Homogeneous vs. heterogeneous transition functions in panel smooth transition regressions

(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.