Mortality and Life Expectancy Forecast for (Comparatively) High - PDF document

Mortality and Life Expectancy Forecast for (Comparatively) High Mortality Countries Ahbab Mohammad Fazle Rabbi ∗ , Stefano Mazzuco † Department of Statistical Sciences, University of Padua, Italy September 27, 2017 Abstract The Lee-Carter method and its later variants are widely accepted extrapolative methods for forecasting mortality and life expectancy in industrial countries due to their simplicity and availability of long time series data with better quality. We compared and contrast the mortality and life expectancy forecast using 7 different variants of Lee-Carter methods for 9 comparatively high mortality countries than industrialized countries along with UN forecast method. The models provided under estimated forecast for high mortality countries compare to comparatively better mortality patterns. Diverging mortality pattern was observed in these countries which is also reflected in future mortality and life expectancy pattern. Better fit of different models in country specific mortality pattern was observed while no models gives better fit uniquely. In the same context, use of probabilistic forecasting technique from Bayesian framework provided better forecast than some of the extrapolative methods. Country specific forecast indicates better fit of certain extrapolative methods may occur in part of the life span rather than that of the whole life span. These findings imply necessity for invention of new forecast method in context of high mortality countries. Keywords: Mortality forecast; Lee-Carter method; Probabilistc forecast; Mortality in Eastern Europe; Bayesian Hirerchical model 1 Introduction Mortality improvements are observed almost all over the world during the 20th century and it is always considered as a positive change for socio-economical advancement of a country. This change has brought new requirements in support-systems for the elderly, such as health-care and pension provision. Aging became the greatest population problem for many industrialized countries since the 1970s (Brouhns et al, 2002). This has resulted in a surge of interest among government policy makers and planners in accurately modeling and forecasting age-specific mortality rates. Policy makers rely greatly on future mortality rates as an indicator of future population structure also. However, besides the developed countries, population aging are also visible in some other countries of the world for which mortality pattern is not same as the the industrialized countries. This sort of different mortality regime may be visible for several Eastern European countries, Russia and some other countries where causes of deaths may play vital role on age-specific deaths (Vallin & Mesl´ e, 2001). Several parametric (both in Frequentist and Bayesian point of view) and nonparametric methods have been proposed over the years for forecasting age-specific mortality rates and ∗ fazlerabbi@stat.unipd.it † mazzuco@stat.unipd.it 1

life expectancy (for instance, Shang, 2012). The simplest way for parametric forecasting is to parametrize the available series of life table and hence to extrapolate each of the parame- ter separately for obtain the forecast from the assumed model (Keyfitz, 1991). Without any doubt, the ground breaking model based on extrapolation was proposed by Lee and Carter (Lee & Carter, 1992). The advantages of the Lee-Carter (LC) method includes its simplicity and robustness in situations where age-specific log mortality rates have linear trends (Booth et al, 2002). LC method attempts to capture the patterns of mortality rates using only one principal component and its scores. However, LC method does not give good results in pres- ence of irregular mortality schedule (Lee & Miller, 2001). The question of whether or how the length of the fitting period affects point forecast accuracy was first identified by Booth et al (2002). These problems made the later studies to impose restriction to start fitting the models from 1950 and following years and other modifications. Also several of studies proposed and compared point and interval forecast accuracy for forecasting age-specific mortality rates and life expectancy at birth (say, Shang, 2012). All of these studies concluded that use of different assumptions leads to different outcomes, and comparing different variants and extensions does not ensure identification of a single best method for all of the countries (Shang, 2012). The reference period used is the main determinant of large differences in outcomes (Pollard 1987), especially when there is considerable non-linearity in the trends or unusual mortality pattern in certain age groups (Stoeldraijer et al, 2013). Thus, the comparison of outcomes from different studies is hampered by differences in the explicit assumptions; such as the choice of the length of the historical period and of the jump-off rates in particular age groups (Stoeldraijer et al, 2013). All these applications and comparisons handled mostly for the industrialized countries. These countries have low mortality regime with high life expectancies; lower adult or early senescence mortality (Shang, 2012). All of the countries studied before for comparing the per- formance of the mortality forecasting models have stable pattern of mortality transition over long period of time; irregular pattern in different age-specific mortality were not the case for any of these countries in the course of demographic transition (except some years off-course). Irregular pattern in age-specific mortality effect forecast of mortality greatly. Distribution of deaths play vital role on modeling mortality, population with lower modal age at deaths sup- posed to have different mortality profile which also have impact on forecast (even for short period). The previous studies also enjoyed the advantages of data quality; most of these coun- tries for illustration have long time series of mortality data with very high quality. For instance, Sweden have series of life tables since 1751 with high quality life tables were available since 1860 (Human Mortality Database, 2016). The available extrapolative methods require certain period of mortality data for fitting the model; data quality of certain time periods often restricts the fitting period. So, performance of these existing mortality models are still subject to analyze in this comparatively high mortality countries. Completely different mortality regime may be observed for several Eastern European coun- tries rather than other developed countries of Europe (Vallin & Mesl´ e, 2001). Several countries of these part of the world have higher mortality regime than the neighbor Western European or other industrialized countries. Accidental mortality and presence of high frequency of cause- specific mortality are common in this region (Monostori et al, 2015). Many of these countries showed increasing trend in life expectancies over the decades, however, irregular trend was also observed. Several of these countries showed decreasing pattern of life expectancy in last century for couple of times (Vallin & Mesl´ e, 2001; Monostori et al, 2015). Another barrier for mod- eling or forecasting mortality for these countries is data quality. Human Mortality Database mentioned country specific caution notes to use the data of some countries during some certain time periods due to data source (Human Mortality Database, 2016). 2