | 47.25 | 11.32
Mental health scale | 12933 | 73.72 | 17.48 | 15987 | 72.18 | 18.23
Physical component summary | 12323 | 49.68 | 10.5 | 15698 | 49.16 | 10.69
Age | 13969 | 43.35 | 17.7 | 17462 | 45.78 | 19.27
Male | 13969 | 0.53 | 0.5 | 17462 | 0.53 | 0.5
Employed full-time | 13969 | 0.42 | 0.49 | 17462 | 0.42 | 0.49
Employed part-time | 13969 | 0.2 | 0.4 | 17462 | 0.21 | 0.41
Neighbourhood quintile of disadvantage | 13969 | 2.94 | 1.44 | 17448 | 3.04 | 1.41
Eqv. household disposable income ($1,000’s) | 13969 | 42.44 | 29.82 | 17462 | 57.61 | 39.58

###  5.1 Sample Data Based on Tenure

Analysis of the HILDA Survey data is performed based on tenure. Specifically,
the data is divided into owners with a mortgage, and renters in the private
rental market. Table 2 shows the summary statistics by tenure for the year
2019. The mean of the two mental health variables are both lower for the
renters compared to owners, with the a mean MCS value of 47.5 for owners, and
44.6 for renters. On average, owners have higher housing costs than renters
with a mean monthly mortgage payment of $2096, compared to monthly rental
payments of $1581. Owners on average have higher incomes, live in less
disadvantaged neighbourhoods, are older, and have slightly lower physical
health.

####  5.1.1 Housing Stress and Financial Hardship Variables

Table 2 shows renters are more likely to be in financial hardship compared to
owners, with 44 percent in hardship compared to 22 percent of owners. This
measure of financial hardship is based on the response to a financial hardship
survey question in HILDA that assesses if individuals are short of money,
combined with a further question assessing their ability to raise emergency
funds.

Specifically, survey participants are first asked Since January did any of the
following happen to you because of a shortage of money? The seven options
survey participants can select are: Could not pay electricity, gas or
telephone bills on time; Could no pay the mortgage or rent on time; Pawned or
sold something; Went without meals; Was unable to heat home; Asked for
financial help from friends or family; and Asked for help from welfare /
community organisations. Multiple options can be chosen from this first
question. The second survey question is Suppose you had only one week to raise
$2000 ($3000 waves nine onwards) for an emergency. Which of the following best
describes how hard it would be for you to get that money? Survey participants
can select one of four responses: I could easily raise the money; I could
raise the money, but it would involve some sacrifices; I would have to do
something drastic to raise the money; I don’t think I could raise the money.

If an individual indicates that any of the seven events in the first question
have occurred, or responds I don’t think I could raise the money to the second
question, they are classified as being in financial hardship.141414Whereas the
first question directly asks about financial hardship events, the the second
question is an indication of financial insecurity. Individuals responding that
they are unable to pay their rent or mortgage on time due to a shortage of
money are classified as being in housing stress, as well as in financial
hardship. Individuals that are not in housing stress, but belonging to any of
the seven other hardship categories, are referred to as being in non-housing
related financial hardship.

The eight financial hardship indicators used for this research, derived from
the two questions discussed above, are identical to the financial stress
experiences collected in the ABS Household Expenditure Survey (HES), except
for the HES collects one extra category regarding non-payment of registration
or insurance.151515The ABS defines financial stress differently to how
financial hardship is defined here, as they combine the questions regarding
financial stress experiences with missing out experiences. These missing out
experiences are not available in the HIDLA Survey.

Figure 1 shows the proportion of renters and owners experiencing each of the
eight financial hardship categories for the year 2019. For both owners and
renters, the most commonly experienced category of financial hardship is
asking for financial help from friends or family; 25 percent of private
renters and 9 percent of owners experienced this hardship. The inability to
pay electricity, gas or telephone bills on time, or to raise money in the case
of an emergency, are also frequently experienced categories. Around 11 percent
of renters in hardship indicate they have missed rental payments due to lack
of money, while 6 percent of owners miss mortgage repayments for the same
reason.

Table 2: Summary Statistics By Tenure, 2019

Tenure | Owners with Mortgage | Private Renters
---|---|---
Variable | N | Mean | SD | N | Mean | SD
Monthly mortgage payments | 6204 | 2097 | 1750 | - | - | -
Monthly rental payments | - | - | - | 4759 | 1581 | 772
Financial hardship | 5572 | 0.22 | 0.41 | 4052 | 0.44 | 0.5
Missed housing payments | 5622 | 0.06 | 0.23 | 4119 | 0.11 | 0.31
Could not pay bills | 5629 | 0.09 | 0.28 | 4137 | 0.2 | 0.4
Sold or pawned something | 5621 | 0.05 | 0.21 | 4124 | 0.12 | 0.33
Went without meals | 5622 | 0.03 | 0.16 | 4125 | 0.09 | 0.29
Went without heating | 5622 | 0.02 | 0.15 | 4118 | 0.06 | 0.23
Sort help from friends or family | 5628 | 0.09 | 0.29 | 4136 | 0.25 | 0.43
Sort help from welfare or community organisation | 5618 | 0.02 | 0.13 | 4122 | 0.08 | 0.27
Unable to raise $2000 ($3000) for emergency | 5662 | 0.08 | 0.28 | 4162 | 0.21 | 0.4
Mental component summary | 5630 | 47.45 | 10.58 | 4166 | 44.61 | 12.14
Mental health scale | 5704 | 72.87 | 17.07 | 4229 | 68.21 | 19.26
Physical component summary | 5630 | 51.67 | 8.77 | 4166 | 50.56 | 10.43
Age | 6204 | 40.48 | 14.49 | 4762 | 36.6 | 15.63
Male | 6204 | 0.51 | 0.5 | 4762 | 0.52 | 0.5
Employed full-time | 6204 | 0.58 | 0.49 | 4762 | 0.49 | 0.5
Employed part-time | 6204 | 0.25 | 0.43 | 4762 | 0.21 | 0.41
Neighbourhood quintile of disadvantage | 6203 | 3.2 | 1.36 | 4761 | 2.88 | 1.41
Eqv. household disposable income ($1,000’s) | 6204 | 67.86 | 40.13 | 4762 | 50.41 | 30.7

Figure 1: Financial Hardship Categories by Tenure, 2019

Notes: Exact questionnaire wording: Since January did any of the following
happen to you because of a shortage of money? Response options: Could not pay
electricity, gas or telephone bills on time; Could no pay the mortgage or rent
on time; Pawned or sold something; Went without meals; Was unable to heat
home; Asked for financial help from friends or family; and Asked for help from
welfare / community organisations. Additional question: Suppose you had only
one week to raise $2000 ($3000 waves nine onwards) for an emergency. Which of
the following best describes how hard it would be for you to get that money?
Response: I don’t think I could raise the money.

