bsvars.org design concept

R packages for Predictive Analyses using Bayesian Structural Vector Autoregressions

\[ \]

by Adam Wang and Tomasz Woźniak

Student’s experience

• make something useful to the world
• collaborate and learn from others
• gain programming experience (especially in C++)
• adds competency to the CV
• being a package developer is fun!

the packages and their working

Structural VARs.

• go-to models for the analysis of policy effects
• facilitate the analysis of dynamic causal effects of a well-isolated cause
• perfect for predictive analyses
• extensively used for: monetary and fiscal policy, financial markets, …
• extendible:
  • non-normality
  • heteroskedasticity
  • time-varying parameters
  • Bayesian hierarchical modelling

the packages and their working

Structural VARs.

\[ \begin{align} \text{VAR equation: } & & y_t & = \mathbf{A} x_{t} + \epsilon_t \\[1ex] \text{structural equation: } & & \mathbf{B}\epsilon_t & = u_t \\[1ex] \text{structural shocks: } & & u_t |Y_{t-1} & \sim N_N\left(\mathbf{0}_N,\text{diag}\left(\boldsymbol\sigma_t^2\right)\right) \end{align} \]

Features.

• system dynamic modelling
• structure of the economy modelled by \(\mathbf{B}\)
• identified structural shocks \(u_t\)
• time-varying variances

the packages and their working

Model specification.

sign_irf[, , 1]

     [,1] [,2] [,3] [,4]
[1,]    1   NA   NA   NA
[2,]   NA   NA   NA   NA
[3,]   -1   NA   NA   NA
[4,]    1   NA   NA   NA

sign_structural

     [,1] [,2] [,3] [,4]
[1,]    1   -1   -1    1
[2,]   NA   NA   NA   NA
[3,]   NA   NA   NA   NA
[4,]   NA   NA   NA   NA

# specify the model
spec <- specify_bsvarSIGN$new(
  Y,
  p = 4,
  sign_irf = sign_irf,
  sign_structural = sign_structural
)

the packages and their working

Estimation.

# sample posterior draws
post <- estimate(spec, S = 5000)

**************************************************|
 bsvarSIGNs: Bayesian Structural VAR with sign,   |
             zero and narrative restrictions      |
**************************************************|
 Progress of simulation for 5000 independent draws
 Press Esc to interrupt the computations
**************************************************|

the packages and their working

Forecasting.

post |>
  forecast(h = 4) |>
  plot(data_in_plot = 0.1)

the packages and their working

Forecast error variance decomposition.

post |>
  compute_variance_decompositions(h = 20) |>
  plot()

the packages and their working

Impulse responses.

post |>
  compute_impulse_responses(h = 20) |>
  plot(probability = 0.68)

the packages and their working

Historical Decompositions.

post |>
  compute_historical_decompositions() |>
  plot()

**************************************************|
bsvars: Bayesian Structural Vector Autoregressions|
**************************************************|
 Computing historical decomposition               |
**************************************************|
 This might take a little while :)                
**************************************************|

target audience

• academic researchers

  • reproducibility, transparency, literature context

• PhD students

  • communication, extendibility, up-to date with the newest developments

• master students

  • simple workflows, documentation and examples, video presentations

• applied economists

  • reliability, speed, incorporating feedback on new features

• economic governance institutions

  • workflow integration, reporting practices, off-the-shelf applications

bsvars.org design concept

\[ \]

1. combine the best of two worlds:

-speed of algorithms written using compiled code, C++

-convenience of data analysis using interpreted code, R

bsvars.org design concept

\[ \]

2. C++ implementation using Rcpp

• provide essential functionality for package development
• manageable dependencies combined with good communication by developers
• simplicity in package setup/compilation/linking/assuring object compatibility lowering the (perceived) entry requirements
• great community support
• super fast on loops (Gibbs sampler in bsvars is a serial job)
• parallel computations using openMP (independent sampler in bsvarSIGNs)

bsvars.org design concept

\[ \]

3. Essential algorithms rely on Armadillo through RcppArmadillo

• frontier package for linear algebra (speed, speed, speed)
• fast and reproducible random number generators
• excellent documentation and support in package development
• makes C++ code as expressive as R’s

bsvars.org design concept

\[ \]

4. Delegate computational tasks to C++ code

• all time intensive tasks are implemented in C++
  • parameter estimation
  • forecasts
  • impulse response functions
  • etc.
• only user interface and data management is done in R
  • R6 objects for specification
  • R wrapper functions for estimation, forecasting, etc.
  • plotting and summary methods

bsvars.org design concept

\[ \]

