The period for this projection is the twenty-five years from 1995 to 2020. The estimates were calculated every five years.

The headship rate method is used for the estimates. The headship rate method is based on the assumption that the number of households is equivalent to the number of householders. The following formula, which multiplies population by headship rate (percentage of householders in the population), is used to estimate the number of households.

(# of households) = (# of householders) = (# of population) * (headship rate)To calculate estimates of households in the future, we need information on the future population and the future headship rate. The future population estimated in the previous publications was used for this new projection. For the future headship rate, we set up assumptions. The assumed headship rate is estimated by prefecture based on the nationwide headship rate with consideration of the relative difference between nationwide headship rate and headship rate by prefecture. This method is discussed in detail in the later section titled, "5. Assumptions of headship rate."

The headship rate varies depending on sex and age. Therefore, the headship rate method employs population and headship rate by sex and age . This estimation deals with various categories of headship rate such as sex(two categories), age (over 15 years old divided into 15 categories), and family type (five categories). Family types consist of" one-person," "couple-only," "couple-and-children," "parent-and-children," and "others."

It should also be noted that we adjusted the number of households by prefecture categorized by sex, age groups, and family type to match the total amount with national estimates.

The initial number of households and population categorized by householders' sex, age, and family type are obtained from the 1995 Census.

In addition, the future population by sex and age of each prefecture is obtained from "Population Projection for Japan by Prefecture (reported on May, 1997)" (abbr.: PPJP). The future number of nationwide households by householder's sex and age is obtained from National Estimates.

The estimates are calculated by householders' sex, age, and family type. The results are presented with numbers and proportions of private households of each prefecture by householder's age and family type (in this report, information on numbers and proportions of private households by family type and prefecture). The estimation was performed for a single case.

As stated in the earlier section, the assumptions for future headship rate need to be determined for the estimation of future households using the headship rate method. In this report, future headship rates by sex, age, and family type, are determined from assumed transitions in the relative difference between the national estimates and the estimates of each prefecture. Details are explained below.

The headship rate method is calculated as follows: the population of sex s at age j in a prefecture i in the year t is estimated by Ps i(t,j); the headship rate of sex s at age j sorted as the family type k is expressed as rs i(t,j,k). Therefore, the following formula is used to estimate the number of households Hs i(t,j,k) of householder's sex s at the age of j:

Because we can use the results of PPJP for the population Ps i(t,j) of sex s at age j in the prefecture i in the year t, the headship rate rs i(t,j,k) in the year t is only needed for the estimation of households Hs i(t,j,k).

Let us move on to a discussion of the relative difference between the national headship rates and the headship rates of each prefecture. The future national headship rate by sex, age, and family type, can be obtained from published National Estimates. Therefore, the next step is to estimate the future fluctuations of the difference between the national headship rates and the headship rates by prefecture in terms of sex, age, and family type. In this way, the future headship rates by prefecture in terms of sex, age, and family type, can be assumed from estimates of national headship rate.

In terms of the headship rate rs i(t,j,k) for sex s at age j in the year t , in family type k, the following formula can be used to determine the relative difference Ds i(t,j,k) between national and prefectural i:

At this point, the national headship rate rs (t,j,k) of the sex s at age j in the year t, in family type k, can be estimated using the following formula if we define: Ps (t,j) as the national population of the sex s in the age of j in the year of t; Hs (t,j,k) as the number of nationwide households of the sex s at age j in the year t categorized as family type k:

Therefore, the following formula can be used on the basis of (2):

Consequently, since the national headship rate rs (t,j,k) has already been estimated, the relative difference Ds i(t,j,k) at future period t is needed to assume the headship rate rs i(t,j,k). In this estimation, the future difference Ds i(t,j,k) is as follows.

In these estimates, we considered regional differences in the headship rate by sex, age, and family type, as well as past trends. As a result, we successfully reflected the recent trend of the headship rate in this projection. Therefore, we observed the transition of the relative difference in each prefecture in terms of headship rates by sex, age, and family type using the national census for 1980, 1985, 1990, and 1995. We performed trial calculations based on several assumptions for the differences in the future, as well as comparing them with national estimates. Accordingly, on the basis of each tendency in the past, we defined these three categories of future trends in the relative difference of headship rates:

[Past trends in relative differences]
[1]: The scale of relative differences has shrunk in the last 5 years (from 1990 to 1995).

[2]: The scale of relative differences has expanded in the past 15 years (from 1980 to 1995).

[3]: Other than [1] and [2]

[1] The scale will continue to decrease in the future.

[2] The scale will be stable at the current level (of 1995).

[3] The scale will decrease gradually in the future.

In the cases of reductions in relative differences (such as [1] and [3]), past trend analyzed by sex, age, and family type was extended to show the future level. For the estimation of [1], to calculate future differences, the average of ratio of headship rate of each prefecture to that of the national estimate is extended into the future by applying an approximate curve to past data at four points in time (1980, 1985, 1990, and 1995). Then, the difference was calculated as the ratio of scale reductions every five years between 2000 and 2020.

In the case of [3], the reduction ratio in the scale of relative differences was set at one half of the estimates of [1]. The number of sections of the headship rate becomes 150 (= two sections by sex * 15 sections by age * five sections by family type). In each section, the headship rates of each prefecture are applied with future fluctuations (level on scale of relative differences) of either [1] , [2], or [3], depending on past fluctuations in relative differences.

Hence, the headship rate rs i(t,j,k) in the prefecture i by the sex s in the age of j of the family type k at the time of t is expressed as follows:

In this formula,s (t,j,k) is the reduction ratio of relative differences in headship rate of the sex s at age j of the family type k at the future time t. In addition, these conditions are applied to this formula: t = 2000, ..., 2020; s = 1, 2; i = 1, ..., 15; k = 1, ..., 5.

The mean size of a household(the average number of members per household) by prefecture can be estimated from "the number of members per private household by prefecture divided by the total number of private households by prefecture." However, because the future population (overall population) obtained from PPJP includes the number of members in institutional households, the number of members in a private household by prefecture needs to be estimated separately for the estimation of the mean size of a household. In this report, the estimated number of members in private households in the future by prefecture was obtained using the ratio of the number of members in private households and that in institutional households to overall population estimated by the National Estimates, and those ratios by prefecture obtained from the 1995 national census.