Figure 2: Severity of Financial Hardship, 2019

Notes: Uses individuals in financial hardship, 2019. For individuals with a
given level of financial hardship severity, displays the frequency of each
financial hardship category. The sum of all eight financial hardship indicator
variables is used as a proxy for the severity of financial hardship (thus,
eight represents maximum hardship). The two most severe hardship categories
are relatively uninformative and not displayed. Left: Private renters. Right:
Owners with a mortgage.

It is informative to consider how each of the financial hardship categories
are associated with the severity of financial hardship. For individuals
experiencing financial hardship in 2019, Figure 2 uses the total number of
financial hardship categories an individual is in as a proxy for severity, and
shows the frequency of each category by severity. For individuals in mild
hardship (experiencing only one financial hardship category), borrowing money
from friends or family and not being able to raise emergency funds are very
frequent occurrences. It is also rare for renters or owners in mild hardship
to miss housing payments. However, the frequency of missed housing payments
increases substantially for individuals in moderate hardship (experiencing
multiple financial hardship categories).

###  5.2 Matched Subsamples

As detailed in section 4.2, matched subsamples are formed for the DID
analysis, resulting in Low, Moderate, and High subsamples for both owners and
renters. Each sample consists of treatment and control group observations,
where the treatment group has an event of housing stress at $t=0$, and the
control group has an event of non-housing related financial hardship. Figure 3
shows the calendar year these events occur for each matched subsample,
illustrating events occur evenly across calendar years.

Figure 3: Time of Event - Matched Subsamples

Notes: The treatment group has an event of housing stress. The control group
has an event of non-housing related financial hardship. The Low subgroup
requires two preceding periods of no financial stress; the Moderate subgroup
has no financial hardship at $t=-2$, and non-housing related financial
hardship at $t=-1$; the High subgroup has two per-treatment periods of non-
housing related financial hardship.

####  5.2.1 Renters and Owners Matched Subsamples

Tables 3, 4, and 5 show the matched subsamples for renters and owners at event
time $t=-1$, split by treatment status. There are differences in the number of
individuals in each subgroup, with as few as 125 individuals in the Moderate
treatment group for renters, and as many as 1460 in the Low control group for
owners. It is worth noting that it is the number of observations in the
treatment group of each subsample that constrains the number of pre-treatment
periods to two.161616The methodology could easily be adapted to include more
pre-treatment periods, given a larger sample size.

The matching methodology is seen to perform well when we compare the averages
of the matched treatment and control observations. For example, the treatment
and control observations of the Low subgroup for renters have similar mean
values for mental health (MCS), disposable income, physical health (PCS),
quintile of neighbourhood disadvantage, and employment. Between the subgroups
we do see differences. As expected, the presence of non-housing related
financial hardship in the pre-treatment periods is associated with decreases
in the average MCS, along with disposable income and other variables.

Table 3: Summary Statisics - Low Matched Subgroups (t = -1)

Subgroup | Renters: Control | Renters: Treat | Owners: Control | Owners: Treat
---|---|---|---|---
Variable | N | Mean | SD | N | Mean | SD | N | Mean | SD | N | Mean | SD
Mental component summary | 913 | 47.33 | 10.46 | 141 | 47.24 | 11.27 | 1460 | 48.12 | 9.85 | 261 | 48.01 | 10.3
Employed full-time | 913 | 0.51 | 0.5 | 141 | 0.57 | 0.5 | 1460 | 0.56 | 0.5 | 261 | 0.62 | 0.49
Employed part-time | 913 | 0.22 | 0.42 | 141 | 0.23 | 0.42 | 1460 | 0.27 | 0.44 | 261 | 0.2 | 0.4
Neighbourhood disadvantage quintile | 913 | 3 | 1.39 | 141 | 2.94 | 1.54 | 1460 | 3.1 | 1.36 | 261 | 3 | 1.41
Disposable income ($1,000’s) | 913 | 47.21 | 22.14 | 141 | 49.4 | 23.82 | 1460 | 56.26 | 26.14 | 261 | 58.13 | 36.47
Physical component summary | 913 | 51.37 | 9.21 | 141 | 52.05 | 8.47 | 1460 | 51.48 | 8.68 | 261 | 51.03 | 8.43

Table 4: Summary Statisics - Moderate Matched Subgroups (t = -1)

Subgroup | Renters: Control | Renters: Treat | Owners: Control | Owners: Treat
---|---|---|---|---
Variable | N | Mean | SD | N | Mean | SD | N | Mean | SD | N | Mean | SD
Mental component summary | 770 | 45.5 | 11.58 | 125 | 45.67 | 11.36 | 898 | 46.46 | 10.67 | 139 | 44.92 | 12.26
Employed full-time | 770 | 0.39 | 0.49 | 125 | 0.45 | 0.5 | 898 | 0.47 | 0.5 | 139 | 0.55 | 0.5
Employed part-time | 770 | 0.25 | 0.44 | 125 | 0.28 | 0.45 | 898 | 0.3 | 0.46 | 139 | 0.24 | 0.43
Neighbourhood disadvantage quintile | 770 | 2.77 | 1.39 | 125 | 2.61 | 1.34 | 898 | 2.91 | 1.34 | 139 | 2.81 | 1.41
Disposable income ($1,000’s) | 770 | 41.86 | 18.74 | 125 | 43.32 | 17.69 | 898 | 50.06 | 24.38 | 139 | 49.73 | 22.57
Physical component summary | 770 | 50.48 | 10 | 125 | 51.95 | 8.66 | 898 | 51.03 | 9.3 | 139 | 50.75 | 9.58

Table 5: Summary Statisics - High Matched Subgroups (t = -1)

Subgroup | Renters: Control | Renters: Treat | Owners: Control | Owners: Treat
---|---|---|---|---
Variable | N | Mean | SD | N | Mean | SD | N | Mean | SD | N | Mean | SD
Mental component summary | 1043 | 43.78 | 11.8 | 466 | 42.74 | 12.4 | 881 | 45.44 | 10.86 | 264 | 44.44 | 11.4
Employed full-time | 1043 | 0.31 | 0.46 | 466 | 0.33 | 0.47 | 881 | 0.39 | 0.49 | 264 | 0.51 | 0.5
Employed part-time | 1043 | 0.25 | 0.43 | 466 | 0.25 | 0.43 | 881 | 0.31 | 0.46 | 264 | 0.23 | 0.42
Neighbourhood disadvantage quintile | 1043 | 2.5 | 1.36 | 466 | 2.47 | 1.27 | 881 | 2.76 | 1.34 | 264 | 2.78 | 1.28
Disposable income ($1,000’s) | 1043 | 37.56 | 17.88 | 466 | 36.98 | 15.28 | 881 | 45.15 | 22.97 | 264 | 47.16 | 21.93
Physical component summary | 1043 | 50.05 | 10.26 | 466 | 48.94 | 10.88 | 881 | 50.55 | 10.13 | 264 | 49.38 | 9.93

