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Local Projections and VARs Estimate the Same Impulse Responses

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  • Mikkel Plagborg-Møller

    (Princeton University)

  • Christian K. Wolf

    (Princeton University)

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 non-invertibility. (iv) Linear VARs are as robust to non-linearities as linear LPs.

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  • Mikkel Plagborg-Møller & Christian K. Wolf, 2020. "Local Projections and VARs Estimate the Same Impulse Responses," Working Papers 2020-16, Princeton University. Economics Department..
    • Handle: RePEc:pri:econom:2020-16
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    Keywords

    external instrument; impulse response function; local projection; proxy variable; structural vector autoregression;
    All these keywords.

    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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