Mid-Year Estimators in Life Table Construction

The life table is the tool most used to synthesize the mortality of a collective, with a paramount influence on public pension systems and life insurances. This is constructed from either death rate, $$m_{x}$$ m x , or death probability, $$q_{x}$$ q x , estimates after assuming some hypothesis regarding to the demographic events (deaths, migrations and births). Both cohort-based and period-based estimators are currently used by statistical agencies. Within the currently most popular period-based estimators, two alternatives coexist for estimating the denominator of $$m_{x}$$ m x : the total number of ‘person-years’ at risk (e.g. [1]) and the average population at risk of dying, measured by mid-year population estimates (e.g. [2]; [3]). Both options give the same solutions under the usual hypotheses of uniformity of demographic events. The effect of uniformity hypotheses has been extensively studied in the first option [4]. In this paper, we explicitly disclose the implicit hypotheses assumed in the latter case, propose alternative estimators free of them and, using a real database from Spain, analyse the impact of the different estimators on some insurance products. Initial results point to the need to include the exact moments of birth in the computation of the period mid-year estimator.