دانلود رایگان مقاله پیش بینی خانواده حفظ الگو سن

abstract

We formulate a time series model of household dynamics for different age groups. We model the shares of the population who are in certain household positions (living alone, living with a partner, etc.). These household positions have very pronounced age patterns. The age profiles change slowly over time, due to changes in the home leaving behaviour of young adults, differences in survival rates of men and women, etc. When forecasting household positions to 2040, we want to preserve the characteristics of the age profiles. We test the Lee–Carter model and the Brass relational method using household data for the Netherlands for the period 1996–2010. Annual shares of the population by household position, age, and sex are modeled as random walks with adrift (RWD). While the Brass model has its limitations, it performs better than the Lee–Carter model in our application. The predicted age patterns based on the Brass model look more reasonable, because the Brass model is a two-parameter model, while the Lee–Carter model contains only one parameter. Also, the model parameters and standard errors of the Brass model are easier to estimate than those of the Lee–Carter model. © 2016 International Institute of Forecasters. Published by Elsevier B.V. All rights reserved.

5. Conclusions and discussion

We have formulated two different time series models for changes over time in the age profiles of six household positions that men and women can occupy at any point in time. These household positions are living alone, cohabiting, living with spouse, lone parent, living in some other private household position, and living in an institution. Preserving the characteristic features of such age profiles while accounting for their changes over time is an important task when predicting the household positions of individuals into the future. Both models are random walk with drift (RWD) models, in which the year-on-year step for the household parameter consists of a certain fixed term (the drift) plus a normally distributed error term with zero expectation. We tested two different versions of the RWD model, namely one based on the Lee–Carter model (LCRWD model), which was originally developed for age patterns of mortality, and the other starting from the Brass relational model, which also stemmed from mortality analyses (Brass-RWD model). When the models are applied to data from the Netherlands for the period 1996–2010, we find that the Brass-RWD model predicts more realistic age profiles of household parameters than the LC-RWD model. This is because of the particular form of the LC-RWD model. When empirical age profiles show a cross-over (a downward trend for some ages, and an upward trend for others), the LC-RWD model is not appropriate, as one of its parameters, namely the b(x)-vector, may have both positive and negative values. This may lead to extrapolated age patterns for future years that are distorted strongly. This distortion becomes more severe for more distant years, because the b(x) values are multiplied by falling or increasing values of a second vector, namely the time index k(t) of the model. Extrapolations obtained using the BrassRWD model did not show these kinds of distortions in our application.