The Box-Cox transformation model has been widely used in applied econometrics, positive accounting, positive finance and statistics. There is a large literature on Box-Cox transformation model with linear structure. However, there is seldom seen on the discussion for such a model with partially linear structure. Considering the importance of the partially linear model, in this paper, a relatively simple semi-parametric estimation procedure is proposed for the Box-Cox transformation model without presuming the linear functional form and without specifying any parametric form of the disturbance, which largely reduces the risk of model misspecification. We show that the proposed estimator is consistent and asymptotically normally distributed. Its covariance matrix is also in a closed form, which can be easily estimated. Finally, a simulation study is conducted to see the finite sample performance of our estimator.
This paper provides an estimation procedure for average treatment effect through a random coefficient dummy endogenous variable model. A leading example of the model is estimating the effect of a training program on earnings. The model is composed of two equations:an outcome equation and a decision equation.Given the linear restriction in outcome and decision equations,Chen(1999) provided a distribution-free estimation procedure under conditional symmetric error distributions. In this paper we extend Chen's estimator by relaxing the linear index into a nonparametric function,which greatly reduces the risk of model misspecification. A two-step approach is proposed:the first step uses a nonparametric regression estimator for the decision variable,and the second step uses an instrumental variables approach to estimate average treatment effect in the outcome equation. The proposed estimator is shown to be consistent and asymptotically normally distributed. Furthermore,we investigate the finite performance of our estimator by a Monte Carlo study and also use our estimator to study the return of college education in different periods of China. The estimates seem more reasonable than those of other commonly used estimators.
