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  • 标题:Spatial analysis of housing stress estimation in Australia with statistical validation.
  • 作者:Rahman, Azizur ; Harding, Ann
  • 期刊名称:Australasian Journal of Regional Studies
  • 印刷版ISSN:1324-0935
  • 出版年度:2014
  • 期号:September
  • 语种:English
  • 出版社:Regional Science Association, Australian and New Zealand Section
  • 摘要:Housing stress has emerged as a widely discussed public policy issue among politicians, academics and policy makers in Australia. With the unprecedented growth in housing prices - and rents - throughout the past decade, many Australians are increasingly finding housing unaffordable (Rahman, 2011; Yates, 2011). Between 1995 and 2005, real house prices in Australia increased by more than 6 percent per year, with an average annual increase of almost 15 percent from 2001 to 2003 (Yates, 2011). This was well above the average annual increase in the 20 years to 1995 of just 1.1 percent and the 50-year average (from 1960 to 2010) of 2.5 percent per year. These data are illustrated in Figure 1 and contrast with the significantly slower growth in Gross Domestic Product (GDP) per capita and average earnings over much of the period. A significant increase of the real house prices is marked from 2001 onwards.
  • 关键词:Australians;Dwellings;Housing

Spatial analysis of housing stress estimation in Australia with statistical validation.


Rahman, Azizur ; Harding, Ann


1. INTRODUCTION

Housing stress has emerged as a widely discussed public policy issue among politicians, academics and policy makers in Australia. With the unprecedented growth in housing prices - and rents - throughout the past decade, many Australians are increasingly finding housing unaffordable (Rahman, 2011; Yates, 2011). Between 1995 and 2005, real house prices in Australia increased by more than 6 percent per year, with an average annual increase of almost 15 percent from 2001 to 2003 (Yates, 2011). This was well above the average annual increase in the 20 years to 1995 of just 1.1 percent and the 50-year average (from 1960 to 2010) of 2.5 percent per year. These data are illustrated in Figure 1 and contrast with the significantly slower growth in Gross Domestic Product (GDP) per capita and average earnings over much of the period. A significant increase of the real house prices is marked from 2001 onwards.

[FIGURE 1 OMITTED]

Compared with other economically advanced nations, Australia is often reported as having experienced relatively rapid growth in real house prices over the past 20 years or so (Tumbarello and Wang, 2010). Just over the five year period from 2000 to 2004, Australia had the third highest rate of house price inflation among Organisation for Economic Co-operation and Development (OECD) member countries, ranking behind only Britain and Spain (Productivity Commission, 2004; The Economist, 2011). Moreover, a recent report of the Australian Bureau of Statistics (ABS) shows that established house prices increased by an average of 33 percent between 2002-03 and 2006-07 (ABS, 2008). Within this time period house rents have also increased rapidly. For instance, within only a 12 month period ending in August 2007, house rents increased in Perth by 36.4 percent, Melbourne by 23.4 percent, Australian Capital Territory by 22.7 percent, Sydney by 18.8 percent, and Brisbane by 13.5 percent (Pearson, 2007). So, housing stress has become an important financial challenge for households, especially for low and middle income groups and an important public policy concern for the national, state and local governments.

About 1.7 million people in this country are in housing stress (Sandel and Wright, 2006). Households with relatively low income and housing costs greater than a certain proportion of household income (for instance, more than or equal to 30 percent) are typically defined as being in housing stress (Rahman, 2009). The concept may also be extended to describe inadequate housing for a proportion of the population. Most of the policy debates on housing stress to date have been confined to the national or state level (Wood et al., 2005; Harding et al., 2004; Nepal et al., 2010; Rahman, 2011; Flood, 2012). This is largely due to the ready availability of data at this coarse geographic level in the sample survey files available from the ABS. However, methodological advances in spatial microsimulation modelling mean that it is now possible to generate synthetic spatial micro-population data (Rahman et al., 2010a).

As in many other countries, substantial spatial differences in socioeconomic growth and wellbeing exist across Australia (Chin et al., 2005; Harding et al., 2006; Stimson et al., 2008). Australian housing programs include subsidising housing costs and rent assistance; mortgage subsidies; and land development planning for housing. All of these policies have had significant impacts on individuals and their living standards, experiences, choices, constraints, decisions and lifestyle preferences (Melhuish et al., 2004; Kelly et al., 2006; Rowley and Ong, 2012; Rahman et al., 2013). In addition, housing acts as a proxy for a host of other factors relevant to economic disadvantage and social inequalities at small area levels. Small area level housing stress statistics also vary with the demographic and socioeconomic conditions of households - and with geography (Rahman, 2011). So, there is a keen interest in understanding who is struggling to afford to buy or rent a house and the impact at small geographic area levels.

This paper studies a spatial analysis of the estimation of statistical local area (SLA) level housing stress in Australia. One of the arguments frequently evoked in the literature is that microsimulation modelling technology based small area estimation lacks vigorous tests of statistical reliability for the microsimulated estimates. So this paper also offers a new statistical approach for validating the results of small area housing stress statistics.

2. A REVIEW OF THE LITERATURE

Typically housing stress describes a financial situation of households where the cost of housing--either as rental, or as a mortgage repayment is considered to be significantly high relative to household income. A range of definitions for describing the situation of housing stress are available in the literature. The following subsections will discuss all methods of measuring housing stress and compare different definitions.

Measures of Housing Stress

Housing stress can be measured by combining two basic quantities - the income and expenditure of a household. A household can be considered under housing stress when it is spending more than an affordable expected proportion of its household income on housing. The affordable expected cut-off point of housing expenditure can vary with the circumstance of households as well as location of dwelling.

As a general rule of thumb, a household spending at least 30 percent of its income on housing can be considered under housing stress (see King, 1994; Landt and Bray, 1997). Some researchers use a different threshold of housing expenditure by restricting the definition to households within different income quintiles. For example, an income threshold of more than 25 percent for housing costs is used by the National Housing Strategy (1991) and Foard et al. (1994). Additionally a commonly used definition of housing stress is specified in Harding et al. (2004), where a threshold of more than 30 percent of housing costs was used, but only for those households having income in the bottom 40 percent (lowest two quintiles) of the equivalised income distribution. Another definition restricts the designation of 'being in housing stress' to those households spending more than 30 percent of their income on housing and belonging to the bottom 10th to 40th income percentile of the income distribution (ABS 2005). It is noted that any threshold-based definition is an arbitrary slice through a continuum, meaning that small area level estimates of a percentage of households in housing stress would be better treated as estimates of small areas with the greatest percentage of households in housing stress. More explicitly, if an area has a very high percentage of households suffering from housing stress under one of the above definitions, the area probably ranks highly on percentage of households suffering from housing stress however defined.

