Structure Change In The Fixed Effects Ordinal Model

This paper takes the fixed effects ordered logit model as an example to study how to test and estimate the structural change in the panel ordinal choice model.Based on the traditional fixed effects ordered logit model,this paper introduces a smooth transition function to describe the structure change process in economics,and constructs fixed effects ordered logit model with smooth transition function.In order to solve the problem of incidental parameters and parameter identification of the model,we use the conditional maximum likelihood estimation method and prove that the conditional maximum likelihood estimators of the model have consistency and asymptotic normality.Before applying the model to the practical problem,we need to test whether the traditional fixed effects ordered logit model has such a structural change.This is equivalent to checking whether the model contains a smooth transition function.We construct a suitable Lagrange multiplier(LM)statistic for this model to test the structural change and give an asymptotic distribution of the LM test statistics.At the same time,the Monte Carlo simulation experiment is used to analyze the LM statistics Size and Power.The simulation results show that the LM statistics established in this paper have good finite sample properties.This article selects the relationship between the income and happiness of Chinese residents as an application example.From a theoretical perspective,we use this model which we construct to verify whether there is a phenomenon of "happiness paradox" among Chinese residents.The"happiness paradox" can be described as the income level increase and reach a certain level,the effect of income on happiness will diminish.We choose age,marriage,health,work status,and education level as the model's control variables to study whether residents' income has such a structural change effect on happiness.The results show that there is a significant nonlinear structural change in the impact of income on happiness.When income growth exceeds the 86%quantile of social income distribution,the effect of income on happiness will be weakened,and the effects of health and education on happiness will increase.