CONTENTS
List of tables

SECTIONS
Preface
Introduction
1. Data sources
2. Proposed classification of living arrangements
3. Method and results
4. Comparison with ABS household estimates
5. Methodological issues
6. Further work
7. Proposed output
References

ADDITIONAL INFORMATION
Appendix 1: 1996 Census, living arrangement distribution
Appendix 2: 1996 Census propensities
Appendix 3: 1996 Census propensities applied to June 1996 ERP
Appendix 4: Generating 1996 household numbers from 1991 propensities

• Step 1: 1991 Census, living arrangement distribution
• Step 2: 1991 Census propensities
• Step 3: 1991 propensities applied to June 1996 ERP
• Step 4: Calculating the number of families
• Step 5: Conversion of family numbers to household numbers
• Step 6: Calculating non-family households
• Step 7: Calculating total households

Appendix 5: Change in Census propensities, 1991-1996


LIST OF TABLES
Table 1: Distribution by living arrangement, 1996 Census count
Table 2: Calculating the number of families
Table 3: Number of families, June 1996
Table 4: Calculating the family to household ratio, 1996 Census
Table 5: Number of family households, June 1996
Table 6: Calculating the number of non-family households
Table 7: Non-family households, June 1996
Table 8: Total households, June 1996
Table 9: Comparison with ABS household estimates, 1996 propensities
Table 10: Comparison with ABS household estimates, 1991 propensities
Table 11: Household of related individuals
Table 12: Disaggregating 'household of related individuals'
Table 13: The effect of including only complete households, 1996 Census living arrangement distribution
Table 14: The effect of including all components of ERP, June 1996


Preface
The Australian Bureau of Statistics is currently developing a method for projecting numbers of households, numbers of families and living arrangements of persons, with the intention of publishing projections by the end of August 1999. This paper provides an overview of the proposed method. The authors would welcome any comments, preferably by 31 May 1999.

The authors can be contacted on (02) 6252 6141, or by writing to:

Demography Section
Australian Bureau of Statistics
PO Box 10
Belconnen ACT

email: Sue.Taylor@abs.gov.au


Introduction

Household and family projections are a complement to the household estimates which have been produced by the ABS since 1996 (See Household Estimates Australia: 1986, 1991-1994 Cat. No. 2710.0. Updated statistics are published in Australian Demographic Statistics, Cat. no. 3101.0). This paper provides an overview of the method proposed by the ABS for producing household and family projections. The first section reviews the sources of data used. The second section outlines the proposed classification, and the third section discusses the method and results of the preliminary work undertaken so far. The fourth section compares the number of households produced by the proposed method for June 1996 with the published household estimates for 1996. Additional methodological issues are discussed in the fifth section. Finally, the last two sections provide an outline of further work and the intended output to be published.


How does the ABS define a 'household'?
A household is defined as a dwelling unit where one or more related or unrelated people reside and make common provision for food or other essentials for living. People live in 'private' dwellings - houses, flats etc. and 'non-private' dwellings - hostels, nursing homes etc. In the census, the population counted in 'private' dwellings is classified according to the type of household (family households or non-family households, the latter is split into lone person and group households). People counted in 'non-private' dwellings have no household type assigned to them.


How does the ABS define a 'family'?
A family is defined as two or more persons, one of whom is at least 15 years of age, who are related by blood, marriage (registered or de facto ), adoption, step or fostering and are resident of the same household. Families are formed by examining the relationship of each person to the household reference person (nominated as Person I or person 2) on the census form, along with additional information for any usual member of the household who happened to be temporarily absent from the household on the census reference date. Families are classified as couple families, lone parent families, and other family types. Some households may contain more than one family.




1. Data Sources
Three main sources of data are used for this project:

• The Census of Population and Housing
• The Estimated Resident Population (ERP)
• Population Projections

Census of Population and Housing
A census of population and housing is held every five years. It produces a count of households, families and individuals at the census reference date.

Prior to the 1986 Census, occupied houseboats in marinas and caravans, tents and cabins in caravan parks and roadside parking areas were treated as non-private dwellings. In the 1986, 1991 and 1996 Censuses, the classification of these dwellings was changed to private dwellings and household and family data were collected from them. For the 1996 Census, dwellings in manufactured Home Estates (MHEs) and self-care units in Accommodation for the Retired or Aged were also classified as private dwellings.