The residual income approach to housing stress measure looks at what different household types can afford to spend on housing after taking into account the other necessary expenditures of living (Stone et al., 2011). Although it is an alternative to benchmarking the income and expenditure ratio measures of housing stress commonly used in Australia, this approach requires an operationalised residual income standard that is not only difficult to quantify but also arbitrary according to varying circumstances of households. This means that a household has a housing related financial stress problem if it cannot meet its non-housing related needs at some minimum level of adequacy after paying for housing (Stone, 2006a). The appropriate indicator of the tension between housing costs and incomes is thus the difference between them - the residual income after paying for housing, rather than the ratio of costs to income.

Defining a residual income standard involves use of a socially-defined standard of adequacy for non-housing items. Thus, while the residual income logic has some conceptual broadness, a particular residual income standard is not universal, but socially grounded in space and time (Stone, 2006b; Stone et al., 2011). Issues involved in selecting such a standard for non-housing necessities can be difficult and complex.

Both the ratio approach and the residual income approach suggest that as the housing costs behaviourally tend to make the first claim on disposable income, a household has a housing stress problem if, after paying for housing, it has insufficient (residual) income to meet its nonshelter needs at some normative level of adequacy. The difference between the two approaches is how they define the normative level of adequacy for non-shelter items. The ratio approach defines it as a fraction of income: traditionally 75 percent. More recently 70 percent has been defined as the minimum share of income that must be available after housing costs in order to avoid hardship in meeting non-shelter needs (Nepal et al., 2010; Rahman, 2011). By contrast, the residual income approach defines the normative level of adequacy for non-shelter items as a monetary amount that is independent of income but very dependent upon household composition and the non-housing cost of living as a function of time and place (Burke et al., 2010).

Types of Ratio Measures

A rationale for the use of the 30/40 rule based ratio measure is given in this subsection. It is noted that this ratio measure not only provides continuity with traditionally used measures, but also it is simple to apply and easy to understand.

The definitions of housing stress by three 'rules'-based ratio measures are as follows:

1) 30-only rule: A household is considered to be in housing stress if it spends more than 30 percent of its disposable or gross income on housing costs;

2) 30/40 rule: A household is considered to be in housing stress if it spends more than 30 percent of its disposable or gross income on housing costs and the household also belongs to the bottom 40 percent of the equivalised disposable income distribution; and

3) 30/(10-40) rule: A household is considered to be in housing stress if it spends more than 30 percent of its disposable or gross income on housing and falls into the bottom 10th to 40th income percentile of the equivalised disposable income distribution.

Although the cut-off point of housing costs for all these definitions is the same, there are some concerns associated with each of these rules. For example, is gross income or disposable income the appropriate base income to calculate housing costs for measuring housing stress? (Gross income is the income of a household from all sources before deducting tax and the Medicare levy, whereas disposable income is the income that remains to a household after deducting the estimated personal income tax and the Medicare levy from gross income.) If a researcher uses 30 percent of gross income as a base, then after possible deductions that figure may be around 40 to 45 percent of actual disposable income. Hence, 30 percent of gross income should equate to a reasonably high proportion of actually received income for housing and other costs. In addition, the 30/40 and 30/(10-40) rules both restrict the definition to those households that are within the bottom 40 percent of the equivalised income distribution. The issue here is: why is the cut-off point at the lowest 40 percent of income distribution? For the latter rule, why are households in the bottom 10 percent of the equivalent income distribution being omitted?

In general, when the individuals have a higher income, they have greater choice in how to spend it. For lower income households, almost all of their income may be spent on basic necessities, including food, clothing and housing. This group is at higher risk of not being able to afford increasing housing costs or they may not have any choice on housing. For the higher income households, paying more than 30 percent income on rent or a mortgage is more likely to be a choice, perhaps to live in a more convenient or desirable area, or to pay off extra on the mortgage to shorten the term of payment. However, there is a possibility that the households in the third quintile (40th to 60th income percentile) of the income distribution - who usually are known as middle class earners - may also have financial hardship in meeting high housing costs, and may have only limited choices to do with housing. By choosing the bottom 40 percent of income distribution as the cut-off, the middle class earning households are excluded from the definitions.

Although middle class income households are at a lower risk of housing stress than low income households, they may be at a level of 'marginal housing stress' because a substantial rise in interest rates, housing prices, or job loss etc. may cause the middle class income households to fall into housing stress. Moreover the 40 percent cut-off is the same regardless of the area in which the individual or household unit is living. Hence no account is taken of housing costs which vary with location; for example the high rents of Canberra and Sydney compared to the low rents of Adelaide are not taken into account in these definitions.

A very severe form of housing stress is the risk of homelessness and may apply to households in the lowest 10 percent of income distribution. This group is quite vulnerable to rising housing costs. Note that many homeless are homeless due to a situation of financial hardship where individuals are unable to afford housing costs or to keep a place to live. Rapidly increasing housing costs could force more of the lowest earning households into homelessness. So the exclusion of households within the lowest income decile from the 30/10-40 rule may overlook this severe form of housing stress. In addition, this definition cannot be used as a means of strategic policy intervention for poverty and housing assistance programs due to its exclusion of the most disadvantaged households. However, some studies do argue that the reported incomes of households in the bottom 10 percent of the income distribution do not always accurately reflect their living standards, and their inclusion in the definition may overestimate housing stress (see ABS, 2005), which is why the ABS argues for the 30/10-40 rule.

A Comparison of Various Ratio Measures

A comparison of the three rules of measuring housing stress is provided in Table 1. Note that none of these definitions takes into account the fact that housing costs vary according to area. The specified rules use relative income of household and the general rule (30 only) uses the absolute household income.

The 30/40 rule is the widely used definition of housing stress in Australia. Although this definition may ignore marginal housing stress, it acknowledges the size of the household income unit by using the equivalised household income distribution. Whereas, the 30/(10-40) rule is also based on equivalised household income distribution, it is more restricted and occasionally uses a definition that ignores both the severe and marginal forms of housing stress. Nevertheless the availability of suitable data, methodological tools and specific research interests in each of these definitions is useful.

It is noted that, in all the definitions, households with negative and nil incomes have been removed from the analysis. In survey data, few households have reported nil or negative incomes. These are often excluded from any analysis related to income distribution and financial well-being, as research from the ABS has shown that the expenditure of these households is similar to that of households earning much more, so these incomes are considered an unreliable measure of a household's standard of living (ABS 2005).

