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This article presents the reply of the author and co-authors to an article about the analysis of differences in the fertility patterns between national populations and over time. In their comments to our paper Osona and Kohler make a number of interesting and potentially helpful points. While their comments do not, in general, appear to be in conflict with our opinions, we are concerned that they have misunderstood one specific point. In their first section, on the analytical relationship between Hadwiger parameters and demographic measures, the authors re-present some known results. Those results, of course, were not the essential point of our paper, which was concerned primarily with the analysis of differences in fertility patterns. The functions were fitted in order to gain understanding of the differences in the patterns between countries and periods. The correspondences between variables to which they refer were used in order to investigate the effects of departures from the models in cases of distorted distributions. In their section dealing with reparameterization the authors propose an alternative to our presentation of the Hadwiger mixture model. Their explicit interpretation of the Hadwiger parameters as the total fertility, the mean age at childbearing, and the variance of the fertility schedule is possibly a step forward for the use of the model in demography.

The paper deals only with the first two of these, which, unlike duration of pregnancy, present unusual problems of estimation. The literature of the past few years contains a number of attempts to deduce values for these determinants from observational data, that is, from observed series of birth intervals, but it is one of the more frustrating aspects of such demographic analyses that the significance of observations often depends as much upon the way in which the data were collected as on the values themselves. Sets of birth intervals can be obtained in a quite remarkable variety of ways and analyzed with correspondingly varied virtuosity. The fecundabilities calculated in various tables are considerably lower than those, which have been derived from other studies. This is largely because of the inclusion in the series of the full range of women in the population; the correction of the harmonic effect also leads to a lower value. A remarkable feature of this series is that some 4% of all intervals were stated as being longer than six years. Intervals of this length are, of course, very much rarer in studies confined to women of high attained parity.