This thesis consists of three essays in macroeconometrics. Each essay is contained in one chapter and can be read as a standalone piece. In Chapter 1, we study estimation and inference of the Forecast Error Variance Decomposition (FEVD) in Structural Vector Autoregressions (SVARs) that are set-identified by internal and external (proxy) restrictions. The paper makes three main contributions. First, we characterize the endpoints of the FEVD as the extreme eigenvalues of a symmetric reduced-form matrix, and propose a consistent plug-in estimator. Second, we use perturbation theory and establish differentiability of the FEVD bounds with respect to reduced-form parameters. Third, we construct a set-length-adjusted delta-method confidence interval that ensures the nominal point-wise coverage. We illustrate the effectiveness of the approach using Monte-Carlo exercises and two empirical applications.

In Chapter 2, I propose an algorithm to summarise the posterior distribution for objects of interest in DSGE models. The paper introduces a Bayesian decision-theoretic framework that constructs a constrained spatial median under the Euclidean norm loss, yielding a well-defined central estimate that is unique and consistent with the theoretical DSGE model while accurately reflecting joint estimation uncertainty. The approach is applied to a large-scale DSGE model, highlighting the limitations of existing practices. Practical guidance on assessing distance concentration, horizon selection and loss function adjustments is also provided.

In Chapter 3, we show that the population equivalence between impulse responses in Vector Autoregressions (VARs) and Local Projections (LPs) extends to (possibly cointegrated) unit roots for an arbitrary large, but finite, lag length p up to horizons less than or equal to p. We also prove that structural estimation with multiple instruments for multiple endogenous regressors (LP-IV) is equivalent to a recursively identified Structural VAR, where the block of instruments is ordered first.