Demographic translation models, initiated by Ryder, give specific relationships between cohort and period fertility. This paper attempts to describe step-by-step evolution of basic models in demographic translation. Two types of models should be distinguished. Cohort models, as formalized by Ryder (1964), specify the way of change in cohort fertility, and period fertility is seen to be dependent on cohort fertility. This determinant/dependent relation is reversed in period models, as by Bongaarts and Feeney (1998). In terms of simplicity, three classes of models are distinguished. The first class allows change in tempo of fertility behavior but quantum is held constant. This class consists of two models. One is the horizontal linear shift model such as Bongaarts-Feeney model, and the other is the vertical linear shift model obtained by reducing Ryder's linear model. The second class allows quantum change but not tempo change. Again, a basic model in this class can be formalized by reducing Ryder's model. Although not in the literature of demographic translation, this paper examines exponential quantum change as another basic model in this class. The third class allows both quantum and tempo changes. Ryder's linear model is one of the most basic models in this class. As another basic model, independent effect model, which combines the horizontal linear shift and exponential quantum change, is examined. For all of these models, the cohort and period relationship in quantum, tempo and rate of change are clarified and translation formulae are compared. This article also examines the performance of such indices as the tempo index and the average cohort fertility by Ryder and the adjusted TFR by Bongaarts-Feeney. It is shown that in some basic models the adjusted TFR fails while Ryder's indices give a reasonable result.

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Overall, the total fertility rate has been decreasing rapidly since 1973 in Japan. A major factor causing low fertility is the fact that it is hard for women to continue their careers while raising children. We do not have enough childcare services to meet women's needs. The more fundamental problem is that our social system is based on the division of labor by gender, where the husband serves as breadwinner and the wife as full-time homemaker. In addition, women's family values have greatly changed with the change of their social role and status. The change in their values under the present social system seems to bring about the tendency to avoid having children. Hence, this paper aims to discuss the following points. Firstly, we examine the impact of a husband's cooperative attitude towards household work or his working style, which enables him to play domestic roles, on fertility behavior and wife's labor supply. We also verify whether such an attitude or a working style will be able to enhance the compatibility of his wife's full-time work with childrearing. Secondly, we analyze the impact of a wife's family values, which are thought to affect the household's decision, on fertility behavior and her labor supply. In particular, this paper discusses upon three typical family values that many sociologists have mentioned as the change of modern women's values, that is, the nontraditional family value (anti-natalism), the individualistic value and the egalitarian value of gender roles. The data used for this study is micro data from "The Survey on a Couple's Life Consciousness" which was conducted by Japan Cultural Institute of Life Insurance in 1994. Considering the limitation of the data, we used three types of models for analysis: (1) Tobit model for the number of children, (2) Multinomial Logit model for a wife's labor participation, (3) Bivariate Probit model for simultaneous choices between childrearing and a wife's full-time work. As the result of these empirical studies, we can show some interesting findings. At first, married women are facing the alternative of their careers or children. However, in the case of husbands' returning home before 7p.m. the probability that married women's full-time work is compatible with childrearing increases. Next, if husbands are working under flextime, the probability of having children may increase. Furthermore, the married women's choice of full-time work is greatly related to their husbands' time allocation in the household rather than their income. With respect to married women's family values, it has been shown that women with an egalitarian value of gender roles tend to choose full-time work and avoid having children. These findings imply that we should change the present social system based on the assumption of traditional gender relationships.

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