基于傅里叶近似的时变门槛模型：估计、检验及其应用

We propose a new class of time-varying threshold models. Traditional threshold models assume that threshold values are constant. However, time-varying threshold models are more suited for many applications and time-varying threshold values are consistent with many economic concepts. Furthermore, our simulations show that ignoring the time-varying features in the threshold could lead to biased estimates and distorted tests. Hence, it is important to construct threshold models with time-varying threshold values. However, the time-varying feature in the threshold might be of unknown form, which can result in a seriously misspecified model and infeasible model specification tests. Based on the fact that a Fourier approximation can often capture the behavior of an unknown time-varying function, we propose time-varying threshold regression models for stationary variables and time-varying threshold cointegration models for nonstationary variables. The main tasks include: ①developing the estimation method for the proposed models and the asymptotic properties of estimators; ②constructing test statistics for threshold effect and threshold constancy, and deriving their limiting distributions; ③assessing the performance of the estimation and testing procedures through Monte Carlo simulations. Moreover, the new models are employed to investigate: ①the relationship between subsidies/tax incentives and firm innovation, and estimate the varying optimal fiscal and tax policy support for firm innovation; ②the relationship between stock index futures and spots, and estimate the time-varying no-arbitrage band. This research can improve methods and theory of threshold models.

本项目提出一组新的时变门槛模型。传统门槛模型假设门槛值为常数，然而，在很多应用中时变门槛模型更符合现实，且时变门槛值与很多经济概念相契合，进一步的模拟表明：忽略门槛时变性会导致参数估计偏差和检验扭曲，因此建立时变门槛模型具有重要意义。但门槛的时变结构常常是未知的，这会引起模型误设并导致模型检验难以实施。近期文献表明傅里叶变换能很好地近似常见时变特征，基于此事实，本项目在平稳和非平稳条件下分别建立时变门槛回归模型和时变门槛协整模型。我们的主要研究任务包括：①发展出模型估计方法并推导参数估计量的大样本特征；②构建门槛存在性和门槛时变性检验统计量并推导极限分布；③使用蒙特卡洛模拟评估模型估计和检验方法的表现。此外，本项目将新模型应用于研究：①政府补贴、税收优惠与企业创新的关系，估计可变的政策力度最优区间；②股指期货与现货的关系，估计时变的无套利区间。本研究有助于完善门槛模型的理论与方法体系。

鉴于经典门槛模型假设门槛值为常数，本项目围绕时变门槛的研究议题展开了深入研究，给出了时变门槛模型的理论方法体系，并将新模型应用于一些重要经济问题，提供了新视角的实证结果，并为时变门槛参数提供了有意义的经济解释。主要研究内容和研究成果简述如下：. 在平稳条件下建立了时变门槛回归模型，在非平稳条件下建立了时变门槛协整模型，分别给出了不同情形下模型的参数估计方法，以及门槛存在性和门槛时变性检验方法，建立了相应的大样本理论并使用蒙特卡洛模拟研究了参数估计和模型检验方法的有限样本表现，模拟结果与相应的大样本理论一致且表明参数估计与模型检验方法具有良好的有限样本表现，而忽略门槛时变性将导致参数估计偏差和检验扭曲。同时，我们将新模型应用于一些重要的实证经济问题，研究结果表明忽略门槛时变性将导致十分不同的实证结果，而时变门槛模型能提供意义丰富的新结果。. 此外，我们还对本项目的研究议题进行了拓展研究，主要研究内容有：将时变门槛概念引入断点回归，建立了具有状态依赖断点的断点回归，为因果推断提供了新的方法；将门槛模型推广到混频数据，建立了混频门槛模型；在门槛模型中引入空间效应，建立了面板门槛空间模型。相关研究成果显示了本项目良好的拓展性，为后续研究提供了方向。