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Modelling Fertility: A Semi-Parametric Approach

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  • Oberhofer, Walter
  • Reichsthaler, Thomas
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    Abstract

    This article presents a categorical model of fertility based on the statistical theory of the Generalised Linear Model (GLM). Focussing on the individual probability of giving birth to a child, we derive distributions which can be embedded in a GLM framework. A major advance of that methodology is the knowledge of the distribution of the random variable, which leads to a Maximum Likelihood estimation procedure. The approach takes into account the smooth shapes of parameter development over the age of the mother as well as over time. The estimation of this semi-parametric approach is done using the Local-Likelihood-method. The presented method provides stable results of the fertility, especially for smaller populations. This is illustrated by using a data set which consists of less than 100,000 inhabitants. Dieser Aufsatz stellt ein kategorielles Modell der Geburtenhäufigkeit auf Basis der statistischen Theorie des Verallgemeinerten Linearen Modells (VLM) vor. Ausgehend von individuellen Gebär-Wahrscheinlichkeiten leiten wir Verteilungen ab, welche in einen VLM-Rahmen eingebettet werden können. Ein besonderer Vorteil dieser Methode ist das Wissen um die Verteilung der Zufallsvariablen, welches ein Maximum-Likelihood Schätzverfahren ermöglicht. Der Ansatz berücksichtigt den gleichmäßigen Verlauf der Parameter-Entwicklung über das Alter der Mutter und über die Zeit. Die Schätzung dieses semi-parametrischen Ansatzes erfolgt mit Hilfe der Local-Likelihood-Methode. Die vorgestellte Methode liefert solide Ergebnisse zur Geburtenhäufigkeit, insbesondere bei kleineren Bevölkerungszahlen. Dies wird anhand eines Datensatzes mit weniger als 100.000 Einwohnern gezeigt.

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    Bibliographic Info

    Paper provided by University of Regensburg, Department of Economics in its series University of Regensburg Working Papers in Business, Economics and Management Information Systems with number 396.

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    Date of creation: 2004
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    Handle: RePEc:bay:rdwiwi:677

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    Keywords: Geburtenentwicklung ; Semiparametrische Schätzung ; Verallgemeinertes lineares Modell;

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    1. Ahlburg, Dennis A. & Land, Kenneth C., 1992. "Population forecasting: Guest editors' introduction," International Journal of Forecasting, Elsevier, vol. 8(3), pages 289-299, November.
    2. Jan Hoem & Dan Madien & Jørgen Nielsen & Else-Marie Ohlsen & Hans Hansen & Bo Rennermalm, 1981. "Experiments in modelling recent Danish fertility curves," Demography, Springer, vol. 18(2), pages 231-244, May.
    3. George B. Roberts, Chairman, Universities-National Bureau Committee for Economic Research, 1960. "Demographic and Economic Change in Developed Countries," NBER Books, National Bureau of Economic Research, Inc, number univ60-2.
    4. Birdsall, Nancy, 1988. "Economic approaches to population growth," Handbook of Development Economics, in: Hollis Chenery & T.N. Srinivasan (ed.), Handbook of Development Economics, edition 1, volume 1, chapter 12, pages 477-542 Elsevier.
    5. Schultz, T. Paul, 1993. "Demand for children in low income countries," Handbook of Population and Family Economics, in: M. R. Rosenzweig & Stark, O. (ed.), Handbook of Population and Family Economics, edition 1, volume 1, chapter 8, pages 349-430 Elsevier.
    6. Harry Haupt & Walter Oberhofer & Thomas Reichsthaler, 2003. "A Varying-Coefficient Approach To Estimation And Extrapolation Of Household Size," Mathematical Population Studies, Taylor & Francis Journals, vol. 10(4), pages 249-273.
    7. Alho, Juha M., 1990. "Stochastic methods in population forecasting," International Journal of Forecasting, Elsevier, vol. 6(4), pages 521-530, December.
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