MATLAB code for large-scale simulation studies on impulse responses using Local Projections, VARs, and several of their variants.
Reference: Montiel Olea, José Luis, Mikkel Plagborg-Møller, Eric Qian and Christian K. Wolf (2025), ''Local Projections or VARs? A Primer for Macroeconomists''
Tested in: MATLAB R2024a on MacBook Pro 2023 (M3 Pro)
Using our code suite, our recommended procedure for computing local projection point estimates and confidence intervals is implemented below.
Use the AIC to select the lag length p by estimating auxiliary VARs of lag length 1 through p_max.
p_max = 20; % Maximum lag length
method = 1; % AIC
p = ic_var(data_y, p_max, method);
Below returns the local projection impulse response function irs of the second variable to the first innovation.
horzs = 0:20; % Horizons of interest
opts_lp = {'resp_ind', 2, 'innov_ind', 1, 'estimator', 'lp',...
'shrinkage', false,...
'bias_corr', true,... % Herbst and Johannsen (2024) bias correction
'alpha', 0.05,... % Significance level
'se_homosk', false}; % Eicker-Huber-White standard errors};
[irs, ses, cis] = ir_estim(data_y, p, horzs, opts_lp{:});
We recommend using the procedure of Herbst and Johannsen (2024) to bias-correct the LP estimator with heteroskedasticity-robust standard errors. Delta method standard errors and confidence intervals are stored in ses and cis respectively.
We find further finite-sample performance gains with the residual block bootstrap of Brüggemann, Jentsch, and Trenkler (2016) using the block length determined by Jentsch and Lunsford (2019).
block_length = ceil(5.03*size(data_y, 1)^(1/4)); % Jentsch and Lunsford (2019) rule of thumb
opts_lp_boot = {'bootstrap', 'var',... % Residual bootstrap
'boot_num', 1000,... % Number of bootstrap draws
'boot_blocklength', block_length};
[~, ~, ~, cis_boot] = ir_estim(data_y, p, horzs, opts_lp{:}, opts_lp_boot{:});
We recommend reporting percentile-t bootstrap confidence intervals, i.e., cis_boot(:,:,3).
_estim/: Impulse response estimation functions
- ir_estim.m: Wrapper function for VAR and LP estimation of impulse responses
- GLP/: Bayesian VAR (Giannone, Lenza, and Primiceri, 2015)
- LP_Penalize/: Penalized LP (Barnichon and Brownlees, 2019)
- lp_biascorr.m: Local projection bias correction as in Herbst and Johannsen (2024)
- var_biascorr.m: VAR bias correction as in Pope (1990)
_dfm/: Functions and scripts used for the encompassing Dynamic Factor Model (DFM) used in the simulation study
- settings/: Folder with simulation settings
- subroutines/: Folder with supporting subroutines used for the simulations
- sw_estim/: DFM code and data adapted from Lazarus, Lewis, Stock and Watson (2018)
illustrations/: Illustrative figures featured in the main text
- plot_dfm_var_vs_lp.m: Plot of LP and VAR impulse response estimands by lag length (Figure 2.1 of the main text)
- plot_emp_var_vs_lp.m: Box plots of VAR-to-LP standard error ratios and normalized point estimate differences based on applications of Ramey (2016) (Figure 3.1 of the main text)
- res_application.mat: Data used in plot_emp_var_vs_lp.m. These are taken from Montiel Olea, Plagborg-Møller, Qian, and Wolf (2024).
- plot_arma.m: Plots of impulse response estimates, absolute bias, and standard deviation (Figures 3.2 and 3.3 of the main text)
- plot_covg_bias.m: Asymptotic coverage of VAR confidence interval as a function of relative VAR bias (Figure 6.1 of the main text)
simulations/: Running and generating figures for the simulation study
- main_dfm.m: Main file for the simulation study
- plot_dfm_paper.m: Plots of bias, standard deviation, MSE, and confidence interval coverage across estimators and DGPs (Figures 5.1, 5.2, and 6.2 in the main text, Figures D.1-D.7 in the supplement).
- plot_varinlpbands.m: Plot of fraction of DGPs for which the VAR point estimates are contained inside the LP confidence interval (Figure E.1 of the supplement).
- Figure 2.1. Run the file plot_dfm_var_vs_lp.m.
- Figure 3.1. Run the file plot_emp_var_vs_lp.m.
- Figures 3.2 and 3.3. Run the file plot_arma.m.
- Figure 6.1: Run the file plot_covg_bias.m.
-
Estimate IRFs from simulated data: This produces raw IRF estimates and confidence intervals for each estimator.
- In _dfm/settings/shared.m, set
settings.simul.n_mcto1000andsettings.specifications.random_n_specto100. - Run the file
simulations/main_dfm.mwith the following settings:- Run combinations of
dgp_type(set togormp) andmode_type(set to3or5). - To produce the appendix results for recursive identification, run the same combinations for
estimand_type='recursive'.
- Run combinations of
- Results will be saved in the directory
simulations/_results/.
- In _dfm/settings/shared.m, set
-
Generate figures: The following steps generate the figures included in the main text and supplement.
- Run the file plot_dfm_paper.m with the following figure-specific header modifications:
- Figures 5.1, 5.2, 6.2, and D.7: Set
dgp_type_plot='both',estimand_type='obsshock', andmode_type=6. - Figures D.1 and D.2: Set
dgp_type_plot='both',estimand_type='recursive', andmode_type=6. - Figures D.3 and D.4: Set
dgp_type_plot='g',estimand_type='obsshock', andmode_type=6. - Figures D.5 and D.6: Set
dgp_type_plot='mp',estimand_type='obsshock', andmode_type=6.
- Figures 5.1, 5.2, 6.2, and D.7: Set
- Figure E.1: Run the file plot_varinlpbands.m.
- Run the file plot_dfm_paper.m with the following figure-specific header modifications:
The simulation study extends that of Li, Plagborg-Møller, and Wolf (2024) with estimation routines based on the replication materials for Montiel Olea, Plagborg-Møller, Qian, and Wolf (2024).
We rely on the BVAR code of Domenico Giannone, Michele Lenza, and Giorgio Primiceri and the penalized LP code of Regis Barnichon and Christian Brownlees. We also use the Dynamic Factor Model code and data of Eben Lazarus, Daniel Lewis, Jim Stock, and Mark Watson, modified to allow for conditional heteroskedasticity of the shocks for both the factors and idiosyncratic disturbances.
Plagborg-Møller acknowledges that this material is based upon work supported by the NSF under Grant #2238049 and by the Alfred P. Sloan Foundation, and W 5715 olf does the same for NSF Grant #2314736.