Estimating Choice Models with Piecewise Smooth Objective Functions: Application to Joint Retirement

This paper studies choice models with piecewise smooth objective functions. By introducing well-defined latent variables derived from regional components (auxiliary functions), we provide conditions under which the choice model can be transformed into a reduced form resembling censored models, with the introduced latent variables as potential outcomes. The potential outcome framework not only serves as an alternative solution method for the choice model, but also facilitates the implementation of the stochastic Expectation-Maximization (SEM) algorithm to obtain MLE. We illustrate the framework using two simple examples: 1) responses to tax and transfers, and 2) the (𝑆, 𝑠) model. We further empirically estimate a joint retirement decision model among European couples based on the interdependent duration model in Honoré and de Paula (2018), applying the proposed solution and estimation methods. The results provide empirical evidence of complementarity between spouses in their transition out of the labor force in Europe