Moreover, the distributions of housing stress measured by the three different rule-based variants are presented in Figure 2. It is obvious from the figure that not only does the percentage of households in housing stress vary under different definitions, but also the density of the SLAs varies with the percentage of housing stress across Australia.

[FIGURE 2 OMITTED]

The graph of the '30/40 rule'- based variant of housing stress shows that approximately 67 percent of the SLAs have housing stress households of 7 to 11 percent, with a mean of 9.52 percent and a coefficient of variation (C.V.) of 34.95. In addition, the graph of the '30/40-10 rule'-based variant shows that most SLAs (about 87 percent) have housing stress households of 3 to 7 percent, with a mean of 4.91 percent and a C.V. of 41.85. The '30 only rule' variant of housing stress reveals that about 51 percent of the SLAs in Australia have households with a rate of housing stress of 13 to 17 percent, with a mean of 14.68 and a C.V. of 36.71.

According to Karl Pearson the C.V. is a very powerful tool for comparing the variability of two or more series of variants (Gupta and Kapoor, 2008), where a variant having the lowest C.V. is considered to be more consistent than the others. In this regard, since the C.V. for the '30/40 rule'-based variant of housing stress estimation is the lowest compared with the variation measures for the other two variants, this variant ('30/40 rule'-based definition) of housing stress estimation is more consistent than the others. Furthermore, in terms of the distributional pattern of these three curves, the '30/40 rule'-based housing stress variant also shows a more rational pattern towards the usual normal curve, while the '30/(40-10) rule' and '30 only rule'-based variants resemble leptokurtic and platykurtic curves respectively. From the statistical point of view, the '30/40 rule'-based housing stress estimation is more consistent and appropriate at small area levels in Australia.

The '30/40 rule'-based definition is also accountable and valid for using socioeconomic policy analyses that link with the housing stress issue. For instance, one of the significant policy implications of this definition is that this rule is widely used as the basis for determining household eligibility for entry to public rental housing and/or receipt of commonwealth rent assistance (CRA). Moreover, the definition has been used by many researchers and public and private organizations including the National Housing Strategy (1992), ABS (2002), Harding et al. (2004), Yates and Gabriel (2006), and recently in estimating figures used by the Australian Prime Minister and subsequently published by the Australian Government Department of Families, Housing, Community Services and Indigenous Affairs (FaHCSIA, 2008). Therefore, this paper uses the '30/40 rule'- based variant to define households in housing stress as those with equivalised household gross income in the lowest two quintiles (bottom 40 percent) of all household incomes in Australia, who are spending more than 30 percent of their gross household income on either renting costs or mortgage repayments.

3. METHODOLOGY

This section briefly presents the research methodology - which is a spatial microsimulation modelling technology (MMT) approach of small area estimation. The method is rapidly becoming popular in the developed world and has now a wide range of applications (see for example, Rahman, 2011; Rahman et al., 2013; Rahman and Harding, 2014) including simulation of the small area impact of changes in income taxes and cash transfers (Ballas and Clarke, 2001; Harding et al., 2009); the development of small area measures of poverty and social exclusion (Tanton et al., 2009; McNamara et al., 2007; Miranti et al., 2011); the small area modelling of activities of daily living status and/or the need for different types of care (Williamson, 1996; Lymer et al., 2008); the development of the SimObesity model to examine small area obesity among children (Procter et al., 2008); small area health-related conditions (Ballas et al., 2006a; Rahman and Harding, 2011; Rahman and Harding, 2013) and the socio-economic impacts of major job gain or loss at the local level (Clarke, 1996; Ballas et al., 2006b).

Spatial-level Microdata Generation

Creation of a synthetic micropopulation dataset at the small area level, such as the SLA level in Australia, is very challenging. Small area estimation technologies have become useful tools to overcome this challenge. Although there are two methods (statistical and geographic) in small area estimation for generating small area microdata, this paper uses the geographic approach also known as spatial microsimulation modelling (SMM). A detailed description of various methods, their properties, suitability and applications are reported in other studies (Rahman, 2009; Harding and Tanton, 2011; Rahman and Harding, 2014). The MMT approach of microdata simulation involves some complex procedures, whose gradual evolution has been described in detail in other research (see for example, Chin and Harding, 2006; Rahman et al., 2010b; Cassells et al., 2010; Rahman, 2011; Rahman et al., 2013).

To produce SLA level housing stress estimates in Australia, a SMM was designed that uses a range of datasets that come from the Australian Bureau of Statistics. These datasets have custom designed tables from the Census. In summary, the ABS sample survey in question is reweighted to match the small area Census benchmark tables, resulting in unit records for households and individuals for each SLA in the model. General discussion about these datasets and various steps of microdata generation are contained in Rahman (2011). The model generates reasonable microdata (by an accuracy index criterion (AIC) illustrated in Rahman, 2011) for 1 397 SLAs which contain more than 99.9 percent households. Among 1 422 SLAs across Australia, the model did not produce reasonable microdata for only 25 SLAs (non-convergent SLAs as per the AIC), which had very small or no populations and were typically located in very remote areas. The overall microdata generation process is depicted in Figure 3.

[FIGURE 3 OMITTED]

Clearly, the process starts by using the SAS language to run the general model file, which contains the path to all input data files and the GREGWT algorithm. The main calculations in the iteration process for the GREGWT algorithm operate separately for each id number of small areas (that is SLA codes). This complex process tracks numerous matrix and/or vector calculations towards achieving convergence for each SLA in the minimum number of iterations. In addition, it also does analysis for extreme data units to determine whether the extreme units have effects on the overall calculations. However, the output keeps records on only the top 30 extremes.

Although the GREGWT program follows the Newton-Raphson approach of iteration, the entire execution process of the model follows just a few successive algorithmic steps, which can be described as:

Step 1: Read in the general model file.

Step 2: Read in benchmark tables, Census data and microdata records from Survey of Income and Housing-Confidentialised Unit Record Files (SIH-CURFs) with SIH-linkage file mentioned in the general model file.

Step 3: Query the individual records within the microdata according to the classifications of the general model file.

Step 4: Change original weights to a new set of weights following a truncated Chi-Square distance function for an appropriate allocation of households/individuals towards the small area benchmarks.

Step 5: Apply the Newton-Raphson method of iteration to determine the best set of new weights by minimising the total distance between the new-synthetic weights and original weights.

Step 6: When convergence has been achieved and/or predefined number of iterations reached, the corresponding new set of synthetic weights is retained by the process and considered as the best reweights.

