Two sex proportional hazard model and marriage market analysis*

Studies of ma rriage market should capture the simultaneous determination of male and female nuptiality by socio-economic characteristics of both sexes. In this line, an extension of Cox proportional hazard model into two sexes is proposed. The basic assumption is that the marital hazard of male and female characteristics (i,j) is proportional to that of reference combination (0,0). Two-sex partial likelihood function is defined by taking not an individual but a pair of male and female as the unit of analysis. The maximum likelihood estimator can be obtained by optimizing the function. Tied data can be treated in the same way as the one-sex model. Some methodological and interpretational problems are discussed. The author cannot provide either a complete computer program or a strict proof of asymptotic efficiency of the two-sex model but a small numerical example. * This is a slightly enlarged version of a paper presented at the poster session, Statistical Demography (S36), The XXIV General Population Conference, Salvador, Bahia, Brazil, in August 2001. 1 1. Issue Figure 1 illustrates the problem that conventional methods cannot examine the effects of marriage market structure on marital hazard. The event history analysis is inherently a one-sex model. Although it is a powerful tool to evaluate the effects of individuals' socio-economic characteristics on marriage, the availability or scarcity of desirable partner is out of the range. It would be essential to assume that a compositional change in characteristics of single males affect not only male nuptiality but also female nuptiality, and vice versa. Marriage market studies have been concentrated on the analysis of contingency table of married couples. Many indices have been applied, including Blau's OM and IM, mobility ratios, Gini's H, Yasuda's y, Gray's v, Yule's Q, Goodman and Kruskal's G, Rockwell's hypergamy ratio, etc. Since 1980's, the log-linear analysis has been the standard method to analyze the contingency table. The problem here is that the contingency table refers to only the result of marriage hazard. Thus, it ignores persons who eventually do not marry, and the analysis of nuptiality change such as recent decline in marital hazard is out of the range. Figure 1. Conventional methods for marriage market analysis Event history analysis of female Event history analysis of male Log-linear analysis of contingency table Socio-economic characteristics of single females Socio-economic characteristics of single males Female marriage hazard Combined socio-economic characteristics of husband and wife Male marriage hazard