Summer School at Lancaster University on:

“A Bayesian Approach to Identification of Structural VAR Models”

June 1-3, 2026

Christiane Baumeister University of Notre Dame NBER and CEPR

This course will focus on estimation and inference in structural vector autoregressive (SVAR) models which are the workhorse models in empirical macroeconomics. The goal of this course is to equip participants with state-of-the art Bayesian methods for empirical research and policy analysis. The course challenges the current practice of identification of VAR models by introducing a more general Bayesian framework that encompasses standard identification approaches as special cases. Drawing structural inference from VAR models requires making use of prior information. This course provides formal tools of Bayesian analysis that allow to incorporate prior beliefs about structural coefficients, the impacts of shocks, and other structural objects of interest in a flexible way. The methods introduced in the lectures will be illustrated with applications to monetary policy, labor market dynamics, and oil price fluctuations as well as hands-on programming in Matlab.

COURSE OUTLINE

Day 1: Identification of Structural VAR Models

We revisit the identification problem in structural VAR models and introduce a general Bayesian framework that nests traditional identification schemes. In particular, we question the current practice of identification in VAR models using inequality constraints. We illustrate the problems that arise from the traditional algorithm based on sign restrictions with an application to modeling the labor market. We introduce a more flexible approach for estimation and inference that is not subject to these concerns.

·         Baumeister, C. and J.D. Hamilton (2015), “Sign Restrictions, Structural Vector Autoregressions, and Useful Prior Information,” Econometrica, 83(5), 1963-1999.

·         Baumeister, C. and J.D. Hamilton (2020), “Drawing Conclusions from Structural Vector Autoregressions Identified on the Basis of Sign Restrictions,” Journal of International Money and Finance, 109, article 102250.

·         Baumeister, C., and J.D. Hamilton (2024), “Advances in Using Vector Autoregressions to Estimate Structural Magnitudes,” Econometric Theory, 40(3), 472-510.

·         Hamilton, J.D. (2026), Vector Autoregressions, Cambridge University Press, Chapters 11 and 12.

·         Brinca, P., J.B. Duarte, and M. Faria-e-Castro (2021), “Measuring Labor Supply and Demand Shocks during COVID-19,” European Economic Review, 139, article 103901.

·         Rubio-Ramirez, J.F., D.F. Waggoner, and T. Zha (2010), “Structural Vector Autoregressions: Theory of Identification and Algorithms for Inference,” Review of Economic Studies, 77(2), 665-696.

Day 2: The Role of Prior Information

We illustrate this new method for identification by revisiting the role of oil supply and demand shocks in generating historical fluctuations in the price of oil and highlight several shortcomings of traditional approaches to identification of oil supply and demand shocks with a particular focus on the estimation of behavioral elasticities.

·         Baumeister, C. and J.D. Hamilton (2019), “Structural Interpretation of Vector Autoregressions with Incomplete Identification: Revisiting the Role of Oil Supply and Demand Shocks,” American Economic Review, 109(5), 1873-1910.

·         Baumeister, C. and J.D. Hamilton (2022), “Structural Vector Autoregressions with Imperfect Identifying Information,” AEA Papers and Proceedings, 112, 466-470.

·         Caldara, D., M. Cavallo, and M. Iacoviello (2016), “Oil Price Elasticities and Oil Price Fluctuations,” Journal of Monetary Economics, 103, 1-20.

·         Kilian, L. (2009). “Not all Oil Price Shocks Are Alike: Disentangling Demand and Supply Shocks in the Crude Oil Market,” American Economic Review, 99, 1053-1069.

·         Kilian, L., and D.P. Murphy (2012), “Why Agnostic Sign Restrictions Are Not Enough: Understanding the Dynamics of Oil Market VAR Models,” Journal of the European Economic Association, 10(5), 1166-1188.

Day 3: Inference in Set-Identified SVAR Models

We show how to supplement prior information about structural parameters with prior knowledge about the impacts of structural shocks and external instruments. We apply this idea to the study of the dynamic effects of monetary policy, its role in business cycle fluctuations, and the estimation of structural policy response coefficients in an interest-rate rule. We also show how to construct credibility sets for impulse response functions, variance decompositions, and historical decompositions.

·         Baumeister, C. and J.D. Hamilton (2018), “Inference in Structural Vector Autoregressions When the Identifying Assumptions are Not Fully Believed: Re-evaluating the Role of Monetary Policy in Economic Fluctuations,” Journal of Monetary Economics, 100, 48-65.

·         Belongia, M.T., and P.N. Ireland (2021), “A Classical View of the Business Cycle,” Journal of Money, Credit, and Banking, 53(2-3), 333-366.

·         Nguyen, Lam (2025), “Bayesian Inference in Proxy SVARs with Incomplete Identification: Re-evaluating the Validity of Monetary Policy Instruments,” Journal of Monetary Economics, 103813.

·         Read, Matthew (2024), “Set-identified Structural Vector Autoregressions and the Effects of a 100 Basis Point Monetary Policy Shock,” Review of Economics and Statistics, forthcoming.

·         Watson, M.W. (2019), “Comment on ‘On the Empirical (Ir)Relevance of the Zero Lower Bound’ by Debortoli, Gali, and Gambetti,” NBER Macroeconomics Annual.

COURSE TIMETABLE

Total: 15 hours

June 1, 2026: Bayesian Analysis of Structural VAR Models

09:00 am – 10:30 am     SVARs: The Identification Problem Revisited

10:45 am – 12:15 pm     Identification Using Inequality Constraints

02:00 pm – 04:00 pm     Matlab Application: Labor Market Dynamics

June 2, 2026: The Role of Prior Information

09:00 am – 10:30 am A Bayesian Interpretation of Traditional Identification Assumptions

10:45 am – 12:15 pm     Inexact prior information about structural elasticities

02:00 pm – 04:00 pm     Matlab Application: Oil Supply and Demand Shocks

June 3, 2026: Inference in Set-Identified SVAR Models

09:00 am – 10:30 am      Credibility Sets for IRFs, Variance, and Historical Decompositions

10:45 am – 12:15 pm      Prior Information about Structural Coefficients, Impacts of Shocks,

                                    and External Instruments

02:00 pm – 04:00 pm      Matlab Application: The Effects of Monetary Policy

Prerequisites: basic knowledge of Bayesian analysis and SVAR models