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lp_var_inference

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LP and VAR inference under potential misspecification

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# lp_var_inference

MATLAB code for inference on impulse responses using Local Projections or VARs.

**Reference:**
[Montiel Olea, José Luis](https://www.joseluismontielolea.com), [Mikkel Plagborg-Møller](https://www.mikkelpm.com), [Eric Qian](https://www.eric-qian.com) and [Christian K. Wolf](https://www.christiankwolf.com/) (2026), "Double Robustness of Local Projections and Some Unpleasant VARithmetic" [(arXiv)](https://arxiv.org/abs/2405.09509)

Tested in: MATLAB R2025b on Macbook Pro 2023 (M3 Pro)

## Contents

**[_data](_data):** Data for our analyses based on [Ramey (2016)](https://www.sciencedirect.com/science/article/pii/S1574004816000045) and [Känzig (2021)](https://www.aeaweb.org/articles?id=10.1257/aer.20190964)

**[_estim](_estim):** Functions for LP and VAR estimation and inference
- [ir_estim.m](_estim/ir_estim.m): Main function for estimates and confidence intervals

**[analytics](analytics):** Figures for analytical results
- [plot_arbias.m](analytics/plot_arbias.m): Plot the least-favorable MA polynomial for the local-to-AR(1) model
- [run_ramey_ses.m](analytics/run_ramey_ses.m): Compute LP and VAR SEs
- [plot_worstcase.m](analytics/plot_worstcase.m): Generate the various analytical worst-case figures

**[documents](documents):** Detailed readme
- [lp_varithmetic_readme.pdf](documents/lp_varithmetic_readme.pdf): Detailed replication instructions plus supplementary information for replication of our empirical literature surveys

**[lit_lags](lit_lags):** Results for our literature review on lag length selection for VARs
- [lit_varlags_raw.csv](lit_lags/lit_varlags_raw.csv): Raw, hand-collected data
- [lit_varlags_eval.m](lit_lags/lit_varlags_eval.m): Plot summary statistics

**[simulations](simulations):** Simulation study
- [_aux](simulations/_aux): Auxiliary simulation-specific routines
- [gen_varma_oil.m](simulations/gen_varma_oil.m): Map oil VAR with 18 lags into a local-to-VAR representation
- [simul_oil.m](simulations/simul_oil.m): Run simulations
- [plot_oil.m](simulations/plot_oil.m): Generate figures

## Detailed replication instructions

- _Figures 4.1-4.3 and A.2-A.3_. First run the file [run_ramey_ses.m](analytics/run_ramey_ses.m). Then execute [plot_worstcase.m](analytics/plot_worstcase.m).
- _Figures 5.1 and D.1_. First run [gen_varma_oil.m](simulations/gen_varma_oil.m). Then execute [simul_oil.m](simulations/simul_oil.m) after setting the option "boot" to "true" for experiments "exp_id=1" and "exp_id=2." The relevant experiment type needs to be selected in [plot_oil.m](simulations/plot_oil.m).
- _Figure A.1_. Run the file [plot_arbias.m](analytics/plot_arbias.m).

## Acknowledgements
Our estimation routines build on the replication materials for [Montiel-Olea and Plagborg-Møller (2021)](https://github.com/jm4474/Lag-augmented_LocalProjections).

Plagborg-Møller acknowledges that this material is based upon work supported by the NSF under [Grant #2238049](https://www.nsf.gov/awardsearch/showAward?AWD_ID=2238049) and by the Alfred P. Sloan Foundation, and Wolf does the same for NSF [Grant #2314736](https://www.nsf.gov/awardsearch/showAward?AWD_ID=2314736).

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