##  6 Empirical Results

###  6.1 Baseline Results

The FE models in equation (1) and equation (2) are estimated for both renters
in the private market, and for owners with a mortgage, using the full HILDA
dataset. After removing missing observations, estimation is performed with
12,644 individuals for the owners’ regressions, and 10,046 individuals for the
renters’ regressions. The mental health dependent variable is represented
using the MCS, and the coefficient representing the additional effect from
housing stress, the key variable of interest, is estimated from equation (2).
In order to explore the impact of omitting financial hardship from the mental
health equation, estimations of equation (1) are provided for comparison. To
assess the individual contribution of each financial hardship indicator, FE
regressions of the MCS on each of the eight financial hardship indicators are
also included. Control variables are used in all the regressions, along with
time FEs (using calendar year dummy variables).

The baseline results are presented in Table 6, with the renters’ regressions
in columns (1) to (3), and the owners’ regressions in columns (4) to (6). The
estimated coefficients for equation (1) are presented in columns (1) and (4),
with the estimates for equation (2) in columns (2) and (5). The results for
including each financial hardship variable separately are found in columns (3)
and (6). Cluster robust standard errors are reported in parentheses, with
clustering at the individual level. The R-squared reported relates to the
within variation only (i.e. the variation remaining after the demeaning has
been performed). The F-statistic reported is for the null hypothesis that the
joint effect of all financial hardship variables together is zero.

Table 6: Baseline Regression Results

Dependent variable: Mental Component Summary
---
| Private Renters | Owners with Mortgage
| (1) | (2) | (3) | (4) | (5) | (6)
Housing stress |  $-$2.27∗∗∗ |  $-$1.79∗∗∗ |  $-$1.01∗∗∗ |  $-$1.52∗∗∗ |  $-$0.86∗∗∗ |  $-$0.50∗
| (0.19) | (0.20) | (0.20) | (0.20) | (0.21) | (0.20)
Financial hardship |  |  $-$1.43∗∗∗ |  |  |  $-$1.18∗∗∗ |
|  | (0.13) |  |  | (0.11) |
Could not pay bills |  |  |  $-$0.98∗∗∗ |  |  |  $-$0.61∗∗∗
|  |  | (0.17) |  |  | (0.15)
Sold/pawned something |  |  |  $-$0.85∗∗∗ |  |  |  $-$1.01∗∗∗
|  |  | (0.22) |  |  | (0.24)
Went without meals |  |  |  $-$1.92∗∗∗ |  |  |  $-$1.75∗∗∗
|  |  | (0.28) |  |  | (0.39)
Went without heating |  |  |  $-$1.46∗∗∗ |  |  |  $-$1.02∗∗
|  |  | (0.31) |  |  | (0.37)
Sort help from friends/family |  |  |  $-$0.64∗∗∗ |  |  |  $-$0.82∗∗∗
|  |  | (0.15) |  |  | (0.15)
Sort help from community |  |  |  $-$0.53∗ |  |  |  $-$1.15∗∗∗
|  |  | (0.25) |  |  | (0.35)
Cannot raise emergency money |  |  |  $-$0.97∗∗∗ |  |  |  $-$0.91∗∗∗
|  |  | (0.17) |  |  | (0.19)
Controls | Yes | Yes | Yes | Yes | Yes | Yes
Individual FEs | Yes | Yes | Yes | Yes | Yes | Yes
Year dummies | Yes | Yes | Yes | Yes | Yes | Yes
Individuals | 10046 | 10046 | 10046 | 12644 | 12644 | 12644
Degrees of freedom | 31095 | 31094 | 31088 | 57135 | 57134 | 57128
R-Squared | 0.0118 | 0.0161 | 0.0261 | 0.0045 | 0.0072 | 0.0108
F-Statistic | 142.46 | 134.33 | 53.46 | 60.18 | 83.38 | 27.712
∗p$<$0.05; ∗∗p$<$0.01; ∗∗∗p$<$0.001

Notes: Individual level cluster robust standard errors are reported in the
parentheses. The F-statistic null hypothesis is all financial hardship
variables are jointly zero. R-Squared values are calculated using within
variation only. Control variables used are the natural logarithm of
equivalised household disposable income, employment status (full-time, part-
time, other), a categorical variable for the neighbourhood quintile of
disadvantage of residence, and the first lag of the PCS score. Disposable
income (in constant 2019 dollars) is at the household level and is equivalised
based on the number of members following OECD equivalence weights.

Before focusing on the estimated additional effect from housing stress, it is
first worth noting that most coefficients have the expected sign (refer to
Table 8 in appendix 9.1 for coefficient estimates of the full model, including
the control variables). The effect from full or part-time employment on mental
health is positive compared to the baseline case of no employment; increases
in disposable income and improvements in physical health both have positive
impacts on mental health; while living in a less disadvantaged neighbourhood
tends to have positive impacts, but not necessarily so.

The Housing Stress coefficient is the one of primary interest from Table 6.
Let us first consider the FE estimates for renters. In column (1), when
financial hardship is omitted from the equation, the Housing stress
coefficient is estimated at $-2.27$ and is highly significant.171717The term
highly significant is used for the $0.1$ percent level of significance. Column
(2) includes the financial hardship variable in the regression, reducing the
magnitude of the Housing stress coefficient, however it is still highly
significant. This coefficient is estimated at $-1.79$, and has the following
interpretation: Housing stress leads to a $0.18$ standard deviation decline in
mental health, compared to non-housing related financial hardship alone. Thus,
this is the additional affect of housing stress for an individual already in
(non-housing related) financial hardship. The conversion to standard
deviations uses the Australian population standard deviation for the MCS of
10. The Financial hardship coefficient estimate of $-1.43$ is also highly
significant, and similar, but slightly less, in magnitude to the Housing
stress estimate. This indicates that the coefficient in column (1)
overestimates the effect of housing stress.

Renters in the private rental market that experience housing stress (and
therefore also financial hardship) are estimated to have a total decline in
the MCS of $(1.79+1.43=)\,3.22$ points on average, or $0.32$ standard
deviations. In contrast, the effect on mental health of financial hardship
without housing stress is estimated to be less than half this magnitude.

