Altersspezifische Querschnittsanalyse der Fertilität in Mecklenburg-Vorpommern mit dem EM-Algorithmus

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• 作者：Benjamin Strohner ; Rafael Weißbach
• 关键词：SchlüsselwörterFertilität ; Inhomogene Markovkette ; Maximum ; Likelihood ; Methode ; EM ; Algorithmus
• 刊名：AStA Wirtschafts- und Sozialstatistisches Archiv
• 出版年：2016
• 出版时间：December 2016
• 年：2016
• 卷：10
• 期：4
• 页码：269-288
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Statistics for Business/Economics/Mathematical Finance/Insurance; Statistics for Social Science, Behavorial Science, Education, Public Policy, and Law; Economics, general;
• 出版者：Springer Berlin Heidelberg
• ISSN：1863-8163
• 卷排序：10

文摘

In this paper the age-specific structure of fertility is modelled and estimated based on cross-sectional data to determine differences between first and second birth. The number of siblings is modelled as a state- and age-discrete and age-specific, i.e. inhomogeneous, Markov chain. The conditional transition probabilities between the states are modelled as asymmetric triangular shape (as a function of age) and allow for differences in the number of already existing siblings. The four parameters of the model are estimated by maximum likelihood. In the application, 26,000 births in Mecklenburg-West Pomerania from the combined cross-sections of 2009 and 2010 are used in combination with the respective population of 740,000 women. Unfortunately, the classification of the population by pre-existing number of siblings is unobserved. However, the EM algorithm is easily applicable, because the logarithmic likelihood is linear in the population. Standard errors are determined with Oakes’ formula. The comparison of the parameter pairs for first and second birth shows, that, adjusted by the age effect, the conditional one-year probability of birth for the second child is relevantly higher than that for the first.