Projecting population, numbers of households and dwelling units in South Africa 2011-2021

Future trends in population, number of households and dwelling units are critical components in strategic planning for future service delivery in South Africa. To aid planning therefore, this study analysed provincial trends in fertility, mortality and net migration as well as trends in the number of households and dwelling units. On the basis of the trends and assumptions about the future, households and dwelling units were projected for the period 2011-2021 using component functional models and ratio method. The results suggest that the size of the population aged 15 years and over in South Africa may increase from 36.4 million in mid-2011 to 42.5 million in mid-2021. Gauteng province is projected to have the largest number of persons in this age group. The number of households nationally is projected to increase from 15 million in mid-2011 to 20 million by mid-2021 with Gauteng having the highest number of households.


Introduction
Population figures are fundamental to planning in all sectors in any population.Household and dwelling unit figures are also fundamental to planning in certain sectors.The census is the traditional source of this information.From a planning perspective, census figures become out dated immediately they are released because population figures are required for the present and the future.
Households and dwelling units numbers have various uses.From a demographic standpoint, households constitute the unit of sampling in multistage sampling.They are also the unit of listing and enumeration in censuses and the basis for apportioning enumeration areas to enumerators (see for example, Statistics South Africa: 2007, Laldaparsad: 2009, Mathetha & Venter: 2007).Because households are often located in dwelling units, information on dwelling units is important.While the unit of analysis in some demographic studies is the household in other studies, their characteristics may constitute contextual explanatory variables (see, Nolunkcwe: 2007, South Africa Institute of Race Relations: 2011, The Housing Development Agency: 2012).Studies in economics dealing with poverty, income, expenditure and wealth sometimes use households as the unit of analysis (see Woolard & Klasen: 2004, Leatt: 2006, Leibbrandt et al: 2010).From a social perspective, information on households enables planners to assess future needs for social services such as the provision of water, electricity, sewage and refuse disposal as well as housing (see Walsh: 2008).While surveys and censuses may provide information on the current stock, they do not provide information about probable future stock of the population, households and dwelling units.
There is a dearth of studies that project future stock of households and dwelling units in South Africa.Few of the studies include the following.Walsh's (2011) study was only suggestive of the methods that may be used to project the number of households into the future but did not provide projected figures.The study suggested that average household size be used to calculate future number of households from projected population figures.A limitation of this approach is that it does not take into consideration variations in the age pattern in household formation and therefore such approach is likely to produce biased estimates.This is because young persons (below the age of 15 years -who are not at risk of forming new households) are included in the computation of average household size.This approach was utilised in van Aardt's (2007) study.His projections were at national and provincial levels.New data especially the 2011 South Africa census have become available since van Aardt's study and hence his projected figures need to be revisited.For example while his projected total population figure on which average household size was applied for 2011 was 48.5 million, the 2011 census results indicated a total population of 51.8 million as of October 2011.It would appear from this that all other things the same, the projected number of households for the projection period in van Aardt's study are underestimates.
Haskins'study utilised data sets from different organisations.The study was confined to Cape Town.It used the annual increase in households between 1996 and 2001 to project the total number of households in 2002-2005 in Cape Town.
The limitations of Haskins' study include the following.Different organisations do not employ the same standards in collecting data thus the data sets used may have been of varying quality.The study was limited in time (terminal end of the projection was 2005) and space (confined to Cape Town).The methodology used -annual growth rate to project householdsdoes not take into account variations in age pattern in household formation (see the methods section on age pattern of household heads).None of the above studies provides projections of households and dwelling units at district municipality levels yet much of planning takes place at this level and at lower levels.

OBJECTIVES OF THE STUDY
The primary objective of this study therefore was to provide projections of households and dwelling units from 2011-2021 nationally, provincially and by district municipality for South Africa to aid planning at these levels.Since the methodology employed in this study requires projections of the population of a certain age range, a secondary objective was to provide projections of the population aged 15 years and over nationally and provincially from 2011-2021 for South Africa.

