This dissertation contains three chapters on empirical macroeconomics and monetary policy. In Chapter 1, I test the forecast performance of a small-scale Dynamic Stochastic General Equilibrium (DSGE) model with sentiment shocks. I relax the benchmark assumption of rational expectations and assume instead that economic agents behave in a near-rational fashion: every period they learn and update their beliefs using a constant gain learning algorithm. Sentiment shocks are captured by exploiting observed data on expectations and are defined as the deviations from the model implied expectations due to exogenous waves of pessimism or optimism. The forecast evaluation is accomplished by comparing the root mean squared prediction error of the canonical 3-equation New Keynesian model at different horizons and under different expectation assumptions: rational expectations, learning, and learning with sentiment. The results show that the model with learning and sentiment shocks is not only able to compete with the other two alternatives, but it is generally better to forecast the output gap and the inflation rate. In Chapter 2, I use a small open economy DSGE model to investigate how Mexico's central bank has conducted its monetary policy in the period 1995-2019. The main objective of the paper is to document the systematic changes in the Bank of Mexico's reaction function by analyzing possible shifts in the parameters of the policy rule. The central bank's policy is modeled using a Taylor rule that relates the nominal interest rate to output, inflation, and the exchange rate. I employ Bayesian computational techniques and conduct rolling-window estimations to explicitly show the transition of the policy coefficients over the sample period. Furthermore, the paper examines the macroeconomic implications of these changes through rolling-window impulse-response functions. The results suggest that the Bank of Mexico's response to inflation has been steady since 1995, while the response to output and the exchange rate has decreased and stabilized after 2002. In Chapter 3, I reconsider whether monetary policy in small open economies responds to exchange rates by studying possible parameter instabilities in a DSGE model. The main focus of the paper is to revisit preceding evidence on the response to exchange rate movements by the Bank of England and determine if its reaction function has remained constant throughout the sample. To this end, I estimate a small open economy general equilibrium model using Bayesian econometric techniques over rolling windows. I find overwhelming evidence of shifts in several parameters, including those related to the policy rule. Furthermore, posterior odds tests reveal a time-varying response to exchange-rate fluctuations by the monetary authorities. The results favor the model with the nominal exchange rate embedded in the policy rule for the initial subsamples. However, the evidence steadily evolves across windows and ultimately changes to prefer the model specification with no exchange rate. The paper also documents evident variations in the model dynamics derived by the instability of parameters via rolling-window impulse response functions and variance decomposition analysis.