Despite finding a strong additional effect of housing stress on renters, the
estimated magnitude for owners is much smaller. The FE coefficient on Housing
Stress for owners, shown in column (5), is estimated to be $-0.86$, around
half the magnitude found for renters, although it is still highly significant.
As with renters, the magnitude of the Housing Stress coefficient is dependent
on inclusion or otherwise of Financial hardship; with Financial hardship
omitted from the regression, the Housing Stress coefficient estimate of
$-1.52$ is almost double the magnitude. Interestingly, the impact of financial
hardship is generally smaller in magnitude for owners, with the effect of non-
housing related financial hardship alone estimated to be $-1.18$. The total
effect of housing stress and financial hardship, an estimated
$(0.86+1.18=)\,2.04$ point MCS decline, is less than two-thirds of that found
for renters.

Columns (3) and (5) of Table 6 provide additional information as to the nature
of financial hardship by including each of the eight hardship variables
separately in a FE regression. These parameter estimates give an idea as to
the possible contribution of each individual indicator towards the total
effect of financial hardship on mental health. Interestingly, for renters
(column (3)), while Housing stress is significant, it is not the largest
financial hardship coefficient; the deprivation variables, Went without meals
and Went without heating, are especially large in magnitude. For example, the
estimated coefficient on Went without meals is $-1.92$, compared to $-1.01$
for Housing stress. For owners (column (6)), the Housing stress coefficient is
the smallest of the eight hardship variables, estimated at $-0.50$, while Went
without meals is once again the largest, with an estimate of $-1.75$.

###  6.2 Difference-in-differences for Matched Subsamples

The DID methodology discussed in Section 4.2 attempts to improve the
robustness to omitted variables and reverse causality by incorporating
matching based on multiple periods, and allowing for explicit testing of the
assumptions required for identification. Additionally, it permits us to
investigate the possibility of heterogeneous effects. These results are
summarised in the two-by-three grid presented in Figure 4. The rows
differentiate based on tenure, with renters on the top row and owners on the
bottom row. DID estimates for each tenure are produced for High, Moderate, and
Low subsamples. All individuals in the High subsamples (left column)
experience non-housing related financial hardship prior in the two pre-
treatment periods; all individuals in the Low subsamples (right column) are
free of financial hardship in the two pre-treatment periods; and individuals
the Moderate subsamples have non-housing related financial hardship in one
pre-treatment period only (at $t=-1$). It is hypothesised that non-housing
related financial hardship in the pre-treatment period will increase the
negative effect of housing related financial hardship on mental health,
compared to a pre-treatment period free from financial hardship.

Figure 4: Matched Difference-in-differences Results

Notes: The predicted MCS values plotted are conditional on event time and
treatment group, and at the mean of control variables for the given time
period. The treatment group has housing related financial hardship and non-
housing related financial hardship at $t=0$, whereas the control group has
non-housing related financial hardship only at $t=0$. All individuals in the
High subsamples (left column) experience non-housing related financial
hardship prior in the pre-treatment periods; all individuals in the Low
subsamples (right column) are free of financial hardship in the pre-treatment
periods; and individuals the Moderate subsamples (middle column) have non-
housing related financial hardship in one pre-treatment period only (at
$t=-1$).

The predicted MCS scores in figure 4 are based on OLS estimation of the DID
model in equation (4) for each subsample. The predictions shown are
conditional on a given treatment or control group status and event time
period; the control variables are predicted at the mean for a given time
period, for the all observations in the subsample. Thus, the plots represent
the treatment and control group differences in the estimates of the key
coefficients of interest (see table 9 in appendix 9.1 for the full set of
coefficient estimates). At event time $t=0$, the treatment group (in red)
experiences housing stress in addition to non-housing related financial
hardship, whereas the control group (green) experiences non-housing related
financial hardship only. Differences in the treatment and control group time
trends from $t=-1$ to $t=0$ are attributed to the effect of the treatment,
given identification assumptions hold.

Prior to discussing the causal estimates of housing stress, we first
investigate the validity of the key parallel trends assumptions by examining
the pre-treatment trends from $t=-2$ to $t=-1$. Inspection of Figure 4 show
the trends in the pre-treatment periods are indeed close to parallel for
treatment and control groups in five of the six panels; the exception being
the Low subgroup for renters. The parallel trends assumption can be formally
tested with a t-test of $\gamma_{2}=0$ from equation (4), representing the
null hypothesis that pre-treatment trends are parallel. The results for each
subgroup are in the top row of Table 7, labelled Parallel Trends. The null of
parallel trends is rejected at the 10 percent level of significance for the
Low subsample for renters, with a p-value of $0.08$. However, for the other
five subsamples, the corresponding p-values are large and there is no evidence
to reject the parallel trends assumption.

Table 7: Difference-in-differences Hypothesis Testing

|  | Renters | Owners
---|---|---|---
Test |  |  Low | Mod | High |  Low | Mod | High
Parallel Trends | Estimate | -1.68 | -0.43 | 0.13 | 0.12 | -0.19 | -0.21
| p-value | 0.08 | 0.70 | 0.88 | 0.87 | 0.88 | 0.83
Treatment Effects | Estimate | -2.67 | -3.45 | -2.05 | -0.36 | 0.03 | -0.96
| p-value | 0.02 | 0.00 | 0.02 | 0.66 | 0.98 | 0.31

Notes: All tests are performed with t-tests of equation (4) using individual
level cluster robust standard errors. Parallel trends is tested with a null of
$\gamma_{2}^{(h)}=0$. Treatment effects are tested with a null of
$\tau^{(h)}=0$.

Having shown the appropriateness of the key identification assumption in five
of the six cases, we can focus on the estimated causal effects from the
matched DID, ignoring the Low subgroup results for renters. Visually
inspecting the High subgroup for renters on the top left of Figure 4, the
parallel trends that hold in the pre-treatment periods are seen to diverge
from $t=-1$ to $t=0$, with a greater downward trend in the treatment group.
The estimated DID treatment effects are shown in Table 7. For renters in the
High subgroup, the estimated additional effect of housing related financial
hardship is $-2.05$, which is significant at the 5 percent significance level.

The Moderate subgroup for renters, seen in the top middle panel of figure 4,
also shows the parallel trends deviating from $t=-1$ to $t=0$. However, some
caution is required in interpreting these results as the power to reject the
parallel trends is lower than in the High subgroup. The estimate of
$\gamma_{2}$ for the Moderate subgroup is $-0.43$, with a standard deviation
of $1.13$, compared to an estimate of $0.13$ and standard deviation of $0.84$
for the High subgroup. The larger standard deviation is due to the small
subsample size; as can see in Table 4 and Table 5, there are only $125$
observations in the Moderate treatment group, compared to $466$ observations
for the High treatment group.181818This sample size problem also illustrates
why only two pre-treatment periods are used, as discussed briefly in Section
5.2.1. Therefore, we should be cautious about placing too much weight on the
effect of housing stress in the Moderate subgroup, estimated to be $-3.45$.
However, this result is still qualitatively consistent with a finding that
housing stress has significant effects on renters, especially for those in
prior financial hardship.

