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Title: Blessing and curse of cross-sectional length on robust estimation for panel data Authors:  Yanrong Yang - The Australian National University (Australia)
Lingyu He - The Australian National University (Australia) [presenting]
Abstract: Cross-sectional dimension (CSD) increases the rate of convergence for common information estimation in panel data models. However, Cross-sectional dependence automatically appears as more cross-sections are involved, which decreases the efficiency of estimation for homogeneous characteristics to some extent. This is the trade-off between the blessing and curse brought by cross-sectional dimensionality. The focus is on this point for robust M-estimation on panel data models. On the one hand, the rate of convergence of a high dimensional coefficient vector common for all cross-sections is provided, which shows that, using cross-sectional data as much as possible is a blessing for extracting homogeneous information. On the other hand, the asymptotic distribution of M-estimator for this parameter vector is established. It can show that the asymptotic variance heavily depends on cross-sectional dependence incurred by cross-sectional length. This interrupts the estimation efficiency. Under different settings for cross-sectional dimensions and dependence, simulations illustrates some common used M-estimation and compare them with the least-squares method. Empirical application on stock returns data from CRSP is provided, which show robust M-estimation is necessary and different cross-sections bring different results.