Census data classified at three levels (households, families and individuals) are used in the projections of households, families and living arrangements.

Limitations of census data for preparing projections
The census question on household relationships solicits information on only one level of household relationship, that of each person in the household to Person 1 or Person 2. In situations where household members are related to each other but not to Person 1 or Person 2, then that second level of relationships may be lost. This may lead to a minor distortion and underestimation of the number of families and family type. The census has been used as the main data source in order to achieve consistency between the household projections and ABS household estimates.

Person level data within the census is based on place of enumeration. Although responses to the census question on persons temporarily absent from the household give person level data for absent usual residents, this is categorised by three broad age groups only. For the purposes of household projections, data are required by five year age groups. Because relationship in household data cannot be allocated back to 5 year age groups, visitors to households on census night are excluded from the projection's data set.

Estimated Resident Population (ERP)
The ABS publishes quarterly estimates of the ERP at the national and State level, and annually at the Statistical Local Area (SLA) level. The ERP is based on census counts of usual residents. It is adjusted for census underenumeration and takes account of the number of Australian residents temporarily overseas at the time of the census.

ERP is obtained by adding to the estimated population at the beginning of each period the components of natural increase (on a usual residence basis) and net overseas intercensal migration. For States and Territories, account is also taken of estimated interstate movements involving a change of usual residence. After each census, estimates for the preceding intercensal period are revised by incorporating an additional quarterly adjustment (intercensal discrepancy) to ensure that the total intercensal increase agrees with the difference between the estimated resident populations at the two respective census dates.

Population Projections
The ABS publishes population projections every two to three years. Projections of the population by age and sex are produced for Australia, the States and Territories. Capital city/balance of State projections are produced for each State and the Northern Territory. The projections are based on a combination of assumptions on future levels of births, deaths and migration to arrive at the size, structure and distribution of Australia's population into the next century. Three main series are published.


2. Proposed classification of living arrangements
A classification of the population by living arrangements is necessary for producing projections using the propensity method. The classification being developed is an adaptation from the classification used by McDonald and Kippen in Household Trends and Projections: Victoria, 1986-2011. Key clients have identified the need for data that are meaningful at a relationship in household level (for example, is a 25 year old male in a two parent family a child or a parent in that family?). The proposed classification fulfils this requirement by identifying the living arrangements of the population at the person level. To achieve this level of classification, three standard ABS census variables have been combined. The resulting classification describes a person as having a relationship type (eg. wife, husband, child), within a family type (eg. couple only family, lone parent family), within a household type (eg. family household, lone person household, group household). The three standard ABS census variables used are:

• Household Type (HHTD)
• Family Type (FMTF)
• Relationship in Household (RLHP)

By combining these three variables, the following classification of living arrangements is obtained:

1. Private Dwellings

1 Family Households
	1 Couple families
		1 Husband, wife or partner (partner) 2 Child under 15, dependent student, non-dependent child (child) 3 Other related individual
	2 Couple families without children
		1 Husband, wife or partner (partner) 2 Other related individual
	3 One parent families
		1 Lone parent, male 2 Lone parent, female 3 Child under 15, dependent student, non-dependent child (child) 4 Other related individual
	4 Other families
		1 Other related individual 2 Unrelated individual
	5 Unrelated individuals living in family households
2 Non-family households
	1 Lone person households
		1 Lone person, male 2 Lone person, female
	2 Group households
		Group household member

2. Non - Private Dwellings

1 Person in a non-private dwelling. 2. Person in an offshore or migratory CD

A number of living arrangements are excluded from the classification, these include:

Private Dwellings
	All Family and non-family households
		Visitor (from within Australia) Overseas visitor
	Non Classifiable households
		Person in a non-classifiable household.

3. Method and results

The proposed projection method is a propensity based method as used by McDonald and Kippen in Household Trends and Projections: Victoria, 1986-2011. Household propensity methods are widely known and used (see Bell, Cooper and Les, 1995). In the proposed method, numbers of families and households are derived from the person level living arrangement classification.