DATA
For the population estimates, the historical trends in fertility and mortality were based in part, on estimates provided by Udjo (2005aUdjo ( , 2005bUdjo ( , 2008)) For the household and dwelling unit projections, the 1996, 2001and 2011censuses (Statistics South Africa 1998, 2003, 2012) data were used, being the three post-apartheid population censuses that have been conducted in South Africa.The overall undercount in the 1996 Census was 11%, which increased to 18% in the 2001 Census but decreased to 14.6% in the 2011 Census.The tabulations of households and dwelling units from these censuses were based on the 2011 provincial boundaries.Several aspects of each of South Africa's post-apartheid censuses are controversial.These controversies have been reported in several studies.See for example, Dorrington (1999), Sadie (1999), Shell (1999), Phillips, Anderson & Tsebe (1999), (Udjo 1999(Udjo , 2004a(Udjo , 2004b)).Some of the controversies pertain to the reported age-sex distributions (especially the 0-4 years age group) and the overall adjusted census figures.A number of the limitations in the data relevant to the present study especially those pertaining to underreporting of fertility and mortality were addressed in Udjo's (2005aUdjo's ( , 2005bUdjo's ( , 2008) ) studies and incorporated in this study.

Definitions
Household: The cooking pot definition is often employed in defining households internationally but the precise definition varies from country to country.According to the multi-lingual demographic dictionary, a household is a group of individuals who share living quarters and their principal meals (van de Walle 1982).The United Nations Economic Commission for Africa (UNECA 1974) defines a household as a group of people who live and eat together.A United Nations Manual, (cited in Casley & Lury 1989) recommends that the concept of 'household' should be based on the arrangements made by persons, individually or in groups, for providing themselves with food or other essentials for living and which may be either a oneperson household or a multi-person household.Statistics South Africa (1998) defines a household as consisting of a single person or a group of people who live together for at least four nights a week, who eat from the same pot and who share resources.These are 'social unit' rather than'physical unit' definitions although a household will usually occupy a physical structure or housing unit.For assessing future needs in housing and social services (such as water and electricity), identification of a physical structure (such as a dwelling or housing unit) is what is needed rather than a social agglomerate of people in time and space.
Dwelling unit: The multi-lingual demographic dictionary defines a dwelling unit as a statistical abstraction denoting housing accommodation appropriate for occupation by one household (Van de Walle 1982).Statistics South Africa defines a dwelling unit as a structure or part of a structure or group of structures occupied or meant to be occupied by one or more than one household.This includes a structure or part of a structure which is vacant and /or under construction but can be lived in at the time of the survey.It also includes units in collective living quarters, unlike a housing unit.Dwelling units may therefore comprise housing units plus units in collective living quarters when applicable.According to Statistics South Africa's definitions, dwelling units include housing units, converted hostels (e.g.family units), residential hotels, homes for the aged, hospitals/medical facilities/clinics, prisons/correctional institutions/police cells, defence force barracks, frail care centres, refugee camps/shelters, convents/monasteries, orphanages/homes for disabled, hotels (including tourist hotel), hostels, student residences/boarding schools (Statistics South Africa 2009).
Housing units constituted about 95% of all enumerated dwelling units in the 2011 Census.The tabulations from the census data utilised in the computations in this study were based on Statistics South Africa's definitions of a 'household' and 'dwelling unit'.

Projecting the Population
Household projections involve 'functional' projection.According to (Kono 1993), "functional population projection is an age-sex population projection that has been transformed or otherwise incorporated into formulas that forecast the future supply or demand for some particular purpose".Functional projections at high levels of aggregation involves two stages: a cohort component projection of the population and a cohort component projection of households using the headship rate.The ratio method may then be used to project households at lower levels of disaggregation.These approaches were utilised in the present study as outlined below.

Provincial, National and district municipality population projections
The cohort component method was used to project the population of each province and the sum of the provincial projections yielded the national total population for each of the projection periods.The base of the projections was the October 2011 Population Census figures adjusted to mid-2011 using geometric interpolation of the exponential form.The terminal end of the projections is 2021.

