GLS Estimation of Local Projections: Trading Robustness for Efficiency

Local projections (LPs) are often regarded as more robust to model misspecification than impulse responses (IRs) derived from forward-iterated dynamic model estimates, as LPs impose fewer restrictions on the underlying dynamics. However, because forecast errors accumulate in the LP errors over the projection horizon, this robustness comes at the price of an increase in variance. To address this, several Generalized Least Squares (GLS) estimators have been proposed to reduce error accumulation and enhance efficiency. We demonstrate, however, that the implied conditioning on dynamic model (horizon-one LP) residuals imposes strong restrictions on the underlying data generating process, undermining the very robustness to misspecification that LPs are valued for. In fact, we show that these GLS LP estimators tend to align more closely with forward-iterated IRs from potentially misspecified models, than with OLS-estimated LPs. Furthermore, we find that conditioning on previous horizon LP residuals fails to deliver efficiency improvements over OLS-estimated LPs.