پیش بینی خانواده: حفظ الگوهای سن   Household forecasting: Preservation of age patterns

1. Motivation Fig. 1 shows, for the case of The Netherlands in 2011, the proportions of women who live with parents, alone, in a consensual union, or with a marital spouse, broken down by five-year age groups. Most adolescents live with their parents. Those who have left home most often live alone or in a consensual union, up to ages around 30. After that, living with a spouse becomes the dominant position, until ages around 70. Some women become lone mothers, due to separation or divorce. Next, increasing numbers lose their husbands because the husband is a few years older (aggravated by the higher mortality of men), and many elderly women live alone, or together with one or more children. Of women over 95, more than half live in an institution (not shown in the graph). Age profiles of the type shown in Fig. 1, and their development over time, help us to understand household dynamics. This in turn, when combined with forecasts offuture age structures, facilitates demographers in projecting the number of households of various types into the future. Combining population forecasts with future values of carefully selected sets of household parameters is a wellestablished method of computing household forecasts; see the extensive review by Holmans (2012). In many countries, the life expectancy of men is increasing faster than that of women. What does that imply for the numbers of elderly men and women who live alone? Business cycles and youth unemployment have effects on the home-leaving behaviour of young adults. Formal marriages have become less important in many Western countries since the 1970s, but did consensual unions fill the gap fully or only partially? These and related issues show that it is important to describe and understand the age profiles of various household parameters, when computing household forecasts to be used by policy makers in such diverse fields as housing, social security, consumption, and energy consumption, to name only a few. Ideally, household forecasts should be based on wellestablished theories of the household behaviours of individuals. Many scholars have tried to develop social, economic and cultural theories to explain why households change over time. The reasons for such changes include a reduced adherence to strict norms; less religiosity and an increase in individual freedom on ethical issues; female education, which has led to women having greater economic independence, and also facilitates divorce; more assertiveness in favour of symmetrical gender roles; the contribution of women to the labour market; increased economic aspirations; and residential autonomy (Lesthaeghe, 1995; Van de Kaa, 1987; Verdon, 1998). In addition, there are also demographic factors, such as falling levels of fertility, and differences in longevity between men and women. However, none of these theories have resulted in formalized models of household behaviour that are general enough and have sufficient explanatory power to be used for forecasting. Two decades ago, Burch (1995) noted that methods for modelling family and household dynamics had made considerable progress, but that theory had lagged behind considerably. The situation is not much better today, which may reflect the complexity of the subject matter. Thus, as a second best to predicting households based on general behavioural theories, we look for regularities in the observed data, try to understand the trends, and extrapolate them into the future by means of formal time series models. Sometimes the forecaster has very little data, perhaps only one year’s worth, upon which the forecast can be based. In that case, a commonly-used approach is simply to keep the parameters of interest constant over the forecast period. One example is the multi-state approach to modelling household dynamics (Van Imhoff & Keilman, 1991), in which the transition probabilities that describe changes among household positions for individuals are kept constant. In the current paper, however, we are able to use time series data over a longer period. This allows us to take possible time trends in the parameters into account explicitly. In addition (though we do not use this here), a time series approach also allows one to make stochastic predictions, and hence to take the prediction uncertainty into account.