The bottom row of figure 4 shows the estimated DID results for owners.
Visually, each panel reveals the trends from $t=-1$ to $t=0$ are similar for
the treatment and control groups. Table 9 shows the treatment effects, which
are estimated to be $-0.36$, $0.03$, and $-0.96$ for the Low, Moderate, and
High subsamples; these estimates are not significantly different from zero.

The results from the DID estimations reveal a consistency with the FE results.
Both methodologies show the impact of housing stress depends on tenure. For
renters, the FE results indicate housing stress has a strong additional effect
on mental health, compared to non-housing related financial hardship alone.
The DID results indicate the same conclusion for individuals who are already
in high financial stress, indicated by non-housing related financial hardship
in the two pre-treatment periods. The estimated additional effect of $-2.05$
is slightly higher than the FE estimate of $-1.79$. For owners, the small
impact reported in the FE regressions is not found in the DID results. This
suggests there is little to no additional impact on mental health of housing
stress for owners.

###  6.3 Robustness

####  6.3.1 Assessing Common Support

The DID results were estimated with matched subgroups based on the matching
rules outlined in Section 4.2. The parallel trends observed in five of the six
panels of Figure 4 provide confidence that the matched treatment and control
groups adequately represent counterfactual outcomes. This is explored further
by considering the similarity between the treatment and control groups based
on observed covariate values. Besides parallel trends, formal proofs of
identification in the DID literature also rely on the so-called common support
assumption (Lechneret al., 2011). Matching methodologies, such as propensity
score matching, typically assess the common support assumption by comparing
distributions of propensity scores between treatment and control groups; the
same assessment is performed on the matched subsamples used in this research.

Figure 5 in the appendix shows the assessment of the common support
assumption, with the rows showing the results for each of the six subsamples.
For a given subsample and event time, the propensity score is estimated for
each observation with a standard logistic regression using the covariates from
the DID analysis.191919The model used to estimate the propensity scores is
$p(W)=logistic(W^{\prime}\theta)$ where $W$ consists of the natural logarithm
of equivalised household disposable income, employment status (full-time,
part-time, other), an indicator for the neighbourhood quintile of
disadvantage, an indicator for the calendar year the event occurs, and the lag
of PCS. The distribution of the predicted propensity scores for the control
and treatment groups is then approximated using histograms, and plotted for
comparability. Each event time period is assessed separately, with the columns
showing event time periods $t=-2,t=-1,$ and $t=0$.

The histograms from Figure 5, representing the probability of being in the
treatment group for each observation, show a high degree of symmetry between
the treatment and control groups. This implies adequate overlap in the
covariate distribution for the treatment and control groups, satisfying the
matching requirement.

Figure 5: Assessment of Common Support Assumption

Notes: The propensity score is the probability of being in the treatment group
for a given event time period, estimated using logistic regression using
covariates: the natural logarithm of equivalised household disposable income,
employment status (full-time, part-time, other), an indicator for the
neighbourhood quintile of disadvantage, an indicator for the calendar year the
event occurs, and the lag of PCS. Disposable income (in constant 2019 dollars)
is at the household level and is equivalised based on the number of members
following OECD equivalence weights.

####  6.3.2 Alternative Dependent Variable

The sensitivity of the FE and DID results to the choice of dependent variable
is also assessed. An alternative outcome measure is available from the SF-36
called the mental health scale. The mental health scale is a narrower measure
of mental health compared to the MCS. It is constructed from summing the
responses to five mental health questions asked in the SF-36, and transforming
the scale to range from 0 to 100. The MCS represents a broader measure of
mental health as it weights responses to additional questions regarding
vitality, social functioning, and role limitations due to emotional
functioning.

Using the mental health scale as the dependent variable, the results are re-
estimated, with the robustness results for the FE regressions provided in
Table 11 in the appendix, and the DID results in figure 6 and Table 12, also
in the appendix. The FE results show a similar direction, magnitude, and
significance as the main reported results. The coefficient magnitudes can be
compared using the mental health scale population standard deviation for
Australia of 16.96 (ABS, 1997). For example, using the mental health scale the
total effect of housing stress for renters is a $0.28$ standard deviation
decline, compared to a $0.32$ standard deviation decline found in the main
results.

Figure 6 shows a consistency with the main DID results. Visually, the Low
subgroup for rents once again does not meet the parallel trends assumption,
and caution is also required for the High and Moderate subgroups for owners.
Despite these precautions, the qualitative results are very similar to the
main DID findings; there is evidence of an additional effect on mental health
from housing stress for renters with financial hardship in the pre-treatment
periods, but little evidence of housing related effects for owners.

##  7 Discussion

###  7.1 Interpretation of Results and Limitations

The FE results have estimated the additional effect of housing stress on
mental health, compared to non-housing related financial hardship alone, after
controlling for income, employment, physical health, neighbourhood effects,
and individual and time FEs. The estimation of equation 2 found a decline of
$0.18$ standard deviations in the MCS. We saw in the FE regressions that
financial hardship also had an impact on mental health, and omitting this
variable biases the magnitude of the Housing stress coefficient upwards. This
highlights the importance of including financial hardship when estimating the
effect of housing stress. The DID framework explicitly matched on financial
hardship experience over multiple periods and allowed for testing of the key
identification assumption (that of parallel trends). There is reassurance that
two different methodologies produce similar conclusions.

The results from the FE regressions suggest the effect on mental health from
housing related financial hardship depends on tenure, with renters more
severely impacted than owners. The DID results suggest that the individuals
most affected by housing stress are renters already exposed to financial
hardship, and owners could be unaffected. These differences based on tenure
could be explained by income and wealth differences. In the sample used for
analysis, owners have higher median incomes, with equivalised disposable
household incomes almost $12 thousand more than renters in 2018.202020The
median of equivalised disposable income across the entire sample in 2018 is
$49 thousand. The median net wealth for a renter is $66 thousand in 2018,
compared to $919 thousand for owners. Owners with missed mortgage repayments
still have a median net wealth of $432 thousand, multiple times more than the
median for renters.212121It is worth noting that owners are on average four
years older than renters, however this can only explain some of these
differences. Considering income and wealth disparities by tenure, there are
likely to be more serious implications for renters in housing stress, compared
with owners.

