Abstract

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.

摘要

尽管平滑过渡（ST）模型已在商业和经济学中流行，但是这些模型中未观察到的异质性的处理受到了有限的关注。我们提出了一个ST有限混合（STFM）模型，该模型可以同时估计面板数据上下文中时变效应和未观察到的异质性的存在。我们的目标是准确地恢复我们感兴趣的独立变量的异质效应，同时使这些效应随时间变化。实现这一目标可能为管理人员和决策者提供宝贵的见解。STFM模型嵌套了几个著名的ST和阈值模型。我们使用贝叶斯方法为STFM模型开发规格，估计和模型选择标准。当样本数随着样本数量的增长而增长时，我们还提供了STFM模型灵活性的理论评估。在广泛的仿真研究中，我们表明忽略未观察到的异质性可能导致参数估计失真，并且当违反基础模型假设时，STFM模型相当健壮。根据经验，我们估算了大联盟棒球中游戏内促销对比赛出勤率的影响。实证结果表明，STFM模型优于其所有嵌套版本。可在线获得本文的补充材料。当违反基本模型假设时，STFM模型相当健壮。根据经验，我们估算了大联盟棒球中游戏内促销对比赛出勤率的影响。实证结果表明，STFM模型优于其所有嵌套版本。可在线获得本文的补充材料。当违反基本模型假设时，STFM模型相当健壮。根据经验，我们估算了大联盟棒球中游戏内促销对比赛出勤率的影响。实证结果表明，STFM模型优于其所有嵌套版本。可在线获得本文的补充材料。