Working Paper

Local Projections, Autocorrelation, and Efficiency

Abstract: 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.

Keywords: Local Projections; Generalized Least Squares;

JEL Classification: C32; C36;

https://doi.org/10.18651/RWP2021-01

Bibliographic Information

Provider: Federal Reserve Bank of Kansas City

Part of Series: Research Working Paper

Publication Date: 2021-03-03

Number: RWP 21-01