A Smooth Transition Finite Mixture Model for Accommodating Unobserved Heterogeneity

While the smooth transition (ST) model has become popular in business and economics, the treatment of unobserved heterogeneity within these models has received limited attention. We propose a ST finite mixture (STFM) model which simultaneously estimates the presence of time-varying effects and unobserved heterogeneity in a panel data context. Our objective is to accurately recover the heterogeneous effects of our independent variables of interest while simultaneously allowing these effects to vary over time. Accomplishing this objective may provide valuable insights for managers and policy makers. The STFM model nests several well-known ST and threshold models. We develop the specification, estimation, and model selection criteria for the STFM model using Bayesian methods. We also provide a theoretical assessment of the flexibility of the STFM model when the number of regimes grows with the sample size. In an extensive simulation study, we show that ignoring unobserved heterogeneity can lead to distorted parameter estimates, and that the STFM model is fairly robust when underlying model assumptions are violated. Empirically, we estimate the effects of in-game promotions on game attendance in Major League Baseball. Empirical results show that the STFM model outperforms all its nested versions. Supplementary materials for this article are available online.