The robustness of the proposed classification and the accuracy of the method for generating numbers of families and households in the base year (1996) has been evaluated. This was done by generating propensities for living arrangements from the 1996 Census and applying these to 30 June 1996 ERP. The results were then compared to the ABS household estimates. Similar calculations were done using 1991 Census based propensities. This investigation involved four steps:

• preparation of the distribution of census counts by living arrangement classification, by five year age groups, from the 1996 Census.
• calculation of the propensities to belong to the various living arrangements, by five year age groups.
• application of the propensities to 1996 ERP.
• calculation of the number of families and households, from the living arrangement classification.

In the following analysis 'census counts' refer to census data, while persons, families and households at June 1996 refer to data generated using ERP.


Step 1 : Producing the distribution of census counts by living arrangement
The 1996 Census counts were classified according to the living arrangement classification listed above, by five year age groups. Appendix 1 gives this distribution. Table 1 below provides an aggregate picture of living arrangements at the 1996 Census. Visitors to households (3.2% of the census count), overseas visitors (0.8%) and people in non-classifiable households (1.3%) are excluded.

Table 1: Distribution by living arrangement, 1996 Census count.

	Living Arrangement	Number of persons
Couple families
	Partner	4 521 880
	Child	4 501 903
	Other related individual	88 993
Couple families without children
	Partner	3 115 948
	Other related individual	45 585
One parent families
	Lone parent, male	104 503
	Lone parent, female	568 366
	Child	1 047 242
	Other related individual	46 543
Other families
	Other related individual	179 061
All families	Unrelated individuals	136 570
Non-family households
	Lone person, male	642 274
	Lone person, female	790 542
	Group household member	606 189
People in non-private dwellings and offshore and migratory CDs		567 039
Total		16 962 638

Step 2: Calculating the propensities to belong to the various living arrangements
From the distribution produced at Step 1, the propensity of people (by five year age groups) to be in different living arrangements was determined. Using the total census count by five year age groups as the denominator, the percentage of the people (propensity) in each age group to live in each living arrangement type was calculated. Appendix 2 shows the propensities. For example, there is a 84.7% likelihood that a 0-4 year old will be a child in a couple family, and a 4.4% likelihood that a 25-29 year old will be a female lone parent in a lone parent family.


Step 3: Application of the propensities to ERP
The propensities calculated at Step 2 were applied to the June 1996 ERP, by five year age groups. Multiplying the propensity to live in each living arrangement type for a given five year age group, by the ERP for that five year age group, gave the distribution of the population at June 1996 by living arrangement types. See Appendix 3 for this distribution. This assumes that people who were not counted in the census but were included in the ERP (at 30 June 1996) had the same propensities of living arrangement types as those counted in the census.


Step 4 : Calculating the number of families and households
In the final step, family and household numbers were derived from the living arrangement types. This involved a number of sequential steps:


Step 4.1 Deriving numbers of families from the living arrangement types
The calculations to derive numbers of families from the living arrangement types are set out in Table 2. A number of assumptions are made in these calculations, for example, that the number of couple families is half the number of partners in couple families, and that the number of one parent families is the number of male lone parents plus the number of female lone parents. The average household size of 'other families' at the 1996 Census is used to calculate the number of 'other families' from the number of persons living in this family type.

Table 2 : Calculating the number of families

Living Arrangement		Number of persons	Number of families
Couple families			=a/2
	Partner	a
	Child(a)	b
	Other related individual(a)	c
Couple families without children			=d/2
	Partner	d
	Other related individual(a)	e
One parent families			= f + g
	Lone parent, male	f
	Lone parent, female	g
	Child(a)	h
	Other related individual(a)	i
Other families			=j / average family size of 'other families' from the 1996 Census
	Other related individual	j
All family households	Unrelated individuals(a)	k
Total Families			Column Total

(a) These living arrangement types do not contribute to the estimation of the number of families


The number of families, derived from the living arrangement types of the population at June 1996 (Appendix 3), is shown below:

Table 3: Number of families, June 1996

Living Arrangement		Number of persons	Number of families
Couple families
	Partner	4 880 858	2 440 429
	Child	4 800 174
	Other related individual	96 868
Couple families without children
	Partner	3 401 852	1 700 926
	Other related individual	49 485
One parent families
	Lone parent, male	112 753	112 753
	Lone parent, female	615 866	615 866
	Child	1 118 487
	Other related individual	50 693
Other families*
	Other related individual	196 812	92 577
All family households	Unrelated individuals	150 078
Total Families		15 473 926	4 962 551

* A division factor of 2.12593, the average family size of 'other' families at the 1996 Census was used in calculating the number of 'other' families.