Spatial Microsimulation Model Outputs: The 1st Stage

Basically there are three outputs from this initial phase of the model. First of all, the core output is the file of synthetic household weights by SLAs in Australia. This file is considered as the most significant output of the model because of its usefulness in the next computational stage of the model (for getting small area microdata and the estimates). The second and third outputs of the model are, respectively, details about residual estimates of the synthetic weights and a convergence report of the model. These two outputs are associated information about the synthetic weights produced by the model. For example, the residual estimates file shows the accuracy of the new weights according to various benchmark classifications. In the spatial microsimulation process, a modeller's expectation is to minimise the overall residual estimates as much as possible, to ensure the consistency and reliability of the synthetic weights. In addition, the convergence report provides information about whether or not the GREGWT reweighting algorithm has converged to the benchmarks for a specific SLA. When the convergence rate seems reasonably low, then the modeller may need to revisit the specification of the model for modification.

Note that the "synthetic weights" file (see Table 2) is the central requirement in the MMT approach of small area estimation. The synthetic weights output file is often known as the synthetic or simulated spatial microdata new-weights, and it is the only output to be used in the next stage of the model for producing ultimate small area estimates. If this stage of the model can generate more accurate synthetic weights at small area levels, then the final small area estimates of interests are likely to be statistically more reliable.

Model Outputs: The 2nd Stage

To produce small area estimates of housing stress we have to run the second stage of the housing stress model. This section describes various parts of the 2nd stage of the model for SLA level housing stress estimation.

Typically, three input files are essential for the second stage of the housing stage model. They are

1) SIH-CURFs;

2) Synthetic weights; and

3) The Consumer Price Index (CPI) file.

These three input files are connected by a SAS program file that is known as the second stage program file. This SAS file not only contains all the linkage paths towards the input files, but also it programs the definition of the housing stress measure, various logic operations and codes of summary statistics for small area estimates. It also indicates a pathway to an outputs folder where the demanded small area estimates could be stored.

The output from the second stage model is the ultimate file for small area housing stress estimates in Australia. This research considers the SLA in Australia as a small area. So, the ultimate output file will contain a range of data for the SLA level housing stress estimation. In particular, the file contains data for the following attributes presented in Table 3.

The output file provides household level estimates of total numbers as well as percentages for each characteristic in the above table. The model can also produce persons' level small area estimates for these variables.

4. RESULTS AND DISCUSSION

This section reports on a selection of the outputs which are produced by the model.

Households and Housing Stress by Tenure Type

The distributions of Australian households and housing stress by tenure are given in Figure 4. About 70 percent of households are living in their own house, with half of them being buyers. Nearly 27 percent of

households are renters, with about 22.5 percent being in private rental. Only 2.9 percent of Australian households are living in other tenures, such as hospital beds, military housing, hotels/hostels etc. Figure 4b reveals that one-third of buyer households (33.2 percent) in Australia are in housing stress. It seems an indication that a proportion of low income households buying their house with the support of first home owners' grant is associated with a high house price, and very low levels of housing supply in many areas, especially in the inner city areas. Additionally, about 59.6 percent private renter households experience housing stress, while just 6.9 percent public renters are in housing stress. So, housing stress estimates for private renters have not only significant influence on the housing stress estimates for renters and overall households, but also have an effect on spatial scales where housing supply is very limited and the demand as well as costs of housing are high for a proportion of low to middle earner households (Rahman, 2011).

Although in theory, households living in public housings are paying less than 30 percent of their assessable income in housing rent (AIHW, 2009), in the equivalised household gross income amount they may be paying more than 30 percent of their income in housing costs. The Commonwealth Rent Assistance eligibility is dependent on recipients being on some form of government transfer payment which is also the primary source of income for public housing households. However, as very low income households, these tenure groups are likely to be in housing stress. For instance, in 2005-06, the proportions of public housing households in Australia with an older resident was 28 percent and with a member with a disability was 29 percent, while substantial percentages (about 29 and 33 percent of households with an older tenant or tenant with a disability respectively) of them were still in housing stress, after the Commonwealth Rent Assistance had been received (see for example, SCRGSP, 2007; AIHW, 2008).

Estimates for Different States and Territories

The model estimates a total of 7 128 035 households in Australia, of which 10.9 percent (i.e., 773 073 households) are in housing stress (Table A1 in Appendix). One-third of Australian households are located in NSW of which about 11.6 percent of households are in housing stress, and the estimated housing stress number for private renters (i.e., 164 089 households) is almost twice the estimated number for buyers (83 894 households). Victoria is the residence of a quarter of Australian households with about 10.4 percent of households being in housing stress, most of which are buyers and renters. Nearly 11.3 percent of 1 387 069 households in Queensland are estimated to be in housing stress with almost 27.9 percent being private renters.

Although Western Australia contains 701 116 households, of which about 9.9 percent are in housing stress, the estimates for public renters are much lower in WA and Tasmania compared to the estimates for other states and territories. The overall rate of housing stress is also higher in South Australia. About 10.1 percent of 181 666 households are experiencing housing stress in Tasmania. Moreover, only 6.6 and 9.2 percent of households located in the Australian Capital Territory and Northern Territory are in housing stress, with the highest prevalence rate (i.e., approximately 20 percent) in the public renters.

Housing Stress by Statistical Division

Table 4 presents the results of housing stress estimates for various statistical divisions (SD) in Australia. An estimated number of 163 655 (21.2 percent) and 135 702 (17.6 percent) households are experiencing housing stress in Sydney and Melbourne SDs. A relatively smaller but significant number of housing stress households are in other major capital city SDs--such as Brisbane: 66 718 (8.6 percent), Perth: 53 766 (7.0 percent) and Adelaide: 46 749 (6.1 percent).

Thus, Sydney, Melbourne, Brisbane, Perth and Adelaide collectively account for about 60.5 percent of the total number of households in housing stress for Australia. In comparison, only 2.4 percent of housing stress households reside in Hobart, Canberra and Darwin. The remaining 37.1 percent of households reside in non-capital SDs. Seven south-east coastal SDs such as Hunter, Illawarra, Mid-North Coast and Richmond-Tweed in the NSW and the Gold Coast, Sunshine Coast and Wide Bay-Burnett in Queensland - have relatively higher estimates than other noncapital SDs (ranging from 11 991 to 25 787 households) and collectively contain 15.8 percent of all housing stress households in Australia.

