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Register a new userForecasting Fertility with Parametric Mixture Models
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Jason Hilton
Publication date
2019
fields
Mathematical Statistics
and research's language is
English
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This paper sets out a forecasting method that employs a mixture of parametric functions to capture the pattern of fertility with respect to age. The overall level of cohort fertility is decomposed over the range of fertile ages using a mixture of parametric density functions. The level of fertility and the parameters describing the shape of the fertility curve are projected foward using time series methods. The model is estimated within a Bayesian framework, allowing predictive distributions of future fertility rates to be produced that naturally incorporate both time series and parametric uncertainty. A number of choices are possible for the precise form of the functions used in the two-component mixtures. The performance of several model variants is tested on data from four countries; England and Wales, the USA, Sweden and France. The former two countries exhibit multi-modality in their fertility rate curves as a function of age, while the latter two are largely uni-modal. The models are estimated using Hamiltonian Monte Carlo and the `stan` software package on data covering the period up to 2006, with the period 2007-2016 held back for assessment purposes. Forecasting performance is found to be comparable to other models identified as producing accurate fertility forecasts in the literature.
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We consider the problem of probabilistic projection of the total fertility rate (TFR) for subnational regions. We seek a method that is consistent with the UNs recently adopted Bayesian method for probabilistic TFR projections for all countries, and works well for all countries. We assess various possible methods using subnational TFR data for 47 countries. We find that the method that performs best in terms of out-of-sample predictive performance and also in terms of reproducing the within-country correlation in TFR is a method that scales the national trajectory by a region-specific scale factor that is allowed to vary slowly over time. This supports the hypothesis of Watkins (1990, 1991) that within-country TFR converges over time in response to country-specific factors, and extends the Watkins hypothesis to the last 50 years and to a much wider range of countries around the world.
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Edmilson Rodrigues Pinto
, Leandro Alves Pereira
, Aurelian Aparecida de Araujo Rodrigues
2015
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