A simple, easy, and flexible way of estimating Bayesian VARs taking into consideration the pandemic period, as a Minnesota prior with time dummies, available in MATLAB, Julia, Python, and R. Codes embed a test for the optimal level of shrinkage for the pandemic period.
Also available MATLAB Pandemic Priors extensions of the Giannone, Lenza, and Primiceri (2015) optimal priors and the Chan (2022) asymmetric conjugate priors.
Paper available at my website: www.danilocascaldigarcia.com
Use of code for research purposes is permitted as long as proper reference to source is given.
This version: February 2023
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
MATLAB:
The main program BVAR_Pandemic_Priors.m performs the Pandemic Priors Bayesian VAR estimation with the time dummies on March to August 2020, and identifies an EBP shock with a recursive Cholesky structure, where EBP is ordered first.
"covid_periods" defines how many monthly dummies to include (starting from and including March 2020). Set to zero to run a conventional Minnesota Prior as in Banbura, Giannone, and Reichlin (2010).
"phi" defines how much signal the econometrician would like to take from the pandemic period. With phi = 999, the value for phi will be the optimal from a marginal likelihood standpoint. With phi close to zero the time dummies are "active," soaking all the pandemics variance; with phi close to infinity the time dummies are "inactive," and the model boils down to a conventional Minnesota Prior.
Dummy observations are created with the auxiliary function pandemicpriors.m.
Optimal phi calculated with the auxiliary function OptimalPhi.m.
Codes written in MATLAB 2022a
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
Julia:
The main program BVAR_Pandemic_Priors.jl performs the Pandemic Priors Bayesian VAR estimation with the time dummies on March to August 2020, and identifies an EBP shock with a recursive Cholesky structure, where EBP is ordered first.
"covid_periods" defines how many monthly dummies to include (starting from and including March 2020). Set to zero to run a conventional Minnesota Prior as in Banbura, Giannone, and Reichlin (2010).
"\phi" defines how much signal the econometrician would like to take from the pandemic period. With \phi =999, the value for \phi will be the optimal from a marginal likelihood standpoint. With \phi close to zero the time dummies are "active," soaking all the pandemics variance; with phi close to infinity the time dummies are "inactive," and the model boils down to a conventional Minnesota Prior.
Auxiliary functions, including the creation of the dummy observations are stored in functions_Pandemic_Priors.jl.
Codes written in Julia v1.8.5
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
Python:
The main program BVAR_Pandemic_Priors.py or BVAR_Pandemic_Priors.ipynb (Jupyter Notebook) performs the Pandemic Priors Bayesian VAR estimation with the time dummies on March to August 2020, and identifies an EBP shock with a recursive Cholesky structure, where EBP is ordered first.
"covid_periods" defines how many monthly dummies to include (starting from and including March 2020). Set to zero to run a conventional Minnesota Prior as in Banbura, Giannone, and Reichlin (2010).
"phi" defines how much signal the econometrician would like to take from the pandemic period. With phi =999, the value for phi will be the optimal from a marginal likelihood standpoint. With phi close to zero the time dummies are "active," soaking all the pandemics variance; with phi close to infinity the time dummies are "inactive," and the model boils down to a conventional Minnesota Prior.
Auxiliary functions, including the creation of the dummy observations are stored in functions_Pandemic_Priors.py.
Codes written in Python 3.9.13 64-bit
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
R:
The main program BVAR_Pandemic_Priors.R performs the Pandemic Priors Bayesian VAR estimation with the time dummies on March to August 2020, and identifies an EBP shock with a recursive Cholesky structure, where EBP is ordered first.
"covid_periods" defines how many monthly dummies to include (starting from and including March 2020). Set to zero to run a conventional Minnesota Prior as in Banbura, Giannone, and Reichlin (2010).
"\phi" defines how much signal the econometrician would like to take from the pandemic period. With \phi =999, the value for \phi will be the optimal from a marginal likelihood standpoint. With \phi close to zero the time dummies are "active," soaking all the pandemics variance; with phi close to infinity the time dummies are "inactive," and the model boils down to a conventional Minnesota Prior.
Auxiliary functions, including the creation of the dummy observations are stored in functions_Pandemic_Priors.R.
Codes written in R 4.3.2 and RStudio 2023.12.0
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% References:
Bańbura, M., Giannone, D., & Reichlin, L. (2010). Large Bayesian vector auto regressions. Journal of applied Econometrics, 25(1), 71-92.
Chan, J. C. (2022). Asymmetric conjugate priors for large Bayesian VARs. Quantitative economics, 13(3), 1145-1169.
Giannone, D., Lenza, M., & Primiceri, G. E. (2015). Prior selection for vector autoregressions. Review of Economics and Statistics, 97(2), 436-451.