Local Projections and VARs Estimate the Same Impulse Responses

Mikkel Plagborg-Møller; Christian K. Wolf

doi:10.3982/ecta17813

journal article Jan 01, 2021

Local Projections and VARs Estimate the Same Impulse Responses

Mikkel Plagborg-Møller Christian K. Wolf

Econometrica Vol. 89 No. 2 pp. 955-980 · JSTOR

View at Publisher Save 10.3982/ecta17813

Abstract

We prove that local projections (LPs) and Vector Autoregressions (VARs) estimate the same impulse responses. This nonparametric result only requires unrestricted lag structures. We discuss several implications: (i) LP and VAR estimators are not conceptually separate procedures; instead, they are simply two dimension reduction techniques with common estimand but different finite‐sample properties. (ii) VAR‐based structural identification—including short‐run, long‐run, or sign restrictions—can equivalently be performed using LPs, and vice versa. (iii) Structural estimation with an instrument (proxy) can be carried out by ordering the instrument first in a recursive VAR, even under noninvertibility. (iv) Linear VARs are as robust to nonlinearities as linear LPs.

Topics

No keywords indexed for this article. Browse by subject →

References

69

[1]

Alloza, M., J. Gonzalo, and C. Sanz (2019): “Dynamic Effects of Persistent Shocks,” Banco de Espana Working Paper No. 1944.

[2]

Almuzara, T., and A. Marcet (2017): “To Diff, or not to Diff?” Preprint.

[3]

Angrist (2009) 10.1515/9781400829828

[4]

Antolín-Díaz American Economic Review (2018) 10.1257/aer.20161852

[5]

Baek, C., and B. Lee (2020): “A Guide to Single Equation Regressions for Impulse Response Estimations,” Manuscript, Hong Kong University of Science and Technology.

[6]

Barakchian Journal of Monetary Economics (2013) 10.1016/j.jmoneco.2013.09.006

[7]

Bernanke (1986)

[8]

Blanchard American Economic Review (1989)

[9]

Blanchard (1986)

[10]

Brockwell (1991) 10.1007/978-1-4419-0320-4

[11]

Brugnolini, L. (2018): “About Local Projection Impulse Response Function Reliability,” Manuscript, University of Rome “Tor Vergata”. 10.2139/ssrn.3229218

[12]

Carriero Journal of Money, Credit and Banking (2015) 10.1111/jmcb.12243

[13]

Chang The Econometrics Journal (2007) 10.1111/j.1368-423x.2007.00216.x

[14]

Chevillon Journal of Economic Surveys (2007) 10.1111/j.1467-6419.2007.00518.x

[15]

Choi Economics Letters (2019) 10.1016/j.econlet.2019.04.017

[16]

Nominal Rigidities and the Dynamic Effects of a Shock to Monetary Policy

Lawrence J. Christiano, Martin Eichenbaum, Charles L. Evans

Journal of Political Economy 2005 10.1086/426038

[17]

Christiano Journal of the European Economic Association (2006) 10.1162/jeea.2006.4.2-3.475

[18]

Dufour Econometrica (1998) 10.2307/2999631

[19]

Fernández-Villaverde American Economic Review (2007) 10.1257/aer.97.3.1021

[20]

Forni Journal of Applied Econometrics (2019) 10.1002/jae.2665

[21]

Frisch (1933)

[22]

Gafarov Journal of Econometrics (2018) 10.1016/j.jeconom.2017.12.004

[23]

Gertler American Economic Journal: Macroeconomics (2015)

[24]

Giacomini, R., and T. Kitagawa (2020): “Robust Bayesian Inference for Set-Identified Models,” cemmap Working Paper CWP13/20.

[25]

Credit Spreads and Business Cycle Fluctuations

Simon Gilchrist, Egon Zakrajšek

American Economic Review 2012 10.1257/aer.102.4.1692

[26]

Inoue International Economic Review (2002) 10.1111/1468-2354.t01-1-00016

[27]

Jarocinski American Economic Journal: Macroeconomics (2020)

[28]

Estimation and Inference of Impulse Responses by Local Projections

ÒSCAR JORDÀ

American Economic Review 2005 10.1257/0002828053828518

[29]

Simultaneous Confidence Regions for Impulse Responses

ÒSCAR JORDÀ

Review of Economics and Statistics 2009 10.1162/rest.91.3.629

[30]

