Hostname: page-component-586b7cd67f-dlnhk Total loading time: 0 Render date: 2024-11-23T21:22:33.629Z Has data issue: false hasContentIssue false
  • English
  • Français

ADVANCES IN USING VECTOR AUTOREGRESSIONS TO ESTIMATE STRUCTURAL MAGNITUDES

Published online by Cambridge University Press:  07 November 2022

Christiane Baumeister Open the ORCID record for Christiane Baumeister [Opens in a new window]  and
James D. Hamilton Open the ORCID record for James D. Hamilton [Opens in a new window]
Christiane Baumeister*
Affiliation:
University of Notre Dame and University of Pretoria
James D. Hamilton
Affiliation:
University of California at San Diego
*
Address correspondence to Christiane Baumeister, Department of Economics, University of Notre Dame, Notre Dame, IN 46556, USA; e-mail: [email protected].
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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.

Type
ET LECTURE
Information
Econometric Theory , Volume 40 , Issue 3 , June 2024 , pp. 472 - 510
Copyright
© The Author(s), 2022. Published by Cambridge University Press

Footnotes

This paper was presented as the Econometric Theory Lecture at the EC$^{2}$ Conference on The Econometrics of Climate, Energy and Resources at CREATES in December 2021. The paper supersedes earlier papers by the authors that were circulated under the titles “Advances in Structural Vector Autoregressions with Imperfect Identifying Information” and “Estimating Structural Parameters Using Vector Autoregressions.” We are thankful to Xin Gu, Frank Kleibergen, Lam Nguyen, Peter C.B. Phillips, Matthew Read, an anonymous co-editor, and three anonymous referees for very useful insights.

