Dynamic Accelerated Failure Time Model with Endogeneity and Heterogeneity: a Control Function approach

We develop a control function method to estimate an Accelerated Failure Time (AFT) model with multiple states, where we account for state dependence, heterogeneity, and endogeneity of covariates. In accounting for state dependency in the structural AFT model and endogeneity of covariates through control functions, we are faced with predetermined covariates in the first stage treatment choice equation, which is a system of regressions for panel data. A concentrated likelihood method has been proposed to estimate a system of regressions with predetermined covariates. The control functions are based on "expected a posteriori" (EAP) values of the correlated random effects, and unlike alternative control function approaches, our approach allows for general instruments.