Fécondité par rang au sein d’une génération en France et au Québec : e
stimation de probabilités d’agrandissement à partir d’un seul recensement

The interest of this research is to observe the differences between the estimates of the fertility rate and the probabilities of enlargement using only the census data, using the indirect “own children method“, which links the Cohabiting children and a potential mother within the household. In the case of France, the method will be validated by comparing the results obtained by the indirect method with those obtained from the 2011 Family and Housing Survey (EFL) data, a survey coupled with the census and interviewing women on the Of the children they had, whether or not the children cohabited with the mother at the time of the census. Concerning Quebec, the results obtained from the indirect method will be compared with those resulting from the operation of the 2011 General Social Survey - Family cycle. Most of the studies developed in order to find the differential factors that affect fertility rate are based on family policies. For this reason, it is important to study and to analyse individual socio demographic variables to characterize the factors that influence the probabilities of become mother or having more children. We are interested in the variables associated with increasing or decreasing probabilities of enlargement. This research examines the relationship between sociodemographic variables available in the different sources of information consulted and probabilities of enlargement. We use the variables: date of birth, sex, and relationship with the head of household to classify and establish relationships (motherchild), and the variables mother's education level and place of birth of the mother to segment and calculate the probabilities of enlargement. The study highlights the underestimation in the probabilities of enlargement and the ISF that use census data (children who live in the household) in comparison with socio-demographic surveys that inform about all children of the main woman in the household. Our results show that, in France and Quebec, more educated women wait longer before becoming mothers and they are less likely to have a large family. Furthermore, they are most likely to remain childless. iv For the mother's place of birth variable, the results are inconclusive. On the one hand, for France, descriptive analyzes of the average age of the mother at first birth and the time elapsed between births are minimal (less than three months). However, the probabilities of enlargement indicate that immigrant women are more likely to have large families (more than three children). On the other hand, for Quebec, the analysis shows that, although women begin their maternity later than women born in Quebec, they are more likely to have a large family (more than three children), especially women from African countries and Maghreb countries. Nevertheless, based on the results of the analysis of variance, there is insufficient statistical evidence to show an effect between the place of birth and the mean time elapsed between the second and third births. We prove that the results of the census underestimate the fertility rates and the probabilities of enlargement cause by the impossibility of counting the total of children born from the main women of the household. The results of this paper provide new perspectives for analyzing fertility trends in subpopulations based on census data. This relatively classical approach distinguishes the ages of women, but also the ranks of birth, which has been more rarely analyzed in previous studies. The results of this research help us to measure the effects of mother's education and birthplace on the probabilities of enlargement. They help us answer a variety of questions, including questions about why women did not have a third child.

Keyphrases: Fertility, Probabilities of enlargement, Own Children method, Indirect method, Fertility rate