Estimates for Various Statistical Subdivisions

To get a much better view at the regional level, the results at the statistical subdivision (SSD) level show that a significantly large number of 20 990 households experiencing housing stress is in the port city Newcastle (Table A2 in Appendix). There are several main geographical regional parts where housing stress is concentrated at SSD level in Sydney, Melbourne, Perth, Adelaide and coastal regions in New South Wales and Queensland. Twelve SSDs making up the western, south western, northern and inner parts of Sydney collectively contain an estimate of 150 775 (19.5 percent of total) housing stress households in Australia. The Fairfield-Liverpool SSD in western Sydney individually has the highest proportion of 16.9 percent households in housing stress.

Although Western Melbourne SSD has the third highest estimated number of 17 098 households, the area's rate of 11.5 percent is relatively low. The Greater Dandenong, Hume and Frankston cities and inner Melbourne have housing stress rates of 14.9, 14.1, 12.6 and 12.3 percent respectively. In addition, several SSDs in north, east and south-east metropolitan Perth and the northern, southern, western and eastern parts of Adelaide have noticeably large estimates of housing stress. Some other major coastal centres such as Wollongong, Richmond-Tweed and Hastings in NSW; Gold Coast, Sunshine Coast, Wide Bay-Burnett and Cairns city in Queensland; and the Hobart SSD also have significant estimates.

It is noticeable that low income households residing in the attractive and a high demand Gold Coast region are more prevalently (an average rate of 14.0 percent) in housing stress. This may be because of a very high level of house prices or rents in the Gold Coast areas.

SLA Level Estimates of Housing Stress across Australia

The spatial analysis depicts estimates by SLAs. Typically, the spatial units of analysis vary greatly in population size and presenting results for the estimated number of households in housing stress usually does not mean a great deal when looking at which areas have housing stress. Thus, only the percentage estimates are considered in spatial analysis, and the spatial graph is depicted in Figure 5. For mapping, the quantile classification is used for geographic distribution of the housing stress (but those SLAs that did not meet the accuracy criterion in the microdata simulation process are treated as missing). This option examines the relativity of all SLAs in Australia. In view of the fact that city areas are very condensed and unseen in the main map, they are presented in separate boxes.

[FIGURE 5 OMITTED]

Findings of the spatial analysis reveal that most of the SLAs in the eastcoast and some SLAs in the west-coast regions in Australia have a relatively higher rate (over 11.2 percent) of households in housing stress. Although many SLAs in inland remote regions throughout the country have the lowest rates of housing stress households, small areas across the mining-boom regions in inland Queensland and Western Australia illustrate relatively higher percentage estimates.

The map also reveals that a number of SLAs located within some major capital cities of Australia have significantly high rates of housing stress (ranging from 16.81 to 28.00 percent). Some SLAs in inner locations of Melbourne, Canberra and Adelaide have the highest percentage estimates. For example, SLAs of inner city in Melbourne and Canberra have estimates of 27.0 percent and 23.2 percent respectively. Perhaps, these results are due to the fact that housing in inner city SLAs is always preferable to many high income households who are in housing stress by choice. Housing supply is very much limited in inner city areas. So the house price and rents are too high, and consequently unaffordable to a high proportion of low to middle income households.

Nevertheless, many SLAs from Brisbane and Sydney, with some others from coastal cities in Queensland and NSW, also have the highest rates. It is evident that few SLAs in Sydney: Fairfield (C) - East, Canterbury (C), Bankstown (C) - North-East and Auburn (A) have a significantly high proportion of housing stress. This is because a large number of households live in these SLAs, with a sizable representation of them from the low income households. Also, small sample size problems appear to exist within many SLAs in Brisbane, where the number of households experiencing housing stress is very low, but the percentage estimate is significantly high due to the small value of the denominator.

5. VALIDATION TOOLS

Validation and the creation of measures of the statistical reliability of small area estimates by microsimulation modelling are challenging (Ballas and Clarke, 2001; Hynes et al., 2006; Edwards and Clarke, 2009; Rahman, 2009; Rahman et al., 2010a). At small area levels, the estimated data are typically unavailable from another source. Accordingly, some researchers have suggested re-aggregating the small area estimates up to larger levels, where reliable data are available to compare the results (Ballas and Clarke, 2001; Kelly, 2004), while others have attempted to use alternative methods to determine the accuracy of their model estimates (Hynes et al., 2006; Edwards and Clarke, 2009). Discussions about various validation methods used by researchers are outlined in detail in other studies (i.e. in Rahman, 2011; Rahman et al., 2013; and Rahman and Harding, 2014). This section offers a new validation tool for testing the accuracy of SLA level housing stress estimates in Australia which are produced by the microsimulation modelling technology.

Absolute Standardised Residual Estimate (ASRE) Analysis

In this approach to validation, we first have to calculate an absolute standardised residual estimate (ASRE) for a small area (in this case SLA level housing stress estimation), and then analyse the values of the ASRE to make a decision about the accuracy. The mathematical formulae for the ASRE use the following standard notations:

[[??].sub.ij] is an observed household total in the jth data at the ith small area;

[Y.sub.ij] is the total households in the jth population at the ith small area;

and

[m.sup.r] is the number of small areas in a rth region and r > i.

The ASRE can be defined as

ASRE = ([[delta].sub.ij])/[square root of AEMSE])

where [[delta].sub.ij] = [absolute value of [Y.sub.ij] - [[??].sub.ij]] and AEMSE = 1/[m.sub.r] [[sigma].sub.m] [([Y.sub.ij] - [[??].sub.ij]).sup.2] where the

AEMSE is the Average Empirical Mean Square Error (see for example, Gomez-Rubio et al., 2008 and Rahman, 2011).

The decision criterion for this validation technique is: 1) when the value of ASRE is close to zero or less than 2 for a SLA then the synthetic household estimate is acceptable (i.e. the performance of the model estimate is good); and 2) when the ASRE value is at least 2, then it is usually considered as a large error (Field, 2000) suggesting that unexplained errors exist in the model estimates and/or the microsimulated datasets.

Results from the ASRE Analysis

Results of ASRE analysis for overall households in housing stress confirm that for 1 205 SLAs out of 1 278 (94.3 percent) in Australia, the model determined very accurate housing stress estimates (Figure 6). There are 73 SLAs that have an ASRE measure of at least 2, and many of these SLAs are located in the capital cities and coastal centres such as Wollongong, Newcastle, Coffs Harbour, Tweed Heads, Gold Coast, Hervey Bay, Mackay etc. For instance, a few SLAs in Ipswich show a high value of ASRE, which indicates that the model has produced statistically non-significant housing stress estimates in this area. In particular the SLA: Ipswich (C) - Central shows an ASRE value of 5.6, which is much bigger than 2. So, for this small area, the estimate of housing stress is not statistically accurate using the ASRE measure.

