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Local Projections and VARs Estimate the Same Impulse Responses

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  • Mikkel Plagborg‐Møller
  • Christian K. Wolf

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.

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  • Mikkel Plagborg‐Møller & Christian K. Wolf, 2021. "Local Projections and VARs Estimate the Same Impulse Responses," Econometrica, Econometric Society, vol. 89(2), pages 955-980, March.
    • Handle: RePEc:wly:emetrp:v:89:y:2021:i:2:p:955-980
    DOI: 10.3982/ECTA17813
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    1. Christina D. Romer & David H. Romer, 2004. "A New Measure of Monetary Shocks: Derivation and Implications," American Economic Review, American Economic Association, vol. 94(4), pages 1055-1084, September.
    2. Karel Mertens & Morten O. Ravn, 2013. "The Dynamic Effects of Personal and Corporate Income Tax Changes in the United States," American Economic Review, American Economic Association, vol. 103(4), pages 1212-1247, June.
    3. Blanchard, Olivier Jean & Quah, Danny, 1989. "The Dynamic Effects of Aggregate Demand and Supply Disturbances," American Economic Review, American Economic Association, vol. 79(4), pages 655-673, September.
    4. Uhlig, Harald, 2005. "What are the effects of monetary policy on output? Results from an agnostic identification procedure," Journal of Monetary Economics, Elsevier, vol. 52(2), pages 381-419, March.
    5. Valerie A. Ramey, 2011. "Identifying Government Spending Shocks: It's all in the Timing," The Quarterly Journal of Economics, Oxford University Press, vol. 126(1), pages 1-50.
    6. Guillaume Chevillon, 2007. "Direct Multi‐Step Estimation And Forecasting," Journal of Economic Surveys, Wiley Blackwell, vol. 21(4), pages 746-785, September.
    7. Lawrence J. Christiano & Martin Eichenbaum & Robert Vigfusson, 2006. "Alternative Procedures for Estimating Vector Autoregressions Identified with Long-Run Restrictions," Journal of the European Economic Association, MIT Press, vol. 4(2-3), pages 475-483, 04-05.
    8. Juan F. Rubio-Ramírez & Daniel F. Waggoner & Tao Zha, 2010. "Structural Vector Autoregressions: Theory of Identification and Algorithms for Inference," Review of Economic Studies, Oxford University Press, vol. 77(2), pages 665-696.
    9. Marcellino, Massimiliano & Stock, James H. & Watson, Mark W., 2006. "A comparison of direct and iterated multistep AR methods for forecasting macroeconomic time series," Journal of Econometrics, Elsevier, vol. 135(1-2), pages 499-526.
    10. Alloza, Mario & Gonzalo Muñoz, Jesus & Sanz, Carlos, 2019. "Dynamic Effects of Persistent Shocks," UC3M Working papers. Economics 29187, Universidad Carlos III de Madrid. Departamento de Economía.
    11. Silvia Miranda Agrippino & Giovanni Ricco, 2018. "Identification with external instruments in structural VARs under partial invertibility," Sciences Po publications 24, Sciences Po.
    12. Atsushi Inoue & Lutz Kilian, 2002. "Bootstrapping Smooth Functions of Slope Parameters and Innovation Variances in VAR (∞) Models," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 43(2), pages 309-332, May.
    13. Issler, João Victor & Linton, Oliver & Timmermann, Allan, 2011. "Annals issue on forecasting--Guest editors' introduction," Journal of Econometrics, Elsevier, vol. 164(1), pages 1-3, September.
    14. James H. Stock & Mark W. Watson, 2012. "Disentangling the Channels of the 2007-09 Recession," Brookings Papers on Economic Activity, Economic Studies Program, The Brookings Institution, vol. 43(1 (Spring), pages 81-156.
    15. Mario Forni & Luca Gambetti & Luca Sala, 2019. "Structural VARs and noninvertible macroeconomic models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 34(2), pages 221-246, March.