Step 4.2 Converting families to family households
Family households can contain more than one family. In order to produce numbers of households, families were converted to households using a ratio which was calculated using the 1996 Census, as shown in Table 4.

Table 4: Calculating the family to household ratio, 1996 Census

	Number of families	Number of family households	Ratio of families to households
1996 Census	4 655 919	4 582 999	0.98433822

This ratio was applied to the number of families produced by the propensity method, to give the number of family households:


Table 5: Number of family households, June 1996

Number of families	Ratio	Number of family households
4 962 551	0.98433822	4 884 828

Step 4.3 Deriving numbers of non-family households from the living arrangement types
As with numbers of families, numbers of non-family households are derived from the living arrangement types. Table 6 sets out the calculations for deriving numbers of non-family households from the living arrangement types. It is assumed that the number of lone person households is the number of male lone persons plus the number of female lone persons, and, that the number of group households is the number of persons in group households divided by the average household size of group households at the 1996 Census.

Table 6: Calculating the number of non-family households

Living Arrangement		Number of persons	Number of households
Non - Family Households
Lone person households			=x + y
	Lone person, male	x
	Lone person, female	y
Group households			= z / average household size of 'group households' at the 1996 Census
	Group household member	z
Total Non-Family Households			Column total

The number of non - family households, derived from the living arrangement types of the population at June 1996 (Appendix 3), is shown in Table 7 below:

Table 7: Non-family households, June 1996

Living Arrangement		Number of persons	Number of households
Lone person households
	Lone person, male	697 940	697 940
	Lone person, female	857 489	857 489
Group households*
	Group household member	668 895	293 518
Total Non-Family Households			1 848 947

* A division factor of 2.278889, which was the average household size for group households in the 1996 Census, was used in calculating the number of group households.



Step 4.4 Deriving the total number of households.
In the final step the total number of households is produced. This is the sum of the number of family households and non-family households.

Table 8 shows the resulting total number of households, for June 1996.

Table 8: Total households, June 1996

Family households	4 884 828
Non-family households	1 848 947
Total Households	6 733 775

4. Comparison with ABS Household Estimates

The ABS has produced household estimates since 1996, using a household size propensity method. For the purposes of household estimates, propensities are derived from the Census of Population and Housing and updated using the monthly Labour Force Survey. Household size propensities are calculated by age, sex, State and part of State, and applied to the resident household population to generate the number and distribution of households by size. Household estimates produce data on household size by number of persons aged 0-14 years and number of persons aged 15 years and over, but do not produce relationship in household data.


Table 9 gives a comparison of the total number of households produced using the proposed method, with ABS household estimates. The table shows that the proposed methodology produces household numbers that are very close to official ABS estimates.

Table 9: Comparison with ABS household estimates, 1996 propensities

1996 Census household count	6 281 817
ABS Household Estimates, June 1996	6 762 115
Total number of households, proposed method, June 1996	6 733 775
Difference from ABS household estimates	28 340
% difference	0.42

The above exercise was repeated using propensities derived from the 1991 Census applied to 1996 ERP (See Appendix 4 for the results of each step). At this stage no trend in propensities over time was considered. Table 10 shows the total number of households produced and compares this figure to ABS Household Estimates.

Table 10: Comparison with ABS household estimates, 1991 propensities

1991 Census household count	5 642 320
ABS Household Estimates, 1996	6 762 115
Total number of households, proposed method, June 1996	6 581 378
Difference from ABS household estimates	180 737
% difference	2.67

5. Methodological issues

1. Classification issues

Given the importance of the underlying classification in producing household projections, the classification used by McDonald and Kippen in Household Trends and Projections: Victoria, 1986-2011 was refined in order to improve accuracy and to more accurately reflect the reality of living arrangements.

McDonald and Kippen grouped together all related and unrelated individuals resident in various family types and classified them as a separate household type, 'household of related individuals'. The division factor used by McDonald and Kippen to produce household numbers from the number of related individuals was based on the 1991 Census (6.2 persons per household). See table 11 below for the number of people and number of households produced in this category at June 1996.

