The Journal of Population Studies

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Population problems have long been centered on relations between the increase of population and productive ability of the economy since "An Essay on the Principle of Population" was published by T.R. Malthus. However, nowadays it is necessary to study taking into consideration on the following two big problems; at first resources and environment, and secondly the change of population structure based on the prolonged average life span of human beings. For the first problem, it will be forced to change the former economic growth line and it will be required not only one country's plan, but also international cooperation in relation to preservation of natural environment and control of rapid increase of population. For the second problem, aging phenomena give the pressure to increase financial demands one hand, and decreasing tendency of number of children will bring labor shortage and reduce effective demands of economy in the future. Therefore, it should be requested to reform the existing industrial structure and socio-economic system which has been established under the precondition of continuing economic growth. From these points, population problems should be switched from the relation between population and economy to co-existence between human beings and nature. Speaking from microscopic aspects, reproduction of population should be considered in relation to a nuclear cycle of human life. The conversion of increasing population to decrease in the first decade of 21st century must be considered as one normal phase of population wave in the long-term historical viewpoints. Then we must design a concrete plan transferring to the new socio-economic system adapting well to the coming zero-economic growth society. We would propose the necessity of Sciences of Seizon, or Life Sciences, to create new order of sustainable existence of human beings.

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The purpose of this paper is to evaluate the four-parameter logit model developed by Ewbank and others, to ascertain the validity and the applicability of this model, and finally to look for a more rational way of estimating the four parameters. For the past few decades, death rate has declined remarkably in both developing and developed countries. However, it is more and more difficult for either the present model life table or any other mathematical model to describe the mortality decline. It is because today's death rate is too low to be described by those models. One of the promising ways of solving this difficulty is to apply relational models. The two-parameter logit model developed by Brass is one of those relational models. But the Brass model sometimes fails to capture the mortality pattern of childhood and old ages. The Ewbank model was developed and designed to cope with this problem. It is not so popular, however, because it is rather difficult to estimate the four parameters of the model. Then, I applied the Ewbank model to Japanese life tables in order to verify the validity of the model, and tried to look for the more rational way of estimating the four parameters of the Ewbank model through various mathematical methods. As a result of the analysis, I found that the Ewbank model captures the mortality pattern of the Japanese, and that the four parameters of the model can be effectively estimated by using Simplex method and Marquardt method. As to the applicability of the Ewbank model, it might be possible to estimate the life table at any point of time from the past to the future by changing the values of the parameters of this model. I ascertained this by altering parameter α. As a result, the feasibility of this model is found to be quite high.

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