Assumptions in the cohort component provincial population projections
The cohort component method of population projections entails separate projections of fertility, mortality (taking into account HIV/AIDS) and net migration.The extrapolation of trends in fertility, mortality and net migration was based on certain assumptions.Although it is customary to produce at least three variants -low, medium and highprojections embodying different sets of assumptions about fertility mortality and net migration, for brevity and ease of interpretation of results, only the medium variant (which is conventionally interpreted as the most likely scenario) projections are presented in this study.The assumptions underlying the medium variant population projections are summarised in Table 1.The basis of the assumptions was the analysis of historical trends and current levels as estimated from various Statistics South Africa data sets.These include the 1995and 1998October Household Surveys (Statistics South Africa 1996, 1999), the 1996 Census (see Udjo 2005a, 2005b), 2007Community Survey (Statistics South Africa 2008), 2001and 2011Censuses (Statistics South Africa 2003, 2013).The trends in fertility, mortality were then extrapolated to 2021.
The linear extrapolation took into consideration the present state of demographic knowledge such that lower and upper limits had to be set for the end of the projection period.The assumptions about net migration were based on the magnitude and trend estimated from the 2011 Census extrapolated to 2021.

District municipality population projections
The ratio method was used in projecting the district municipality populations and consisted of the following steps.Firstly, within each province, population ratios of district municipalities to the provincial population based on the 1996, 2001 and 2011 censuses and based on the 2011 provincial boundaries were computed for all district municipalities.Secondly, the population ratios were linearly extrapolated to 2021.In order to obtain the population estimates for each of the district municipalities, the result of the extrapolated ratio for each time period within the projection period for each district municipality was applied to the provincial population estimates for each time period.The advantage of this approach is that it is not necessary to estimate and project trends in fertility, mortality and net migration at district municipality level where the data are more limited.The approach indirectly takes into account fertility, mortality and net migration because the growth (positive or negative) and hence the size of each district population is due to fertility, mortality and net migration.
For each district municipality, the projection may be expressed algebraically as Where P(i,j,t) is a projected district municipality i, population in a province j, in a specific time period t, P(j,t) is a projected provincial j, population at time t and r(i,t) is a projected ratio of district municipality population to its projected provincial population at time t.

Household Projections National and provincial household projections
The cohort component functional model of household projections may be expressed as HH(x,s,j,t+n) = P(x,s,j, t+n) .HR(x,s,j,t,n) Where: x is a five-year age group starting at 15 or the open ended age group which is 65 years in this study.Although some persons aged 10-14 were reported as household heads, the percentages were negligible (0.41% at national level in 2011) and were excluded from the analysis.Although in some cases, it might be true that some persons aged 10-14 may be household head, it might also be a reflection of the quality of the data.Conventionally however, the age group 15+ is used.s is sex; j is a province; t is the initial time period; t+n is the end of the time period interval; HH(t+n) is the estimated number of household heads (equivalent to the number of households) at the midpoint of the interval; P(t+n) is the projected number of persons in the population at the mid-point of the interval, HR(t,n) is the projected headship rate during the interval.Thus, a cohort component model of functional household projections for each province in this study is therefore expressed as: where HH is the sum of the number of household heads in each five-year age group from 15-64 and the open age interval, 65 years and above for a sex group (i.e.number of households whose heads are in the age-sex group specified).The sum of all the projected provincial households for each period yielded the national total of households for the period.The period for the household projections is 2011-2021.
The Headship rates used in this study were based on the linear extrapolation of the rates observed in 1996, 2001 and 2011 to 2021.The rates observed in 1996, 2001 and 2011 for males at national level are illustrated in figure 2. The headship rates exhibit a distinct age pattern that increase sharply after age 15 and taper off after age 30-34 for males.The increase in headship rates for females was more or less exponential after age 15 (graph not shown).

