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Limitations of Census data for calculating propensities
12 The Census question on relationships in the household collects information on only one level of household relationship, that of each person in the household to Person 1 and/or Person 2 on the Census form. In situations where household members are related to each other but not to Person 1 or Person 2, then that second level of relationship may be lost. This may lead to a distortion and underestimation of the number of families, as well as relationships within the household and family type.
13 Person level data within the Census is based on place of enumeration. For 1991 and 1996, persons temporarily absent from the household on Census night were excluded from the propensities as they were only categorised by three broad age groups only, and therefore could not be allocated to household, family and relationship in household type, by five-year age groups. For consistency, persons temporarily absent from the household in the 2001 and 2006 Censuses were also excluded from the propensities. Visitors to households on Census night were also excluded from the propensities because they are not included in family coding in the Census.
30 June 2006 estimated resident population (ERP)
14 Estimated resident population is based on Census counts of usual residents at the national, state and Statistical Local Area (SLA) levels. Account is taken of Census underenumeration and the number of Australian residents temporarily overseas at the time of the Census.
15 Estimated resident population does not distinguish between persons resident in private and non-private dwellings (NPDs). Household and family projections are concerned exclusively with the population usually resident in private dwellings. Therefore, for the purposes of these projections, the proportion of the Census count in NPDs is identified and excluded from the calculation of numbers of households and families but they are included in the analysis of living arrangements.
30 June 2006 household estimates
16 In this publication, household estimates for 30 June 2006 are used to constrain the number of households for 2006 derived from 2006 Census living arrangements of persons. See paragraphs 35 to 38 below.
17 Household estimates for 30 June 2006 are derived from the 2006 Census of Population and Housing, with adjustments for dwelling undercount and dwelling misclassification.
18 The ABS produces population projections every two to three years, with the most recent set being published in Population Projections, Australia, 2006 to 2101 (cat. no. 3222.0) in September 2008. Projections are produced for Australia, the states, territories, capital cities and balances of state (excluding Balance of Australian Capital Territory), disaggregated by age and sex.
19 The projections are based on a combination of assumptions on future levels of fertility, mortality and migration to arrive at the size, structure and distribution of Australia's future population. A range of possible future populations are therefore produced.
20 The Series B population projection from Population Projections, Australia, 2006 to 2101 (cat. no. 3222.0) has been chosen as the future population of Australia and the states and territories, and assumes:
21 Using only one population projection series as the future population of Australia ensures that differences in different series of projections of households, families and living arrangements of people reflect changes in living arrangements only.
22 Chapter 5 - What If...? discusses the results of using two other projections of the population, the Series A and Series C projections from Population Projections, Australia, 2006 to 2101 (cat. no. 3222.0), as the assumptions about the future population of Australia and the states and territories.
Overview and assumptions
23 The ABS uses a propensity method to project numbers of households, families and persons in different living arrangements. The method identifies propensities (proportions) from the Census of Population and Housing for people to belong to different living arrangement types. Trends observed in the propensities over the last four Censuses are assumed to continue into the future, and applied to a projected population. Numbers of households and families are then derived from the projected living arrangements of the population.
24 The projection method initially produces household numbers in the base year (2006) that differ from ABS household estimates for 2006 published in Australian Demographic Statistics (cat. no. 3101.0). As a consequence, before the Census trends can be projected forward, living arrangements in the base year must be 'reconciled' such that the number of households derived from them are consistent with ABS household estimates. To ensure the discrepancy that arises between the two methods is not carried through the projected years, reconciled base year living arrangement propensities, as opposed to Census propensities, are used as the basis for obtaining projected propensities which are then applied to the projected population to derive projected living arrangements.
25 A household is defined as one or more persons, at least one of whom is at least 15 years of age, usually resident in the same private dwelling. The Census categorises households as discrete units, thus the projection method is based on the assumption that households are discrete units. It is acknowledged that some living arrangements are fluid and that because of study, work or shared care arrangements, a family member may be associated with more than one household. For example, full-time students living away from home may still be dependent on their family household.
26 This method assumes that trends observed over the four Censuses accurately reflect underlying changes in living arrangement characteristics over that time period.
27 Before choosing to base living arrangement trends on four Censuses (that is, 1991 to 2006), observed propensities for five (1986 to 2006) and three (1996 to 2006) Censuses were analysed to assess the influence of more, or fewer, data points upon the living arrangement trends. On one hand, more data points might be considered a stronger indicator of trends over the long-term. Conversely, fewer data points might provide greater sensitivity in the projections to more recent changes in trends in living arrangements. In this issue, four Census data points have been used to incorporate both long-term and more recent trends, without an undue influence by either.
28 Living arrangement propensities were calculated using a large proportion (95% in 2006) of the Census count of Australian usual residents. People not counted in the Census, or not included in the classification of living arrangements, but included in the projected population were proportionally distributed across the living arrangement types. This assumes that these people have the same living arrangement distribution as those included in the calculation of the propensities.
