RELATIONSHIPS BETWEEN COHORT AND PERIOD DEMOGRAPHIC INDICATORS

Demographers commonly distinguish between period indices which refer to observations at a point in time and cohort indices which refer to generations. In this study we are concerned with establishing relationships that make it possible to switch from one type of index to the other. We first look at renewable events whose frequency is measured by rates, and then at non-renewable events whose frequency is measured by probabilities. The hypothesis on which our method is based is that the variation frequencies over time can be approximated by polynomials over time intervals with a duration equal to that of an individual's exposure to risk. The quality of the relationships which are thus established between period and cohort values is evaluated by looking at fertility in France during the past hundred years: the results are considered satisfactory when based on the assumption that the approximating polynomial is a cubic. These relationships highlight the determining role played by variations of timing in the phenomenon studied, namely, the average age at childbirth, and its first derivative with respect to time, and the second derivative of the variance.