Panel Influence Matrix for Outliers Detection and Robust Estimation of Unbalanced Panel Data Regression

The estimation of a panel data regression model can be biased due to outliers. Meanwhile, the robust estimation method for an unbalanced panel data regression model is limited. In general, the robust estimation method proposed in previous studies did not consider the panel data structure, which consists of several cross-sections and time-series units. As a consequence, the trimming process for observations seen as outliers can completely remove all observations from a cross-section unit. This trimming process may result in biased cross-section unit estimation. Based on these problems, in this study, we proposed a panel influence matrix for detecting outliers and determining robust estimates of a one-way unbalanced panel data regression model with a fixed-effects approach. This method considers an unbalanced panel data structure formed of several cross-section units. We applied our proposed robust procedure to three unbalanced panel data schemes. The robust estimate results obtained using the panel influence matrix were compared to those obtained using the within transformation and the influence matrix, disregarding the cross-section and time-series units in the panel data. Based on Mean Squared Error (MSE) value, the robust estimation result using the panel influence matrix gave the best results for all the research data schemes with the smallest MSE value compared to other methods.