Basic Models of Demographic Translation

Abstract

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.