LocalProjections.jl

Local projection methods for impulse response estimation

LocalProjections.jl is a Julia package for estimating impulse response functions with local projection methods. It follows the latest development in the econometric literature and pursues reliable and efficient implementation.

Features

A growing list of features includes the following:

Ordinary least squares local projections as in Jordà (2005)
Instrumental variable (LP-IV) estimation and unit effect normalization as in Stock and Watson (2018)
Smooth local projections as in Barnichon and Brownlees (2019)
Equal-weighted cosine (EWC) test for HAR inference as in Lazarus et al. (2018)

Quick Start

Example data are included in this package for convenience.

To reproduce the empirical illustration from Barnichon and Brownlees (2019):

using LocalProjections, CSV
# Read example data from Barnichon and Brownlees (2019)
df = CSV.File(datafile(:bb))
# Specify names of the regressors
ns = (:ir, :pi, :yg)
# Specify the smooth local projection estimator
est = SmoothLP(:ir, 3, 2, search=grid(194.0.*(1:0.5:10)), criterion=LOOCV())
# Conduct the estimation with the default variance-covariance estimator
r = lp(est, df, :yg, xnames=ns, wnames=ns, nlag=4, nhorz=20, minhorz=1)
# Collect the estimated impulse response function
f = irf(r, :yg, :ir)

To reproduce the cumulative multipliers from Ramey and Zubairy (2018):

using LocalProjections, CSV
# Read example data from Ramey and Zubairy (2018)
df = CSV.File(datafile(:rz))
# Replicate results in their Table 1 (baseline linear specification with news shock)
r = lp(df, Cum(:y), xnames=Cum(:g), wnames=(:newsy, :y, :g), iv=Cum(:g)=>:newsy,
    nlag=4, nhorz=17, addylag=false, firststagebyhorz=true)
f = irf(r, Cum(:y), Cum(:g))

References

Barnichon, Regis and Christian Brownlees. 2019. "Impulse Response Estimation by Smooth Local Projections." The Review of Economics and Statistics 101 (3): 522-530.

Jordà, Òscar. 2005. "Estimation and Inference of Impulse Responses by Local Projections." American Economic Review 95 (1): 161-182.

Lazarus, Eben, Daniel J. Lewis, James H. Stock, and Mark W. Watson. 2018. "HAR Inference: Recommendations for Practice." Journal of Business & Economic Statistics 36 (4): 541-559.

Li, Dake, Mikkel Plagborg-Møller and Christian K. Wolf. 2021. "Local Projections vs. VARs: Lessons from Thousands of DGPs." Unpublished.

Montiel Olea, José Luis and Mikkel Plagborg-Møller. 2021. "Local Projection Inference is Simpler and More Robust Than You Think." Econometrica 89 (4): 1789-1823.

Plagborg-Møller, Mikkel and Christian K. Wolf. 2021. "Local Projections and VARs Estimate the Same Impulse Responses." Econometrica 89 (2): 955-980.

Ramey, Valerie A. and Sarah Zubairy. 2018. "Government Spending Multipliers in Good Times and in Bad: Evidence from US Historical Data." Journal of Political Economy 126 (2): 850-901.

Stock, James H. and Mark W. Watson. 2018. "Identification and Estimation of Dynamic Causal Effects in Macroeconomics Using External Instruments." The Economic Journal 128 (610): 917-948.