基于傅里叶近似的时变门槛拐点回归模型及其应用

本文通过引入时变门槛值扩展了Hansen的拐点回归,使用傅里叶近似捕捉时变门槛构建了具有时变门槛值的拐点回归,探讨了模型估计、门槛存在性和门槛常数性检验等问题,并使用蒙特卡洛模拟实验方法研究了忽略门槛时变性的后果以及新方法的表现,结果表明:忽略门槛时变性会导致参数估计偏差,当门槛值为常数而误用时变门槛模型时,参数估计仍是无偏的。最后,将新时变门槛模型用于研究政府债务与经济增长的关系,研究发现:债务门槛具有明显的时变性,而忽略门槛时变性会错误估计债务对经济增长的影响以及最优债务门槛值。

Regression Kink with a Time-varying Threshold Based on Fourier Approximation and Its Application

This paper extends Hansen’s regression kink by allowing for a time-varying threshold,in which the time-varying threshold is approximated using a Fourier approximation.The estimation of the model is proposed,and the statistics for threshold effect and threshold constancy are constructed.We also employ Monte Carlo simulations to examine the performance of the model and the consequence that may arise from ignoring the time-varying features in the threshold.The simulation results show that overlooking the time-varying features would lead to biased estimates,while the proposed approach can lead to unbiased estimates even when the true model contains a constant threshold.Then,the proposed model is used to investigate the relationship between debt and growth.The empirical results support that there is a debt-threshold effect,and ignoring the time-varying features can result in misleading estimates of the optimal debt threshold and the effect of debt on growth.