In this recent paper, Olea, Plagborg-Møller, Qian and Wolf “provide a formal proof of Jordà’s claim that conventional LP confidence intervals for impulse responses are surprisingly robust to misspecification.” The paper demonstrates the superiority of LP’s impulse responses function versus VAR’s impulse response functions (quotes are italics).
Olea, J. L. M., Plagborg-Møller, M., Qian, E., & Wolf, C. K. (2024). Double Robustness of Local Projections and Some Unpleasant VARithmetic (No. w32495). National Bureau of Economic Research.
https://www.nber.org/papers/w32495
“In general, the only way to guarantee robustness of conventional VAR inference is thus to include so many lags that the VAR estimator is asymptotically equivalent with LP. If instead the VAR confidence interval is much shorter (as is typically the case in applied practice), then VAR confidence intervals will severely undercover even for a misspecification term that: (i) is small in magnitude; (ii) has dynamic properties that cannot be ruled out ex ante based on economic theory; and (iii) is difficult to detect ex post with model specification tests. Instead of increasing the lag length, coverage can also be restored by using a larger bias-aware critical value (Armstrong and Kolesár, 2021), but we show that the resulting confidence intervals are so wide that one may as well report the LP interval.”
The recommendations for applied researchers:
- When the goal is to construct confidence intervals for impulse responses that have accurate coverage in a wide range of empirically relevant DGPs—as opposed to minimizing MSE— then the smaller bias of LPs documented in simulations by Li, Plagborg-Møller, and Wolf (2024) is more valuable than the smaller variance enjoyed by VAR estimators.
- Researchers who use LP should control for those lags of the data that are strong predictors of the outcome or impulse variables. This is important even if the researcher directly observes a near-perfect proxy for the shock of interest. However, it is not necessary to get the lag length exactly right to achieve correct coverage. To select the number of lags to control for in the LP, it suffices to run a VAR in all variables used in the analysis and select the lag length that minimizes conventional information criteria (such as AIC). Our results complement the finding of Montiel Olea and Plagborg-Møller (2021) that lag-augmented LP confidence intervals are also more robust than VAR intervals to persistence in the data and to the length of the impulse response horizon.
- There is no free lunch for VARs: if an estimated VAR yields confidence intervals that are substantially narrower than the corresponding LP intervals, we recommend increasing the VAR lag length until that is no longer the case, to guarantee robust confidence interval coverage. Conventional tests of correct VAR specification do not suffice to guard against coverage distortions.
The bold letters are mine. The LP are more valuable as they provide correct coverage (lower bias). In addition, LP are more robust for confidence intervals than VAR for persistent data and for the horizon of the impulse response. The LPs are robust to misspecification, while VARs are not. From the third take-away, you may think that should always use LPs if you think that your model suffers from various form misspecification…