Although the results suggest renters face additional mental health impacts
from housing stress, they do not necessarily mean that housing stress has a
larger impact than other aspects of financial hardship, despite the specific
features of housing expenditure discussed earlier. The FE regressions found
that non-housing related financial hardship also has significant negative
impacts on mental health. Additionally, a regression that simply adds each of
the eight categories of financial hardship as separate variables suggests all
aspects of financial hardship impact on mental health, and that deprivation,
such as going without meals or heating, could have a larger impact than
housing stress. Further conclusions are limited by the simultaneous nature by
which financial hardship indicators are determined. For example, although
deprivation appears to have large mental health impacts, burdensome housing
costs could be a cause of this deprivation.

A limitation of this study is that, despite highly significant results, the FE
model only describes a small amount of the within variation used for
estimation. Leaving a large fraction of the variance unexplained increases the
possibility of omitted variable bias. Reverse causality is also a concern in
the FE regressions. For example, increasingly erratic or impulsive behaviour
associated with worsening mental health could cause financial hardship
problems, or missed housing payments. This problem is mitigated to some degree
by the timing of these variables. The HILDA Survey questions for the MCS are
asked in relation to the previous month, whereas seven of the eight financial
hardship indicators refer to events that have occurred since the start of the
interview year.222222The majority of the HILDA interviews take place between
July and October of each year. The FE results also use the first lag of the
PCS to reduce the problem of simultaneously determined mental and physical
health.

Although the DID has the advantage over the FE regressions of matching over
multiple periods, and being able to test the identification assumption, once
matching is performed there are a limited number of observations in some
subsamples. This reduces the ability to reject the parallel trends assumption,
and increases the standard errors around the parameter estimating the effect
size. Despite these concerns, the similarity of the FE and DID results provide
reassurance as to the robustness of the main findings.

###  7.2 The Broader Literature and Policy Implications

This research fits within a broader field that seeks a better understanding of
the social determinates of health, which include income, education, housing,
and others (Mikkonen & Raphael, 2010). This area has gained in importance due
to the inability for traditional explanations, such has individual health
behaviours, poverty, and access to health care, to fully explain mortality,
morbidity, and other health gradients, including mental health, that are found
in most countries across socioeconomic status (Marmot & Allen, 2014; Smith,
1999). There are a number of reasons to suspect that social constructs that
contribute to socioeconomic status are also important causes of the health
gradient. These reasons include chronic arousal of stress pathways leading to
physiological disregulation, and increases in psychosocial stressors due to
positioning within the social hierarchy (Deaton & Paxson, 2001; McEwen &
Gianaros, 2010).

One criticism of the literature on the social determinant of health is a lack
of emphasis on strong causal methodology. And due to the highly correlated
nature of many of these variables, such as income, education and wealth, the
exact causal pathways are difficult to ascertain. For example, unequal health
outcomes in adults attributed to income could be caused by health shocks early
in life that reduce lifetime earnings (Smith, 1999). In order to correctly
inform policy makers, more studies with a causal focus are needed. This
research contributes to the literature by addressing methodological concerns
in the literature investigating the effect of housing stress on mental health.

The results presented in this research provide support for government
intervention to alleviate housing stress for renters, especially those in
persistent financial hardship, in order to reduce the negative impacts on
mental health. Increasing the supply of affordable housing options, or
increasing rental supplements, would both appear to have mental health
benefits. However, it is worth noting that the evidence presented in this
research does not necessarily favour housing interventions over other welfare
policies that may reduce financial hardship more broadly. For instance, the
results suggest that experiences of deprivation could have especially large
negative mental health impacts.

The effectiveness of policy to reduce the impact of housing stress and
financial hardship on mental health may benefit from looking beyond the usual
policy prescriptions. Inspired by behavioural economics, some researchers have
started asking how economic decisions change under financial hardship. For
example, Carvalho et al. (2016) finds that individuals are more present bias
before payday than after payday. Potentially short term financial problems can
become overly salient in the minds of decision makers, leading to behaviours
that result in a long term poverty trap. This appears to open up new policy
directions for improving financial mobility, and therefore mental health, such
as interventions to help initial asset accumulation that could assist with
escaping a poverty trap (Bernheim et al., 2015).

##  8 Conclusion

Housing expenditure tends to be sticky and costly to adjust, and makes up a
large proportion of household expenditure. Additionally, the loss of housing
can have catastrophic consequences. These specific features of housing
expenditure imply that housing stress could cause negative mental health
impacts. This research finds that housing stress does have an effect on mental
health, with larger declines estimated for renters than for owners. Especially
impacted are renters that have prior experience with financial hardship. For
these individuals, the DID estimates a $0.2$ standard deviation decline in the
MCS. This is the additional impact of housing stress, compared to non-housing
related financial hardship alone. The estimated impact of housing stress on
owners with a mortgage is small or not different from zero. This research also
suggests that the mental health impact of housing stress is more important
than some, but not all, aspects of financial hardship.

