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  • SIMULATING THE EFFECT OF DEMOGRAPHIC EVENTS ON THE HOUSEHOLD COMPOSITIONAuthor(s): Keith Spicer, Ian Diamond and Maire Ni BhrolchainSource: Journal of the Australian Population Association, Vol. 9, No. 2 (November 1992), pp.173-184Published by: SpringerStable URL: .Accessed: 14/06/2014 08:10

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  • Vol.9, No.2, 1992 Journal of the Australian Population Association


    Keith Spicer, Ian Diamond and Maire Ni Bhrolchain Department of Social Statistics University of Southampton

    Southampton S09 5NH, England

    The aim of this paper is to measure the effects on household composition of changes in demographic events, e.g. mortality, fertility, marriage, divorce. British household data are taken from the General Household Survey and aged by simulation to 2001 using a 'Most Likely* model. Subsequently different assumptions of each demographic event are taken from 1991 so that the effects of perturbations within each event can be studied. Special features of the simulation model are the differentiations between cohabitation and marriage and separation and divorce, and the detailed breakdowns of household types such as lone parents into single and previously married women and men with children aged 0-4, 5-15 and 16 and over.

    Introduction The most commonly used method for projecting the number and type of

    households is the headship rate method For example, Bell (1992) reports that in Australia, there are a number of different household projections at both national and subnational levels, the majority of which use a headship rate. The Australian Bureau of Statistics publishes population projections at national and state level but has not published projections for the numbers of households and the number of persons residing in households (Ironmonger and Lloyd-Smith 1990). United Nations (1973) provides full descriptions of the most common household projection methods.

    A headship rate is the proportion of people in a certain subpopulation who are heads of households, thus the headship rate for single males aged 20-24 is 0.4 if 40 per cent of such males are heads of households. In the forecasting and projection of these rates, groups are normally distinguished by age, sex and marital status. The usual procedure (Rees 1986) is to forecast future marital behaviour within the groups: the proportion of single males aged 20- 24 that will marry in the next five years or the proportion of married males that will divorce in that time. In essence one is finding probabilities of individuals making a transition from one status to another. In conjunction with an independent population projection over the same period, projected headship rates are then used to project the number of household heads and hence the number of households.

    Material from the General Household Survey was made available through the Office of Population Censuses and Surveys and the ESRC Data Archive has been used by permission of the Controller of H.M. Stationery Office.


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  • Despite their widespread use, headship rates have a number of disadvantages. Murphy (1986) pointed out that a great drawback is that demographic and socioeconomic characteristics of the other members of the household are completely ignored and that, anyway, the choice of a head within the household is crucial as regards the output household composition. Bell and Cooper (1990) reported that the output displayed by the headship rate methods is often confined to the total number of households and the age- sex distribution of heads. Often other assumptions, such as the household distribution (by type) of single males aged 20-24, for example, have to be made to project the household composition with sufficient information for planning purposes. Indeed, as Murphy, Sullivan and Brown (1989) stated, the headship rate approach describes a state rather than modelling a process.

    Moreover, the crucial drawback is that it is difficult to incorporate demo- graphic period effects into the headship rate approach. For example, if marriage rates decrease by five per cent and divorce rates increase by five per cent at certain ages, how does one transfer those assumptions into headship assumptions?

    Household Simulation

    Studying the effect of demographic factors on the household composition is therefore not trivial. Simulation at the individual level can handle all demo- graphic events by taking each household, one at a time, simulating each possible event (using a Monte Carlo method) for each individual within each household for each year over a number of years. Our methodology is similar to that of Brass (1983), taking a 'marker' individual as the head of the house- hold. The marker is taken as the senior woman, that is the oldest married woman or, if there is none, the oldest non-married woman or, if there are no adult women, the oldest man. The marker can only leave the household by death or abdication: the latter only applies to the case of a man, who abdicates when he enters a relationship with a woman and is deemed to be 'owned1 by another marker. If any other members leave the household, they are kept in the simulation in their new household, although in the case of a man, he dis- appears when he enters a relationship. There is thus a balance in the number of men, since we introduce men as relationships commence, though there may be small discrepancies introduced in some demographic attributes such as the age distribution of men. Women who form new households become new markers.

    Special consideration in our simulation is given to the marriage process. We use an 'open population* model in that when a woman marries, or cohabits, her partner's age and marital status are simulated, thereby ensuring that there is always a partner available for her to form a relationship with. Alternative models in the past, notably Galler (1988) and Hammel et al. (1976), have attempted to use a 'closed population', searching for the most suitable partners in the other households; but there are immense problems in determining a 'scoring system' for prospective partners, and forming the methodology for when no suitable partners are available.


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  • We also split the marriage process itself into two parts: cohabitation and marriage. Since cohabitation is now widespread1 we must incorporate it into our simulation. The average length of the cohabitation period is just under two years for first marriage and three years for second marriage (GHS data, various years) so we must adjust our marriage rates to account for cohabiting unions two and three years earlier. In addition, many such unions do not end in marriage. Bumpass and Sweet (1989) estimate this is so for around 40 per cent involving single women in the United States. Spicer (1992) showed that British cohabitation behaviour is very similar, using data taken from Haskey and Kiernan (1989) by comparing lengths of current cohabitations and also the length of time prior to marriage spent in a cohabiting union. The US Cohabitation Life Table (shown in Table 1) is therefore used for British cohabiting unions in our simulation.

