Local Projections vs. VARs

Interesting paper, showing an interesting LP (higher variance) vs. VAR (higher bias) tradeoff.

The authors conclude that "Unless researchers are overwhelmingly concerned with bias, shrinkage via Bayesian VARs or penalized LPs is attractive."  

A key point in terms of whether researchers are "overwhelmingly concerned with bias" is that it's not so much about researchers' preferences (innate feelings about bias) as it is about the data -- dynamic environments with large moving-average roots force concern with bias, because that's where low-ordered VARs are poor approximations, injecting large amounts of bias.

So: Much depends on how important large moving-average roots are in macroeconomic dynamics.  In principle they can be be very important (so un-penalized LP may be attractive).  In practice, well, usually it seems not so much (in which case penalized LP may be attractive).

Local Projections vs. VARs: Lessons From Thousands of DGPs

By:	Dake Li; Mikkel Plagborg-M{\o}ller; Christian K. Wolf
Abstract:	We conduct a simulation study of Local Projection (LP) and Vector Autoregression (VAR) estimators of structural impulse responses across thousands of data generating processes (DGPs), designed to mimic the properties of the universe of U.S. macroeconomic data. Our analysis considers various structural identification schemes and several variants of LP and VAR estimators, and we pay particular attention to the role of the researcher's loss function. A clear bias-variance trade-off emerges: Because our DGPs are not exactly finite-order VAR models, LPs have lower bias than VAR estimators; however, the variance of LPs is substantially higher than that of VARs at intermediate or long horizons. Unless researchers are overwhelmingly concerned with bias, shrinkage via Bayesian VARs or penalized LPs is attractive.
Date:	2021–04
URL:	http://d.repec.org/n?u=RePEc:arx:papers:2104.00655&r=ets