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##  9 Appendix

###  9.1 Full Regression Results

Table 8: Baseline Regression Results - Full Model

| Dependent variable:
---|---
| Mental Component Summary
| Renters | Owners
| (1) | (2) | (3) | (4) | (5) | (6)
Housing stress |  $-$2.27∗∗∗ |  $-$1.79∗∗∗ |  $-$1.01∗∗∗ |  $-$1.52∗∗∗ |  $-$0.86∗∗∗ |  $-$0.50∗
| (0.19) | (0.20) | (0.20) | (0.20) | (0.21) | (0.20)
Financial hardship |  |  $-$1.43∗∗∗ |  |  |  $-$1.18∗∗∗ |
|  | (0.13) |  |  | (0.11) |
Could not pay bills |  |  |  $-$0.98∗∗∗ |  |  |  $-$0.61∗∗∗
|  |  | (0.17) |  |  | (0.15)
Sold/pawned something |  |  |  $-$0.85∗∗∗ |  |  |  $-$1.01∗∗∗
|  |  | (0.22) |  |  | (0.24)
Went without meals |  |  |  $-$1.92∗∗∗ |  |  |  $-$1.75∗∗∗
|  |  | (0.28) |  |  | (0.39)
Went without heating |  |  |  $-$1.46∗∗∗ |  |  |  $-$1.02∗∗
|  |  | (0.31) |  |  | (0.37)
Sort help from friends/family |  |  |  $-$0.64∗∗∗ |  |  |  $-$0.82∗∗∗
|  |  | (0.15) |  |  | (0.15)
Sort help from community |  |  |  $-$0.53∗ |  |  |  $-$1.15∗∗∗
|  |  | (0.25) |  |  | (0.35)
Cannot raise emergency money |  |  |  $-$0.97∗∗∗ |  |  |  $-$0.91∗∗∗
|  |  | (0.17) |  |  | (0.19)
Household Disposable income | 0.22 | 0.14 | 0.07 |  0.53∗∗∗ |  0.46∗∗∗ |  0.42∗∗∗
| (0.12) | (0.12) | (0.12) | (0.11) | (0.11) | (0.11)
Employed full-time |  1.54∗∗∗ |  1.36∗∗∗ |  1.18∗∗∗ |  0.85∗∗∗ |  0.78∗∗∗ |  0.73∗∗∗
| (0.20) | (0.20) | (0.20) | (0.16) | (0.16) | (0.16)
Employed part-time |  1.24∗∗∗ |  1.17∗∗∗ |  1.07∗∗∗ |  0.83∗∗∗ |  0.80∗∗∗ |  0.77∗∗∗
| (0.19) | (0.19) | (0.19) | (0.15) | (0.15) | (0.15)
Physical component summary |  0.04∗∗∗ |  0.04∗∗∗ |  0.04∗∗∗ |  0.02∗∗∗ |  0.02∗∗∗ |  0.02∗∗∗
| (0.01) | (0.01) | (0.01) | (0.01) | (0.01) | (0.01)
Neighbourhood (Q2) | 0.11 | 0.13 | 0.10 | 0.29 | 0.31 | 0.29
| (0.23) | (0.23) | (0.22) | (0.30) | (0.30) | (0.30)
Neighbourhood (Q3) |  $-$0.12 |  $-$0.13 |  $-$0.15 | 0.09 | 0.11 | 0.11
| (0.24) | (0.24) | (0.23) | (0.29) | (0.29) | (0.29)
Neighbourhood (Q4) | 0.12 | 0.13 | 0.08 |  $-$0.32 |  $-$0.29 |  $-$0.31
| (0.25) | (0.25) | (0.25) | (0.30) | (0.30) | (0.30)
Neighbourhood (Q5) | 0.22 | 0.22 | 0.18 |  $-$0.02 | 0.004 |  $-$0.01
| (0.28) | (0.28) | (0.28) | (0.33) | (0.33) | (0.33)
Year dummies | Yes | Yes | Yes | Yes | Yes | Yes
Individuals | 10046 | 10046 | 10046 | 12644 | 12644 | 12644
Degrees of freedom | 31095 | 31094 | 31088 | 57135 | 57134 | 57128
∗p$<$0.05; ∗∗p$<$0.01; ∗∗∗p$<$0.001

Notes: Cluster robust standard errors (individual level) reported in the
parentheses. R-Squared values are calculated using within variation only.
Income is natural logarithm of equivalised household disposable income
(constant 2019 dollars), equivalised by household members using OECD
equivalence weights. The PCS is lagged by one period.

Table 9: Difference-in-differences Results - Full Model

| Dependent variable:
---|---
| Mental Component Summary
| Renters | Owners
| (1) | (2) | (3) | (4) | (5) | (6)
| Low | Mod | High | Low. | Mod. | High.
Treat:1[t=0] |  $-$2.67∗ |  $-$3.45∗∗ |  $-$2.05∗ |  $-$0.36 | 0.03 |  $-$0.96
| (1.11) | (1.21) | (0.87) | (0.81) | (1.35) | (0.94)
Treat:1[t=-1] |  $-$1.68 |  $-$0.43 | 0.13 | 0.12 |  $-$0.19 |  $-$0.21
| (0.97) | (1.13) | (0.84) | (0.71) | (1.21) | (0.95)
Treat | 1.64 | 0.31 |  $-$1.14 |  $-$0.13 |  $-$1.47 |  $-$0.59
| (0.99) | (1.09) | (0.86) | (0.75) | (1.27) | (0.96)
1[t=-1] |  $-$0.61 |  $-$0.93∗ |  $-$0.78 |  $-$0.47 |  $-$0.82∗ |  $-$0.15
| (0.37) | (0.47) | (0.53) | (0.29) | (0.42) | (0.52)
1[t=0] |  $-$1.56∗∗∗ |  $-$0.87 |  $-$0.96 |  $-$1.82∗∗∗ |  $-$1.39∗∗ |  $-$0.74
| (0.41) | (0.45) | (0.55) | (0.32) | (0.43) | (0.54)
Disposable income |  $-$0.31 |  $-$1.47∗ |  $-$0.10 | 0.43 |  $-$0.42 |  $-$0.06
| (0.54) | (0.60) | (0.48) | (0.41) | (0.64) | (0.57)
Employed full-time |  1.76∗ |  3.00∗∗∗ |  2.77∗∗∗ |  2.01∗∗∗ |  3.44∗∗∗ |  2.95∗∗∗
| (0.69) | (0.72) | (0.61) | (0.59) | (0.78) | (0.73)
Employed part-time | 0.55 | 0.05 |  2.18∗∗∗ |  1.73∗∗ |  2.69∗∗∗ |  2.15∗∗
| (0.72) | (0.78) | (0.62) | (0.61) | (0.80) | (0.74)
Physical component summary | 0.002 |  $-$0.02 |  0.06∗ |  0.06∗ | 0.02 |  0.07∗
| (0.03) | (0.03) | (0.03) | (0.02) | (0.03) | (0.03)
Neighbourhood (Q2) |  $-$0.74 | 0.28 |  1.66∗ | 0.02 | 0.90 |  $-$0.76
| (0.77) | (0.87) | (0.65) | (0.65) | (0.86) | (0.81)
Neighbourhood (Q3) |  $-$0.65 |  $-$0.30 |  $-$0.07 |  $-$0.74 |  $-$0.12 |  $-$1.10
| (0.81) | (0.92) | (0.77) | (0.64) | (0.92) | (0.87)
Neighbourhood (Q4) |  $-$0.25 |  1.87∗ |  $-$0.31 |  $-$0.98 | 1.00 |  $-$1.17
| (0.86) | (0.91) | (0.86) | (0.66) | (0.94) | (0.92)
Neighbourhood (Q5) |  $-$1.70∗ | 1.04 |  $-$0.03 |  $-$1.50∗ | 0.56 |  $-$0.45
| (0.86) | (0.96) | (0.92) | (0.67) | (0.94) | (0.92)
Event Year Fixed Effects | Yes | Yes | Yes | Yes | Yes | Yes
Individuals | 1078 | 928 | 1552 | 1774 | 1069 | 1183
Observations | 2885 | 2441 | 3748 | 4698 | 2782 | 2869
∗p$<$0.05; ∗∗p$<$0.01; ∗∗∗p$<$0.001

Notes: Cluster robust standard errors (individual level) reported in the
parentheses. Income is natural logarithm of equivalised household disposable
income (constant 2019 dollars), equivalised by household members using OECD
equivalence weights. Colons represent interaction terms and $1[\cdot]$ are
indicator variables for the stated event time. Event year fixed effects for
the actual calendar year the event occurs, and are added using dummy variables
for 2004-2019.

