Shrinkage estimation of common breaks in panel data models via adaptive group fused Lasso

In this paper we consider estimation and inference of common breaks in panel data models via adaptive group fused Lasso. We consider two approaches—penalized least squares (PLS) for first-differenced models without endogenous regressors, and penalized GMM (PGMM) for first-differenced models with endogeneity. We show that with probability tending to one, both methods can correctly determine the unknown number of breaks and estimate the common break dates consistently. We establish the asymptotic distributions of the Lasso estimators of the regression coefficients and their post Lasso versions. We also propose and validate a data-driven method to determine the tuning parameter used in the Lasso procedure. Monte Carlo simulations demonstrate that both the PLS and PGMM estimation methods work well in finite samples. We apply our PGMM method to study the effect of foreign direct investment (FDI) on economic growth using a panel of 88 countries and regions from 1973 to 2012 and find multiple breaks in the model.