References

REFERENCES

Aastveit, K.A., Bjørnland, H.C., & Cross, J.L. (2022) Inflation expectations and the pass-through of oil prices. Review of Economics and Statistics . https://doi.org/10.1162/rest_a_01073.Google Scholar
Amir-Ahmadi, P. & Drautzburg, T. (2021) Identification and inference with ranking restrictions. Quantitative Economics 12(1), 1–39.CrossRefGoogle Scholar
Andrews, D.W.K. & Kwon, S. (2019). Inference in Moment Inequality Models That Is Robust to Spurious Precision under Model Misspecification. Cowles Foundation Discussion Paper No. 2184.Google Scholar
Antolín-Díaz, J. & Rubio-Ramírez, J.F. (2018) Narrative sign restrictions for SVARs. American Economic Review 108, 2802–2829.CrossRefGoogle Scholar
Arias, J.E., Caldara, D., & Rubio-Ramírez, J.F. (2019) The systematic component of monetary policy in SVARs: An agnostic identification procedure. Journal of Monetary Economics 101, 1–13.CrossRefGoogle Scholar
Arias, J.E., Rubio-Ramírez, J.F., & Waggoner, D.F. (2021) Inference in Bayesian proxy-SVARs. Journal of Econometrics 225(1), 88–106.CrossRefGoogle Scholar
Aruoba, S.B., Mlikota, M., Schorfheide, F., & Villalvazo, S. (2022) SVARs with occasionally-binding constraints. Journal of Econometrics . https://doi.org/10.1016/j.jeconom.2021.07.013.CrossRefGoogle Scholar
Basher, S.A., Haug, A.A., & Sadorsky, P. (2018) The impact of oil-market shocks on stock returns in major oil-exporting countries. Journal of International Money and Finance 86, 264–280.CrossRefGoogle Scholar
Baumeister, C. (2018). Matlab code for “Inference in Structural Vector Autoregressions When the Identifying Assumptions Are Not Fully Believed: Re-Evaluating the Role of Monetary Policy in Economic Fluctuations”. https://drive.google.com/uc?export=download&id=1Dh34goEM1neTjykrwdpa60jvyU92nBg1.Google Scholar
Baumeister, C. & Derdzyan, A. (2021) Structural Changes in Energy Markets: A New Approach to Modeling Time-Varying Dynamics. Working paper, University of Notre Dame.Google Scholar
Baumeister, C. & Hamilton, J.D. (2015) Sign restrictions, structural vector autoregressions, and useful prior information. Econometrica 83, 1963–1999.CrossRefGoogle Scholar
Baumeister, C. & Hamilton, J.D. (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.CrossRefGoogle Scholar
Baumeister, C. & Hamilton, J.D. (2019a) Structural interpretation of vector autoregressions with incomplete information: Revisiting the role of oil supply and demand shocks. American Economic Review 109, 1873–1910.CrossRefGoogle Scholar
Baumeister, C. & Hamilton, J.D. (2019b) Replication Data for: Structural Interpretation of Vector Autoregressions with Incomplete Identification: Revisiting the Role of Oil Supply and Demand Shocks. https://www.openicpsr.org/openicpsr/project/113108/version/V1/view.Google Scholar
Belongia, M.T. & Ireland, P.N. (2021) A classical view of the business cycle. Journal of Money, Credit and Banking 53, 333–366.CrossRefGoogle Scholar
Bernanke, B.S. (1986) Alternative explanations of the money-income correlation. Carnegie-Rochester Conference Series on Public Policy 25, 49–99.CrossRefGoogle Scholar
Braun, R. & Brüggemann, R. (2022) Identification of SVAR models by combining sign restrictions with external instruments. Journal of Business and Economic Statistics . https://doi.org/10.1080/07350015.2022.2104857.Google Scholar
Brinca, P., Duarte, J.B., and Faria-e-Castro, M. (2021) Measuring sectoral supply and demand shocks during COVID-19. European Economic Review 139, 103901.CrossRefGoogle ScholarPubMed
Caldara, D., Cavallo, M., & Iacoviello, M. (2019) Oil price elasticities and oil price fluctuations. Journal of Monetary Economics 103, 1–20.CrossRefGoogle Scholar
Caldara, D. & Herbst, E. (2019) Monetary policy, real activity, and credit spreads: Evidence from Bayesian proxy SVARs. American Economic Journal: Macroeconomics 11(1), 157–192.Google Scholar
Campbell, J.R., Evans, C.L., Fisher, J.D.M., & Justiniano, A. (2012) Macroeconomic effects of Federal reserve forward guidance. Brookings Papers on Economic Activity 43(1), 1–80.CrossRefGoogle Scholar
Chao, J.C. & Phillips, P.C.B. (2002) Jeffreys prior analysis of the simultaneous equations model in the case with $n+1$ endogenous variables. Journal of Econometrics 111, 251–283.CrossRefGoogle Scholar
Christiano, L.J., Eichenbaum, M., & Evans, C. (1999) Monetary policy shocks: What have we learned and to what end? In Taylor, J. B. & Woodford, M. (eds.), Handbook of Macroeconomics , vol. 1, pp. 65–148. Elsevier.CrossRefGoogle Scholar