Ipswich is one of the fastest growing regions in Brisbane and the population characteristics are quite different to the Australian average. In particular, a significantly large number of working population families (about 60 percent) are Technicians & trades workers, Community & personal service workers, Clerical & administrative workers, and Labourers, who tend to have lower incomes (ABS, 2007). But the housing costs in this area are relatively high. The supply of housing in this area is also inadequate with growing housing demand for increasing populations. As a result, the model simulates significantly high estimates of housing stress for the region by considering the micro-level attributes.

[FIGURE 6 OMITTED]

To get an idea of why a non-significant value of ASRE arises for some of these small area estimates, we may check detailed micro-level results for an SLA (such as Petermann-Simpson in Alice Springs, NT) along with its geographic characteristics. For the Petermann-Simpson SLA, the ASRE value of 8.5 has revealed that the model overestimated the housing stress for overall households. It is noted that Petermann-Simpson is one of the functional economic and strategic growing areas in rural central Australia (ABS, 2007; Rahman, 2011). Economic growth in this SLA results from the flow-on effects of providing regional support services to major national projects such as tourism, culture and heritages conservation, mining development, defence construction, forestry and horticultural trials, and a transport and logistics hub servicing the central Australia railway. However, residential land release and housing supply is not consistently adequate in this remote area with its growing population. High demands for housing increase the house price and rents in the area that increase noticeably the money allocated to housing for lower income households and perhaps skew the estimate of housing stress. Sharply increasing housing costs (the average annual change for 2008-09 is estimated as 27 percent) for a large group of low income households (having median weekly income of 961 AUD) residing in Petermann-Simpson has influence over a high rate of housing stress.

6. CONCLUSIONS

This paper has empirically examined the statistical local area level housing stress estimates across Australia using a synthetically simulated micro-dataset and analysed the results. It has also demonstrated a new method for validating the results of small area housing stress statistics.

According to our findings housing stress estimate is greatest within several-hotspot areas in Australia. One of the key findings using outputs from the spatial microsimulation model was that in 2011 around one in ten Australian households were experiencing housing stress, with large numbers of these households residing in the east coast states of New South Wales, Victoria and Queensland. When looking at housing stress at a higher geographic disaggregation, findings from the model outputs have revealed that households experiencing housing stress were mostly residents of the Sydney, Melbourne, Brisbane, Perth, Adelaide, Gold Coast, Hunter, Illawarra, Mid-North Coast statistical divisions, along with some other statistical divisions located across the coastal centres of New South Wales and Queensland. The Canberra, Hobart and Darwin statistical divisions all have relatively low housing stress levels.

Breaking the geographic classifications down to a finer level, we find greater heterogeneity in housing stress estimates, but still the households are concentrated in these main locations or spots. Areas with a high proportion of households living in housing stress were those concentrated in the outer fringes of capital cities along the east coast of Australia. Of particular interest was Newcastle, which has the largest estimated number of households (20 990) in housing stress among all of the statistical subdivisions in Australia. More explicitly, the range of estimated numbers of housing stress was from 1 886 households for Newcastle (C) Outer West to 2 826 households for Newcastle (C)--Inner City among the nine SLAs in this statistical subdivision. Although the estimated number is the highest for Newcastle, the percentage estimate (about 11.4 percent) was relatively lower than in many hotspot SSDs within the capital and non-capital cities. Some other non-capital coastal cities--such as Wollongong, Richmond-Tweed, Hastings and Clarence etc in New South Wales and Gold Coast, Sunshine Coasts, Wide Bay-Burnett and Cairns City in Queensland - have spatial subdivisions with much higher rates of housing stress. In addition, many statistical subdivisions within capital cities have also demonstrated large estimated figures. Basically, these regional subdivisions are located in the greater western and northern regions of Sydney, in the western, inner, eastern middle, southern and northern outer regions of Melbourne, in the north-west, south-east and Logan City regions of Brisbane, in the north, east and south-east metropolitan regions of Perth, as well as in the northern, southern, western and eastern regions of Adelaide.

Breaking the geographic scale down even further to one of the smallest and administratively helpful areas--the SLA--we can really see which small areas are suffering the most from housing stress. Findings have demonstrated that a large number of SLAs in the New South Wales coastal cities, including Sydney, had the highest numbers of households in housing stress. Most of the SLAs in Melbourne, Adelaide, and Hobart also had significantly high estimates. Moreover, the rapidly growing mining areas around inland locations in different states have resulted in many SLAs with relatively higher estimates of housing stress. This could be because of a significant lack in the supply of housing within these quickly growing mining areas, which in turn creates a high demand of housing and then increasing housing costs for mainly low and middle income households. In contrast, significantly large numbers of SLAs in Brisbane, Canberra and Darwin have much lower numbers of households in housing stress. This is probably because these SLAs are not only small in size but also have relatively smaller household populations. The results of the percentage estimates reveal somewhat opposite results to the number count estimates: that is, many small SLAs with few households show high percentages of households in housing stress, but there are actually only a few households in stress in these locations. Nonetheless, various SLAs in different capital cities indeed confirm significantly large values in housing stress for both number counts as well as percentages.

The validation tool outlined in this paper is the ASRE analysis, where an ASRE for the SLA level housing stress estimate has been calculated and then analysed using a standard cut-off criteria for making a decision. Results have demonstrated statistically accurate estimates for a very high number of SLAs (about 94.3 percent). There are a number of SLAs with statistically insignificant values of ASRE, and most of them are geographically located in the capital cities, including Melbourne, Brisbane, Canberra and Darwin, as well as major coastal centres in the Eastern part of Australia. Additionally, findings suggest that the proposed validation tools can not only check the statistical validity of an SLA level estimate, but can also identify and describe the possible features of the SLAs that may have insignificant results. The SLAs with ASRE values significantly bigger than 2 demonstrate inaccurate housing stress estimates for the respective SLAs. In such a case researchers would undertake further analysis of these micro-level data for these SLAs, along with their geographic attributes.

Looking at future research directions, we are currently finalising estimates of SLA level housing stress estimates by tenure types within eight major capital cities in Australia, comparing the estimates of housing stress between the cities as well as looking at different SLAs within a specific major city. In addition, a proposed technique for estimating confidence intervals around the housing stress estimates will also be explored. Finally, using groupings of various housing costs such as 0-10, 10-20, 20-30 percent etc of the households' income, a new study would estimates the housing stress for different income deciles and then map the estimates within these groups at a chosen spatial scale such as local government area.

