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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 458 Rahman and Harding 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 Spatial Analysis of Housing Stress Estimation Within 459 Australia with Statistical Validation 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.

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

–  –  –

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. Distribution of Housing Stress for Three Variants in Australia.

Source: Rahman, (2011).

Spatial Analysis of Housing Stress Estimation Within 461 Australia with Statistical Validation 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 462 Rahman and Harding 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 Spatial Analysis of Housing Stress Estimation Within 463 Australia with Statistical Validation 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.

–  –  –

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 Analysis of Housing Stress Estimation Within 465 Australia with Statistical Validation Spatial Microsimulation Model Outputs: The 1st Stage Basically there are three outputs from this initial phase of the model.

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