Evaluation of the variants of the Lee-Carter method of forecasting mortality: a multi-country comparison

Abstract

The Lee-Carter (LC) method of mortality forecasting is well known and widely used. Two recent variants are the Lee-Miller (LM) variant and the Booth-Maindonald-Smith (BMS) variant. Both aim to improve the performance of the method. These two variants and the original LeeCarter method are evaluated using data for twenty populations for 19002001, with the fitting period ending in 1985 and the forecast period beginning in 1986. Forecast errors are compared and decomposed, and uncertainty is examined. For these short-term forecasts, the two variants are generally more accurate than the LC method with narrower prediction intervals; and BMS marginally outperforms LM on these criteria overall. Further evaluation using different fitting periods is required. s Keyfitz observed in 1981, one might have thought that population forecasters would be obsessed with eagerness to see how well they have done in the past, and that users would demand reports on the error of current forecasts; but “no such obsession or demand is to be seen” (Keyfitz 1981:580). Population futures have always been a central concern of demographers and those who use their work, from the studies of Malthus in the eighteenth century to those of Pearl and Reed in the twentieth. But, perhaps as a result of the failure of these and other authors to correctly foretell the demographic future, demographers for most of the last century retreated into non-committal scenario-building projections: demographic forecasting based on formal statistical methods has developed only in the last two decades. Actuaries similarly are centrally concerned with the future survival of current lives, but again formal * Correspondence to [e-mail] A 14 BOOTH, TICKLE AND SMITH statistical methods of mortality forecasting are a comparatively recent development. The publication of the Lee-Carter method (Lee and Carter 1992) marked the beginning of a new era of interest in mortality forecasting. Since then several other methods have been developed, but the Lee-Carter method is still regarded as among the best currently available and is now widely used. On the basis of this method, Tuljapurkar, Li and Boe (2000) identified a universal pattern of constant rates of mortality decline in the world’s most developed countries, with rates of decline higher than those incorporated in official projections, leading to higher forecast levels of life expectancy. The Lee-Carter method uses matrix decomposition to reduce annual age-specific death rates to a time-dependent index of level of mortality, and a set of time-independent parameters which modify the overall level at particular ages. It uses standard time series methods to model and forecast the level index over time. As with time-series-based forecasting in general, the philosophy of the Lee-Carter approach is that the past is the best guide to the future. Thus accurate modelling of past trends is an essential basis for forecasting future levels of mortality, and accurate modelling of the past variability of mortality is an essential basis for estimating the uncertainty of the forecast. In this context, a central issue is: how much of the past provides the best guide to how much of the future? Even in the context of a statistical forecast, judgment will be required to answer this question, but the objective is to minimise the role of judgement and maximise the role of formal theory on the one hand, and formal evaluation on the other. Modifications to the Lee-Carter method have been proposed by Lee and Miller (2001) and Booth, Maindonald and Smith (2002). These address the choice of fitting period, the method for the adjustment of the level parameter and the choice of jump-off rates. The three variants of the Lee-Carter method have not been comprehensively evaluated. This paper presents the results of an evaluation of the Lee-Carter, Lee-Miller and BoothMaindonald-Smith variants based on data by sex for ten countries. The evaluation involves fitting the different variants to data up to 1985, forecasting for the period since that date, and comparing the forecasts with actual mortality in that period. EVALUATION OF LEE-CARTER METHOD OF FORECASTING 15