Bias in Local Projections

35 Pages Posted: 14 May 2020

See all articles by Edward Herbst

Edward Herbst

Board of Governors of the Federal Reserve System

Benjamin K. Johannsen

Board of Governors of the Federal Reserve System

Date Written: January 31, 2020

Abstract

Local projections (LPs) are a popular tool in applied macroeconomic research. We survey the related literature and find that LPs are often used with very small samples in the time dimension. With small sample sizes, given the high degree of persistence in most macroeconomic data, impulse responses estimated by LPs can be severely biased. This is true even if the right-hand-side variable in the LP is iid, or if the data set includes a large cross-section (i.e., panel data). We derive a simple expression to elucidate the source of the bias. Our expression highlights the interdependence between coefficients of LPs at different horizons. As a byproduct, we propose a way to bias-correct LPs. Using U.S. macroeconomic data and identified monetary policy shocks, we demonstrate that the bias correction can be large.

Keywords: Local projections; Bias

JEL Classification: C20; E00

Suggested Citation

Herbst, Edward and Johannsen, Benjamin K., Bias in Local Projections (January 31, 2020). FEDS Working Paper No. 2020-010 https://doi.org/10.17016/FEDS.2020.010 , Available at SSRN: https://ssrn.com/abstract=3600410

Edward Herbst (Contact Author)

Board of Governors of the Federal Reserve System ( email )

20th Street and Constitution Avenue NW
Washington, DC 20551
United States

Benjamin K. Johannsen

Board of Governors of the Federal Reserve System ( email )

20th Street and Constitution Avenue NW
Washington, DC 20551
United States

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