Dynamic central bank credibility: a Kalman Filter–Recursive Least Squares approach for emerging markets

We develop a state-space framework that jointly estimates central bank credibility as a scalar latent variable and the associated time-varying monetary policy reaction function. The Kalman filter extracts an unobservable credibility index from observed inflation expectations, while Recursive Least Squares continuously updates the reaction function coefficients using the Kalman innovations sequence, ensuring that parameter estimation operates on long-run trend components rather than transitory fluctuations. Under standard regularity conditions, we establish consistency of the credibility estimator and show that the reaction function coefficients attain the Cramer-Rao bound when the innovation variance is constant; a GLS variant achieves efficiency in the heteroskedastic case. Applying the framework to Banco de Mexico over 2002-2024, we identify four distinct credibility regimes: a consolidation phase following the adoption of inflation targeting (2002-2008), a transitory shock during the global financial crisis (2008-2009), a sustained high-credibility equilibrium (2010-2020), and a stress episode associated with post-pandemic inflation (2021-2023) followed by partial recovery. The time-varying reaction coefficients reveal that Banco de Mexico's responsiveness to the inflation gap is itself a function of its credibility state: stronger anchoring permits a more measured policy response, while credibility deterioration triggers sharper, front-loaded adjustments. These findings have direct implications for the optimal design of monetary policy communication in emerging markets and for the broader debate on whether central bank credibility generates real persistent effects beyond its role in expectation coordination.