Advances in Using Vector Autoregressions to Estimate Structural Magnitudes

Abstract

This paper surveys recent advances in drawing structural conclusions from vector autoregressions (VARs), providing a unified perspective on the role of prior knowledge. We describe the traditional approach to identification as a claim to have exact prior information about the structural model and propose Bayesian inference as a way to acknowledge that prior information is imperfect or subject to error. We raise concerns from both a frequentist and a Bayesian perspective about the way that results are typically reported for VARs that are set-identified using sign and other restrictions. We call attention to a common but previously unrecognized error in estimating structural elasticities and show how to correctly estimate elasticities even in the case when one only knows the effects of a single structural shock.

Not All Energy Transitions Are Alike: Disentangling the Effects of Demand and Supply-Side Policies on Future Oil Prices

“…In the Notes: The impulse response function-based (IRF) supply and demand elasticities are estimated as the impact production response relative to the impact price response after an oil-specific demand and oil supply shock, respectively (see Kilian and Murphy, 2014). The impact demand and supply elasticities are obtained directly from the B 0 matrix (see Baumeister and Hamilton, 2023).…”

“…More specifically, this concept is an impulse response-based ratio of equilibrium impacts. It is defined as the oil output response relative to the price response given an oil-specific or aggregate demand shock as defined byKilian and Murphy (2014) Baumeister and Hamilton (2023). note that this concept does not entail the usual ceteris paribus assumption of an elasticity because an oil-specific demand shock does not only trigger a response in price but also a response in other variables.…”

“…note that this concept does not entail the usual ceteris paribus assumption of an elasticity because an oil-specific demand shock does not only trigger a response in price but also a response in other variables. A supply elasticity that takes into account the ceteris paribus requirement is obtained directly from the impact elasticity in the structural B 0 matrix (seeBaumeister and Hamilton, 2023). The relevant normalized element of this matrix indicates the simultaneous response of oil output to a change in the oil price holding all other variables constant.…”

Pandemic, War, Inflation: Oil Markets at a Crossroads?

“…At the onset of the COVID-19 pandemic, oil prices collapsed reaching a trough of $18 per barrel in April 2022. The lift-off of oil 14 For a non-technical introduction to the econometric methodology, please refer to Baumeister and Hamilton (2022); for a thorough treatment, please refer to Baumeister and Hamilton (2023a). Both papers use a model of the global oil market for illustration.…”

A new posterior sampler for Bayesian structural vector autoregressive models

“…Kilian and Lütkepohl (2017) take the view that applied researchers can frequently express prior beliefs on impulse responses. Baumeister and Hamilton (2015, forthcoming) show cases in which sign restrictions are naturally expressed on the contemporaneous response of the variables of the model, for instance, structural elasticities. Baumeister and Hamilton (2018) propose a hybrid approach that jointly accommodates sign restrictions on both the impulse responses and the structural relations among variables.…”