Forecasting with Bayesian Hierarchical Panel VARs • bvarPANELs

An R package for Forecasting with Bayesian Hierarchical Panel Vector Autoregressions

Provides Bayesian estimation and forecasting of dynamic panel data using Bayesian Hierarchical Panel Vector Autoregressions (VARs). The model includes country-specific VARs that share a global prior distribution. Under this prior expected value, each country’s system follows a global VAR with country-invariant parameters. Further flexibility is provided by the hierarchical prior structure that retains the Minnesota prior interpretation for the global VAR and features estimated prior covariance matrices, shrinkage, and persistence levels. Bayesian forecasting is developed for models including exogenous variables, allowing conditional forecasts given the future trajectories of some variables and restricted forecasts assuring that rates are forecasted to stay positive and less than 100. The package implements the model specification, estimation, and forecasting routines, facilitating coherent workflows and reproducibility. Beautiful plots, informative summary functions, and extensive documentation complement all this. An extraordinary computational speed is achieved thanks to employing frontier econometric and numerical techniques and algorithms written in C++. The bvarPANELs package is aligned regarding objects, workflows, and code structure with the R packages bsvars by Woźniak (2024) and bsvarSIGNs by Wang & Woźniak (2024), and they constitute an integrated toolset.

Features

Bayesian Hierarchical Panel Vector Autoregressions

The model in the bvarPANELs package features a country-specific Vector Autoregressive equation for the country-specific:
- dependent variables Yc,
- lagged dependent variables Xc,
- error terms Ec,
- autoregressive parameters Ac, and
- error term covariance matrix Sc.
```
     Yc = Ac Xc + Ec         (VAR equation)
Ec | Xc ~ MN(0, Sc, I)       (error term normality)
```
The error terms feature a zero-mean matrix-variate normal distribution with row-specific covariance matrix Sc and column-specific covariance equal to the identity matrix I.
The Hierarchical Panel VAR model features a sophisticated hierarchical prior structure that grants the model flexibility, interpretability, and improved forecasting performance.
The country-specific parameters follow a prior distribution that, at its mean value, represents a global VAR model with a global autoregressive parameter matrix A and a global error term covariance matrix S:

       Yc = A Xc + Ec          (VAR equation)
  Ec | Xc ~ MN(0, S, I)        (error term normality)

See more details in this presentation

Simple workflows

Specify the models using the specify_bvarPANEL$new() function
Estimate the models using the estimate() method
Predict the future using the forecast() method
Compute forecast error variance decompositions using function compute_variance_decompositions()
Use plot() and summary() methods to gain the insights into the core of the empirical problem.

Fast and efficient computations

Extraordinary computational speed is obtained by combining
- the application of frontier econometric and numerical techniques, and
- the algorithms 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:

**************************************************|
bvarPANELs: Forecasting with Bayesian Hierarchical|
            Panel Vector Autoregressions          |
**************************************************|
 Progress of the MCMC simulation for 10000 draws
    Every draw is saved via MCMC thinning
 Press Esc to interrupt the computations
**************************************************|
0%   10   20   30   40   50   60   70   80   90   100%
[----|----|----|----|----|----|----|----|----|----|
*************************************

The hexagonal logo

This beautiful logo can be reproduced in R using this file.

Resources

a reference manual
a website of the family of packages bsvars.org
presentations:
- for the International Labour Organization given March 2025 featuring bvarPANELs 0.2]

Start your Bayesian analysis of data

The beginnings are as easy as ABC:

library(bvarPANELs)                                     # load the package

spec = specify_bvarPANEL$new(                           # specify the model
  ilo_dynamic_panel,                                    # data
  exogenous = ilo_exogenous_variables,                  # exogenous variables
  stationary = c(FALSE, FALSE, FALSE, TRUE),            # stationarity (determines prior mean)
  type = c("real", "rate", "rate", "rate")              # variable types
)

burn = estimate(spec, S = 10000)                        # run the burn-in
post = estimate(burn, S = 10000)                        # estimate the model

fore = forecast(                                        # forecast the model 
  post,                                                 # estimation output
  horizon = 6,                                          # forecast horizon
  exogenous_forecast = ilo_exogenous_forecasts,         # forecasts for exogenous variables
  conditional_forecast = ilo_conditional_forecasts      # gdp projections
)

plot(fore, "COL", main = "Forecasts for Colombia")
summary(fore, "COL")$variable2

post |>                                                 # estimation output
  compute_variance_decompositions(horizon = 6) |>       # compute variance decompositions
  plot(which_c = "COL")                                 # plot variance decompositions

The bvarPANELs package supports a simplified workflow using the |> pipe:

ilo_dynamic_panel |>                                    # data
  specify_bvarPANEL$new(                                # specify the model
    exogenous = ilo_exogenous_variables,                # exogenous variables
    stationary = c(FALSE, FALSE, FALSE, TRUE),          # stationarity (determines prior mean)
    type = c("real", "rate", "rate", "rate")            # variable types
  ) |> 
  estimate(S = 10000) |>                                # run the burn-in
  estimate(S = 10000) -> post                           # estimate the model

post |> forecast(                                       # forecast the model 
  horizon = 6,                                          # forecast horizon
  exogenous_forecast = ilo_exogenous_forecasts,         # forecasts for exogenous variables
  conditional_forecast = ilo_conditional_forecasts      # gdp projections
) |> plot("COL", main = "Forecasts for Colombia")

Now, you’re ready to analyse your model!

Installation

The first time you install the package

You must have a cpp compiler. Follow the instructions from Section 1.3. by Eddelbuettel & François (2023). In short, for Windows: install RTools, for macOS: install Xcode Command Line Tools, and for Linux: install the standard development packages.

Once that’s done:

Just open your R and install the package from its developer’s repository by typing:

devtools::install_github("bsvars/bvarPANELs")

Development

The package is under intensive development. Your help is most welcome! Please, have a look at our issues to learn what we’re working on. 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.