APPENDIX
Table A1. Number of Households and Housing Stress Estimates by
Tenure Types for the States and Territories in Australia, 2011.

States   Overall     Owners    Buyers    Public    Private   Other
&        Total                           Renters   Renters   tenure
Terri-   HH (1)      HH        HH        HH        HH        HH
tories   (HS% (2))   (HS)      (HS)      (HS)      (HS)      (HS)

NSW      2328200     836696    760241    114423    548464    68376
         (11.57)     (0.098)   (11.04)   (17.84)   (29.92)   (0.135)
VIC      1781601     665595    649015    57158     364009    45824
         (10.42)     (0.074)   (11.00)   (17.23)   (28.53)   (0.103)
QLD      1387069     452587    480441    49455     362374    42211
         (11.29)     (0.127)   (9.80)    (15.66)   (27.90)   (0.142)
WA       701116      226922    270603    29681     151063    22847
         (9.91)      (0.087)   (8.90)    (14.91)   (26.94)   (0.153)
SA       583284      208924    208090    42311     104603    19356
         (10.54)     (0.064)   (9.94)    (15.19)   (32.66)   (0.103)
TAS      181666      70923     62269     10912     32428     5134
         (10.11)     (0.059)   (10.31)   (14.04)   (31.96)   (0.136)
ACT      116911      35567     45761     9453      24101     2027
         (6.59)      (0.008)   (4.52)    (20.05)   (15.44)   (0.000)
NT       48188       8432      18174     4533      14668     2380
         (9.35)      (0.43)    (7.08)    (19.32)   (15.67)   (0.042)
AUS      7128035     2505646   2494594   317926    1601710   208155
         (10.85)     (0.091)   (10.30)   (16.72)   (28.74)   (0.13)

Note: (1) No. of Households; (2) Proportion of Households in Housing
Stress. Source: the Authors.

Table A2. Lists of the Thirty-Five SSDs with the Highest Estimated
Numbers, and Highest Percentages of Households, Experiencing Housing
Stress across Australia, 2011.

ID      SSD Name               HS1     %

11005   Newcastle              20990   11.4
10525   Fairfield-Liverpool    17464   16.9
20510   Western Melbourne      17098   11.5
50515   North Metropolitan     16090   10.1
10520   CanterburyBankstown    15935   16.1
40505   Northern Adelaide      15626   11.9
10540   CentralWestern Syd.    15352   15.2
10515   St George-Sutherland   14748   9.8
10505   Inner Sydney           14589   12.1
10570   Gosford-Wyong          14365   13.0
20505   Inner Melbourne        14264   12.3
50525   South Eastern Metro.   13417   11.0
20565   Southern Melbourne     13338   9.1
40520   Southern Adelaide      12689   10.0
20550   Eastern Middle Melb.   12316   8.3
30715   Gold Coast West        11732   14.1
10545   Outer Western Syd.     11640   11.2
10553   Blacktown              11322   13.2
30905   Sunshine Coast         11195   14.0
11505   Wollongong             11142   11.6
50520   South Western Metro.   11003   9.9
30710   Gold Coast East        10889   15.5
20580   SuthEast Outer Melb.   10446   11.9
40510   Western Adelaide       9800    11.6
30507   Nrthwest Outer Bris.   9339    8.4
20530   Northern Mid. Melb.    9199    10.1
10555   Lower Northern Syd.    9140    8.2
50510   East Metropolitan      8934    10.1
10530   Outer SuthWest Syd.    8837    11.9
10560   Central North Sydney   8815    6.6
40515   Eastern Adelaide       8634    9.8
10510   Eastern Suburbs        8568    9.8
30511   Sutheast Outer Bris.   8345    10.5
60505   Greater Hobart         7856    10.3
20555   Eastern Outer Melb.    7826    9.1

ID      SSD Name               HS      %2

10525   Fairfield-Liverpool    17464   16.9
12501   Coffs Harbour          3055    16.7
10520   Canterbury-Bankstown   15935   16.1
30710   Gold Coast East        10889   15.5
12007   Lismore                1758    15.4
10540   CentralWestern         15352   15.2
          Sydney
12005   Tweed Heads&Coast      3611    15.1
20575   Greater Dandenong      6384    14.9
          City
12010   RichmondTweed SDBal    7311    14.9
12503   Port Macquarie         2338    14.6
20535   Hume City              6453    14.1
30715   Gold Coast West        11732   14.1
12505   Clarence(excl.         5146    14.0
          CoffsHarb)
31507   Hervey Bay City        2589    14.0
          Part A
30905   Sunshine Coast         11195   14.0
30705   Gold Coast North       2533    13.9
30520   Caboolture Shire       6324    13.8
30545   Redcliffe City         2806    13.6
12510   Hastings(excl.Prt      5238    13.5
          Macqu)
30530   Logan City             7670    13.4
10553   Blacktown              11322   13.2
31505   Bundaberg              2954    13.2
14515   Lower South Coast      3362    13.0
30910   Sunshine Coast         3066    13.0
          SD Bal
10570   Gosford-Wyong          14365   13.0
14003   Bathurst               1381    12.7
20585   Frankston City         5484    12.6
11507   Nowra-Bomaderry        1433    12.6
35005   Cairns City Part A     5485    12.5
23005   Mildura Rural City A   2110    12.4
30720   Gold Coast SD Bal      633     12.4
30501   Inner Brisbane         4227    12.4
20505   Inner Melbourne        14264   12.3
24005   Greater Shepparton A   1948    12.1
10505   Inner Sydney           14589   12.1

Note: (1) Arranged by No. of Households Experiencing Housing Stress,
and (2) Arranged by Percentage of Households Experiencing Housing
Stress. Source: the Authors.


ACKNOWLEDGEMENTS: This paper utilises the methodological research that has been undertaken as part of the PhD of Dr Rahman, based on the three prestigious scholarships: an E-IPRS from the Commonwealth of Australia, the ACT - Land Development Agency Postgraduate Research Scholarship from the Government of Australian Capital Territory (ACT) and the Australian Housing and Urban Research Institute (AHURI) and the NATSEM Top-Up Scholarship from the University of Canberra (UC). Special thanks are due to Robert Tanton and Shuangzhe Liu at UC, and Mark Morrison, Kenneth Russell and peoples involved in the CSIRO workshop at CSU in Australia for their valuable comments and stimulus.

