Effects of Age Shift on the Tempo and Quantum of Non-Repeatable Events

Effects of age shift on the tempo and quantum of non-repeatable demographic events are examined. The purpose is to develop a period index theory based on the survival model and to provide a mathematically consistent interpretation of Bongaarts and Feeney's tempo adjustment arguments. The survival model for non-repeatable events is introduced. In the time-inhomogeneous case, three types of period survival models are considered. McKendrick equation is used to formulate the risk population dynamics. The tempo and quantum indices for three period survival models are computed when the period age shift occurs for the hazard, the incidence, and the survival rates. Bongaarts and Feeney's tempo adjustment arguments are consistently based on the scenario of the period age shift on the survival rate, and they give translation formulae between period indices without referring to cohort. Traditional demographic translation formulae between cohort and period indices are reviewed to clarify differences between cohort- and period-oriented translation procedures.