Bayesian Estimation of Structural Vector Autoregressive Models • bsvars

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).

Features

Structural Vector Autoregressions

All the models in the bsvars package consist of the Vector Autoregressive equation, with autoregressive parameters A and error terms E, and the structural equation with structural shocks U

    Y = AX + E           (VAR equation)
   BE = U                (structural equation)

The models are identified via exclusion restrictions, heteroskedasticity, or non-normality
Autoregressive parameters A and the structural matrix B are 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

Simple workflows

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(), and compute_structural_shocks() respectively
Analyse the fitted values, time-varying volatility, and volatility regimes using functions compute_fitted_values(), compute_conditional_sd(), and compute_regime_probabilities() respectively

Fast and efficient computations

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%
[----|----|----|----|----|----|----|----|----|----|
*************************************

Start your Bayesian analysis of data

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 model

Starting 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 model

Now, you’re ready to analyse your model!

Installation

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")

Development

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!

About the author

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.