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CMI Working Paper 25

Stochastic projection methodologies: Lee-Carter model features, example results and implications

CMI Working Paper 25 includes detail on the Lee-Carter methodology and is analogous to CMI Working Paper 20 which addressed similar areas for the P-spline methodology

The paper includes:

  • a description of the models and datasets used;
  • a guide to using the output from the Lee-Carter modelling software made available by the CMI;
  • a discussion of various features of the Lee-Carter model;
  • sample annuity values for use in 2004 produced using the Lee-Carter model and data to 2003 which are then compared to annuity values based on the interim cohort projections, plus how the equivalent sample annuity values for use in each year between 1993 and 2004 would have progressed as more data became available over the period;
  • results of some initial investigations into the features of the extension by Renshaw and Haberman of the age-period Lee-Carter model to an age-period-cohort model;
  • an assessment of the P-Spline, Lee-Carter and the Lee-Carter age-period-cohort models against some high-level objectives desirable of projection models; and
  • a summary of the Working Party's views on the three models.

With this paper, the CMI's Mortality Projections Working Party has completed its work on projection methodologies

There remain many areas regarding projection models that are worthy of further investigation and research and the CMI will retain an interest (and may commission further work) in these areas. The development of projection methodologies and publication of projections are of course areas for the wider profession, and not merely the CMI. Given the importance of projections, the actuarial profession may wish to consider how this should be taken on, perhaps by a Research Group or Working Party.

The CMI has sought to make the research more accessible to actuaries through CMI Working Paper 30 and the CMI Library of Mortality Projections.

From 2005 to 2008, the CMI made available the illustrative software it used in its research into mortality projections. The software is not commercial grade but was intended to allow users to experiment with the methodologies. The software uses the statistical package R, together with the R(D)COM interface.  The illustrative software was withdrawn for new users early in 2009 after the CMI became aware that it is not compatible with newer versions of R and/or the interface but is now available on request to anyone able to locate appropriate versions of R and the interface.

Subsequent to the publication of CMI Working Paper 25, the CMI became aware that the dataset for permanent assurances for male lives used included initial exposures but was used as if these were central exposures. As a result, the results published in CMI Working Paper 25 (and CMI Working Papers 20 and 27) that used this dataset were inaccurate. During the re-work the CMI found an error in the projection software in the calculation of deviance residuals used in boot-strapping simulations for the Lee-Carter models which also affects some of the values in CMI Working Paper 25.

To obtain more details on these two issues and their impact, please see the Errata to CMI Working Papers 20, 25 and 27 on Mortality Projections

CMI Working Paper 25 has been revised to take account of these issues.  Please note that this version of CMI Working Paper 25 has NOT been updated for any developments subsequent to its original publication, other than the noted errata. Should you require a copy of the original version, please contact the CMI.

After the original version of this paper was finalised, the CMI became aware of a development by JP Morgan of LifeMetrics which also makes software available illustrating various methodologies and contains a research paper comparing these methodologies. Rather than delay the publication of CMI Working Paper 25, the CMI did not undertaken comparisons between the conclusions of the papers nor of the results of using the different software.

The Exposure note contains an Important update regarding CMI work on mortality projections (Nov 2007).

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