Del Negro, M. & Schorfheide, F. (2008) Forming priors for DSGE models (and how it affects the assessment of nominal rigidities). Journal of Monetary Economics 55, 1191–1208.CrossRefGoogle Scholar
Doan, T., Litterman, R.B., & Sims, C.A. (1984) Forecasting and conditional projection using realistic prior distributions. Econometric Reviews 3, 1–100.CrossRefGoogle Scholar
Drèze, J.H. (1975) Bayesian theory of identification in simultaneous equations models. In Fienberg, S.E. & Zellner, A. (eds.), Studies in Bayesian Econometrics and Statistics . North-Holland.Google Scholar
Fry, R. & Pagan, A. (2011) Sign restrictions in structural vector autoregressions: A critical review. Journal of Economic Literature 49, 938–960.CrossRefGoogle Scholar
Gafarov, B., Meier, M., & Olea, J.L.M. (2018) Delta-method inference for a class of set-identified SVARs. Journal of Econometrics 203, 316–327.CrossRefGoogle Scholar
Galí, J. (2008) Monetary Policy, Inflation, and the Business Cycle: An Introduction to the New Keynesian Framework and Its Applications . Princeton University Press.Google Scholar
Gertler, M. & Karadi, P. (2015) Monetary policy surprises, credit costs, and economic activity. American Economic Journal: Macroeconomics 7, 44–76.Google Scholar
Giacomini, R. & Kitagawa, T. (2021) Robust Bayesian inference for set-identified models. Econometrica 89, 1519–1556.CrossRefGoogle Scholar
Giacomini, R., Kitagawa, T., & Read, M. (2021a) Identification and Inference under Narrative Restrictions. Working paper, Brown University.CrossRefGoogle Scholar
Giacomini, R., Kitagawa, T., & Read, M. (2021b) Robust Bayesian Analysis for Econometrics. CEPR Discussion Paper 16488.CrossRefGoogle Scholar
Giacomini, R., Kitagawa, T., & Uhlig, H. (2019) Estimation under Ambiguity. CEMMAP Working paper CWP24/19.CrossRefGoogle Scholar
Giacomini, R., Kitagawa, T., & Volpicella, A. (2022) Uncertain identification. Quantitative Economics 13(1), 95–123.CrossRefGoogle Scholar
Grisse, C. (2020) The Effect of Monetary Policy on the Swiss Franc: An SVAR Approach. Working paper 2020-02, Swiss National Bank.Google Scholar
Güntner, J.H.F. (2014) How do oil producers respond to demand shocks? Energy Economics 44, 1–13.CrossRefGoogle Scholar
Gustafson, P. (2009) What are the limits of posterior distributions arising from nonidentified models, and why should we care? Journal of the American Statistical Association 104, 1682–1695.CrossRefGoogle Scholar
Gustafson, P. (2015) Bayesian Inference for Partially Identified Models: Exploring the Limits of Limited Data , Monographs on Statistics & Applied Probability. Chapman & Hall/CRC and Taylor & Francis.CrossRefGoogle Scholar
Hamilton, J.D. (1994) Time Series Analysis . Princeton University Press.CrossRefGoogle Scholar
Herrera, A.M. & Rangaraju, S. (2020) The effect of oil supply shocks on US economic activity: What have we learned? Journal of Applied Econometrics 35, 141–159.CrossRefGoogle Scholar
Inoue, A. & Kilian, L. (2022) Joint Bayesian inference about impulse responses in VAR models. Journal of Econometrics . https://doi.org/10.1016/j.jeconom.2021.05.010.CrossRefGoogle Scholar
Jeffreys, H. (1946) An invariant form for the prior probability in estimation problems. Proceedings of the Royal Society of London, Series A, Mathematical and Physical Sciences 186, 453–461.Google ScholarPubMed
Kédagni, D., Li, L., & Mourifié, I. (2021) Discordant Relaxations of Misspecified Models. CEMMAP Working paper CWP19/21.Google Scholar
Kilian, L. (2008) Exogenous oil supply shocks: How big are they and how much do they matter for the U.S. economy? Review of Economics and Statistics 90, 216–240.CrossRefGoogle Scholar
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.CrossRefGoogle Scholar
Kilian, L. (2022) Understanding the estimation of oil demand and oil supply elasticities. Energy Economics 107, 105844.CrossRefGoogle Scholar
Kilian, L. & Lütkepohl, H. (2017) Structural Vector Autoregressive Analysis . Cambridge University Press.CrossRefGoogle Scholar
Kilian, L. & Murphy, D.P. (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.CrossRefGoogle Scholar
Kilian, L. & Murphy, D.P. (2014) The role of inventories and speculative trading in the global market for crude oil. Journal of Applied Econometrics 29, 454–478.CrossRefGoogle Scholar
Kleibergen, F. & Zivot, E. (2003) Bayesian and classical approaches to instrumental variable regression. Journal of Econometrics 114, 29–72.CrossRefGoogle Scholar
Lindley, D.V. (1972) Bayesian Statistics: A Review . Society for Industrial and Applied Mathematics.CrossRefGoogle Scholar
