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Opening the black box of local projections

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  • Klieber, Karin
  • Coulombe, Philippe Goulet

Abstract

Local projections (LPs) are widely used in empirical macroeconomics to estimate impulse responses to policy interventions. Yet, in many ways, they are black boxes. It is often unclear what mechanism or historical episodes drive a particular estimate. We introduce a new decomposition of LP estimates into the sum of contributions of historical events, which is the product, for each time stamp, of a weight and the realization of the response variable. In the least squares case, we show that these weights admit two interpretations. First, they represent purified and standardized shocks. Second, they serve as proximity scores between the projected policy intervention and past interventions in the sample. Notably, this second interpretation extends naturally to machine learning methods, many of which yield impulse responses that, while nonlinear in predictors, still aggregate past outcomes linearly via proximity-based weights. Applying this framework to shocks in monetary and fiscal policy, global temperature, and the excess bond premium, we find that easily identifiable events—such as Nixon’s interference with the Fed, stagflation, World War II, and the Mount Agung volcanic eruption—emerge as dominant drivers of oftenheavily concentrated impulse response estimates. JEL Classification: C32, C53, E31, E52, E62

Suggested Citation

  • Klieber, Karin & Coulombe, Philippe Goulet, 2025. "Opening the black box of local projections," Working Paper Series 3105, European Central Bank.
  • Handle: RePEc:ecb:ecbwps:20253105
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    1. Alan J. Auerbach & Yuriy Gorodnichenko, 2012. "Measuring the Output Responses to Fiscal Policy," American Economic Journal: Economic Policy, American Economic Association, vol. 4(2), pages 1-27, May.
    2. 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.
    3. Markus K. Brunnermeier & Yuliy Sannikov, 2014. "A Macroeconomic Model with a Financial Sector," American Economic Review, American Economic Association, vol. 104(2), pages 379-421, February.
    4. Hidehiko Ichimura & Whitney K. Newey, 2022. "The influence function of semiparametric estimators," Quantitative Economics, Econometric Society, vol. 13(1), pages 29-61, January.
    5. Valerie A. Ramey, 2011. "Identifying Government Spending Shocks: It's all in the Timing," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 126(1), pages 1-50.
    6. Christiano, Lawrence J & Eichenbaum, Martin & Evans, Charles, 1996. "The Effects of Monetary Policy Shocks: Evidence from the Flow of Funds," The Review of Economics and Statistics, MIT Press, vol. 78(1), pages 16-34, February.
    7. Victor Chernozhukov & Denis Chetverikov & Mert Demirer & Esther Duflo & Christian Hansen & Whitney Newey & James Robins, 2018. "Double/debiased machine learning for treatment and structural parameters," Econometrics Journal, Royal Economic Society, vol. 21(1), pages 1-68, February.
    8. Joshua D. Angrist & Òscar Jordà & Guido M. Kuersteiner, 2018. "Semiparametric Estimates of Monetary Policy Effects: String Theory Revisited," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 36(3), pages 371-387, July.
    9. Ben S. Bernanke & Mark Gertler & Mark Watson, 1997. "Systematic Monetary Policy and the Effects of Oil Price Shocks," Brookings Papers on Economic Activity, Economic Studies Program, The Brookings Institution, vol. 28(1), pages 91-157.
    10. Angrist, Joshua D. & Krueger, Alan B., 1999. "Empirical strategies in labor economics," Handbook of Labor Economics, in: O. Ashenfelter & D. Card (ed.), Handbook of Labor Economics, edition 1, volume 3, chapter 23, pages 1277-1366, Elsevier.
    11. Haroon Mumtaz & Michele Piffer, 2022. "Impulse response estimation via flexible local projections," Papers 2204.13150, arXiv.org.
    12. Michael W. McCracken & Serena Ng, 2016. "FRED-MD: A Monthly Database for Macroeconomic Research," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 34(4), pages 574-589, October.
    13. Drechsel, Thomas, 2023. "Estimating the Effects of Political Pressure on the Fed: A Narrative Approach with New Data," CEPR Discussion Papers 18612, C.E.P.R. Discussion Papers.
    14. Aruoba, Boragan & Drechsel, Thomas, 2022. "Identifying Monetary Policy Shocks: A Natural Language Approach," CEPR Discussion Papers 17133, C.E.P.R. Discussion Papers.
