Estimating coefficient-by-coefficient breaks in panel data models

Abstract

When estimating structural breaks, existing econometric methods adopt an a approach in which either all parameters change simultaneously, or they remain the same. In this paper, we consider the estimation of panel data models when an unknown subset of coefficients is subject to breaks. The challenge lies in estimating the breaks for each coefficient. To tackle this, we propose a new estimator for panel data, the “Coefficient-by-Coefficient Lasso” break estimator. This estimator is derived by penalizing the coefficients with a fused penalty and using component-wise adaptive weights. We present this estimator for two scenarios: those with homogeneous breaks and those with heterogeneous breaks. We show that the method identifies the number and dates of breaks for all coefficients with high probability and that the post-selection estimator is asymptotically normal. We examine the small-sample properties of the method through a Monte Carlo study and further apply it to analyze the influence of socioeconomic factors on crime.