29 Distributing by this method is likely to lead to an underestimation of lone person households. If an entire household is absent on Census night, that household can be missed. However, if some members of the household are at home, the household type can be coded based on the information of those members remaining at home, and the information provided for members temporarily absent. It is therefore more likely for a household to be missed if that household consists of only one member.
30 The method for obtaining household and family projections is outlined in detail in paragraphs 31 to 50 below. The procedure consists of four main parts: (1) obtaining the rate of change in living arrangement propensities; (2) reconciling base year living arrangements to align with ABS household estimates; (3) obtaining projections of living arrangements; and (4) deriving numbers of households and families from the projected living arrangements.
Step 1: Using Census data to obtain the rate of change in living arrangement propensities
31 Census counts from the past four Censuses, classified by living arrangement type and five-year age group, were used to obtain the rate of change in living arrangement propensities. There are 15 living arrangement types, as shown in summary tables in Chapter 3 - Projection results, Australia and Chapter 4 - Projection results, States and Territories.
Step 1.1 Population distribution by living arrangement
32 Using the 1991, 1996, 2001 and 2006 Census datasets, Census counts were classified by living arrangement and five-year age groups. Visitors to households, overseas visitors and people in non-classifiable households were excluded.
Step 1.2 Calculation of propensities
33 From the distribution produced at step 1.1, the propensity of persons in each five-year age group to live in each living arrangement was calculated using the total count of persons by five-year age group as the denominator. Propensities for Australia for the 1991, 1996, 2001 and 2006 Censuses are provided in data cube Living arrangement propensities, Australia.
Step 1.3 Rate of change in propensities
34 A line of best fit was calculated for each living arrangement and age group, using the observed 1991, 1996, 2001 and 2006 propensities (calculated in step 1.2). The annual rate of change for each line of best fit was calculated. A condition to measure the closeness of fit of each straight line was employed. If the fitted straight line produced an r-square value of greater than 0.2, it was assumed that there was an observable trend in that particular living arrangement and age group, which was assumed to continue into the future at the rates specified in Table 2.1. If the fitted straight line produced an r-square value of less than 0.2, it was assumed there had been no change in propensity between 1991 and 2006, and therefore the 2006 propensity for that living arrangement and age group was assumed to remain constant throughout the projection period. See Graph 2.2 for an illustration of this method.
Step 2: Reconciling base year living arrangements with ABS household estimates
35 Numbers of persons by living arrangement type in the base year (2006) was adjusted such that numbers of households derived from them were consistent with ABS 2006 household estimates.
Step 2.1 Obtaining the number of households from the projection method
36 The 2006 Census propensities were applied to 2006 ERP to obtain 2006 ERP disaggregated by living arrangement and five-year age group. From these living arrangements, the number of households and families were obtained using the method outlined in step 4.1 to 4.4.
Step 2.2 Reconciling living arrangements with household estimates
37 The numbers of lone person households and total households for 2006 obtained from the projection method were replaced with 2006 ABS household estimates of the number of lone person households and total households. The difference between the total numbers of households and lone person households was proportionally distributed amongst family and group households. The number of families and then persons by living arrangement were derived from the scaled household estimates, using the method outlined in step 4 in reverse. For example, to obtain the number of persons in a group household from the number of group households, the reconciled number of group households was multiplied by the average size of a group household based on the 2006 Census (as opposed to dividing the number of persons in group households by this ratio to obtain the number of group households).
38 The 2006 reconciled counts by living arrangement were proportionally distributed across the five-year age groups according to the 2006 Census propensities (as generated in step 1.2). The distribution was constrained to sum to 2006 ERP (by age) and the reconciled totals for each living arrangement.
Step 2.3 Calculating reconciled propensities
39 The propensity to live in each living arrangement and age group from the reconciled 2006 counts by living arrangement and age group was calculated. Reconciled propensities are provided in data cube Living arrangement propensities, Australia.
Step 3: Obtaining projected number of persons by living arrangement
40 The 2006 reconciled propensities were used as the basis for obtaining the projected propensities.
Step 3.1 Applying Census trends to obtain projected propensities
41 Assumed rates of change, generated in step 1.3, were applied to the 2006 reconciled propensities (generated in step 2.3) to give projected propensities for the period 2007 to 2031. This produced three series of 'projected propensities'. Projected propensities were subsequently adjusted to add to 100% in each five-year age group.
Step 3.2 Applying projected propensities to the projected population
42 For each living arrangement and age group, the projected propensities were then multiplied by the projected population of each age group, for each year from 2007 to 2031, to obtain the three series of projected population by living arrangement type.
Step 3.3 Constraining of sub-state and state totals to Australian totals
43 Propensities were produced for Australia, the states, territories, capital cities and each balance of state (excluding Balance of Australian Capital Territory) and applied to the respective projected population. As the propensities were projected independently at each geographical level, after they were applied to the projected population their sum did not equal the distribution of living arrangements for Australia. In order to ensure consistency in the projected number of persons, constraints were applied to person level data to ensure that the sum of the sub-states and states add to that of Australia.
