Two Essays on Maximum Likelihood Estimation

In recent years, a vast macroeconomic and finance literature has been devoted to building DSGE models to explain the impact of various macroeconomic shocks on output, inflation and interest rates. The DSGE models that have numerous frictions and different types of shocks are the standard tool in macroeconomic analysis, and they appear to reproduce the data in many important dimensions. This work consists of two essays on maximum likelihood estimation of DSGE models. The first essay focuses on a monetary DSGE model of term structure, and the estimation of its structural parameters, while the second essay explores and compares three different versions of New Keynesian DSGE models. A general background is provided for the models, and their estimation techniques along with a review of the term structure models and New Keynesian models.