Table 11: Household of related individuals

	Persons	Households
Related and unrelated individuals living in a family household	543 871	87 721

In the proposed ABS classification, the category 'household of related individuals' has been disaggregated, for two main reasons:

1. Other related persons living in a family household were counted back to the family type to which they belonged on Census night, rather than being grouped together to form an artificial household. As these people were allocated back to existing households, they did not contribute to the calculation of the number of households.

2. People classified by ABS as living in 'other families' (eg a brother and sister living together) were identified as a distinct family type and contributed to the calculation of the number of households using a division factor of 2.12593, which was the average family size for this family type in the 1996 Census.


The disaggregation produced the results shown in Table 12.

Table 12: Disaggregating 'household of related individuals'

	Persons	Families
Other related persons in a couple family	96 868
Other related person in a couple family without children	49 485
Other related persons in a lone parent family	50 693
Related persons living in other family types	196 812	92 577
Unrelated individual in a family household	150 078
Total	543 936	92 577

Therefore, the number of 'other families' produced by the ABS classification is 4 856 higher than the number of households of 'related individuals' produced by McDonald and Kippen's classification.

2. Data Issues

i. The proposed ABS method produces numbers of families and households from person level data. This method assumes that the number of couple families is half the number of partners in couple families (that is a ratio of 2 partners to 1 couple family) and that the number of couple families without children is half the number of partners within couple families without children (that is a ratio of 2).

Within both the 1991 and 1996 Censuses, the ratio has been different (1.96). This is because family coding in the census is based on usual residence, whereas person coding is based on place of enumeration. If a given dwelling usually contains a couple family, a couple family will be coded, even if one of the partners is temporarily absent on census night. That family will only have 1 husband/wife/partner, and the other partner will be picked up as a visitor in whichever dwelling he/she was enumerated. Because visitors cannot be allocated back to 5 year age groups and to living arrangement type, they are excluded from the propensities and therefore do not contribute to the estimates of household numbers.

Two options addressing this issue have been discussed:

1. Applying the 1996 Census ratio of 1.96, rather than the ratio of 2, to calculate the number of couple families and couple families without children. This would, however, be inconsistent with the apparent logic of the method.

2. Including only persons enumerated in complete households on census night in the calculation of propensities.
Investigation of this option indicates that there is variation in the likelihood of households being incomplete, by living arrangement type. While overall there is a 5% difference in the number of people counted if only those in complete households on census night are included, the difference varies across living arrangement types. For example, the difference for male lone parents is 9.9%, the difference for partners in couple families is 7.2%, and the difference for partners in couples families without children is 2.2%.

The variation in percentage difference across living arrangement types suggests there is differential bias depending on whether persons in complete households, or all persons at home on census night, are counted. Any bias in the distribution of census counts by living arrangement type would be carried through to numbers of families and households, which are generated from the person level data.

Diagram 1 (attached at the end of this document) shows the different census counts used in calculating propensities when persons in complete households, or all persons at home on census night, are counted.

Table 13 shows the difference in persons counted across living arrangement types when persons in complete households, or all persons at home on census night, are counted.

Table 13: The effect of including only complete households, 1996 Census living arrangement distribution

Living Arrangement		Counting all persons at home	Counting persons at home in complete families only	Difference	% Difference
Couple families
	Partner	4 521 880	4 196 185	325 695	7.2
	Child	4 501 903	4 206 926	294 977	6.6
	Other related individual	88 993	82 340	6 653	7.5
Couple families without children
	Partner	3 115 948	3 047 339	68 609	2.2
	Other related individual	45 585	43 808	1 777	3.9
One parent families
	Lone parent, male	104 503	94 171	10 332	9.9
	Lone parent, female	568 366	533 496	34 870	6.1
	Child	1 047 242	1 015 550	31 692	3.0
	Other related individual	46 543	44 534	2 009	4.3
Other families
	Other related individual	179 061	178 921	140	0.1
Unrelated individuals in family household		136 570	127 637	8 933	6.5
Non - family households
Lone person households
	Lone person, male	642 274	642 274	0	_
	Lone person, female	790 542	790 542	0	_
Group household
	Group household member	606 189	576 036	30 153	5.0
Total		16 395 599	15 579 759	815 840	5.0

ii. The proposed classification excludes overseas visitors, Australian usual residents who are visitors to the household on census night, and persons who are coded to 'unclassifiable' households. The ERP, to which the propensities are applied, excludes only overseas visitors.

