关键词: 随机效应半参数logit模型, Laplace近似, 惩罚似然估计, 收入差距假说

Abstract: In order to study the contestable income inequality effect on health, we propose a semi-parametric logit model with random effects which can reduce both model specification bias and omitted variable bias. Its nonparametric specification can also be used to exploratory data analysis. Then the estimation procedures are established, where the difficulty lies in evaluation of the intractable integral introduced by random effects, and the existence of nonparametric parts makes it even tougher. We solved it by the fourth order Laplace approximation together with penalized spline method, and the penalized maximum likelihood estimators are obtained by approximate Newton_Raphson algorithm. Meanwhile, we propose a selection method of smoothing parameter based on cross validation. Real application supports the weak version of income inequality hypothesis, and the nonparametric estimation results show evidence of validity of U-type function. Corresponding compares show the accuracy of our estimation method.

Key words: Semi-parametric Logit Model with Random Effects, Laplace Approximation, Penalized Likelihood Estimation, Income Inequality Hypothesis