District municipality household projections
In theory, one could apply the cohort component model of functional household projections to district municipality household projections but this is computationally heavy and tedious.Also, the data required to do this are sparser and less reliable at this level.Hence the ratio method was applied as follows.Within each province, household head ratios in district municipalities to total provincial household heads in 1996, 2001 and 2011 censuses were computed for all district municipalities based on the 2011 provincial boundaries.Secondly, the computed household head ratios were linearly extrapolated to 2021.In order to obtain estimates of the number of households for each of the district municipalities from mid-2012 to mid-2021, the result of the extrapolated ratio for each period for each district municipality was applied to the total provincial household estimates for the period.The method may be expressed algebraically as:

HH(i,j,t) = HH(j,t) * p(i,t)
Where HH(i,j,t) is a projected district municipality i, number of household heads in a province j, in a specific time period t, HH(j,t) is a projected provincial j, number of household heads at time t and p(i,t) is a projected ratio of district municipality number of household heads to its projected provincial number of household heads at time t.

Assumptions in the district municipality projections
The underlying assumption in the district municipality household projections was that the trend in the ratio of household heads in district municipalities to total provincial household heads in 2012-2021 will be similar to the trend observed in the ratios in 1996, 2001 and 2011.

Dwelling Units Projections
The ratio method was used in all the dwelling unit projections as follows.

Provincial and National dwelling unit projections
The base count of the dwelling units used in the estimation was the aggregated number of enumerated dwelling units based on the following questions: Which type of dwelling does this household occupy?(1996 Census).What is the type of these living quarters?(2001 and2011 Censuses).At the provincial level and for each province, the ratio of the total number of dwelling units to housing units in 1996, 2001 and 2011 were computed from the census data based on the 2011 provincial boundaries.The ratios for 2001 and 2011 were then linearly extrapolated to 2021 (the ratios for 1996 were much higher and inconsistent with those for 2001 and 2011).The result of the extrapolated ratios for each province was applied to the estimated total provincial number of household heads for the period to obtain the total number of dwelling units in a province for each period in the projection interval.The method may be expressed algebraically as: DU(,j,t) = HH(j,t) * R(i,t) Where DU(,j,t) is a projected number of dwelling units in a province j, in a specific time period t, HH(j,t) is a projected number of household heads in a province at time t and R(i,t) is a projected ratio of the total number of dwelling units to housing units in the province at time t.The sum of the projected dwelling units for all provinces for each period yielded the national total number of dwelling units for the period.

District municipality dwelling unit projections
Regarding district municipalities in each province, the ratio of dwelling units in a municipality to the total provincial dwelling units in 1996 2001 and 2011 were computed.These ratios were linearly extrapolated to 2021.To obtain the total number dwelling units in a district municipality, the extrapolated ratios for each period was applied to its estimated total provincial number of dwelling units for the period.The method may be expressed algebraically as:

du(i,j,t) = DU(j,t) * R(i,t)
Where du(i,j,t) is a projected district municipality i, number of dwelling units in a province j, in a specific time period t, DU(j,t) is a projected provincial j, number of dwelling unts at time t and R(i,t) is a projected ratio of dwelling units in a municipality to its projected total provincial dwelling units at time t.

Assumptions in the dwelling unit projections
The assumptions underlying the dwelling unit projections were: (1) the trend in the ratio of the total number of provincial dwelling units to housing units in 2012-2021 will be similar to the trend observed in the ratios in 2001 and 2011; (2) the trend in the ratio of dwelling units in a district municipality to the total provincial dwelling units in 2012-2021 will be similar to the trend observed in the ratios in 1996, 2001 and 2011.

PROJECTED POPULATION Projected National and Provincial Population (aged 15 years and over) 2011-2021
The annual rate of population growth resulting from age-sex cohort changes provides an overall measure of the balance in the components of population growth.Figure 1 summarises the projected growth rate in the population aged 15 years and over.Persons aged 15 years and over in the context of this study constitute the 'population at risk of becoming household heads' (though a negligible percentage of persons aged 10-14 may be household heads).The graph suggests that if the assumptions underlying the population projections hold, annual growth of the population aged 15 years and over nationally may increase from about 1.4% during the period 2011-2012 to about 2.0% during the period 2020-2021.In absolute terms, it is projected that the population aged 15 years and over nationally may increase from about 36.4 million in mid-2011 to about 42.5 million in mid-2021.Gauteng province is projected to have the largest number of persons in this age group -increasing from about 9.3 million in mid-2011 to about 10.6 million in mid-2021 with the Northern Cape projected to have the least number of persons in this age group during the projection period (see Table 2).Gauteng, Mpumalanga, Limpopo and North West are projected to have the highest annual growth rate (about 3% or higher) in the number of households.

