Modeling Household Fertility Decisions: A Nonlinear Simultaneous Probit Model

Abstract This article proposes new methods for modeling household fertility decisions. Much of the demographic literature on this subject suggests that decisions relating to fertility are influenced by the orientations (attitudes, desires, intentions) of both husbands and wives, but the methods used in previous work do not indicate how wife's (husband's) orientation influences husband's (wife's) orientation, nor how these separate phenomena are combined to produce a joint decision. As such, these methods cannot be used to model the process by which husbands and wives come to have similar or dissimilar orientations or to assess one of the key issues in the literature, namely, the relative influence of the husband (wife) on the subsequent decision. To address these issues, we construct and estimate a nonlinear simultaneous equation probit that has not been considered in previous statistical work. Specifically, we model the trivariate distribution of wife's stated desire for additional children, husband's stated desire for additional children, and subsequent fertility. In the model, the stated desire of the husband (wife) is viewed as an indicator of the husband's (wife's) latent disposition toward subsequent fertility. The husband's (wife's) disposition is allowed to depend on the wife's (husband's) disposition. The two dispositions are then combined to generate the couple's propensity for subsequent fertility. We show how such models can be estimated and tested and how the parameters can be used to assess the relative influence of each partner on the propensity. To illustrate the approach, we reanalyze data on post–World War II fertility from the Princeton Fertility Study. We find that recursive models do not fit the data, that both partners’ dispositions influence subsequent fertility and (under additional assumptions) that the relative influence of each partner on the couple's propensity is .5. Next, we show how to extend the basic framework to treat other types of decision making. Specifically, we take up the case where the observed variables are not necessarily binary, as in the example, and we discuss differences between the binary case and the more general cases. For such cases we also propose a number of new models that have not been considered in previous work. We also show how the framework can be extended to the case where the latent variables have multiple indicators, the case where multiple decisions are jointly made, and the case where the decision(s) depends on three or more decision makers.