The ageing of the population at a high speed has the following influences on social security as well as on the balance and growth of the economy. First of all, as the cost of social security (including social services) increases remarkably at the earlier stage of ageing, the disposable (after tax) income and private consumption of the present labour force generation tend to increase at a lower growth rate than that of the GNP. At this stage a Keynesian policy is required. Secondly if pension systems are based on terminal funding scheme, the ageing of the population increases savings (net increase of the amount of the pension funds) at the earlier stage of the ageing of the population. Thirdly, there is a time lag between the increase of social security benefits and the decrease in the personal savings ratio. The high ratio of savings and the shortage of aggregate demand as well as the high pressure for export in the recent Japan can partly be attributed to the above factors. It is important to note that no invisible hand works to adjust the investment/savings gap. However, Japan will proceed to the next stage of the ageing of the population in the 1990s, when the Japanese economy may fall in "the Japanese disease" which will be caused mainly by supply-side factors. Five policies to cope with the coming difficulties in the Japanese economy are suggested in the last section of the paper.

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Migration of population can be classified into "individual migration" and "group migration". So far, the study of migration of population has been focussed mainly on the individual migration. Compared with the aspects of individual migration, therefore, those of family or household migration, a typical type of group migration, have scarcely been disclosed. This paper aims to introduce some aspects of household migration, which can make a step for grasping the aspects of family migration, in this country, basing the data derived mainly from 1980 Population Census and 1978 and 1983 Housing Surveys. As the results, the following main aspects of the household migration in this country were drawn; (1) Residential mobility of the ordinary households is higher than that of population, or individual persons. (2) The smaller in size of the household, the greater in the residential mobility. (3) Overall residential mobility of the households has been declining in recent years. (4) Nearly half of the migrated households in this country moved due to the reason of "housing".

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Co-residence of parents and grown-up (especially married) children has been one of the most important factors that affect the trends in household formation in recent Japan. This article reports the proportion co-residing (proportion of co-resident population in a cohort), using a nation-wide large-sample household survey data set containing about 300,000 persons in each year. The results are as follows. The proportion of parents who co-reside with children (proportion co-residing of parents with children) had remarkably decreased during the period, 1975 to 1985, especially for younger elders regardless of their marital status. Consequently, in 1985, the proportion co-residing of married elders aged 65-79 was nearly constant (around 55%), while its proportion of unmarried elders gradually increased in accordance with their age from 65 to 79 (60-70%). On the contrary, the proportion co-residing of married children aged 20-39 with their parents had been constant or slightly rising (around 30%) during the same period. These two opposite trends can be interpreted as follows: though the preference for co-residence has declined both for parents and for children, the child availability for parents has barely changed and the downward trend in preference has directly appeared as the proportion co-residing; while the parent availability for children has increased owing to the decrease in number of siblings to be balanced with the decreasing preference. The nature of co-residence seems to have been undergoing some change asmuch as the headship rate for co-resident children has been decreasing, which means that parents in a higher status relative to their children due to their resources such as owned houses have been more likely to co-reside with their children. Therefore, the co-residence is esteemed to have been shifting from the obligatory one to a strategic one.

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Spline interpolations and the examples of their application to demographic data were introduced first by H. S. Shryock, J. S. Siegel et al. and then D. R. McNeil et al. Though these are very useful, no further detailed introduction has been done. But there are many other formulas of interpolation and curve fitting with spline functions. From these, the one-and-two-dimensional useful formulas and examples of their applications to demographic data will be introduced in a somewhat orderly form. Formulas introduced here are the following ones. (a) Interpolation and curve fitting with a cubic spline function. (b) Interpolation and curve fitting with B-spline functions. (c) Interpolation with a rational spline function by Spath. (d) Quasi Hermite interpolation with a piecewise cubic polynomial by Akima. (e) Curve fitting with a piecewise cubic polynomial (automatic method) by Yoshimoto et al. The formula (c) is the one for one-dementional data. In (d) and (e), the continuity of interpolation functions and their derivatives are assurned. (b) is comprehensive and most useful, but it is not easy for us to use, because users should be skilled in deciding the number and position of knots. So its computing procedure should be done with big computers. (a) is a special case of (b) with a polynomial of degree three, and is widely used because of its moderate precision and easiness for use. But (a) may provide us unfavourable results for certain specific data. In such cases, formulas (c)-(e) may be used instead of (a). Examples of application are as follows. (1) Interpolating and smoothing values of life table functions, e.g. survivorship function (l_x) and mortality rates (q_x). (2) Interpolating births by five-year age groups of mothers into single ages. Angular transformation and (c) are used for it. (3) Interpolating cause-specific deaths by five-year age groups into single ages. (a) is usually used, but (c) and (d) may be necessary for deaths by certain specific causes of death. (4) Interpolating and smoothing two-demensional demographic data e. g. mortality rates and expectations of life by year and age. Depicting spatial patterns of demographic data using contour map and spline surface. It should be noted that a certain model explaining the data (one-or two-demensional) is taken into consideration whenever these formulas are used. It is interesting that we apply the formulas of interpolation or curve fitting with two-demensional B-spline function of degree k in x and l in x (not necessarily k=l) to two-demensional demographic data. In interpolating population by year and age as a two-demensional demographic data, interpolation by birth cohort may have to be taken into account.

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