Projected Absolute numbers of households and average household size
The absolute numbers of projected households are shown in table 3.In absolute terms, it is projected that the number of households nationally may increase from about 15 million in mid-2011 to about 20 million in mid-2021.Gauteng province is projected to have the highest number of households -increasing from about 4.1 million in mid-2011 to about 5.7 million in mid-2021 with the Northern Cape projected to have the least number of households -increasing from about 315,000 in mid-2011 to about 396,000 in mid-2021.
The projections indicate that average household size (the number of persons per household) may decline.At the national level, average household size is projected to decrease from about 3.4 persons per household in 2011 to about 2.9 persons per household by 2021.KwaZulu-Natal is projected to have the highest average household size -4.0 in 2011, 3.6 in 2016 and 3.3 by 2021 -while Gauteng the lowest -3.0 in 2011, 2.7 in 2016 and 2.5 by 2021.Projected household size by 2021 in other provinces are: Eastern Cape (3.3), Free State (2.7), Limpopo (3.1), Mpumalanga (3.0), Northern Cape (3.2), North West (2.7) and Western Cape (3.0).

Projected Sex composition of Household Heads
At the base period (2011), the Eastern Cape Province had the highest percentage (50.3%) of households that were headed by females in comparison with other provinces.This is higher than the national average of 40.9%.Limpopo and KwaZulu-Natal provinces also had higher percentages of households that were headed by females than the national average in 2011.Gauteng province had the lowest percentage (34%) of households headed by females in comparison with other provinces in 2011.It is projected that the percentage of households headed by females may decline in the Eastern Cape (from 50.3% in 2011 to 48.6% in 2021), Limpopo (from 49.5% in 2011 to 44.1% in 2021), Mpumalanga (from 40.1% in 2011 to 38.6% in 2021) and North West (from 36% in 2011 to 33.8% in 2021).In the other provinces, the percentage may either increase (KwaZulu-Natal, the Northern Cape, the Western Cape, Gauteng) or remain more or less stable (the Free State).Consequently, KwaZulu-Natal is projected to have the highest percentage (48.7%) of households that are headed by females by 2021.

Median age of household heads
The median is a useful measure of the age composition of household heads.In general, the projections indicate that female heads of households are older on average (46.8 years in 2011 and 48.2 years in 2021) than male heads of households (41.9 years in 2011 and 43.1 years in 2021).At the national level, female heads of households were about 4.9 years older than male heads of households in 2011.This age gap is projected to widen slightly to 5.1 years by 2021 nationally.The higher median age for females is partly due to widowhood.In every human population, the force of mortality is higher among males than females.Consequently, some females would become heads of household at the death of their spouse/partner.
At The median age of female household heads is projected to increase in the Northern Cape, Western Cape, North West, Free State and Mpumalanga while it is projected to decrease in the Eastern Cape and Limpopo.The median age of male household heads is projected to increase in all provinces except in KwaZulu-Natal where it is projected to be more or less stable, as among female household heads in the province.

2021.
Figure 3 shows the results of the projected number of households in district municipalities ranked from the lowest to the highest by 2021.It is projected that of all the district municipalities in the country, the Central Karoo district municipality located in the Western Cape would have the lowest number of households (24,175) by 2021, while the City of Johannesburg located in Gauteng would have the highest number of households (2,158,528) by 2021.  4 summarises the results of the projected number of dwelling units at national and provincial levels.As seen in the table, it is projected that the number of dwelling units nationally will increase from about 15.8 million in 2011 to about 21.3 million in 2021.This implies an average annual growth rate of about 3.0% per annum during the period 2011-2021.Gauteng is projected to have the highest number of dwelling units (6.2 million) by 2021, implying an average annual growth rate of about 3.0% per annum during the period 2011-2021.The Northern Cape is projected to have the lowest number of dwelling units (417,798) by 2021, implying an average annual growth rate of about 2.3% per annum during the period.

