RWP 21-01, March 2021
It is well known that Local Projections (LP) residuals are autocorrelated. Conventional wisdom says that LP have to be estimated by OLS with Newey-West (or some type of Heteroskedastic and Autocorrelation Consistent (HAC)) standard errors and that GLS is not possible because the autocorrelation process is unknown and/or because the GLS estimator would be inconsistent. I derive the autocorrelation process of LP and show that it can be corrected for using a consistent GLS estimator. Estimating LP with GLS has three major implications: 1) LP GLS can be less biased, more efficient, and generally has better coverage properties than estimation by OLS with HAC standard errors. 2) Consistency of the LP GLS estimator gives a general counterexample showing that strict exogeneity is not a necessary condition for GLS. 3) Since the autocorrelation process can be modeled explicitly, it is now possible to estimate time-varying parameter LP.
JEL Classification: C32, C36
Article Citation
- Lusompa, Amaze. 2021. “Local Projections, Autocorrelation, and Efficiency.” Federal Reserve Bank of Kansas City, Research Working Paper no. 21-01, March. Available at External Linkhttps://doi.org/10.18651/RWP2021-01