In this study, we attempt to develop a mortality model that reflects the improvements in the mortality rate of Japan’s elderly since 1970, using the Japanese Mortality Database （JMD） life tables organized according to prefecture.

Specifically, we first apply the Flexible Two-dimensional Model （Flexible Model） by Wilmoth et al. （2012） to the JMD life tables per prefecture. We use the coefficients of the Flexible Model, which are derived from 719 life tables in the Human Mortality Database （2021）. As a result, it is confirmed that the estimation error of the Flexible Model becomes larger particularly in the elderly age group of 65 years and older, and that the estimation error tends to increase as the life expectancy at age 65 increases.

Based on these observations, the estimation errors of the Flexible Model in the age group of 50 years and above are stored in the form of a matrix, and we apply Singular Value Decomposition to the matrix. Then, we derive the first singular value and the corresponding left and right singular vectors and fix the product of the first singular value and the left singular vector as coefficient of the proposed model （Modified Model） for the usage of indirect estimations. This Modified Model is also compared with Clark’ s （2019a） model.

Finally, the Modified Model proposed in this study is applied to the Japanese Ministry of Health, Labour and Welfare's Municipal Life Tables from 2015, and it is confirmed that the mortality rate can be estimated accurately. Therefore, it is suggested that the Modified Model can be applied to future population projection at the municipal level.

The child–woman ratio (CWR) is frequently used as a fertility parameter in projecting the regional population and is commonly calculated as the value obtained by dividing the number of children aged 0–4 years by the number of women aged 15–49 years. However, to improve the accuracy of population projections, the CWRs are suggested to be calculated using different denominator ages based on the following two ideas: the deviation in age-specific fertility rate and the strength of correlation between total fertility rate and CWR at the prefectural level. These ideas remain merely hypotheses because empirical analysis of them is lacking. This study aimed to verify the validity of previous hypotheses using the model population projections of all municipalities and propose a new analytical framework that expresses the logical relationship between the denominator age of the CWR and the accuracy of regional population projections.

By analyzing the projection error of the population aged 0–4 years using different denominator ages of the CWR through model population projections, these hypotheses are valid in the projection beginning with the 1980 Population Census but are invalid in that beginning with the 1990 or 2000 Population Census. The reason for this is thought to be that the influence of age structure changes was not taken into consideration. Therefore, for grasping the influence of age structure changes, projection errors of the population aged 0–4 years were decomposed to the following three projection errors: the age-specific CWR, age structure ratio, and the population of denominator age of women. This is the new analytical framework between the projection accuracy and the denominator age of CWR. The denominator age with high projection accuracy cannot be determined before projection even if this framework is used. However, the difference in projection errors by selecting the denominator age of the CWR will be reduced, since age structure changes become smaller as reflected by the decreased number of births in the past. In other words, the significance of selecting the denominator age diminishes for the future. Thus, this study recommends the use of the most common CWR with a denominator age of 15–49 years in regional population projections.

The purpose of this paper was to calculate the average number of live births （ANLB） to women who continued in their first marriage during the birth period and to evaluate complete fertility in Japan during the period between World War I and World War II using the ANLB.

I first calculated the ANLB of the nation, cities and counties based on birth-cohort data for five groups: “before 1890”, “1891–1895”, “1896–1900”, “1901–1905” and “1906–1910”, using the population census of the 1950 special report: “The Fertility of Japanese Women” （Prime Minister's Office Statistics Bureau 1957）. The calculated ANLB of birth cohorts in the “before 1890” and “1906–1915” groups were unreliable. Therefore, I estimated the relevant ANLB.

Next, I estimated the ANLB of women whose husbands worked in a primary industry （ANLB-P） and that of women whose husbands worked in a non-primary industry （ANLB-NP） based on city and county data for ANLB. The national ANLB declined slightly for the birth cohorts from “1891–1895” to “1901–1905” ; live births in the ANLB-P group rose whereas live births in the ANLB-NP group declined. The national ANLB could be calculated as the weighted average of the ANLB-P and ANLB-NP groups if the correct proportions of the two values are known.

I concluded that national marital fertility showed a slight downward trend during the period between World War I and World War II while marital fertility by occupation varied. When ANLB, ANLB-P and ANLB-NP were considered to derive an index of complete fertility, the marital fertility of those whose husbands worked in primary industries rose while that of those whose husbands worked in non-primary industries declined. I also concluded that the slight overall decline in national marital fertility resulted from the decline in the marital fertility of those whose husbands worked in non-primary industries offsetting the increase in the marital fertility of those whose husbands worked in primary industries.