Forecasting Mortality for Small Populations by Mixing Mortality Data

33 Pages Posted: 1 Aug 2013

See all articles by Ales Ahcan

Ales Ahcan

University of Ljubljana - Faculty of Economics

Darko Medved

JMD Consulting Ltd

Annamaria Olivieri

University of Parma - Dipartimento di Scienze Economiche e Aziendali

Ermanno Pitacco

MIB Trieste School of Management

Date Written: July 30, 2013

Abstract

In this paper we address the problem of projecting mortality when data are severely affected by random fluctuations, due in particular to a small sample size, or when data are scanty. Such situations may emerge when dealing with small populations, such as small countries (possibly previously part of a larger country), a specific geographic area of a (large) country, a life annuity portfolio or a pension fund, or when the investigation is restricted to the oldest ages. The critical issues arising from the volatility of data due to the small sample size (especially at the highest ages) may be made worse by missing records; this is the case, for example, of a small country previously part of a larger country, or a specific geographic area of a country, given that in some periods mortality data could have been collected just at an aggregate level.

We suggest to 'replicate' the mortality of the small population by mixing appropriately the mortality data obtained from other populations. We design a two-step procedure. First, we obtain the average mortality of 'neighboring' populations. Three alternative approaches are tested for the assessment of the average mortality; conversely, the identification and the weight of the neighboring populations are obtained through (standard) optimization techniques. Then, following a sort of credibility approach, we mix the original mortality data of the small population with the average mortality of the neighboring populations.

In principle, the approach described in the paper could be adopted for any population, whatever is its size, aiming at improving mortality projections through information collected from other groups. Through backtesting, we show that the procedure we suggest is convenient for small populations, but not necessarily for large populations, nor for populations not showing noticeable erratic effects in data. This finding can be explained as follows: while the replication of the original data implies the increase of the size of the sample, it also involves a smoothing of data, with a possible loss of specific information relating to the group referred to. In the case of small populations showing major erratic movements in mortality data, the advantages gained from the larger sample size overcome the disadvantages of the smoothing effect.

Keywords: Mortality projections, Mortality trends, Multi-population mortality models

JEL Classification: G22

Suggested Citation

Ahcan, Ales and Medved, Darko and Olivieri, Annamaria and Pitacco, Ermanno, Forecasting Mortality for Small Populations by Mixing Mortality Data (July 30, 2013). Available at SSRN: https://ssrn.com/abstract=2303796 or http://dx.doi.org/10.2139/ssrn.2303796

Ales Ahcan

University of Ljubljana - Faculty of Economics ( email )

Kardeljeva ploscad 17
Ljubljana, 1000
Slovenia

Darko Medved

JMD Consulting Ltd ( email )

Perovo 2A
1241 Kamnik
Slovenia

Annamaria Olivieri (Contact Author)

University of Parma - Dipartimento di Scienze Economiche e Aziendali ( email )

via Kennedy 6
Parma, 43125
Italy

Ermanno Pitacco

MIB Trieste School of Management

Trieste, Trieste 34100
Italy

Do you have a job opening that you would like to promote on SSRN?

Paper statistics

Downloads
169
Abstract Views
813
Rank
326,172
PlumX Metrics