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Altersspezifische Querschnittsanalyse der Fertilität in Mecklenburg-Vorpommern mit dem EM-Algorithmus
[Age-Specific Cross-Sectional Analysis of the Fertility in Mecklenburg-West Pomerania with the EM Algorithm]

Author

Listed:
  • Benjamin Strohner

    (Universität Rostock)

  • Rafael Weißbach

    (Universität Rostock)

Abstract

Zusammenfassung In diesem Aufsatz soll die altersspezifische Struktur der Fertilität modelliert und aus Querschnittsdaten geschätzt werden, um Unterschiede zwischen erster und zweiter Geburt zu bestimmen. Es wird die Kinderzahl einer Frau als zustandsdiskrete altersspezifische, also inhomogene, Markovkette modelliert. Ökonomische Theorie legt nahe, dass die bedingten Übergangswahrscheinlichkeiten zwischen den Zuständen einer im Alter asymmetrischen Dreiecksgestalt folgen. Ferner nehmen wir an, dass sie sich nach der Anzahl der vorhandenen Kinder unterscheiden können. Die insgesamt entstehenden vier Parameter werden mittels Maximum-Likelihood geschätzt. Aus dem Doppeljahrgang 2009/2010 werden dafür 26.000 Geburten in Mecklenburg-Vorpommern mit dem Bevölkerungsbestand von 740.000 Frauen kombiniert. Die Gliederung des Bestandes der Frauen nach der Anzahl vorhandener Kinder ist allerdings unbekannt. Frühere Geburten liegen nur aggregiert vor. Weil die Loglikelihoodfunktion linear in diesen Frauenbeständen ist, wird der EM-Algorithmus anwendbar. Die Standardfehler werden mit der Formel von Oakes bestimmt. Der Vergleich der Parameterpaare für erste und zweite Geburten zeigt, dass, adjustiert um den Alterseffekt, die bedingte einjährige Geburtenwahrscheinlichkeit für das zweite Kind relevant höher ist als die des ersten Kindes.

Suggested Citation

  • Benjamin Strohner & Rafael Weißbach, 2016. "Altersspezifische Querschnittsanalyse der Fertilität in Mecklenburg-Vorpommern mit dem EM-Algorithmus [Age-Specific Cross-Sectional Analysis of the Fertility in Mecklenburg-West Pomerania with the ," AStA Wirtschafts- und Sozialstatistisches Archiv, Springer;Deutsche Statistische Gesellschaft - German Statistical Society, vol. 10(4), pages 269-288, December.
    • Handle: RePEc:spr:astaws:v:10:y:2016:i:4:d:10.1007_s11943-016-0184-2
    DOI: 10.1007/s11943-016-0184-2
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    References listed on IDEAS

    as
    1. Weißbach, Rafael & Mollenhauer, Thomas, 2011. "Modelling Rating Transitions," VfS Annual Conference 2011 (Frankfurt, Main): The Order of the World Economy - Lessons from the Crisis 48698, Verein für Socialpolitik / German Economic Association.
    2. Kremer, Alexander & Weißbach, Rafael, 2014. "Asymptotic normality for discretely observed Markov jump processes with an absorbing state," Statistics & Probability Letters, Elsevier, vol. 90(C), pages 136-139.
    3. Alexander Kremer & Rafael Weißbach, 2013. "Consistent estimation for discretely observed Markov jump processes with an absorbing state," Statistical Papers, Springer, vol. 54(4), pages 993-1007, November.
    4. James J. Heckman & Robert J. Willis, 1976. "Estimation of a Stochastic Model of Reproduction: An Econometric Approach," NBER Chapters, in: Household Production and Consumption, pages 99-146, National Bureau of Economic Research, Inc.
    5. Weißbach, Rafael & Walter, Ronja, 2010. "A likelihood ratio test for stationarity of rating transitions," Journal of Econometrics, Elsevier, vol. 155(2), pages 188-194, April.
    6. James J. Heckman & James R. Walker, 1989. "Forecasting Aggregate Period Specific Birth Rates: The Time Series Properties of a Microdynamic Neoclassical Model of Fertility," NBER Working Papers 3133, National Bureau of Economic Research, Inc.
    7. Nestor E. Terleckyj, 1976. "Household Production and Consumption," NBER Books, National Bureau of Economic Research, Inc, number terl76-1.
    8. Yongdai Kim & Lancelot James & Rafael Weissbach, 2012. "Bayesian analysis of multistate event history data: beta-Dirichlet process prior," Biometrika, Biometrika Trust, vol. 99(1), pages 127-140.
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    Cited by:

    1. Ralf Thomas Münnich, 2016. "Vorwort des Herausgebers," AStA Wirtschafts- und Sozialstatistisches Archiv, Springer;Deutsche Statistische Gesellschaft - German Statistical Society, vol. 10(4), pages 197-203, December.
    2. Felix Rösel & Julia Sonnenburg, 2016. "Politisch abgehängt? Kreisgebietsreform und AfD Wahlergebnis in Mecklenburg-Vorpommern," ifo Dresden berichtet, ifo Institute - Leibniz Institute for Economic Research at the University of Munich, vol. 23(06), pages 06-13, December.

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