    16. Sylvain Leduc & Daniel Wilson, 2017. "Are State Governments Roadblocks to Federal Stimulus? Evidence on the Flypaper Effect of Highway Grants in the 2009 Recovery Act," American Economic Journal: Economic Policy, American Economic Association, vol. 9(2), pages 253-292, May.
    17. Marek Jarociński & Peter Karadi, 2020. "Deconstructing Monetary Policy Surprises—The Role of Information Shocks," American Economic Journal: Macroeconomics, American Economic Association, vol. 12(2), pages 1-43, April.
    18. Mikkel Plagborg-Møller & Christian K. Wolf, 2021. "Instrumental Variable Identification of Dynamic Variance Decompositions," Working Papers 2021-40, Princeton University. Economics Department..
    19. James H. Stock & Mark W. Watson, 2018. "Identification and Estimation of Dynamic Causal Effects in Macroeconomics Using External Instruments," Economic Journal, Royal Economic Society, vol. 128(610), pages 917-948, May.
    20. Sims, Christopher A, 1980. "Macroeconomics and Reality," Econometrica, Econometric Society, vol. 48(1), pages 1-48, January.
    21. Joshua D. Angrist & Jörn-Steffen Pischke, 2009. "Mostly Harmless Econometrics: An Empiricist's Companion," Economics Books, Princeton University Press, edition 1, number 8769.
    22. √Íscar Jord√Ä & Moritz Schularick & Alan M. Taylor, 2013. "When Credit Bites Back," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 45(s2), pages 3-28, December.
    23. Lutz Kilian & Daniel P. Murphy, 2012. "Why Agnostic Sign Restrictions Are Not Enough: Understanding The Dynamics Of Oil Market Var Models," Journal of the European Economic Association, European Economic Association, vol. 10(5), pages 1166-1188, October.
    24. Andrea Carriero & Haroon Mumtaz & Konstantinos Theodoridis & Angeliki Theophilopoulou, 2015. "The Impact of Uncertainty Shocks under Measurement Error: A Proxy SVAR Approach," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 47(6), pages 1223-1238, September.
    25. Lewis, Richard & Reinsel, Gregory C., 1985. "Prediction of multivariate time series by autoregressive model fitting," Journal of Multivariate Analysis, Elsevier, vol. 16(3), pages 393-411, June.
    26. Lawrence J. Christiano & Martin Eichenbaum & Charles L. Evans, 2005. "Nominal Rigidities and the Dynamic Effects of a Shock to Monetary Policy," Journal of Political Economy, University of Chicago Press, vol. 113(1), pages 1-45, February.
    27. Mark Gertler & Peter Karadi, 2015. "Monetary Policy Surprises, Credit Costs, and Economic Activity," American Economic Journal: Macroeconomics, American Economic Association, vol. 7(1), pages 44-76, January.
    28. Lutz Kilian, 2009. "Not All Oil Price Shocks Are Alike: Disentangling Demand and Supply Shocks in the Crude Oil Market," American Economic Review, American Economic Association, vol. 99(3), pages 1053-1069, June.
    29. Pesaran, M. Hashem & Pick, Andreas & Timmermann, Allan, 2011. "Variable selection, estimation and inference for multi-period forecasting problems," Journal of Econometrics, Elsevier, vol. 164(1), pages 173-187, September.
    30. Jean-Marie Dufour & Eric Renault, 1998. "Short Run and Long Run Causality in Time Series: Theory," Econometrica, Econometric Society, vol. 66(5), pages 1099-1126, September.
    31. Mertens, Elmar, 2012. "Are spectral estimators useful for long-run restrictions in SVARs?," Journal of Economic Dynamics and Control, Elsevier, vol. 36(12), pages 1831-1844.
    32. Schorfheide, Frank, 2005. "VAR forecasting under misspecification," Journal of Econometrics, Elsevier, vol. 128(1), pages 99-136, September.
    33. Choi, Chi-Young & Chudik, Alexander, 2019. "Estimating impulse response functions when the shock series is observed," Economics Letters, Elsevier, vol. 180(C), pages 71-75.
    34. Newey, Whitney K, 1994. "The Asymptotic Variance of Semiparametric Estimators," Econometrica, Econometric Society, vol. 62(6), pages 1349-1382, November.
