Bayesian VECM — III. Money demand — R cross-check¶

Vector autoregressions, Part 6c (R)¶

Validates bvecm_money_python.ipynb. The series are genuinely I(1) (so cointegration is well-defined), but the Johansen trace test should return $r=0$: the classic long-run money-demand relation has broken down. urca's ur.df (unit-root tests) and ca.jo (Johansen) confirm the Python finding.

Data: bvecm_money_data.csv — log real M2, log real GDP, 3-month rate, quarterly 1959–2019 (FRED).

In [1]:
.libPaths('C:/Users/user/R/win-library/4.6')
suppressMessages(library(urca))
d <- read.csv('bvecm_money_data.csv'); Y <- d[, c('realM2','realGDP','tbill')]
for (nm in colnames(Y)) {
  s <- summary(ur.df(Y[[nm]], type = 'drift', lags = 4, selectlags = 'AIC'))
  cat(sprintf('ADF %-8s: stat %6.2f  (5%% crit %.2f)  -> %s\n', nm, s@teststat[1], s@cval[1,2],
              ifelse(s@teststat[1] > s@cval[1,2], 'I(1)', 'I(0)')))
}
jo <- ca.jo(Y, type = 'trace', ecdet = 'none', K = 2, spec = 'transitory')
cat('\nJohansen trace test:\n'); print(round(cbind(trace = jo@teststat, jo@cval), 1))
cat('\ncross-check -> Python: all three I(1), but Johansen r=0 -> money-demand cointegration has BROKEN DOWN\n')

ADF realM2  : stat  -0.36  (5% crit -2.88)  -> I(1)
ADF realGDP : stat  -1.81  (5% crit -2.88)  -> I(1)
ADF tbill   : stat  -2.26  (5% crit -2.88)  -> I(1)

Johansen trace test:

         trace 10pct 5pct 1pct
r <= 2 |   0.5   6.5  8.2 11.7
r <= 1 |   5.6  15.7 18.0 23.5
r = 0  |  18.1  28.7 31.5 37.2

cross-check -> Python: all three I(1), but Johansen r=0 -> money-demand cointegration has BROKEN DOWN

Same verdict: the relation is gone¶

  • ur.df confirms all three series are I(1) — genuine candidates for cointegration, so (unlike the Fisher case) the test is meaningful.
  • ca.jo finds $r=0$. Even the first trace statistic falls short of its critical value: there is no cointegrating vector. Maximum likelihood and the Bayesian VECM agree — no stable long-run money demand over this sample.
  • Together with Parts 6a–6b, the three R cross-checks reproduce the full spectrum: $r=2$ (yields), full rank (Fisher), $r=0$ (money) — the rank is the whole story, and it replicates across method and software.

References¶

  • Pfaff, B. (2008). Analysis of Integrated and Cointegrated Time Series with R. Springer.
  • Friedman, B. M. & Kuttner, K. N. (1992). American Economic Review 82, 472–492.