Multivariate life table methodology for estimating the effect of child mortality on the total fertility rate and its components

This paper develops, validates, and applies new multivariate methodology to assess the effect of child mortality on both period and cohort measures of fertility. The methodology, which can be applied to period data as well as cohort data, is based on discrete-time survival models of parity progression that enable construction of a multivariate life table of fertility covering all parity transitions. The five dimensions of this life table are woman's age, parity, duration in parity, and two dimensions representing lagged child mortality (number of dead children at the beginning and end of the previous year when the woman was one year younger). Additional socioeconomic predictor variables are also included in the underlying survival models. The life table is multivariate in the sense that it can be specified for values or categories of one socioeconomic predictor variable while holding other socioeconomic predictors constant. The life table yields a number of measures of both the quantum and the tempo of fertility and child mortality. It also yields a replacement rate, which measures the extent to which child deaths are replaced by additional births. Because the life table is multivariate, all measures calculated from it are also multivariate. By way of illustration, the methodology is applied to three Indian National Family Health Surveys conducted in 1992-93 (NFHS-1), 1998-99 (NFHS-2), and 2005-06 (NFHS-3). Major findings are that dead children are incompletely replaced, and that the replacement rate rises as the total fertility rate falls over the three surveys, reflecting women's increasing ability to achieve their wanted number of surviving children.