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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.

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

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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


2) Synthetic weights; and

3) The Consumer Price Index (CPI) file.

Spatial Analysis of Housing Stress Estimation Within 467 Australia with Statistical Validation 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.

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

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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.


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

Households and Housing Stress by Tenure Type

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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).

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22.47 0.04 26.93 0.34 0.30 4.46 6.88 33.23 35.15 Figure 4. Distribution of Households and Housing Stress Estimates by Tenure Types in Australia, 2011. Source: the Authors.

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 Spatial Analysis of Housing Stress Estimation Within 469 Australia with Statistical Validation 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).

470 Rahman and Harding Table 4. Housing Stress Estimates by the Statistical Division in Australia, 2011.

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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 RichmondTweed in the NSW and the Gold Coast, Sunshine Coast and Wide BayBurnett 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.

Spatial Analysis of Housing Stress Estimation Within 471 Australia with Statistical Validation

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 472 Rahman and Harding 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.

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Figure 5. Estimated Proportion of Households in Housing Stress by the Statistical Local Area in Australia, 2011.

Source: the Authors.

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 Spatial Analysis of Housing Stress Estimation Within 473 Australia with Statistical Validation 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.


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;

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