5. R6 management of the input object

• minimal scripting specify_bsvar$new() provides basic setup of:
  • starting values
  • identification
  • data matrices
  • prior hyper-parameters (each of them are lists with R6 structure)
• ample modelling choices managed by arguments of specify_bsvar$new()
• possibility of coherent customisation using in functions R6 public elements
• essential specification variables managed by R6 private elements

bsvars.org design concept

\[ \]

5. R6 management of the input object

• R6 is R’s object-oriented programming system
• both spec and spec$prior are R6 objects
• modify a public field

spec$prior$A[1, 1] <- 0
spec$prior$A

     [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13] [,14]
[1,]    0    0    0    0    0    0    0    0    0     0     0     0     0     0
[2,]    0    1    0    0    0    0    0    0    0     0     0     0     0     0
[3,]    0    0    1    0    0    0    0    0    0     0     0     0     0     0
[4,]    0    0    0    1    0    0    0    0    0     0     0     0     0     0
     [,15] [,16] [,17]
[1,]     0     0     0
[2,]     0     0     0
[3,]     0     0     0
[4,]     0     0     0

• call a public method

spec$prior$estimate_hyper()

**************************************************|
 Adaptive Metropolis MCMC: hyper parameters       |
**************************************************|

bsvars.org design concept

\[ \]

6. Establish a set of generics in bsvars

• provide model-specific methods in other packages
• assure similar workflows
• implement through Depends: and Imports:

bsvars.org design concept

\[ \]

7. S3 methods

• R’s native object-oriented programming system
• simple workflows

... |>
  plot()

• same method for different objects
• applies to objects generated from both packages bsvars and bsvarSIGNs

bsvars::plot.Forecasts
bsvars::plot.PosteriorFEVD
bsvars::plot.PosteriorIR
bsvars::plot.PosteriorHD

bsvars.org design concept

\[ \]

7. S3 generics and methods

• simple workflows

us_fiscal_lsuw |>
  specify_bsvar$new(p = 4) |>
  estimate(S = 5000) -> post

• full transparency on what model is used

bsvars::estimate

bsvars::estimate.BSVAR              bsvars::estimate.PosteriorBSVAR
bsvars::estimate.BSVART             bsvars::estimate.PosteriorBSVART
bsvars::estimate.BSVARMIX           bsvars::estimate.PosteriorBSVARMIX
bsvars::estimate.BSVARMSH           bsvars::estimate.PosteriorBSVARMSH
bsvars::estimate.BSVARSV            bsvars::estimate.PosteriorBSVARSV

bsvarSIGNs::estimate.BSVARSIGN

bsvars.org design concept

\[ \]

8. export all C++ functions in a library

• for developers to access all code for their R package development using C++ code
• implement through LinkingTo: and Depends:
• pointer management
• assure consistency in object declarations
• assignment by reference not working across packages

bsvars.org design concept

\[ \]

9. Outputs and workflows to target various users

• provide all the outputs, posterior draws
  • insightful users can can compute demanded quantities not provided in the packages
• provide all the basic functionality with well-designed workflows
  • plot and summary methods for users valuing simplicity in scripting
  • It’s amazing how much you do with a few lines of code!

bsvars.org design concept

\[ \]

10. Extensive resources

• documentation pitched to users of various level of advancement
• pkgdown website with package features, social media chanels, and updates on the most recent presentations!
• a vignette to be sent to the Journal of Statistical Software or the R Journal

future developments

\[ \]

bsvars and bsvarSIGNs

• bsvars include more models non-normal and heteroskedastic
• bsvars provide computations for more outputs (cummulative IRF and HD, connectedness measures)
• bsvars include more model verification techniques
• bsvarSIGNs include COVID modelling
• bsvarSIGNs implement parallel computations for independence sampler
• bsvarSIGNs improve hyperparameter estimation
• bsvarSIGNs implement some user-demanded features
• bsvars and bsvarSIGNs JSS submissions
• bsvars and bsvarSIGNs forecasting performance evaluation ??

future developments

\[ \]

upcoming packages

• bvarPANELs - Bayesian Panel VAR forecasting of labour market outcomes for the International Labour Organization
• bsvarTVPs with Annika Camehl - Time-varying identification of Structural VARs as an extension to bsvars
• bsvarCFs with Dan Zhu - Bayesian forecasting with VARs subject to soft and hard restrictions as an extension to bsvars and bsvarSIGNs
• bvarGIGs with Rui Liu and Andres Ramirez Hassan - Bayesian forecasting with VARs with flexible shrinkage
• bsmars with Longcan Li - Bayesian forecasting with Matrix Autoregression