Time dependency in diffusion models: Gamma-Diffusion Models as an alternative to the Hernes Model

Jean-Marie Le Goff, Université de Lausanne

Marriage process in a cohort is sometimes analyzed with a Hernes model. This model presents a convenient property that clearly allows one to distinguish the quantum effect in the cohort from the tempo effect. In its original paper, Hernes (1972) formulates his model in terms of diffusion or contagion of the idea of marriage from people already married to those not yet married. The spread of the proportion of married people in the cohort has an increasing effect on the risk of marriage. However, this increasing effect is slowed down by the fact that unmarried people progressively cease to be attractive on the marriage market when aging. Hernes mentions that this decreasing force could be related to another mechanism: Each individual in the cohort is heterogeneous in his or her susceptibility to get married. Persons who have a better susceptibility to marry will marry early, and the weight of individuals with worse susceptibility will be higher and higher as time goes on. The consequence of the heterogeneity in susceptibility is a negative effect on the risk to marry, which slows down the increasing effect due to the mechanism of diffusion. We believe that this second mechanism no longer corresponds to the model formally specified by Hernes. This paper shows models corresponding to this mechanism, the gamma-logistic and the gamma-mixed influence diffusion models. These models are estimated on data of the Wisconsin Longitudinal Study.