DISCUSSION, IMPLICATIONS FOR PLANNING AND CONCLUSION
There is very limited information with which to compare the results of this study due to a dearth of studies on household projections in South Africa.The few available studies suggest approaches that may be used in household projections without providing projected household numbers.Statistics South Africa, the provider of official statistics in South Africa has never undertaken household or dwelling units projections.
One study however, with which to compare the results of this study with is van Aardt's (2007) study which provided household projections up to 2021.Whereas van Aardt projected the number of households to be 17,379,366 by 2021, this study projects 20,075,006 households by 2021.The differences in the numbers projected numbers lie in methodology and data.Whereas van Aardt's study used average household size for the projections, this study utilised the cohort component functional approach.Newer data have become available since van Aardt's projections.Furthermore, van Aardt's projections were at national and provincial levels and did not project dwelling units.This study projected households and dwelling units at national, provincial and district municipality levels.Our knowledge of households and dwelling units projections in the context of South Africa is therefore enhanced by this study.The results from this study should aid planning in some sectors at lower geographical levels in South Africa.
The results have socioeconomic implications in different sectors nationally, provincially and in district municipalities.Increasing numbers of households and dwelling units imply that in the future, there would be increased demand for electricity, water supply as well as toilet and waste disposal facilities.This needs to be taken into consideration in planning in these sectors.For example the implication of the projections for the Electricity Supply Commission of South Africa (ESKOM -the main supplier of electricity for South African households) entails among others, the following.In planning for energy supply for dwelling units by 2021, the company would have to take into consideration the current load of backlog as at 2014 (i.e. the total number of dwelling units that have applied for electricity connection but still not connected as at 2014).On top of this load, the company would have to take into consideration the projected number of new dwelling units (which is the projected number of dwelling units by 2021 minus the projected number of dwelling units as at 2014).The sum of these two numbers (i.e.backlog load at a specific time period plus the projected number of new dwelling units by the end of the projection period) constitutes the increase in future demand for electricity.This scenario applies to other social service sectors as well at any level of geographical disaggregation.Aside these socioeconomic implications, the results should inform planning for the next census in South Africa with regard to housing and dwelling units listing, demarcation of enumerator areas as the figures provide some indications of the expected workload in these regard.
It should be noted, that in this study, all types of dwelling or housing units were lumped together in the projections as the focus of the study was not on quality of dwelling or housing units but on numbers.Thus, informal dwellings (such as shacks) and formal dwellings or housing units were given the same treatment in this study.This is perhaps a weakness of the study.Lumping different types of dwelling or housing units together may be unsatisfactory as this may be of concern to certain sectors such as electricity supply (e.g.ESKOM) and government departments such as the Department of Human Settlement from a planning perspective.Although computationally heavy, future studies may consider doing the projections by type of housing and dwelling units.

Figure 1 :
Figure 1: Projected annual percentage growth rate of the population aged 15 years and over by province

Figure 3 :
Figure 3: Projected number of households in district municipalities by 2021

Figure 4 :
Figure 4: Projected number of dwelling units in district municipalities by 2021 , that utilised the 1996 Census (Statistics South Africa 1998), 1997 and 1998 October Household Survey as well as the 2007 Community Survey data.The 2011 South Africa Census (Statistics South Africa 2012) was used to estimate current levels of fertility, mortality as well as current trends in net migration.The population estimates incorporate HIV/AIDS through the use of the INDEPTH (2004) model life tables.

Total fertility rate; E0 = Life expectancy at birth (years, both sexes); Net Mig = Net migration (Internal and international)
provincial level, the Eastern Cape had the highest median age (50.2 years) of female household heads in 2011 and is also projected to have the highest median age (51.1 years) of female household heads by 2021 in comparison with other provinces.Gauteng had the lowest median age (43.5 years) in 2011 and is also projected to have the lowest median age (46.4 years) of female household heads by 2021 in comparison with other provinces.