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.

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)
• Cumulative effects and state dependency as in Ramey and Zubairy (2018)
• Panel local projections with fixed effects as in Jordà, Schularick and Taylor (2015)
• Smooth local projections as in Barnichon and Brownlees (2019)
• Equal-weighted cosine (EWC) test for HAR inference as in Lazarus et al. (2018)

Estimation for a given specification is conducted by calling the function lp. An impulse response function with respect to a specific variable is then obtained via irf. 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)
# By default, conduct least-squares estimation
# Lags for the outcome variable and variables in `wnames` are included automatically
r_ls = lp(df, :yg, xnames=ns, wnames=ns, nlag=4, nhorz=20, minhorz=1)
# Collect the estimated impulse response function with respect to ir
f_ls = irf(r_ls, :yg, :ir)

# For smooth local projections, specify the estimator
est = SmoothLP(:ir, 3, 2, search=grid(194.0.*(1:0.5:10)), criterion=LOOCV())
r_sm = lp(est, df, :yg, xnames=ns, wnames=ns, nlag=4, nhorz=20, minhorz=1)
f_sm = irf(r_sm, :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
# `Cum()` is for cumulative effects
r1 = lp(df, Cum(:y), xnames=Cum(:g), wnames=(:newsy, :y, :g), iv=Cum(:g)=>:newsy,
    nlag=4, nhorz=17, addylag=false, firststagebyhorz=true)
f1 = irf(r1, Cum(:y), Cum(:g))

# State-dependent specification with both news shock and Blanchard-Perotti shock
# Interactions with states are handled automatically for variables in `wnames`
# For other variables, interactions with states need to be constructed before calling `lp`
r2 = lp(df, Cum(:y), xnames=(Cum(:g,:rec), Cum(:g,:exp), :rec), wnames=(:newsy, :y, :g),
        iv=(Cum(:g,:rec), Cum(:g,:exp))=>(:recnewsy, :expnewsy, :recg, :expg),
        states=(:rec, :exp), nlag=4, nhorz=16, minhorz=1, addylag=false, firststagebyhorz=true)
# Collect the estimated impulse response functions in each state separately
f2rec = irf(r2, Cum(:y), Cum(:g,:rec))
f2exp = irf(r2, Cum(:y), Cum(:g,:exp))

For panel local projections, specify the variable identifying each unit:

using LocalProjections, CSV
# Example from Jordà's website using the macrohistory database
df = CSV.File(datafile(:jst))
ws = (:dlgrgdp, :dlgcpi, :dstir)
# Country fixed effects are included by default
# Compute cluster-robust standard errors via Vcov.jl
r = lp(df, :dlgrgdp, wnames=ws, nlag=3, nhorz=5, panelid=:iso, vce=cluster(:iso))
f = irf(r, :dlgrgdp, :dlgrgdp, lag=1)

For more details, enter the help mode.

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.

Jordà, Òscar., Moritz Schularick, and Alan M. Taylor. 2015. "Betting the House." Journal of International Economics 96 (S1): S2-S18.

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.