The thesis consists of three chapters on econometrics analysis, both theoretical and applied. In the first chapter, which is coauthored with Andrea Carriero, Todd Clark and Massimiliano Marcellino, we propose a hierarchical shrinkage approach for multi-country VAR models. To make the approach operational, we consider three different scale mixtures of Normals priors --- specifically, Horseshoe, Normal-Gamma, and Normal-Gamma-Gamma priors. We provide new theoretical results for the Normal-Gamma prior. Empirically, we use a quarterly data set for G7 economies to examine how model specifications and prior choices affect the forecasting performance for GDP growth, inflation, and a short-term interest rate. We find that hierarchical shrinkage, particularly as implemented with the Horseshoe prior, is very useful in forecasting inflation. It also has the best density forecast performance for output growth and the interest rate. Adding foreign information yields benefits, as multi-country models generally improve on the forecast accuracy of single-country models. In the second chapter, which is coauthored with George Kapetanios and Massimiliano Marcellino, we develop kernel-based non-parametric estimation and inferential theory for large heterogeneous panel data models with stochastic time-varying coefficients. We propose mean group and pooled estimators, derive asymptotic distributions and show the uniform consistency and asymptotic normality of path coefficients. We extend the procedures to the case with possibly endogenous regressors and propose a time-varying version of the Hausman exogeneity test. Proposed estimators are investigated through a Monte Carlo study. We also present two empirical applications, exploring time-varying price elasticity of U.S. gasoline demand functions and estimating the panel versions of time-varying backward-looking and forward-looking Phillips curves. In the third chapter, I develop time-varying continuously updated GMM estimation and inferential theory for moment conditional models whose coefficients vary stochastically over time. Then, I extend overidentification test, Wald-type test for restrictions on model parameters to time-varying setting and propose the uniform version of these tests and a test for parameter stability. After deriving the asymptotic properties of the estimators and test statistics, I assess their finite sample performance by an extensive Monte-Carlo study and illustrate their application by an empirical example on conditional asset pricing models with SDF representation.