An R package for Bayesian Estimation of Structural Vector Autoregressive Models
This package provides efficient algorithms for Bayesian estimation of Structural Vector Autoregressive (SVAR) models via Markov chain Monte Carlo methods. A wide range of SVAR models is considered, including homo- and heteroskedastic specifications and those with non-normal structural shocks. All models include three-level equation-specific local-global hierarchical prior distribution for the estimated level of shrinkage for autoregressive and structural parameters. Additionally, the package facilitates predictive and structural analyses with a variety of tools and methods.
The heteroskedastic SVAR model setup is similar as in Woźniak & Droumaguet (2015) and Lütkepohl & Woźniak (2020). The sampler of the structural matrix follows Waggoner & Zha (2003), whereas that for autoregressive parameters follows Chan, Koop, Yu (2022). The specification of Markov switching heteroskedasticity is inspired by Song & Woźniak (2021), and that of Stochastic Volatility model by Kastner & Frühwirth-Schnatter (2014).
- All the models in the bsvars package consist of the Vector
Autoregressive equation, with autoregressive parameters
Aand error termsE, and the structural equation with structural shocksU
Y = AX + E (VAR equation)
BE = U (structural equation)
- The models are identified via exclusion restrictions, heteroskedasticity, or non-normality
- Autoregressive parameters
Aand the structural matrixBare feature a three-level local-global hierarchical prior that estimates the equation-specific level of shrinkage - In five models the structural shocks are conditionally normal with
zero mean and diagonal covariance matrix with variances that are:
- equal to one
- time-varying following non-centred Stochastic Volatility
- time-varying following centred Stochastic Volatility
- time-varying with stationary Markov Switching
- time-varying with sparse Markov Switching where the number of volatility regimes is estimated
- In two more models non-normal structural shocks following
- a finite mixture of normal components and component-specific variances
- a sparse mixture of normal components and component-specific variances where the number of states is estimated
- Specify the models using
specify_bsvar_*()functions, for instance,specify_bsvar() - Estimate the models using the
estimate()method - Predict the future using the
predict()method - Provide structural analyses using impulse responses, forecast
error variance decompositions, historical decompositions, and
structural shocks using functions
compute_impulse_responses(),compute_variance_decompositions(),compute_historical_decompositions(), andcompute_structural_shocks()respectively - Analyse the fitted values, time-varying volatility, and volatility
regimes using functions
compute_fitted_values(),compute_conditional_sd(), andcompute_regime_probabilities()respectively
- Extraordinary computational speed is obtained by combining
- the implementation of frontier econometric techniques, and
- compiled code written in cpp
- It combines the best of two worlds: the ease of data analysis with R and fast cpp algorithms
- The algorithms used here are very fast. But still, Bayesian estimation might take a little time. Look at our beautiful progress bar in the meantime:
**************************************************|
bsvars: Bayesian Structural Vector Autoregressions|
**************************************************|
Gibbs sampler for the SVAR-SV model |
Non-centred SV model is estimated |
**************************************************|
Progress of the MCMC simulation for 1000 draws
Every 10th draw is saved via MCMC thinning
Press Esc to interrupt the computations
**************************************************|
0% 10 20 30 40 50 60 70 80 90 100%
[----|----|----|----|----|----|----|----|----|----|
*************************************
The beginnings are as easy as ABC:
library(bsvars) # upload the package
data(us_fiscal_lsuw) # upload data
spec = specify_bsvar_sv$new(us_fiscal_lsuw, p = 4) # specify the model
burn_in = estimate(spec, 1000) # run the burn-in
out = estimate(burn_in, 50000) # estimate the modelStarting from bsvars version 2.0.0 a simplified workflow using the
|> pipe is possible:
library(bsvars) # upload the package
data(us_fiscal_lsuw) # upload data
us_fiscal_lsuw |>
specify_bsvar_sv$new(p = 4) |> # specify the model
estimate(S = 1000) |> # run the burn-in
estimate(S = 50000) -> out # estimate the modelNow, you’re ready to analyse your model!
Just open your R and type:
install.packages("bsvars")
The developer’s version of the package with the newest features can be installed by typing:
devtools::install_git("https://github.com/bsvars/bsvars.git")
The package is under intensive development. Your help is welcome! Please, have a look at the roadmap, discuss package features and applications, or report a bug. Thank you!
Tomasz is a Bayesian econometrician and a Senior Lecturer at the University of Melbourne. He develops methodology for empirical macroeconomic analyses and programs in R and cpp using Rcpp.