Data driven robust estimation methods for fixed effects panel data models

The panel data regression models have gained increasing attention in different areas of research including econometrics, environmental sciences, epidemiology, behavioural and social sciences. However, the presence of outlying observations in panel data may often lead to biased and inefficient estimates of the model parameters resulting in unreliable inferences when the least squares method is applied. We propose extensions of the M-estimation and Exponential squared loss function-based approaches with a data-driven selection of tuning parameters to achieve desirable level of robustness against outliers without loss of estimation efficiency. The consistency and asymptotic normality of the proposed estimators have also been proved under some mild regularity conditions. The finite-sample performance of our proposed methods have been examined via several Monte Carlo experiments and their results are compared with the ones from existing methods. In addition, a macroeconomic dataset is analysed using the proposed methods to demonstrate their superiorities.