Local Projections, Autocorrelation, and Efficiency

It is well known that Local Projections (LP) residuals are autocorrelated. Conventional wisdom says that LP have to be estimated by OLS with Newey and West (1987) (or some type of Heteroskedastic and Autocorrelation Consistent (HAC)) standard errors and that GLS is not possible because the autocorrelation process is unknown. I show that the autocorrelation process of LP is known and that autocorrelation can be corrected for using GLS. Estimating LP with GLS has three major implications: 1) LP GLS can be substantially more efficient and less biased than estimation by OLS with Newey-West standard errors. 2) Since the autocorrelation process can be modeled explicitly, it is possible to give a fully Bayesian treatment of LP. That is, LP can be estimated using frequentist/classical or fully Bayesian methods. 3) Since the autocorrelation process can be modeled explicitly, it is now possible to estimate time-varying parameter LP.