Centro de Gestión de la Calidad y del Cambio
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- PublicationPricing reverse mortgages in Spain(Springer Verlag (Germany), 2013-07) Debón Aucejo, Ana María; Montes, F.; Sala, R.; Facultad de Administración y Dirección de Empresas; Dpto. de Estadística e Investigación Operativa Aplicadas y Calidad; Centro de Gestión de la Calidad y del Cambio; Ministerio de Ciencia e Innovación[EN] In Spain, as in other European countries, the continuous ageing of the population creates a need for long-term care services and their financing. However, in Spain the development of this kind of services is still embryonic. The aim of this article is to obtain a calculation method for reverse mortgages in Spain based on the fit and projection of dynamic tables for Spanish mortality, using the Lee and Carter model. Mortality and life expectancy for the next 20 years are predicted using the fitted model, and confidence intervals are obtained from the prediction errors of parameters for the mortality index of the model. The last part of the article illustrates an application of the results to calculate the reverse mortgage model promoted by the Spanish Instituto de Crédito Oficial (Spanish State Financial Agency), for which the authors have developed a computer application.
- PublicationMortality forecasting in Colombia from abridged life tables by sex(Springer, 2018) Diaz-Rojo, Gisou; Debón Aucejo, Ana María; Giner Bosch, Vicent; Facultad de Administración y Dirección de Empresas; Dpto. de Estadística e Investigación Operativa Aplicadas y Calidad; Escuela Técnica Superior de Ingeniería Industrial; Centro de Gestión de la Calidad y del Cambio; Ministerio de Economía y Empresa[EN] BACKGROUND: An adequate forecasting model of mortality that allows an analysis of different population changes is a topic of interest for countries in demographic transition. Phenomena such as the reduction of mortality, ageing, and the increase in life expectancy are extremely useful in the planning of public policies that seek to promote the economic and social development of countries. To our knowledge, this paper is one of the first to evaluate the performance of mortality forecasting models applied to abridged life tables. OBJECTIVE: Select a mortality model that best describes and forecasts the characteristics of mortality in Colombia when only abridged life tables are available. DATA AND METHOD: We used Colombian abridged life tables for the period 1973-2005 with data from the Latin American Human Mortality Database. Different mortality models to deal with modeling and forecasting probability of death are presented in this study. For the comparison of mortality models, two criteria were analyzed: graphical residuals analysis and the hold-out method to evaluate the predictive performance of the models, applying different goodness of fit measures. RESULTS: Only three models did not have convergence problems: Lee-Carter (LC), Lee-Carter with two terms (LC2), and Age-Period-Cohort (APC) models. All models fit better for women, the improvement of LC2 on LC is mostly for central ages for men, and the APC model's fit is worse than the other two. The analysis of the standardized deviance residuals allows us to deduce that the models that reasonably fit the Colombian mortality data are LC and LC2. The major residuals correspond to children's ages and later ages for both sexes. CONCLUSION: The LC and LC2 models present better goodness of fit, identifying the principal characteristics of mortality for Colombia.Mortality forecasting from abridged life tables by sex has clear added value for studying differences between developing countries and convergence/divergence of demographic changes.
- PublicationMultivariate Control Chart and Lee-Carter Models to Study Mortality Changes(MDPI AG, 2020-11) Diaz-Rojo, Gisou; Debón Aucejo, Ana María; Mosquera, Jaime; Facultad de Administración y Dirección de Empresas; Dpto. de Estadística e Investigación Operativa Aplicadas y Calidad; Centro de Gestión de la Calidad y del Cambio; Universidad del Tolima; Universitat Politècnica de València; Ministerio de Economía y Competitividad[EN] The mortality structure of a population usually reflects the economic and social development of the country. The purpose of this study was to identify moments in time and age intervals at which the observed probability of death is substantially different from the pattern of mortality for a studied period. Therefore, a mortality model was fitted to decompose the historical pattern of mortality. The model residuals were monitored by the T-2 multivariate control chart to detect substantial changes in mortality that were not identified by the model. The abridged life tables for Colombia in the period 1973-2005 were used as a case study. The Lee-Carter model collects information regarding violence in Colombia. Therefore, the years identified as out-of-control in the charts are associated with very early or quite advanced ages of death and are inversely related to the violence that did not claim as many victims at those ages. The mortality changes identified in the control charts pertain to changes in the population's health conditions or new causes of death such as COVID-19 in the coming years. The proposed methodology is generalizable to other countries, especially developing countries.
- PublicationTemporal evolution of some mortality indicators: Application to Spanish data(Taylor & Francis (Routledge): SSH Titles - no Open Select, 2012) Debón Aucejo, Ana María; Martínez Ruiz, F; Montes, F; Facultad de Administración y Dirección de Empresas; Dpto. de Estadística e Investigación Operativa Aplicadas y Calidad; Centro de Gestión de la Calidad y del Cambio; Universitat Politècnica de València; Ministerio de Ciencia e Innovación[EN] In Spain, as in other developed countries, significant changes in mortality patterns have occurred during the 20th and 21st centuries. One reflection of these changes is life expectancy, which has improved in this period, although the robustness of this indicator prevents these changes from being of the same order as those for the probability of death. If, moreover, we bear in mind that life expectancy offers no information as to whether this improvement is the same for different age groups, it is important and necessary to turn to other mortality indicators whose past and future evolution in Spain we are going to study. These indicators are applied to Spanish mortality data for the period 1981–2008, for the age range 0–99. To study its future evolution, the mortality ratios have to be projected using an adequate methodology, namely, the Lee-Carter model. Con- fidence intervals for these predictions can be calculated using the methodology that Lee and Carter apply in their original article for expected lifetime confidence intervals, but they take into account only the error in the prediction of the mortality index obtained from the ARIMA model adjusted to its temporal series, excluding other sources of error such as that introduced by estimations of the other parameters in the model. That is why bootstrap procedures are preferred, permitting the combination of all sources of uncertainty.