    35. Pascal Paul, 2020. "The Time-Varying Effect of Monetary Policy on Asset Prices," The Review of Economics and Statistics, MIT Press, vol. 102(4), pages 690-704, October.
    36. Lutz Kilian & Robert J. Vigfusson, 2011. "Are the responses of the U.S. economy asymmetric in energy price increases and decreases?," Quantitative Economics, Econometric Society, vol. 2(3), pages 419-453, November.
    37. Frank Smets & Rafael Wouters, 2007. "Shocks and Frictions in US Business Cycles: A Bayesian DSGE Approach," American Economic Review, American Economic Association, vol. 97(3), pages 586-606, June.
    38. Kilian,Lutz & Lütkepohl,Helmut, 2018. "Structural Vector Autoregressive Analysis," Cambridge Books, Cambridge University Press, number 9781107196575, November.
    39. Simon Gilchrist & Egon Zakrajsek, 2012. "Credit Spreads and Business Cycle Fluctuations," American Economic Review, American Economic Association, vol. 102(4), pages 1692-1720, June.
    40. Mikkel Plagborg-M{o}ller & Christian K. Wolf, 2020. "Instrumental Variable Identification of Dynamic Variance Decompositions," Papers 2011.01380, arXiv.org, revised Jul 2021.
    41. Tucker McElroy, 2015. "When are Direct Multi‐step and Iterative Forecasts Identical?," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 34(4), pages 315-336, July.
    42. Luca Brugnolini, 2018. "About Local Projection Impulse Response Function Reliability," CEIS Research Paper 440, Tor Vergata University, CEIS, revised 09 Jun 2018.
    43. Sydney C. Ludvigson & Sai Ma & Serena Ng, 2020. "COVID-19 and The Macroeconomic Effects of Costly Disasters," NBER Working Papers 26987, National Bureau of Economic Research, Inc.
    44. Valerie A. Ramey & Sarah Zubairy, 2018. "Government Spending Multipliers in Good Times and in Bad: Evidence from US Historical Data," Journal of Political Economy, University of Chicago Press, vol. 126(2), pages 850-901.
    45. Gafarov, Bulat & Meier, Matthias & Montiel Olea, José Luis, 2018. "Delta-method inference for a class of set-identified SVARs," Journal of Econometrics, Elsevier, vol. 203(2), pages 316-327.
    46. Barakchian, S. Mahdi & Crowe, Christopher, 2013. "Monetary policy matters: Evidence from new shocks data," Journal of Monetary Economics, Elsevier, vol. 60(8), pages 950-966.
    47. Lutz Kilian & Yun Jung Kim, 2011. "How Reliable Are Local Projection Estimators of Impulse Responses?," The Review of Economics and Statistics, MIT Press, vol. 93(4), pages 1460-1466, November.
    48. Emi Nakamura & Jón Steinsson, 2018. "Identification in Macroeconomics," Journal of Economic Perspectives, American Economic Association, vol. 32(3), pages 59-86, Summer.
    49. Miranda-Agrippino, Silvia & Ricco, Giovanni, 2019. "Identification with External Instruments in Structural VARs under Partial Invertibility," The Warwick Economics Research Paper Series (TWERPS) 1213, University of Warwick, Department of Economics.
    50. Pao-Li Chang & Shinichi Sakata, 2007. "Estimation of impulse response functions using long autoregression," Econometrics Journal, Royal Economic Society, vol. 10(2), pages 453-469, July.
    51. James H. Stock & Mark W. Watson, 2012. "Disentangling the Channels of the 2007-09 Recession," Brookings Papers on Economic Activity, Economic Studies Program, The Brookings Institution, vol. 44(1 (Spring), pages 81-156.
    52. James H. Stock & Mark W. Watson, 2012. "Disentangling the Channels of the 2007-2009 Recession," NBER Working Papers 18094, National Bureau of Economic Research, Inc.
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    JEL classification:

    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C36 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Instrumental Variables (IV) Estimation

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