###  9.2 MCS and PCS Construction

To construct the MCS and PCS, this research uses the ABS National Health
Survey, 1995. This provides the SF-36 summary statistics for the Australian
population, along with weighting coefficients derived from principal
components factor analysis (see table 10). Following the procedure outlined in
Ware et al. (2001), the eight category scores of the SF-36 are first
standardised using the ABS’s population mean and standard deviation estimates.
The ABS weighting coefficients are then used to take linear combinations of
the eight category scores to form mental and physical component summaries. In
the final step, the two aggregate measures are transformed to have a mean of
50, and a standard deviation of 10 in the general population.

Table 10: MCS and PCS Creation

SF-36 Scale | Pop. Mean | Pop. Std. Dev. | PCS Coeff. | MCS Coeff.
---|---|---|---|---
Physical function | 83.46 | 23.23 | 0.47 | -0.24
Role limits (physical) | 80.28 | 34.84 | 0.38 | -0.13
Bodily pain | 76.94 | 24.84 | 0.37 | -0.12
General health | 71.82 | 20.35 | 0.19 | 0.05
Vitality | 64.48 | 19.77 | -0.02 | 0.27
Social function | 85.06 | 22.29 | -0.01 | 0.26
Role limits (emotion) | 83.19 | 32.15 | -0.15 | 0.36
Mental health | 75.98 | 16.96 | -0.27 | 0.49

Columns (left to right): Australian population means, Australian population
standard deviations, weighting coefficients for PCS, weighting coefficients
for MCS. Weighting coefficients are the principal components weighting
coefficients for the eight scales of the SF-36 in the Australian population
(ABS, 1997).

###  9.3 Robustness - Mental Health Scale Dependent Variable

Table 11: Fixed Effects Robustness - Mental Health Scale Dependent Variable

Dependent variable: Mental Health Scale
---
| Private Renters | Owners with Mortgage
| (1) | (2) | (3) | (4) | (5) | (6)
Housing stress |  $-$3.32∗∗∗ |  $-$2.54∗∗∗ |  $-$1.46∗∗∗ |  $-$2.52∗∗∗ |  $-$1.44∗∗∗ |  $-$0.85∗∗
| (0.30) | (0.31) | (0.31) | (0.31) | (0.33) | (0.32)
Financial hardship |  |  $-$2.29∗∗∗ |  |  |  $-$1.93∗∗∗ |
|  | (0.21) |  |  | (0.18) |
Could not pay bills |  |  |  $-$1.32∗∗∗ |  |  |  $-$1.01∗∗∗
|  |  | (0.27) |  |  | (0.23)
Sold/pawned something |  |  |  $-$1.59∗∗∗ |  |  |  $-$1.77∗∗∗
|  |  | (0.34) |  |  | (0.38)
Went without meals |  |  |  $-$2.87∗∗∗ |  |  |  $-$2.19∗∗∗
|  |  | (0.44) |  |  | (0.61)
Went without heating |  |  |  $-$2.13∗∗∗ |  |  |  $-$1.92∗∗∗
|  |  | (0.49) |  |  | (0.58)
Sort help from friends/family |  |  |  $-$0.86∗∗∗ |  |  |  $-$1.46∗∗∗
|  |  | (0.23) |  |  | (0.22)
Sort help from community |  |  |  $-$0.80∗ |  |  |  $-$1.79∗∗
|  |  | (0.40) |  |  | (0.55)
Cannot raise emergency money |  |  |  $-$1.57∗∗∗ |  |  |  $-$1.48∗∗∗
|  |  | (0.28) |  |  | (0.30)
Controls | Yes | Yes | Yes | Yes | Yes | Yes
Year dummies | Yes | Yes | Yes | Yes | Yes | Yes
Individuals | 10046 | 10046 | 10046 | 12644 | 12644 | 12644
Degrees of freedom | 31095 | 31094 | 31088 | 57135 | 57134 | 57128
R-Squared | 0.0108 | 0.0152 | 0.0238 | 0.0046 | 0.0076 | 0.0112
F-Statistic | 125.57 | 123.63 | 45.45 | 64.56 | 90.23 | 29.246
∗p$<$0.05; ∗∗p$<$0.01; ∗∗∗p$<$0.001

Notes: The mental health scale sums five questions from the SF-36 and
transforms the scale to range from 0-100. Individual level cluster robust
standard errors are reported in the parentheses. The F-statistic null
hypothesis is included financial hardship variables are jointly zero.
R-Squared values are calculated using within variation only. Control variables
used are the natural logarithm of equivalised household disposable income,
employment status (full-time, part-time, other), a categorical variable for
the neighbourhood quintile of disadvantage of residence, and the first lag of
the PCS score. Disposable income (in constant 2019 dollars) is at the
household level and is equivalised based on the number of members following
OECD equivalence weights.

Figure 6: Matched DID Results - Mental Health Scale Dependent Variable

Notes: Dependent variable is the mental health scale, rather than the MCS.
Mental health scale predicted values plotted are conditional on event time and
treatment group, and at the mean of control variables for the given time
period. The pre-treatment periods are $t=-2$ and $t=-1$. In the pre-treatment
periods individuals are in non-housing related financial hardship, but no
housing related financial hardship. The post-treatment period is $t=0$. The
treatment group has housing related financial hardship and non-housing related
financial hardship at $t=0$, whereas the control group has non-housing related
financial hardship only.

Table 12: DID Hypothesis Testing - Alternative dependent variable

Test |  | Renters:Low | Mod | High | Owners:Low | Mod | High
---|---|---|---|---|---|---|---
Parallel Trends | Estimate | -1.67 | -0.70 | -0.43 | 0.06 | 1.17 | -1.24
| p-value | 0.26 | 0.69 | 0.75 | 0.95 | 0.57 | 0.42
Treatment Effects | Estimate | -3.53 | -4.86 | -2.64 | -1.20 | 1.06 | -2.02
| p-value | 0.05 | 0.01 | 0.06 | 0.36 | 0.62 | 0.18

Notes: Dependent variable is the mental health scale, rather than the MCS. All
tests are performed with t-tests of equation (4) using individual level
cluster robust standard errors. Parallel trends is tested with a null of
$\gamma_{2}^{(h)}=0$. Treatment effects is tested with a null of
$\tau^{(h)}=0$.