Research

We study the Structural Vector Autoregressions (SVARs) that impose internal and external restrictions to set-identify the Forecast Error Variance Decomposition (FEVD). This object measures the importance of shocks for macroeconomic fluctuations and is therefore of first-order interest in business cycle analysis. We make the following contributions. First, we characterize the endpoints of the FEVD as the extreme eigenvalues of a symmetric reduced-form matrix. A consistent plug-in estimator naturally follows. Second, we use the perturbation theory to prove that the endpoints of the FEVD are differentiable. Third, we construct confidence intervals that are uniformly consistent in level and have asymptotic Bayesian interpretation. We also describe the conditions to derive uniformly consistent confidence intervals for impulse responses. A Monte-Carlo exercise demonstrates the approach properties in finite samples. An unconventional monetary policy application illustrates our toolkit. 

Presented at: Econometric Society European Summer Meeting (Erasmus University), 28th European Association for Young Economists Annual Meeting (Paris School of Economics), 2nd Time Series Workshop (University of East Anglia).

Presented by co-authors: 4th Sailing the Macro Workshop (Ortygia Foundation), Bristol Econometric Study Group (University of Bristol) Econometric Society North American Summer Meeting (Vanderbilt), 8th RCEA Time Series Workshop (Brunel University), Scotish Econometric Society Conference (University of Glasgow), Society for Nonlinear Dynamics and Econometrics (University of Padova)

Bayesian estimation of DSGE models is standard in macroeconomics, yet commonly reported objects of interest — impulse response functions and forecast error variance decompositions — often misrepresent uncertainty and model structure. This paper introduces a Bayesian decision-theoretic framework that constructs a constrained spatial median under the Euclidean norm loss, yielding a good central estimate that is consistent with the 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 horizon selection and loss function adjustments is also provided.

Presented at: Virtual Workshop for Junior Researchers in Time Series, MMF PhD Conference (Loughborough University), QMUL Economics and Finance PhD Workshop (Queen Mary University of London), European Association for Young Economists Annual Meeting (King's College London), International Association for Applied Econometrics Conference (University of Torino), European Economic Association Annual Meeting (Bordeaux School of Economics), University of Oxford, University of Pavia.

We show that the equivalence in population between impulse responses in Vector Autoregressions (VARs) and Local Projections (LPs) can be extended to cointegrated unit roots with unrestricted lag structure. We also prove that structural estimation with multiple instruments for multiple endogenous regressors is equivalent to a recursively block-identified Structural VAR, where the block of instruments is ordered first.

Presented at: ISCTE Business School, Central Bank of Ireland.

We propose a machinery to incorporate Dynamic Stochastic General Equilibrium (DSGE) models as a prior for Local Projections (LPs). First, relative to Vector Autoregressions (VARs) and standard Bayesian LPs, our framework successfully deals with the bias-variance trade-off, can be effectively used for policy analysis and forecasts well. Second, it enables posterior inference with respect to DSGE model parameters, where the posterior mode can be interpreted as a minimum distance estimator by projecting the LP coefficients onto the DSGE restrictions.

This paper explores a phenomena that has so far been mostly overlooked by applied macroeconomists when estimating the effects of monetary policy shocks; the central bank does not have full information about the current state of the economy when making policy decisions. We show that ignoring this leads to misidentification for identification schemes that rely on internal identification, i.e, approaches that do not make use of data that are external to the VAR for identification. The external instrument approach remains valid in population, although suffers from an increase in finite sample bias. We demonstrate the results using a simple simulation exercise, before turning to an empirical application focused on the US. Although the consequences of the information gap are documented here in a VAR setting, the same issue carries over to estimated DSGE models.