Simple Semiparametric Estimation of Ordered Response Models: With an Application to the Interdependent Durations Model

Abstract

We propose two simple semiparametric estimation methods for ordered response models with an unknown error distribution. The proposed methods do not require users to choose any tuning parameter and they automatically incorporate the monotonicity restriction of the unknown distribution function. Fixing finite dimensional parameters in the model, we construct nonparametric maximum likelihood estimates (NPMLE) for the error distribution based on the related binary choice data or the entire ordered response data. We then obtain estimates for finite dimensional parameters based on moment conditions given the estimated distribution function. Our semiparametric approaches deliver root-n consistent and asymptotically normal estimators of the regression coefficient and threshold parameter. We also develop valid bootstrap procedures for inference. We apply our methods to the interdependent durations model in Honore and de Paula (2010), where the social interaction effect is directly related to the threshold parameter in the corresponding ordered response model. The advantages of our methods are borne out in simulation studies and a real data application to the joint retirement decision of married couples.