Statistical Inference And Application For Instrumental Variable Linear Regression Model With Longitudinal Data

Statistical analysis of longitudinal data is more and more aroused people’s concern, the main reason is the dataset for the characteristics and advantages of time series data and cross section data, better reflect the change of the difference between individual and individual, as a result, it has been widely applied to the economy, biology, medicine and other fields. The key point is how to analyze within-subject correlation for longitudinal data. When we analyze the dataset by using the statistical models, we often assume that the explanatory variables in the model are exogenous. But in practical applications, the models with the exogenous variables are not satisfied and the explanatory variables are the endogenous variables, the existing statistical analysis methods are no longer applicable. If we ignore the endogenous variables, the estimates will be biased and be not consistent. In order to solve the problem, in this paper, we consider the statistical inference for instrumental variable linear regression models with longitudinal data. The main work is as follows:First, to solve the problem of endogenous variables, we introduce the instrumental variables. Second, in order to deal with the within-subject correlation for longitudinal data, we use the quadratic inference function method to construct the objective function. Under some regularity conditions, we show that the proposed estimation is consistent and asymptotically normal. The finite sample properties of the proposed method are evaluated via the simulation studies. Simulation studies show that the proposed method eliminates the effect of endogenous variable, and improves the efficiency whether or not the work correlation matrix is correctly specified. Finally, the proposed method is applied to explore the relationship between trade openness and economic growth, the results show that we use the foreign markets close degree as an instrumental variable, trade openness and economic growth has the stronger positive correlation.