Assessment of cross-sectional and longitudinal components of a difference with an algorithm of contour replacement

This study proposes a new decomposition method which permits a difference in an aggregate measure at a final time point to be split into additive components corresponding to the initial differences in the event-rates of the measure and differences in trends in these underlying event-rates. The method is an extension of the existing algorithm of stepwise replacement. We provide a full description of the method and two examples of its application with mortality and fertility data. The outcome of these two decompositions are: 1) age-specific contributions of initial conditions and trends to the Japan-USA life expectancy gap in 2009 with a reference time point at 1970; and 2) age-specific contributions of initial conditions and trends to the difference in Czech-Russian age variations in fertility for the 1970 female birth cohorts with reference to the 1955 cohorts.