44 Constraining was conducted using two-dimensional iterative proportional fitting (IPF). To constrain to Australian totals, a matrix was constructed for person counts for each five-year age group for each state/territory and living arrangement type. The figures in the body of the matrix were proportionally scaled across rows and columns simultaneously constraining to the Australian living arrangement totals in the final column and age totals in the final row. The scaling process was repeated several times until stability was attained within the matrix. Decimals produced by the scaling process were then rounded, with column and row totals preserved. The final matrix was fed back into the extrapolation process, forming the base for the next year's projections.
45 This procedure was then conducted at the sub-state level. The same process was followed, with the matrix constrained simultaneously to state or territory living arrangement totals and sub-state age totals. For a more detailed description of the IPF procedure, see Purcell, N. J. and Kish, L., (1979), Estimations for small domains, Biometrics, 35, pp. 365-384.
Step 4: Calculating the number of families and households
46 Three series of projected numbers of households and families were derived from the three series of living arrangement projections. When calculating the number of 'other families', family households and group households, ratios from the 2006 Census were applied to account for varying household and family sizes in these categories. These ratios were generated and applied at the capital city/balance of state level, from which state and Australia level data were aggregated. The ratios are presented in the following table.
Step 4.1 Deriving numbers of families from the living arrangement types
47 The number of couple families (with or without children) were calculated as half the number of partners in couple families (with or without children). The number of one-parent families were calculated as the number of male lone parents plus the number of female lone parents. The number of 'other families' were calculated by dividing the number of persons living in 'other families' by the average size of 'other families' at the 2006 Census.
Step 4.2 Converting families to family households
48 Family households can contain more than one family. In order to obtain numbers of family households, families were converted to households using the family households to families ratio.
Step 4.3 Deriving numbers of non-family households
49 Numbers of non-family households were also derived from the living arrangement types. The number of lone person households were calculated as the number of male lone persons plus the number of female lone persons. The number of group households were calculated by dividing the number of persons in group households by the average size of group households at the 2006 Census.
Step 4.4 Deriving the total number of households
50 Family and non-family households were added to produce the total number of households.
DIFFERENCE BETWEEN 2006 ESTIMATES OF FAMILIES IN THIS PUBLICATION AND 2006 CENSUS COUNTS OF FAMILIES
51 It should be noted that the 2006 estimates of families in Australia and the states and territories in this publication differ from the number of families according to the 2006 Census of Population and Housing. The 2006 estimate of the number of families in Australia in this publication (5,735,051) is greater than the 2006 Census count of families (5,219,165) published in various 2006 Census publications. This is due to estimates of families in this publication being based on 2006 estimated resident population as well as 2006 Census living arrangement propensities. The 2006 ERP of Australia is greater than the 2006 Census count of people in Australia as it includes Census net undercount and residents temporarily overseas, and as a result, the number of families based on 2006 ERP is greater than the number of families from the 2006 Census.
52 The propensities were derived using the area boundaries as they existed at the relevant reference points (1991, 1996, 2001 and 2006). It is considered that the use of such propensities (rather than based on revised areas) would not have had a significant effect on the comparability of the propensities over time. For example, the 2006 Australian Standard Geographical Classification (ASGC) incorporated a number of boundary changes to the Statistical Division of Brisbane. Analysis of the propensities for Brisbane and the Balance of Queensland found there was little to no change in the propensities for each living arrangement and age group when calculated using 2006 ASGC boundaries compared to previous boundaries.
53 Generally, in this publication, figures of less than one million are rounded in the text to the nearest thousand while figures of more than one million are rounded to the nearest one hundred thousand.
54 Changes in population over time are commonly discussed in terms of average annual growth rates. In this publication, however, changes are for the most part presented as percentage increases or decreases over the entire 25-year period (from 2006 to 2031), in order to make differences between projected numbers (of households, families and people in different living arrangements) more discernible.
COMPARISON WITH STATE GOVERNMENT HOUSEHOLD PROJECTIONS
55 The following table has been provided for comparative purposes. It gives details of ABS and state and territory government household projections at the capital city and balance of state level for 2016. Note that ABS and New South Wales, Victoria and Queensland government projections are 2006-based, while Western Australian projections are 1996-based. Not all state and territory governments produce household projections.
56 ABS publications draw extensively on information provided freely by individuals, businesses, governments and other organisations. Their continued cooperation is very much appreciated; without it, the wide range of statistics published by the ABS would not be available. Information received by the ABS is treated in strict confidence as required by the Census and Statistics Act 1905.
RELATED PUBLICATIONS AND REFERENCES
57 Users may also wish to refer to the following ABS products:
ADDITIONAL STATISTICS AVAILABLE
58 As well as the statistics included in this and related publications, the ABS may have other relevant data available on request. Inquiries should be made to the National Information and Referral Service on 1300 135 070.
59 ABS products and publications are available free of charge from the ABS web site <https://www.abs.gov.au>. Click on Statistics to gain access to the full range of ABS statistical and reference information.
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