A Markov-Switching DSGE model for measuring the output gap in Brazil

The output gap, while inherently unobservable, plays a pivotal role in informing policymakers due to its significant implications for forecasting inflation rates and understanding the mechanisms of monetary policy transmission. Traditional filters frequently employed in estimating the output gap face criticism for being purely statistical and lacking economic theory. Conversely, estimates derived from Dynamic Stochastic General Equilibrium (DSGE) models encounter challenges stemming from the assumption of constant parameters over time. This study focuses on estimating the output gap for Brazil, employing a full specified DSGE model that incorporates Markov-Switching elements (MS-DSGE) to account for potential regime shifts. We introduce four model versions, some of which incorporate variations in volatilities and Taylor's rule parameters. In order to compare our output gap estimate with other approaches, we perform prediction tests, both with the central bank's reaction function and with the free price inflation Phillips curve. Our results in the first test indicate that the HP (Hodrick-Prescott) filter estimate performs better in the short and mid-term, but the MS-DSGE estimate presented better results in the long run. In the second exercise, no output gap series stands out among the approaches considered. In this context, the estimated output gap from the MS-DSGE framework emerges as a valuable asset within the arsenal available to policymakers, contributing meaningfully to their analytical toolkit.