Specification test in panel ordered response models - Chen, Yongwei; Li, Kunpeng; Zhang, Jie (Communications in statistics. Simulation and computation, 2025)
This paper develops a new simple method to simultaneously test the threshold effect and the correlation between unobserved individual effects and covariates in a panel ordered response model. We first use logistic function to represent the threshold effect, and use Mundlak's projection formula to characterize the potential correlation between individual effect and covariates. We then construct Wald statistics to test the existence of such correlation and threshold effect separately, and then to test whether the two phenomena exist simultaneously by controlling the false discovery rate (FDR). The advantage of using FDR approach is that we can accurately know the specific form that the model should adopt when rejecting the multiple hypotheses. Simulation results show that our method can effectively capture the actual model even in the finite sample. We apply our method to test the relationship between income and happiness using data from the survey of China Family Panel Studies. While the findings suggest that income is significantly correlated with unobserved individual effect, no evidence is found in support of the threshold effect between income and happiness.