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Reconciling forecasts of age distribution of death counts: Application to fixed-term annuity pricing

22nd June 2017 3pm, University of Southampton, Building 54, Room 5027

Hanlin Shang, Australian National University

A joint S3RI and CPC seminar: The different constituents of age-specific life-table death counts can be represented by a random vector called compositions with non-negative components that sum to a radix. Data in which the observations are compositions, are called compositional data. An example of which is the age-specific life-table death counts, where the radix is the fixed annual number of births in the life-table population. Age-specific life-table death counts are often disaggregated by different attributes, such as sex, state, ethnic group and socioeconomic status. In making social policies and pricing annuity at national and subnational levels, it is important not only to forecast age distribution of death counts accurately, but also to ensure that forecasts at the subnational level add up to the forecasts at the national level. This motivates recent developments in grouped forecasting methods (Shang and Hyndman, 2017, Shang and Haberman, 2017) to reconcile age-specific mortality forecasts. We extend the grouped forecasting methods to reconcile forecasts at the national and subnational levels, where a compositional data-analytic approach is adapted to forecast age distribution of death counts. Using the regional age-specific life-table death counts in Japan obtained from the Japanese Mortality Database (2017), we investigate the difference in point forecast accuracy between the independent and grouped forecasting methods. The grouped forecasting methods are shown not only to be useful for reconciling forecasts of age-specific life-table death counts at national and subnational levels, but they are able to improve forecast accuracy. The improved forecast accuracy of life-table death counts is of great interest to demographers and actuaries for estimating life expectancy and annuity prices, in particular at the level of population subgroups, defined by key factors such as sex, region, and socioeconomic grouping.