Statistical inference for the Panel data model with errors-in-variables

In this paper, the Panel data model with errors-in-variables is considered, and the parameter estimation and testing problem of restricted condition are studied. Firstly, a corrected least squares method is proposed to estimate the unknown parameter vector, and the asymptotic property of the obtained estimator is shown under some regularity conditions. Then, to test the validity of linear restriction, a test statistic based on the difference of the corrected residual sum of squares under the null and alternative hypotheses is constructed, and its limiting distribution is derived. The effectiveness of the proposed methods is assessed by some simulation studies.