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Local Projections or VARs? A Primer for Macroeconomists

In: NBER Macroeconomics Annual 2025, volume 40

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  • José Luis Montiel Olea
  • Mikkel Plagborg-Møller
  • Eric Qian
  • Christian K. Wolf

Abstract

What should applied macroeconomists know about local projection (LP) and vector autoregression (VAR) impulse response estimators? The two methods share the same estimand, but in finite samples lie on opposite ends of a bias-variance trade-off. While the low bias of LPs comes at a quite steep variance cost, this cost must be paid to achieve robust uncertainty assessments. Hence, when the goal is to convey what can be learned about dynamic causal effects from the data, VARs should only be used with long lag lengths, ensuring equivalence with LP. For LP estimation, we provide guidance on selection of lag length and controls, bias correction, and confidence interval construction.
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Suggested Citation

  • José Luis Montiel Olea & Mikkel Plagborg-Møller & Eric Qian & Christian K. Wolf, 2025. "Local Projections or VARs? A Primer for Macroeconomists," NBER Chapters, in: NBER Macroeconomics Annual 2025, volume 40, National Bureau of Economic Research, Inc.
    • Handle: RePEc:nbr:nberch:15140
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    References listed on IDEAS

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    1. 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.
    2. ChaeWon Baek & Byoungchan Lee, 2022. "A Guide to Autoregressive Distributed Lag Models for Impulse Response Estimations," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 84(5), pages 1101-1122, October.
    3. Braun, Phillip A. & Mittnik, Stefan, 1993. "Misspecifications in vector autoregressions and their effects on impulse responses and variance decompositions," Journal of Econometrics, Elsevier, vol. 59(3), pages 319-341, October.
    4. Dake Li & Mikkel Plagborg-Møller & Christian K. Wolf, 2021. "Local Projections vs. VARs: Lessons From Thousands of DGPs," Working Papers 2021-55, Princeton University. Economics Department..
    5. Li, Dake & Plagborg-Møller, Mikkel & Wolf, Christian K., 2024. "Local projections vs. VARs: Lessons from thousands of DGPs," Journal of Econometrics, Elsevier, vol. 244(2).
    6. 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.
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    Cited by:

    1. Sarah Vella, 2025. "Constructing a country-specific indicator for cyclical systemic risk," Economic Change and Restructuring, Springer, vol. 58(3), pages 1-63, June.
    2. Andrea Recine & Massimiliano Tancioni, 2025. "Macroeconomic Effects of Government Defense and Non-Defense R&D," Working Papers in Public Economics 262, Department of Economics and Law, Sapienza University of Roma.

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    More about this item

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • 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

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