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Azizur Rahman

Lecturer, School of Computing and Mathematics, Charles Sturt University, Wagga Wagga, NSW, 2678, Australia. Email: azrahman@csu.edu.au

Adjunct Associate Professor, University of Canberra, Canberra, ACT 2601, Australia. Email: azizur.rahman@canberra.edu.au

Ann Harding

Professor, National Centre for Social and Economic Modelling (NATSEM), University of Canberra, Canberra, ACT, 2601, Australia. Email: ann.harding@natsem.canberra.edu.au
Figure 4. Distribution of Households and Housing Stress Estimates
by Tenure Types in Australia, 2011.

a. Australian Households.

Owners          35.15
Buyers          35.00
Other tenure     2.92
                 26.93
Renters public   22.47
Renters private   4.46

b. Households in Housing Stress.

Renters public    6.88
Buyers           35.00
Renters private  59.55
                  0.34
Owners            0.30
Other tenure      0.04

Source: the Authors.

Note: Table made from pie graph.

Table 1. A Comparison of the Different Measures of Housing Stress.

30 only rule             30/40 rule             30/10-40 rule

General definition--     Specified              More specified
a household is in        definition--'a         definition--a
housing stress if it     household is in        household is in
spends more than 30      housing stress if it   housing stress if it
percent of its income    spends more than 30    spends more than 30
on housing costs'.       percent of its         percent of its
                         income on housing      income on housing
                         costs and the          and places into the
                         household also         bottom 10th to 40th
                         belongs to the         income percentile of
                         bottom 40 percent of   the equivalised
                         the equivalised        income
                         income                 distribution'.
                         distribution'.

Assessing all forms of   Ignores any marginal   Ignores both the
housing stress in one    housing stress.        marginal and severe
flag.                                           housing stress.

Only the absolute        The relative income    The relative income
household income is      of the household is    of the household is
considered.              taken into account.    used.

It is free from          It is based on         It is based on
equivalised household    equivalised            equivalised
income cut-off.          household income       household income
                         cut-off by the         between 10 to 40
                         bottom 40 percent.     percentiles.

Has been used in the     Widely used in         Used on a few
past.                    Australia.             occasions.

No account is given to   Proper treatment is    Proper treatment is
the size of income       given to the size of   given of the size of
unit.                    the household income   the household income
                         unit.                  unit.

Source: Rahman, (2011).

Table 2. An Illustration of Households Synthetic Weights Produced by
the GREGWT Algorithm for SLA level Microdata at in Australia.

Turning the national level household            Household (HH)
weights in the Survey of Income                 synthetic weights
and Housing (SIH)--CURFs data into              for the SLA
                                                levels microdata

Unit    HH  Wkly    Wkly  Other     HH         NSW   NSW    NSW   Other
record  ID  income  rent  variable  weight     SLA1  SLA2   SLA3  SLA

1        1     7       3      ...     1029     0     10.2   0      ...
2        2    11       4      ...     157      0     0      0      ...
3        3    11       4      ...     157      0     0      0      ...
4        4    11       4      ...     157      0     0      0      ...
5        5    11       0      ...     1003     2.45  9.64   16.38  ...
6        6    11       0      ...     1003     2.45  13.54  16.38  ...
...      ...  ...      ...    ...                    ...    ...    ...
...      ...  ...      ...    ...                    ...    ...    ...

...           ...      ...    ...     GREGWT         ...    ...    ...
                                      Re-
                                      weight-
                                      ing
53220         ...      ...    ...

                                      8.4      12465  25853  27940  ...
                                      million

                                      No. of   No. of households in
                                      HHs in   SLAs
                                      AUS

Source: Rahman, (2011).

Table 3. Attributes of the Final Outputs file of the Model.

* SLA ID;         * Renter private           * Buyer in housing
* Total number    households;                stress;
of households;    * Other tenure type        * Renter public in
* Fully owner     households                 housing stress;
households;       (i.e., hospital, hostel,   * Renter private in
* Buyer           military tenure etc);      housing stress;
households;       * Total housing stress;    * Other tenure
* Renter public   * Owner in housing         households in
households;       stress;                    housing stress.

Source: the Authors.

Table 4. Housing Stress Estimates by the Statistical Division in
Australia, 2011.

ID    SD (1) Name         HS (2)   %

105   Sydney              163655   21.17
205   Melbourne           135702   17.55
305   Brisbane            66718    8.63
505   Perth               53766    6.95
405   Adelaide            46749    6.05
307   Gold Coast          25787    3.34
110   Hunter              24764    3.20
115   Illawarra           17058    2.21
125   Mid-North Coast     15777    2.04
309   Sunshine Coast      14261    1.84
120   Richmond-Tweed      12680    1.64
315   Wide Bay-Burnett    11991    1.55
210   Barwon              9783     1.27
350   Far North           9055     1.17
320   Darling Downs       8011     1.04
605   Greater Hobart      7856     1.02
510   South West          7742     1.00
145   South Eastern       7716     1.00
805   Canberra            7700     1.00
240   Goulburn            7339     0.95
235   Loddon              6794     0.88
130   Northern            6654     0.86
345   Northern            6654     0.86
140   Central West        6568     0.85
255   Gippsland           5959     0.77
220   Central Highlands   5621     0.73
330   Fitzroy             5609     0.73
615   Northern            5339     0.69
150   Murrumbidgee        5234     0.68
410   Outer Adelaide      4500     0.58

ID    SD Name             HS       %

340   Mackay              4368     0.57
155   Murray              4292     0.56
135   North Western       4204     0.54
620   Mersey-Lyell        3912     0.51
230   Mallee              3404     0.44
245   Ovens-Murray        3339     0.43
215   Western District    3203     0.41
705   Darwin              3171     0.41
250   East Gippsland      3016     0.39
312   West Moreton        2825     0.37
420   Murray Lands        2657     0.34
435   Northern            2637     0.34
425   South East          2153     0.28
535   Central             1870     0.24
515   LowerGreat South    1848     0.24
415   YorkeLower Nrth     1612     0.21
225   Wimmera             1486     0.19
525   Midlands            1423     0.18
710   NT -Bal             1334     0.17
610   Southern            1266     0.16
530   South Eastern       1245     0.16
430   Eyre                1147     0.15
160   Far West            727      0.09
545   Kimberley           685      0.09
325   South West          575      0.07
355   North West          529      0.07
540   Pilbara             449      0.06
520   UpperGreat South    430      0.06
335   Central West        224      0.03
000   Australia           773073   100

Note: (1) Statistical Division; (2) Total No. of Households in
Housing Stress. Source: the Authors.
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