Interdependent Durations

Abstract

This paper studies the identification of a simultaneous equation model involving duration measures. It proposes a game theoretic model in which durations are determined by strategic agents. In the absence of strategic motives, the model delivers a version of the generalized accelerated failure time model. In its most general form, the system resembles a classical simultaneous equation model in which endogenous variables interact with observable and unobservable exogenous components to characterize an economic environment. In this paper, the endogenous variables are the individually chosen equilibrium durations. Even though a unique solution to the game is not always attainable in this context, the structural elements of the economic system are shown to be semi‐parametrically identified. We also present a brief discussion of estimation ideas and a set of simulation studies on the model.

Interdependent durations in joint retirement

“…which gives the same timing choice for the first retiree as in Honoré and de Paula (2010) but an earlier one for the second spouse. A similar set of calculations is obtained for…”

“…In contrast, the equilibrium joint retirement date for a given realization of (K 1 , K 2 ) is uniquely pinned down in the setup here. Because Nash bargaining implies Pareto efficiency and because T is the Pareto dominant outcome among the possible multiple equilibria in the game analyzed by Honoré and de Paula (2010), it should be the case that joint retirement in the Nash bargaining model occurs on or before T .…”

“…For the first two, we use a standard proportional hazard model for each spouse with a Weibull baseline hazard and the usual specification for the covariate function. For the third, we use an ordered logit model as suggested by our paper Honoré and de Paula (2010). We present the models in detail below.…”

Identification of Social Interactions

“…Identification is formally proved for the model and evidence is adduced that bunching in desertions occurred in a way that is consistent with social interactions. This work is extended to an elegant discussion of semiparametric identification of interdependences in duration models in Honoré and de Paula (2010).…”

Econometric analysis of games with multiple equilibria

“…The idea of identifying certain (non-exhaustive) outcomes with the occurrence of multiple equilibria is pursued by Honoré and de Paula (2010) for the identification of a complete information timing game. In that paper, outcomes y are duration variables chosen by individuals to model circumstances where timing decisions by one person a↵ect the payo↵ of another individual (e.g., joint migration, joint retirement, technology adoption).…”