Threshold effects in nonlinear models with an application to the social capital-retirement-health relationship

This paper considers the relationship between social capital and health in the years before, at and after retirement. This adds to the current literature that only investigates this relationship in either the population as a whole or two subpopulations, pre-retirement and post-retirement. We now investigate if there are further additional subpopulations in the years to and from retirement. We take an information criteria approach to select the optimal model of subpopulations from a full range of potential models. This approach is similar to that proposed for linear models. Our contribution is to show how this may also be applied to nonlinear models and without the need for estimating subsequent subpopulations conditional on previous fixed subpopulations. Our main finding is that the association of social capital with health diminishes at retirement, and this decreases further 10 years after retirement. We find a strong positive significant association of social capital with health, although this turns negative after 20 years, indicating potential unobserved heterogeneity. The types of social capital may differ in later years (e.g., less volunteering) and hence overall social capital may have less of an influence on health in later years.