Before revision:  We do not find strong support for the hypothesis that having an independent central bank for a long period of time necessarily lowers inflation. Simulation studies evaluate the sensitivity of the proposed methods in complex settings when certain assumptions are violated and highlight the importance of working with appropriate learning algorithms for estimation.
After revision:  We do not find strong support for the hypothesis that CBI causes lower inflation. If a country had legislated CBI for every year between 1998 and 2008, it would have had an average reduction in inflation of -0.63 (-2.33; 1.07) percentage points in 2010.