Litterman, R.B. (1986) Forecasting with Bayesian vector autoregressions—Five years of experience. Journal of Business and Economic Statistics 4(1), 25–38.Google Scholar
Ludvigson, S.C., Ma, S., & Ng, S. (2017) Shock Restricted Structural Vector-Autoregressions. NBER Working paper 23225, National Bureau of Economic Research.CrossRefGoogle Scholar
Lukmanova, E., & Rabitsch, K. (2021) New Evidence on Monetary Transmission: Interest Rate versus Inflation Target Shocks. Working paper, KU Leuven.CrossRefGoogle Scholar
Mertens, K. & Ravn, M.O. (2013) The dynamic effectsof personal and corporate income tax changes in the United States. American Economic Review 103, 1212–1247.CrossRefGoogle Scholar
Moon, H.R. & Schorfheide, F. (2012) Bayesian and frequentist inference in partially identified models. Econometrica 80, 755–782.Google Scholar
Nakamura, E. & Steinsson, J. (2018) High frequency identification of monetary non-neutrality: The information effect. Quarterly Journal of Economics 133, 1283–1330.CrossRefGoogle Scholar
Nguyen, L. (2019) Bayesian Inference in Structural Vector Autoregression with Sign Restrictions and External Instruments. Working paper, University of California, San Diego.Google Scholar
Phillips, P.C.B. (1991) To criticize the critics: An objective Bayesian analysis of stochastic trends. Journal of Applied Econometrics 6, 334–364.CrossRefGoogle Scholar
Plagborg-Møller, M. & Wolf, C.K. (2021) Local projections and VARs estimate the same Impule responses. Econometrica 89, 955–980.CrossRefGoogle Scholar
Poirier, D.J. (1998) Revising beliefs in nonidentified models. Econometric Theory 14(4), 483–509.CrossRefGoogle Scholar
Riggi, M. & Venditti, F. (2015) The time varying effect of oil Price shocks on euro-area exports. Journal of Economic Dynamics and Control 59, 75–94.CrossRefGoogle Scholar
Robert, C.P. (2007) The Bayesian Choice , Springer Texts in Statistics, Springer.Google Scholar
Rubio-Ramírez, J., Waggoner, D.F., & Zha, T. (2010) Structural vector autoregressions: Theory of identification and algorithms for inference. Review of Economic Studies 77(2), 665–696.CrossRefGoogle Scholar
Shapiro, M.D. & Watson, M.W. (1988) Sources of business cycle fluctuations. In Fischer, S. (ed.), NBER Macroeconomics Annual , vol. 3, pp. 111–156. MIT Press.Google Scholar
Shiller, R.J. (1973) A distributed lag estimator derived from smoothness priors. Econometrica 41(4), 775–788.CrossRefGoogle Scholar
Sims, C.A. & Zha, T. (1998) Bayesian methods for dynamic multivariate models. International Economic Review 39, 949–968.CrossRefGoogle Scholar
Sims, C.A. & Zha, T. (1999) Error bands for impulse responses. Econometrica 67, 1113–1155.CrossRefGoogle Scholar
Smets, F. & Wouters, R. (2007) Shocks and frictions in US business cycle: A Bayesian DSGE approach. American Economic Review 97, 586–606.CrossRefGoogle Scholar
Stock, J.H. & Watson, M.W. (2012) Disentangling the channels of the 2007–09 recession. Brookings Papers on Economic Activity 43(1), 81–156.CrossRefGoogle Scholar
Stock, J.H. & Watson, M.W. (2016) Factor models and structural vector autoregressions in macroeconomics. In Taylor, J. B. & Uhlig, H. (eds.), Handbook of Macroeconomics , vol. 2, pp. 415–525. Elsevier.Google Scholar
Stock, J.H. & Watson, M.W. (2018) Identification and estimation of dynamic causal effects in macroeconomics using external instruments. Economic Journal 128, 917–948.CrossRefGoogle Scholar
Uhlig, H. (2005) What are the effects of monetary policy on output? Results from an agnostic identification procedure. Journal of Monetary Economics 52, 381–419.CrossRefGoogle Scholar
Uhlig, H. (2017) Shocks, sign restrictions, and identification. In Honoré, B., Pakes, A., Piazzesi, M., & Samuelson, L. (eds), Advances in Economics and Econometrics , vol. 2, pp. 95–127. Cambridge University Press.CrossRefGoogle Scholar
Valenti, D., Manera, M., & Sbuelz, A. (2020) Interpreting the oil risk premium: Do oil price shocks matter? Energy Economics 91, 104906.CrossRefGoogle Scholar
Watson, M. (2019). Comment on “On the Empirical (Ir)Relevance of the Zero Lower Bound” by Debortoli, D., Gali, J., and Gambetti, L.. In: NBER Macroeconomics Annual 2019 , vol. 34, pp. 182–193. National Bureau of Economic Research.Google Scholar
Wolf, C.K. (2020) SVAR (mis-)identification and the real effects of monetary policy shocks. American Economic Journal: Macroeconomics 12(4), 1–32.Google Scholar
Woodford, M. (2003) Interest and Prices . Princeton University Press.Google Scholar
Zhou, X. (2020) Refining the workhorse oil market model. Journal of Applied Econometrics 35, 130–140.CrossRefGoogle Scholar