When Credit Bites Back

ÒSCAR JORDÀ, MORITZ SCHULARICK, Alan M. Taylor

Journal of Money, Credit and Banking 2013 10.1111/jmcb.12069

[31]

Betting the house

ÒSCAR JORDÀ, MORITZ SCHULARICK, Alan M. Taylor

Journal of International Economics 2015 10.1016/j.jinteco.2014.12.011

[32]

Jordà Journal of Monetary Economics (2020) 10.1016/j.jmoneco.2019.01.021

[33]

Kilian, L. (2006): “Not All Oil Price Shocks Are Alike: Disentangling Demand and Supply Shocks in the Crude Oil Market,” CEPR Discussion Paper 5994.

[34]

Kilian Review of Economics and Statistics (2011) 10.1162/rest_a_00143

[35]

Kilian (2017) 10.1017/9781108164818

[36]

Kilian Journal of the European Economic Association (2012) 10.1111/j.1542-4774.2012.01080.x

[37]

Kilian Quantitative Economics (2011) 10.3982/qe99

[38]

Leduc American Economic Journal: Economic Policy (2017)

[39]

Lewis Journal of Multivariate Analysis (1985) 10.1016/0047-259x(85)90027-2

[40]

Ludvigson, S. C., S. Ma, and S. Ng (2020a): “Covid19 and the Macroeconomic Effects of Costly Disasters,” NBER Working Paper No. 26987. 10.3386/w26987

[41]

Ludvigson, S. C., S. Ma, and S. Ng (2020b): “Shock Restricted Structural Vector-Autoregressions,” Manuscript, New York University.

[42]

Marcellino Journal of Econometrics (2006) 10.1016/j.jeconom.2005.07.020

[43]

McElroy Journal of Forecasting (2015) 10.1002/for.2321

[44]

Meier, A. (2005): “How Big Is the Bias in Estimated Impulse Responses? A Horse Race Between VAR and Local Projection Methods,” Manuscript, European University Institute.

[45]

Mertens Journal of Economic Dynamics and Control (2012) 10.1016/j.jedc.2012.06.007

[46]

Mertens, K. (2015): “Advances in Empirical Macroeconomics, Lecture 2,” Lecture slides, Bonn Summer School.

[47]

The Dynamic Effects of Personal and Corporate Income Tax Changes in the United States

Karel Mertens, Morten O Ravn

American Economic Review 2013 10.1257/aer.103.4.1212

[48]

Miranda-Agrippino, S. (2017): “Unsurprising Shocks: Information, Premia, and the Monetary Transmission,” Manuscript, Bank of England. 10.2139/ssrn.2865585

[49]

Miranda-Agrippino, S., and G. Ricco (2019): “Identification With External Instruments in Structural VARs Under Partial Invertibility,” Manuscript, Bank of England.

[50]

Identification in Macroeconomics

Emi Nakamura, Jón Steinsson

Journal of Economic Perspectives 2018 10.1257/jep.32.3.59

Showing 50 of 69 references

Cited By

553

The impact of increasing labour market rigidity on employment growth in OECD countries

Rasmus Wiese, João Tovar Jalles · 2025

Economic Analysis and Policy

Local Projections

ÒSCAR JORDÀ, Alan M. Taylor · 2025

Journal of Economic Literature

Bias in local projections

Edward P. Herbst, Benjamin K. Johannsen · 2024

Journal of Econometrics

Local Projections and VARs Estimate the Same Impulse Responses

Mikkel Plagborg-Møller, Christian K. Wolf · 2021

Econometrica

Household debt, consumption and inequality

Berrak Bahadir, Kuhelika De · 2020

Journal of International Money and...

Metrics

553

Citations

69

References

Details

Published: Jan 01, 2021
Vol/Issue: 89(2)
Pages: 955-980

Authors

M

Mikkel Plagborg-Møller

Department of Economics, Princeton University

C

Christian K. Wolf

Becker Friedman Institute, University of Chicago

Funding

National Science Foundation

Cite This Article

Mikkel Plagborg-Møller, Christian K. Wolf (2021). Local Projections and VARs Estimate the Same Impulse Responses. Econometrica, 89(2), 955-980. https://doi.org/10.3982/ecta17813

Local Projections and VARs Estimate the Same Impulse Responses

You May Also Like