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This article describes a semiparametric estimation method for a discrete duration model with autoregressive random effects using Markov chain Monte Carlo techniques, and analyzes the duration of ten monthly economic times series which are components of the Japanese leading diffusion index. By introducing common time-dependent random effects to the individual duration, we capture a co-movement among durations that represents external macroeconomic factors. A dynamic modelling approach is employed assuming smoothness conditions on the baseline hazard function for long duration times with sparse observations.

Discrete Duration Model Having Autoregressive Random Effects with Application to Japanese Diffusion Index