This dissertation is comprised of three chapters. Chapter 1 is a reprint of my job market. The chapter considers the efficient estimation of opinion pools in the Bayesian paradigm and extends their application to cases where the number of competing models exceeds the number of observations. An appropriate Bayesian formulation and estimation algorithm is proposed which 1) accommodates any proper scoring rule and 2) allows the weights to shrink towards any possible combination. This flexibility makes the Bayesian opinion pool relevant for applications related to model averaging and model selection and improves stability compared to the ones estimated using scoring rules in a small sample setting. Results from a simulation study reveal that the proposed Bayesian opinion pool methodology improves prediction accuracy. An application involving the Survey of Professional Forecasters demonstrates that the Bayesian opinion pool's inflation forecast competes well with the equal-weight aggregated inflation forecast published by the Federal Bank of Philadelphia. The application showcases the usefulness of the Bayesian solution in situations where traditional opinion pools fail.

Chapter two introduces a non-parametric vector autoregressive model with dynamic factor (DF-NPVAR) through a hierarchical Bayesian approach. The chapter considers the specification, identification and estimation of the DF-NPVAR model, allowing it to be efficiently fit via MCMC algorithms. The model aims at effectively capturing dynamic relationships among variables and enabling the incorporation of extensive information sets. Issues related to model comparison and extensions to settings with autocorrelated errors and qualitative variables are also considered. In an application employing post-war US data, the DF-NPVAR model successfully identifies non-linear associations between macroeconomic variables and the dynamic factor captures the business cycle component, which aligns with officially declared recession periods.

Chapter three discusses a Bayesian estimation for the FAVAR models using the precision-based algorithm. The model is fully identified under the identification restrictions of \cite{bai2016estimation}. The approach increases the efficiency of the Gibbs sampler and avoids slow convergence and poor mixing (\cite{chan2009efficient}). This article then contrasts the Bayesian approach with the one-step and two-step estimation techniques proposed in \cite{bernanke2005measuring}. The simulation study finds that the Bayesian approach recovers the unobservable factor in a simple FAVAR framework compared to estimation techniques proposed in \cite{bernanke2005measuring}.