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Modelling Fertility: A Semi-Parametric Approach

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  • Oberhofer, Walter
  • Reichsthaler, Thomas

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.

Suggested Citation

  • Oberhofer, Walter & Reichsthaler, Thomas, 2004. "Modelling Fertility: A Semi-Parametric Approach," University of Regensburg Working Papers in Business, Economics and Management Information Systems 396, University of Regensburg, Department of Economics.
  • Handle: RePEc:bay:rdwiwi:677
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    File URL: https://epub.uni-regensburg.de/4511/1/rdisb396.pdf
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    References listed on IDEAS

    as
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    More about this item

    Keywords

    Geburtenentwicklung ; Semiparametrische Schätzung ; Verallgemeinertes lineares Modell;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General

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