    We have no similar information for previously married women but the proportion of non-marrying unions is probably lower, say around 25 per cent. The problem is similar to that for single women but we have to make some assumptions since many women are ineligible to marry through being separated and not divorced. We assume that separated women who are cohabiting at the time of divorce have cohabited, on average, for half the period of separation; and that about one half of all divorced women who ever cohabit as divorced are cohabiting at the time of divorce. These assumptions tie in with GHS data that 20-25 per cent of separated women are cohabiting. Our life table is formed in Table 2.

    Table 1 Cohabitation life table (single women)

    No. of years Split Marry Still cohabiting

    0 0 0 100 0-1 12 26 62 1-2 10 16 36 2-3 6 7 23 3-4 4 4 15 4-5 3 3 9 5-10 5 3 1

    10+ 0 1 0

    Table 2 Cohabitation life table (previously married women)

    No. of years Split Marry Still cohabiting

    0 0 0 100 0-1 9 21 70 1-2 9 17 44 2-3 5 13 26 3-4 1 11 14

    4+ 1 13 0

    1 Nearly half of all first marriages are preceded by cohabitation as are over two-thirds of later marriages in Great Britain (GHS 1986-1989 data).


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  • We must also differentiate between separation and divorce. Murphy (1984) estimated that around 13 per cent of British women who separate never divorce; Bloom et al. (1975) estimated ten per cent in the US. Therefore we must correct the divorce rates by two years, the approximate average length of time between separation and divorce (GHS data), to give separation rates and also by a factor of 100/87 to account for those not divorcing. We can then use the distribution of time from separation to divorce to model divorce as a separate event

    The third special feature in our simulation is the treatment of ex-nuptial fertility. Using Bachrach's (1987) model II, incorporating age and parity, we can approximately estimate fertility for single cohabiting, single non- cohabiting, previously married cohabiting and previously married non- cohabiting women. Because Bachrach (1987) did not specifically give fertility rates but the probability of women (in given marital statuses at the start of the period) giving birth within the following five years, we must first correct her probabilities to one-year birth probabilities and then correct to the vital registration rates for overall ex-nuptial fertility.

    Each individual in each household is thus exposed to each possible event in turn, though some events are clearly not applicable to some individuals, e.g. a male giving birth, a non-married woman divorcing, a married woman marrying. Individuals can be subject to leaving the parental home, giving birth, moving into a relationship (either cohabitation or marriage), leaving cohabitation (either to a marriage or splitting), separating (if married), divorcing (if separated), going to an institution or dying. Other events involve 'introducing' a new member into the population, for example gaining an elderly relative. These events are simulated using characteristics of the marker and other data. For the example of gaining an elderly relative, and institutionalization, information is taken from the work of Grundy (1986, 1989) using Longitudinal Study data. The Longitudinal Study (LS) links one per cent of the population through the comparison of two successive censuses, in these cases, 1971 and 1981, to monitor individual change.

    The General Household Survey The General Household Survey (GHS) is a continuous British voluntary

    household survey covering about 12,000 households a year. Interviewing takes place throughout the year and results are published annually. The topics covered include household composition, marriage and fertility history as well as occupation, education and contraception. Response has been fairly consistent in the 1970s and 1980s at around 80 per cent, though for the contraception section this is slightly lower.

    For the actual simulation, we have taken a sample of 10,000 households from the 1971 General Household Survey, split into ten smaller samples each of 1,000 households. The data quality was remarkably good with only 70 households in total needing any manipulation. Over half of these were due to marriage data being given but the date of marriage left blank. On these occasions, the couples were deemed to be cohabiting as suggested in the codebook. The majority of the other households needing manipulation had the


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  • age of one member missing. In these cases the missing age was estimated using the ages and relationships of the other members.

    The age-sex structures of our sample and the 1971 Census were similar but only after correcting for non-response by household size using the rates given in Barnes and Birch (1975) and then correcting by age. The distributions of household size and type were then deemed to be similar enough to those given in the census to continue the analysis.

    Calibration After running each of our ten samples five times (a total initial sample of

    50,000 households) the results we obtain for 1981 are shown in Table 3, the household type distribution for 1981. Although it could be argued that no one type of household is very closely in agreement in terms of the percentage distributions exhibited by the simulation and the census, it could also be argued that no one type is particularly inaccurately measured. Two additional independent repetitions of the simulation (each of the ten samples run five times in each case) using different random number seeds also led to no error being greater than 1.1 per cent of all households in any instance.

    As regards more up-to-date comparisons, we can compare our simulated distribution to that from the 1987 GHS. However, the General Household Survey data do not account for non-response errors so we must instead study the changes in the GHS between 1981 and 1987 and compare these with the changes in the simulation distribution over the same period. Table 4 shows that the shifts in the distribution from 1981 to 1987 are similar to a d...


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