Wolpin’s Model of Fertility Responses to Infant/Child Mortality

Suppose that births are biological feasible in the first two periods of a family’s life cycle, but that the woman is infertile in the third period. Each offspring may die in either of the first two periods of life, as an “infant” or as a “child”, with probabilities given by p1 (infant mortality) and p2 (child mortality). Within periods, deaths occur subsequent to to decisions about births. Thus, an offspring born in the first period of the family’s life cycle may die in its infancy (its first period of life) before the second period fertility decision is made. Such a death can not be “replaced” by a birth in the third period, because the woman is infertile. For the same reason, a birth in period 2 is not replaceable even if its death occurs in that period (infant).1 It is assumed that conditional on surviving the first two periods non–adult periods, is unity. The family is assumed to derive utility only from those offspring who survive to adulthood.2