De Vos, I. and Everaert, G. (2026). GLS estimation of local projections: Trading robustness for efficiency Journal of Econometrics, 253:1--20.

Local projections (LPs) are widely used for estimating impulse responses (IRs) as they are considered more robust to model misspecification than forward-iterated IRs from dynamic models such as VARs. However, this robustness comes at the cost of higher variance, particularly at longer horizons. To mitigate this trade-off, several GLS transformations of LPs have been proposed. This paper analyzes two broad strands of GLS-type LP estimators: those that condition on residuals from an auxiliary VAR, and those that condition on residuals from previous-horizon LPs. We show that the former impose a VAR structure, which leads them to align with VAR IRs, while the latter preserve the unrestricted nature of LPs but end up replicating LP OLS estimates. Consequently, the intended efficiency gains are either not achieved or come at the expense of the very robustness that motivates the use of LPs.