The impact of using lee-carter cohort life tables on pension schemes: a case ofPoland

Barbara Więckowska, Social Insurance Department, Warsaw School of Economics
Jakub Bijak, University of Southampton

Population ageing, especially in the developed countries, will very likely enforce the reform of pension systems – a switch from defined-benefit schemes towards defined-contribution ones. Due to these changes, the pension benefits will depend, among others, on the estimated future life expectancy at the age of retirement. The calculations based on period life tables published by national statistical authorities would lead to pension fund deficit, because they underestimate the risk of surviving subsequent years after retirement by prospective pensioners. This is due to the fact that such tables do not take into account the lengthening of the human lifespan for the subsequent cohorts of population. The paper aims at filling the above-mentioned methodological gap by proposing to produce cohort life tables based on mortality forecasts obtained using a modified version of the Lee-Carter model. The approach is stochastic and enables to accommodate three sources of uncertainty concerning future mortality developments: Poisson variability of the numbers of deaths, estimation of the parameters of the model, as well as the trend extrapolation. The analysis based on the uncertainty of forecasts allows to estimate the risk of adverse selection in the insurance portfolio. An empirical illustration concentrates on the second and third pillars of the Polish pension scheme (fully-funded ones). The obtained Lee-Carter forecasts allow for comparing the pension benefits calculated on the basis of period and cohort life tables. The results for Poland indicate a discrepancy between both approaches, reaching in some cases more than 8 percent. Additionally, sensitivity of the results is assessed with respect to different variables (retirement age, sex, initial capital, interest rates and length of the guaranteed benefit period), as well as to the assumed stochastic structure of the model, all being presented in a variety of alternative scenarios.