Investigation using the same population components in calculating the propensities as included in ERP, (that is, excluding only overseas visitors from the classification), produced a dramatic reduction in the number of households. This is because the addition of Australian visitors and persons in 'non classifiable' households to the propensities reduces the propensities of those persons who live in the other types of living arrangements. Comparative results are shown in table 14.

Table 14: The effect of including all components of ERP, June 1996

	Using the proposed classification	Including all components of ERP
Number of households, June 1996	6 733 775	6 415 823
Difference with ABS household estimates	28 340	346 292
% Difference with household estimates	0.42	5.1

iii. Australian residents temporarily overseas, and Australian visitors to households on census night are not included in the census propensities. Their inclusion in ERP and the calculation of household numbers assumes that they have the same propensities to be in each living arrangement type as those counted at home in the census.


iv. O'Leary, in his paper 'Estimating the Number of Household in Victoria As At 30th June 1996', has raised the following issues:

• Overcount within the census of usual residents in non-private dwellings

O'Leary argues that this overcount is a result of McDonald and Kippen including visitors to NPDs on census night as usual residents of NPDs. Persons in NPDs are counted in the proposed classification of living arrangements. This category is included in the census counts and propensities, to project the likelihood to live in an NPD at different ages. However, the category is not included in the household population, or in the calculation of household numbers. An overcount of persons living in NPDs will therefore result in an undercount of the household population and an undercount of the number of households.

While the working paper has not addressed this issue, it is intended that ABS will investigate this further.

• Bias in the census towards overcounting one parent families and lone person households, and undercounting couple families and couple families without children

O'Leary argues that lone parent families and lone person households may be overestimated if the census question reallocating absent household members to their household of usual residence is incorrectly coded. If absent partners are not correctly coded to their usual relationship in household, the remaining partner may be incorrectly included in the living arrangement 'lone parent' or 'lone partner'.

While plausible, this is not something that can be quantified and, therefore, taken into account.


6. Further work
The household projections project will continue work in a number of areas:

1. Take account of comments received.

2. Consultation within the ABS to finalise our classification and terminology.

3. Examine propensities at State and substate level.

4. Projections of living arrangements, families and households.
Given that the proposed method produces numbers of households very close to ABS household estimates at the base year (1996), the next stage is to project propensities by living arrangements. This will involve:

• deriving the propensities at the 1986 Census.
• trend analysis of the change in propensities, by age, across the three Census (1986, 1991 and 1996)
• application of propensities to the Projected Population.

7. Proposed Output
The projection method being developed will yield output for Australia, State and capital city/balance of State. The proposed time horizon is 2021. The proposed output will be by five year age groups, to age 85+ years. Output will be at the person, family and household level:

• The living arrangement characteristics of the projected total population, by age eg. the number of persons by age and sex who are lone parents in a family household, or the number of people aged 25-29 years who live 'at home' with two parents.
• The propensity of the population to live under various living arrangements, by age eg. the propensity for an 80-84 year old female to live alone, or the propensity of a male 25-29 years to be a lone parent.
• The projected number of families, and the projected numbers of family types eg. the number of couple families or the number of lone parent families
• The projected number of households, and the projected numbers of household types eg. the number of family households or the number of lone person household.

References
Australian Bureau of Statistics (1996) Household Estimates Australia: 1986, 1991-1994, Catalogue No. 2710.0. Canberra.

Australian Bureau of Statistics (1997) Australian Demographic Statistics (Issued quarterly), Catalogue No. 3101.0. Canberra.

Bell, M., Cooper, J. & Les, M. (1995) Household and Family Forecasting Models - A Review, Commonwealth Department of Housing and Regional Development.

Dugbaza, T. (1996) Estimating Families: An Examination of Methodological Issues, Data Sources and Provisional Estimates, Demography Working Paper 96/3, Australian Bureau of Statistics, Canberra.

McDonald, P. & Kippen, R. Household Trends and Projections: Victoria, 1986-20, Demography Program, Australian National University, Canberra.

O'Leary, Estimating the Number of Households in Victoria As At 30th June 1996, Research Unit, Department of Infrastructure, Victoria.



Please Note: Diagram 1 and the Appendices are attached below.