A new model for interdependent durations with an application to joint retirement

This paper introduces a bivariate version of the generalized accelerated failure time model. It allows for simultaneity in the econometric sense that the two realized outcomes depend structurally on each other. Another feature of the proposed model is that it will generate equal durations with positive probability. The motivating example is retirement decisions by married couples. In that example it seems reasonable to allow for the possibility that each partner's optimal retirement time depends on the retirement time of the spouse. Moreover, the data suggest that the wife and the husband retire at the same time for a nonnegligible fraction of couples. Our approach takes as a starting point a stylized economic model that leads to a univariate generalized accelerated failure time model. The covariates of that generalized accelerated failure time model act as utility-flow shifters in the economic model. We introduce simultaneity by allowing the utility flow in retirement to depend on the retirement status of the spouse. The econometric model is then completed by assuming that the observed outcome is the Nash bargaining solution in that simple economic model. The advantage of this approach is that it includes independent realizations from the generalized accelerated failure time model as a special case, and deviations from this special case can be given an economic interpretation. We illustrate the model by studying the joint retirement decisions in married couples using the Health and Retirement Study. We provide a discussion of relevant identifying variation and estimate our model using indirect inference. The main empirical finding is that the simultaneity seems economically important. In our preferred specification the indirect utility associated with being retired increases by approximately 5% when one's spouse retires. The estimated model also predicts that the marginal effect of a change in the husbands' pension plan on wives' retirement dates is about 3.3% of the direct effect on the husbands'.