Modelling and Prediction of the Gross Mortality Rate in Ecuador

Authors

  • Mónica Mite University of Guayaquil
  • Sandra Garcia-Bustos
  • Marcela Pincay
  • Ana Debón
  • Francisco Santoja

DOI:

https://doi.org/10.24203/ajas.v6i3.5383

Keywords:

Mortality, Lee-Carter Model, Plat Model, StMoMo, ARIMA

Abstract

This paper presents the results obtained from the modelling of the mortality data in Ecuador from 1990 to 2010, using the StMoMo library in the open source programming language R. This library was developed based on the Generalized Age-Period-Cohort Models (GAPC), among which is the Lee-Carter model, which has been widely applied in the actuarial area. The gross mortality rate of men and women in an age range of 1 to 85 years was modelled for the data of Ecuador, in the period 1990-2010. Of a total of eight models, two models have been selected because they present a good fit of the data for both genders. The first is the basic model of Lee-Carter and the second, the Plat model, which incorporates the cohort effect. A comparison was made with the two models to determine which one has a better forecast in a horizon of 20 years for specific ages. Both models show and predict the decrease in mortality in Ecuador of both genders, a decrease that is more pronounced, in general, for women at certain ages. In determining the uncertainty of the models, the bootstrap technique was used to define the confidence intervals of the adjusted model. The GAPC and ARIMA models were also compared; the former improve the mortality forecasting.

Author Biography

Mónica Mite, University of Guayaquil

Facultad de Matematicas y Fisicas

References

“ECLAC (2015). Economic Center for Latin America and the Caribbean 2015, URL https://www.cepal.org/es/publicaciones/39965-panorama-social-america-latina- 2015,†p. 39965, 2015.

B. K. Defo, “Demographic, epidemiological, and health transitions: are they relevant to population health patterns in {Africa}?,†Glob. Health Action, vol. 7, 2014.

P. D. Shagñay-Huaraca, “Ajuste y estimación de tablas de mortalidad dinámicas de la población ecuatoriana hasta el año 2030,†Quito: EPN, 2014., 2014.

H. C. and K. Lara, “CONSTRUCCIÓN DE TABLAS DE MORTALIDAD DE LA POBLACIÓN ECUATORIANA CON BASE EN EL CENSO 2001 Y ESTADÃSTICAS VITALES,†Consult. CIMACYT, pp. 1–7, 2004.

J. Sanchez, “Construcción de una tabla de mortalidad para la población ecuatoriana,†Repos. Dsp., 2000.

R. D. Lee and L. Carter, “Modelling and forecasting {U.S.} mortality,†J. Am. Stat. Assoc., vol. 87, no. 419, pp. 659–671, 1992.

A. M. Villegas, P. Millossovich, and V. K. Kaishev, “StMoMo: An R Package for Stochastic Mortality Modelling.†2016.

R Core Team, “R: A Language and Environment for Statistical Computing.†Vienna, Austria, 2015.

A. Delwarde and M. Denuit, “Importance de la période d’observation et des ages consideres dans la projection de la mortalité selon la methode de Lee-Carter.,†Belgian Actuar. Bull., vol. 1, no. 1, pp. 1–21, 2003.

A. Hunt and D. Blake, “On the structure and classification of mortality models,†Pension Inst. Work. Pap., 2015.

I. D. Currie, “On fitting generalized linear and non-linear models of mortality,†Scand. Actuar. J., vol. 2016, no. 4, pp. 356–383, 2016.

H. Turner and D. Firth, “Generalized nonlinear models in R: An overview of the gnm package.†2015.

N. Brouhns, M. Denuit, and J. K. Vermunt, “A {Poisson} log-bilinear regression approach to the construction of projected lifetables,†Insur. Math. Econ., vol. 31, no. 3, pp. 373–393, 2002.

A. Debón, F. Montes, and F. Martínez-Ruiz, “A geostatistical approach for dynamic life table: The effect of mortality on remaining lifetime and annuities.,†Insur. Math. Econ., vol. 47, no. 3, pp. 327–336, 2010.

G. E. P. and J. Box, Time Series Analysis: Forecasting and Control., Revised ed. 1970.

R. Plat, “On stochastic mortality modeling,†Insur. Math. Econ., vol. 45, no. 3, pp. 393–404, 2009.

A. J. G. Cairns et al., “A quantitative comparison of stochastic mortality models using data from England and Wales and the United States,†North Am. Actuar. J., vol. 13, no. 1, pp. 1–35, 2009.

A. Debón, F. Montes, J. Mateu, E. Porcu, and M. Bevilacqua, “Modelling residuals dependence in Dymanic Life Tables,†Comput. Stat. Data Anal., vol. 52, no. 3, pp. 3128–3147, 2008.

B. Efron and R. J. Tibshirani, An introduction to the boostrap. Chapman & Hall, New York & London, 1993.

M. Koissi, A. Shapiro, and G. Hognas, “Evaluating and extending the {Lee-Carter} model for mortality forecasting confidence interval,†Insur. Math. Econ., vol. 38, no. 1, pp. 1–20, 2006.

R. Hyndman, “demography: Forecasting mortality and fertility data.†2005.

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Published

2018-06-28

How to Cite

Mite, M., Garcia-Bustos, S., Pincay, M., Debón, A., & Santoja, F. (2018). Modelling and Prediction of the Gross Mortality Rate in Ecuador. Asian Journal of Applied Sciences, 6(3). https://doi.org/10.24203/ajas.v6i3.5383

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