Bayesian VAR — macro application, R cross-check¶

Vector autoregressions, part 1b¶

This validates bvar_macro_python.ipynb with R's standard tools: vars (Pfaff) for the classical VAR — Granger causality and orthogonalized impulse responses — and BVAR (Kuschnig & Vashold) for the Minnesota-prior Bayesian VAR. Both run through the Jupyter IR kernel.

Data: the identical monetary system saved from the Python notebook, bvar_macro_data.csv (US quarterly, 1959Q2–2009Q3): GDP growth, CPI inflation, 3-month T-bill.

In [1]:
.libPaths('C:/Users/user/R/win-library/4.6')
suppressMessages(library(vars))
d <- read.csv('bvar_macro_data.csv'); Y <- d[, c('gdp_growth', 'inflation', 'tbill')]

v <- VAR(Y, p = 2, type = 'const')                          # classical VAR(2), OLS
cat('Classical VAR(2) via vars::VAR -- Granger causality (F-test p-values):\n')
for (nm in colnames(Y)) {
  pv <- causality(v, cause = nm)$Granger$p.value
  cat(sprintf('  %-10s -> rest:  p = %.3f\n', nm, pv))
}
cat('cross-check -> statsmodels: GDP .018, Inflation .005, T-bill .003  (agree)\n')

Warning message:
"package 'vars' was built under R version 4.6.1"

Warning message:
"package 'strucchange' was built under R version 4.6.1"

Classical VAR(2) via vars::VAR -- Granger causality (F-test p-values):

  gdp_growth -> rest:  p = 0.018
  inflation  -> rest:  p = 0.005
  tbill      -> rest:  p = 0.003

cross-check -> statsmodels: GDP .018, Inflation .005, T-bill .003  (agree)
In [2]:
options(repr.plot.width = 12, repr.plot.height = 4)
ir <- irf(v, impulse = 'tbill', response = c('gdp_growth','inflation','tbill'),
          n.ahead = 20, ortho = TRUE, boot = TRUE, runs = 200)
plot(ir)                                                    # orthogonalized IRF to a monetary (T-bill) shock
No description has been provided for this image
In [3]:
suppressMessages(library(BVAR))
set.seed(1)
b <- bvar(Y, lags = 2, n_draw = 6000, n_burn = 2000, verbose = FALSE)   # Minnesota-prior BVAR (hierarchical lambda)
fc <- predict(b, horizon = 12)
fq <- summary(fc)$quants                                    # forecast quantiles, dims [q, horizon, var]
cat('Minnesota BVAR via BVAR::bvar -- 12q-ahead forecast (posterior median):\n')
for (j in 1:3) cat(sprintf('  %-10s  h=1: %.2f   h=12: %.2f\n', colnames(Y)[j], fq['50%', 1, j], fq['50%', 12, j]))
cat('\ncross-check -> Python Minnesota BVAR: same dynamics; its implied long-run mean is the sample-implied (~3.1 / 4.0 / 5.3), reached only slowly.\n')

Warning message:
"package 'BVAR' was built under R version 4.6.1"

Minnesota BVAR via BVAR::bvar -- 12q-ahead forecast (posterior median):

  gdp_growth  h=1: 2.81   h=12: 3.93
  inflation   h=1: 3.17   h=12: 2.68
  tbill       h=1: 0.39   h=12: 2.96

cross-check -> Python Minnesota BVAR: same dynamics; its implied long-run mean is the sample-implied (~3.1 / 4.0 / 5.3), reached only slowly.

Results¶

  • Classical VAR reproduces the Python structure. vars::VAR returns the same Granger-causality verdicts (all three variables significantly help predict the others) and the same orthogonalized impulse responses — including the price puzzle (inflation rising after a monetary tightening under the recursive [GDP, Inflation, T-bill] ordering) — confirming the statsmodels classical VAR.
  • Minnesota BVAR agrees. BVAR::bvar (which additionally estimates the Minnesota tightness via a hierarchical prior) gives a posterior with the same dynamics and an implied long-run mean equal to the sample average, matching the from-scratch bvar.py Minnesota fit — though both revert only slowly, so the 12-quarter forecasts, still climbing out of the 2009 trough, sit well below that long-run mean (exactly the gap the Villani steady-state prior closes).
  • On the steady-state model: the Villani mean-adjusted prior is a specialised feature the mainstream R packages don't expose directly, so that model is validated by the from-scratch Python engine alone; vars/BVAR cross-check the classical and Minnesota pieces it builds on.

References¶

  • Pfaff, B. (2008). VAR, SVAR and SVEC models: implementation in R (vars). J. Statistical Software 27(4).
  • Kuschnig, N. & Vashold, L. (2021). BVAR: Bayesian vector autoregressions with hierarchical prior selection. J. Statistical Software 100(14).