Dealing With Endogeneity in Threshold Models Using Copulas
提出一种基于Copula理论的新方法，解决结构阈值回归模型中阈值变量的内生性问题，无需假设阈值变量服从正态分布，并通过蒙特卡洛研究验证了方法的稳健性。
We suggest a new method dealing with the problem of endogeneity of the threshold variable in structural threshold regression models based on copula theory. This method enables us to relax the assumption that the threshold variable is normally distributed and to capture the dependence structure between the threshold regression error term and the threshold variable independently of the marginal distribution of the threshold variable. For Gaussian and Student’s t copulas, this dependent structure can be captured by copula-type transformations of the distribution of the threshold variable, for each regime of the model. Augmenting the threshold model under these transformations can control for the endogeneity problem of threshold variable. The single-factor correlation structure of the threshold regression error term with these transformations allows us to consistently estimate the threshold and the slope parameters of the model based on a least squares method. Based on a Monte Carlo study, we show that our method is robust to nonlinear dependence structures between the regression error term and the threshold variable implied by the Archimedean family of copulas. We illustrate the method by estimating a model of the foreign-trade multiplier for seven OECD economies.