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Differences From Differencing: Should Local Projections With Observed Shocks Be Estimated in Levels or Differences?

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  • Jeremy Piger
  • Thomas Stockwell

Abstract

We show there are large finite‐sample estimation improvements from estimating local projections (LP) in a cumulated differences (long‐differenced) specification vs. a specification in levels when the impulse response of interest is to an externally identified (“observed”) shock. The long‐differenced specification substantially reduces, and in many cases eliminates, estimation bias, as well as significantly improves confidence interval coverage. These improvements increase for more persistent processes, at longer horizons, and for smaller sample sizes and extend to the instrumental variable LP (LP‐IV) setting where the observed shock is an instrument for an endogenous variable of interest. We demonstrate these results via simulations as well as illustrative analytic results.

Suggested Citation

  • Jeremy Piger & Thomas Stockwell, 2025. "Differences From Differencing: Should Local Projections With Observed Shocks Be Estimated in Levels or Differences?," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 40(7), pages 759-787, November.
    • Handle: RePEc:wly:japmet:v:40:y:2025:i:7:p:759-787
    DOI: 10.1002/jae.70003
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    Cited by:

    1. Eric Fortier, 2026. "Specification Choice in Local Projections: Evidence from Monetary Policy Shocks," Discussion Papers dp26-01, Department of Economics, Simon Fraser University.
    2. Mavrogiannis, Christos & Tagkalakis, Athanasios, 2025. "The effects of structural reforms on gross capital inflows in OECD countries," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 104(C).
    3. Marc Burri & Daniel Kaufmann, 2026. "Multiple monetary policy shocks from daily data: A heteroskedasticity IV approach," IRENE Working Papers 26-06, IRENE Institute of Economic Research.

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