    15. Christiano, Lawrence J. & Eichenbaum, Martin & Evans, Charles L., 1999. "Monetary policy shocks: What have we learned and to what end?," Handbook of Macroeconomics, in: J. B. Taylor & M. Woodford (ed.), Handbook of Macroeconomics, edition 1, volume 1, chapter 2, pages 65-148, Elsevier.
    16. Adrien Bilal & Diego R. Känzig, 2024. "The Macroeconomic Impact of Climate Change: Global vs. Local Temperature," NBER Working Papers 32450, National Bureau of Economic Research, Inc.
    17. Hauzenberger, Niko & Huber, Florian & Klieber, Karin & Marcellino, Massimiliano, 2025. "Machine learning the macroeconomic effects of financial shocks," Economics Letters, Elsevier, vol. 250(C).
    18. Nadav Ben Zeev & Valerie A. Ramey & Sarah Zubairy, 2023. "Do Government Spending Multipliers Depend on the Sign of the Shock?," AEA Papers and Proceedings, American Economic Association, vol. 113, pages 382-387, May.
    19. Regis Barnichon & Christian Matthes & Alexander Ziegenbein, 2022. "Are the Effects of Financial Market Disruptions Big or Small?," The Review of Economics and Statistics, MIT Press, vol. 104(3), pages 557-570, May.
    20. Alberto Alesina & Francesco Giavazzi, 2012. "Introduction to "Fiscal Policy after the Financial Crisis"," NBER Chapters, in: Fiscal Policy after the Financial Crisis, pages 1-18, National Bureau of Economic Research, Inc.
    21. Philippe Goulet Coulombe & Maxime Leroux & Dalibor Stevanovic & Stéphane Surprenant, 2022. "How is machine learning useful for macroeconomic forecasting?," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 37(5), pages 920-964, August.
    22. Nadav Ben Zeev & Evi Pappa, 2017. "Chronicle of a War Foretold: The Macroeconomic Effects of Anticipated Defence Spending Shocks," Economic Journal, Royal Economic Society, vol. 127(603), pages 1568-1597, August.
    23. Emi Nakamura & Jón Steinsson, 2018. "High-Frequency Identification of Monetary Non-Neutrality: The Information Effect," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 133(3), pages 1283-1330.
    24. Haroon Mumtaz & Michele Piffer, 2022. "Impulse response estimation via fexible local projections," Working Papers 938, Queen Mary University of London, School of Economics and Finance.
    25. Gonçalves, Sílvia & Herrera, Ana María & Kilian, Lutz & Pesavento, Elena, 2024. "State-dependent local projections," Journal of Econometrics, Elsevier, vol. 244(2).
    26. Philippe Goulet Coulombe, 2024. "The macroeconomy as a random forest," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 39(3), pages 401-421, April.
    27. Silvia Goncalves & Ana María Herrera & Lutz Kilian & Elena Pesavento, 2024. "Nonparametric Local Projections," Working Papers 2414, Federal Reserve Bank of Dallas.
    28. Sergio Firpo & Nicole M. Fortin & Thomas Lemieux, 2009. "Unconditional Quantile Regressions," Econometrica, Econometric Society, vol. 77(3), pages 953-973, May.
    29. 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.
    30. Ben S. Bernanke & Jean Boivin & Piotr Eliasz, 2005. "Measuring the Effects of Monetary Policy: A Factor-Augmented Vector Autoregressive (FAVAR) Approach," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 120(1), pages 387-422.
    31. 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.
    32. Marcus Buckmann & Andreas Joseph, 2023. "An Interpretable Machine Learning Workflow with an Application to Economic Forecasting," International Journal of Central Banking, International Journal of Central Banking, vol. 19(4), pages 449-522, October.
    33. 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.
    34. James Cloyne & Òscar Jordà & Alan M. Taylor, 2023. "State-Dependent Local Projections: Understanding Impulse Response Heterogeneity," Working Paper Series 2023-05, Federal Reserve Bank of San Francisco.
    35. Jeffrey C. Chen & Abe Dunn & Kyle Hood & Alexander Driessen & Andrea Batch, 2019. "Off to the Races: A Comparison of Machine Learning and Alternative Data for Predicting Economic Indicators," NBER Chapters, in: Big Data for Twenty-First-Century Economic Statistics, pages 373-402, National Bureau of Economic Research, Inc.
    36. Alan J. Auerbach & Yuriy Gorodnichenko, 2013. "Corrigendum: Measuring the Output Responses to Fiscal Policy," American Economic Journal: Economic Policy, American Economic Association, vol. 5(3), pages 320-322, August.
