The purchasing power of Finnish statutory earnings-related pensions is maintained by making annual index adjustments, which depend linearly on inflation and the development of general earnings levels, to accrued pension rights. A key part of the financial planning of pension systems is to forecast the time series of annual pension expenditure E(t). As index adjustments have a direct impact on pension expenditure, assumed future index development is commonly used as a parameter in a pension expenditure forecast model.

This exercise presents a formula by which the effect of assumed future index adjustments on a pension expenditure forecast can be determined outside the forecast model. The determination of the quantities present in the formula itself is approached from the perspective of an inverse problem and a solution is presented to it.

While the problem set up deals with index adjustments, the solution leads to a number of interesting side results. From the quantities present int he formula, it can be deduced how pension rights develop in the forecast model. This information can be used both in the analysis of the forecast model and, for example, in examining the impact of the earnings trend of the forecast population. The quantities also provide a way of examining the intergenerational effects of changes in pension laws. The formula itself can also be applied to the study of the stochastic behaviour of index dependence.

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