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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.

It has been demonstrated for many pre-industrial populations that the age at marriage, or marriage duration, influences age-specific marital fertility but the reason for this remains unclear. Among the several mechanisms that may be responsible, the following are often cited: secondary sterility or increased sub fecundity associated with parity; declining coital frequency; the age difference between the spouses; and, importantly, parity-dependent fertility control. If the latter mechanism were partly responsible for the marriage-duration effect in pre-transition populations, it would contradict the concept of the modern fertility transition as the evolution (or revolution) from parity-independent to parity-dependent fertility. The study presented in this paper investigates the relative importance of these alternative explanations. The application of multivariate Poisson regression to the fertility data from two birth cohorts in the Belgian city of Leuven shows that a linearly declining or even concave age-specific fertility pattern, disaggregated by age at marriage, does not imply parity-dependent fertility limitation. [ABSTRACT FROM AUTHOR]

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.

In a recent examination of data from 13 family reconstitutions drawn from parish registers E.A. Wrigley and R.S. Schofield have discussed the patterns of marital fertility prevalent in pre-industrial England. In their article the authors noted that earlier evidence of the practice of family limitation in pre-industrial England was limited in time and place and suggested that natural fertility was the predominant form of childbearing within marriage. In a situation of family limitation, as couples reach their desired family size or parity, they make efforts to reduce or cease further childbearing, and thus lower fertility. For this reason, fertility rates fall more rapidly as age, and thus parity, increases. It will be noted that the level of fertility can vary enormously between different groups, in the presence of both natural fertility and family limitation, thus the age pattern of fertility rather than its level is the key to identifying the underlying regime. Pre-marital conceptions leading to post-marital births inflate the marital fertility rate artificially, since in calculating the period in observation all women are regarded as only being at risk of conceiving from the date of marriage. For women who conceive before marriage this is clearly false. Thus the length of time they are exposed to the risk of conception is underestimated, and the marital fertility rate overestimated.