    37. Daniel Borup & Philippe Goulet Coulombe & Erik Christian Montes Schütte & David E. Rapach & Sander Schwenk-Nebbe, 2022. "The Anatomy of Out-of-Sample Forecasting Accuracy," FRB Atlanta Working Paper 2022-16, Federal Reserve Bank of Atlanta.
    38. Brissimis, Sophocles N. & Magginas, Nicholas S., 2006. "Forward-looking information in VAR models and the price puzzle," Journal of Monetary Economics, Elsevier, vol. 53(6), pages 1225-1234, September.
    39. Mario Forni & Luca Gambetti & Nicolò Maffei‐Faccioli & Luca Sala, 2024. "Nonlinear Transmission of Financial Shocks: Some New Evidence," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 56(1), pages 5-33, February.
    40. Lin, Yi & Jeon, Yongho, 2006. "Random Forests and Adaptive Nearest Neighbors," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 578-590, June.
    41. Simon Gilchrist & Egon Zakrajsek, 2012. "Credit Spreads and Business Cycle Fluctuations," American Economic Review, American Economic Association, vol. 102(4), pages 1692-1720, June.
    42. repec:cdl:econwp:qt8w31z6qx is not listed on IDEAS
    43. Whitney Newey & Kenneth West, 2014. "A simple, positive semi-definite, heteroscedasticity and autocorrelation consistent covariance matrix," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 33(1), pages 125-132.
    44. Marcelo C. Medeiros & Gabriel F. R. Vasconcelos & Álvaro Veiga & Eduardo Zilberman, 2021. "Forecasting Inflation in a Data-Rich Environment: The Benefits of Machine Learning Methods," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 39(1), pages 98-119, January.
    45. Geert Mesters & Régis Barnichon, 2025. "Innovations Meet Narratives -Improving the Power-Credibility Trade-off in Macro," Working Papers 1475, Barcelona School of Economics.
    46. Nordhaus, William D., 1993. "Rolling the 'DICE': an optimal transition path for controlling greenhouse gases," Resource and Energy Economics, Elsevier, vol. 15(1), pages 27-50, March.
    47. Philippe Goulet Coulombe & Maximilian Goebel & Karin Klieber, 2024. "Dual Interpretation of Machine Learning Forecasts," Papers 2412.13076, arXiv.org.
    48. Emi Nakamura & Jón Steinsson, 2018. "Identification in Macroeconomics," Journal of Economic Perspectives, American Economic Association, vol. 32(3), pages 59-86, Summer.
    49. Yuriy Gorodnichenko & Byoungchan Lee, 2020. "Forecast Error Variance Decompositions with Local Projections," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 38(4), pages 921-933, October.
    50. Melissa Dell & Benjamin F. Jones & Benjamin A. Olken, 2012. "Temperature Shocks and Economic Growth: Evidence from the Last Half Century," American Economic Journal: Macroeconomics, American Economic Association, vol. 4(3), pages 66-95, July.
    51. Nathan S. Balke & Kenneth M. Emery, 1994. "Understanding the price puzzle," Economic and Financial Policy Review, Federal Reserve Bank of Dallas, issue Q IV, pages 15-26.
    52. Nadav Ben Zeev & Evi Pappa, 2017. "Chronicle of a War Foretold: The Macroeconomic Effects of Anticipated Defence Spending Shocks," Economic Journal, Royal Economic Society, vol. 127(603), pages 1568-1597, August.
    53. 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.
    54. Hanson, Michael S., 2004. "The "price puzzle" reconsidered," Journal of Monetary Economics, Elsevier, vol. 51(7), pages 1385-1413, October.
    55. 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.
    56. Herbst, Edward P. & Johannsen, Benjamin K., 2024. "Bias in local projections," Journal of Econometrics, Elsevier, vol. 240(1).
    57. José Luis Montiel Olea & Mikkel Plagborg‐Møller, 2021. "Local Projection Inference Is Simpler and More Robust Than You Think," Econometrica, Econometric Society, vol. 89(4), pages 1789-1823, July.
    58. Yitzhaki, Shlomo, 1996. "On Using Linear Regressions in Welfare Economics," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(4), pages 478-486, October.
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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
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
    • E31 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Price Level; Inflation; Deflation
    • E52 - Macroeconomics and Monetary Economics - - Monetary Policy, Central Banking, and the Supply of Money and Credit - - - Monetary Policy
    • E62 - Macroeconomics and Monetary Economics - - Macroeconomic Policy, Macroeconomic Aspects of Public Finance, and General Outlook - - - Fiscal Policy; Modern Monetary Theory

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