Long-Run Effects in Large Heterogeneous Panel Data Models with Cross-Sectionally Correlated Errors

This paper develops a cross-sectionally augmented distributed lag (CS-DL) approach to the estimation of long-run effects in large dynamic heterogeneous panel data models with cross-sectionally dependent errors. The asymptotic distribution of the CS-DL estimator is derived under coefficient heterogeneity in the case where the time dimension ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" altimg="si10.gif"> <mml:mtext>T</mml:mtext> </mml:math>) and the cross-section dimension ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" altimg="si11.gif"> <mml:mtext>N</mml:mtext> </mml:math>) are both large. The CS-DL approach is compared with more standard panel data estimators that are based on autoregressive distributed lag (ARDL) specifications. It is shown that unlike the ARDL-type estimator, the CS-DL estimator is robust to misspecification of dynamics and error serial correlation. The theoretical results are illustrated with small sample evidence obtained by means of Monte Carlo simulations, which suggest that the performance of the CS-DL approach is often superior to the alternative panel ARDL estimates, particularly when <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" altimg="si12.gif"> <mml:mtext>T</mml:mtext> </mml:math>is not too large and lies in the range of 30–50.