A Markov Chain Model of the Contribution Behavior of the National Pension Insured Persons

Ki-Hong Choi

This paper applies the methodology of Markov chain work-life table in modelling the contribution behavior of National Pension insured persons. This model enables us to model the transition pattern between types of coverage, namely workplace based insured or individually insured in the National Pension system. It is well known that there are significant differences in the amount of monthly contributory incomes as well as in the intensity of contribution by types of coverage, which has been major troubles in constructing realistic models of contribution behavior for the insured persons. In theory, this paper proves that the backward recursion formular of Hoem(1977) and the forward recursion formular of BLS in the work-life expectancy literature have identical solution and identified the closed form solution. The solution provides the formular for expected sojourn time at each age since the insured person enters the National Pension system. The expected sojourn time at each age also provides weighted averaged contributory incomes as well as the cumulative insured period net of non-contribution period due to unemployment etc. This Markov chain contribution model combined with actuarial pension benefit model can make a complete probabilistic contribution-pension benefit model for the National Pension system of Korea.

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