Abstract (Panel) Smooth Transition Regressions substantially gained in popularity due to their flexibility in modeling regression coefficients as homogeneous or heterogeneous functions of various transition variables. In the estimation process, however, researchers typically face a tradeoff in the sense that a single (homogeneous) transition function may yield biased estimates if the true model is heterogeneous, while the latter specification is accompanied by convergence problems and longer estimation time, rendering their application less appealing. This paper proposes a Lagrange multiplier test indicating whether the homogeneous smooth transition regression model is appropriate or not. We provide time series and panel versions of the test and discuss the joint N, T limiting behavior of the test statistic under cross-sectional dependence and heteroskedasticity. The empirical size and power of the test are evaluated by Monte Carlo simulations. An application to US stock return predictability illustrates the practical usefulness of the proposed procedure.

中文翻译：

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面板平滑过渡回归中的同质与异质过渡函数

摘要（面板）平滑过渡回归因其在将回归系数建模为各种过渡变量的同质或异质函数方面的灵活性而大受欢迎。然而，在估计过程中，研究人员通常面临一种权衡，即如果真实模型是异质的，单个（同构）转移函数可能会产生有偏估计，而后者的规范伴随着收敛问题和更长的估计时间，使得他们的应用不太吸引人。本文提出了一个拉格朗日乘数检验，表明齐次平滑过渡回归模型是否合适。我们提供测试的时间序列和面板版本并讨论联合 N，横截面相关性和异方差下检验统计量的 T 限制行为。测试的经验大小和功效通过蒙特卡罗模拟进行评估。对美国股票回报可预测性的应用说明了所提议程序的实际用途。