5. Conclusions
On the basis of the comparison of various estimators of the variance of the idiosyncratic error, two new tests are constructed for the existence of random effects in linear panel data models with no distributional assumptions. The resultant tests are one-sided, and asymptotically normally distributed under the null hypothesis. Power study shows that the tests can detect local alternatives distinct at the parametric rate from the null. Due to the first difference and orthogonal transformations used in the construction of variance estimators of the idiosyncratic error, the two proposed tests are robust to the presence of one effect and the possible correlation between the covariates and the error components when the other one is tested. As argued in Remark 1, the method can be used to construct tests for a time trend. Moreover, different from the method of Wu and Li (2014), the method suggested in this paper can be easily extended to construct test statistrics for the existence of random effects in the two-way error component models with unbalanced panels. Specifically, we use the difference operator to eliminate the time effect and then use the same method of Wu et al. (2015) to construct test statistics for the existence of random effects in the error component models with unbalanced panels. We leave this for further study.
