Estimation of A Partial Linear Model with Instrumental Variable for the Longitudinal Data

Abstract

Abstract A partial linear model with instrumental variables was developed for longitudinal data. In the partially linear model, the explanatory variable is an endogenous variable, which is correlated with the error term. The endogenous variable was expressed by an instrumental variable and an error item. The endogenous variable was estimated by the instrumental variable through the least square method. B-spline regression combined with QR decomposition was used to approximate the nonparametric function. For the estimation of parametric, the Quadratic inference function and Secant method were applied. Under some conditions, the estimator was consistent and asymptotic normality. Some simulation was conducted to prove the finite sample behavior of the estimator.