Kenny-Meyler-Quinn (1998) Bayesian VAR Models for Forecasting Irish Inflation

Summary

Kenny, Meyler, and Quinn (1998) evaluate Bayesian vector autoregression (VAR) models for forecasting Irish Harmonised Index of Consumer Prices (HICP) inflation ahead of Economic and Monetary Union (EMU) accession in January 1999. They first screen candidate indicators using Cecchetti's (1995) predictability regressions, then construct three Bayesian VAR (BVAR) models of increasing complexity using the Minnesota (Doan-Litterman-Sims) random-walk prior implemented via Theil mixed estimation. The paper's central finding is that a parsimonious three-variable small-open-economy (SOE) BVAR — domestic prices, foreign prices, and the exchange rate — dominates all larger specifications, while unrestricted OLS VARs with five variables perform worse than a naïve no-change forecast at short horizons.

Key Claims

External prices dominate. Import-weighted and trade-weighted foreign price indices are the only variables significant at all five forecast horizons (1Q to 3-4 years); the nominal effective exchange rate (EER) is significant from 1Q through 3 years, implying near-complete pass-through within three years.
M3 is uninformative. Money supply growth is not significant at any horizon in the Cecchetti regressions; capacity utilisation and unemployment are significant but temporally unstable in sub-samples.
Parsimony wins. BVAR1 ( $\{P, P^*, E\}$ , $\gamma=0.4$ , $w=0.8$ ) achieves Theil $U = 0.71$ (1–4Q) and $0.55$ (5–8Q) — best among all models. Adding wages and retail sales (BVAR2) or short rate and domestic credit (BVAR3) marginally worsens short-horizon performance.
Bayesian priors are essential. Unrestricted 5-variable OLS VAR (LVAR2): Theil $U = 1.21$ (1–4Q) — worse than naïve. BVAR3 with the same five variables: Theil $U = 0.85$ , i.e., priors cut the error by ${\sim}44\%$ .
General prior fails. Restricting foreign price equations to univariate AR processes (treating P* and E as exogenous, as in Artis-Zhang 1990) did not improve any of the three BVARs.
Forecast uncertainty is large. The best 95% confidence interval spans approximately $\pm 1.6\%$ per quarter, limiting policy usefulness.
Temporal instability. Many indicators significant in full sample lose significance in sub-sample tests; rolling evaluation from 1992Q1 covers only $T=24$ forecasts, limiting statistical power.

Indicator Screening (Cecchetti 1995 Framework)

For each candidate indicator $X_t$ and lag horizon pair $(l,k)$ , estimate:

$\pi_{t+l,t+k} = a(L)\pi_t + b(L)X_t + \varepsilon_t$

over the sample 1979Q1–1998Q1, then apply a Newey-West Wald test of $H_0: b(L) = 0$ .

Indicator	1Q	2Q	4Q	8Q	12–16Q
Import-weighted foreign prices	✓	✓	✓	✓	✓
Trade-weighted foreign prices	✓	✓	✓	✓	✓
Nominal EER	✓	✓	✓	✓	(fades)
Unemployment rate	✓	✓	✓	✓	✓
Capacity utilization	✓	✓	✓	(fades)	(fades)
M3	✗	✗	✗	✗	✗
Industrial production	✗	✗	✗	✗	✗

BVAR Model Specifications

Minnesota random-walk prior: $y_{n,t} = \mu_n + y_{n,t-1} + \varepsilon_{n,t}$ . Standard deviations:

$S(i,j,l) = \bigl[\gamma \cdot g(l) \cdot f(i,j)\bigr] \cdot \frac{s_i}{s_j}$

where $g(l) = l^{-d}$ ( $d=1$ fixed), $f(i,j) = 1$ if $i=j$ and $w_{ij}$ otherwise; $s_i/s_j$ rescales by residual standard deviations.

Model	Variables	$\gamma$	$w$	Description
BVAR1	{P, P*, E}	0.4	0.8	Small open economy
BVAR2	{P, P*, E, W, RS}	0.3	0.3	Augmented SOE
BVAR3	{P, P*, E, r^s, DC}	0.2	0.4	Monetary

$P$ = domestic HICP; $P^*$ = foreign prices (import-weighted); $E$ = nominal EER; $W$ = wages; RS = retail sales; $r^s$ = short-term interest rate; DC = domestic credit.

Forecast Results (Theil U vs. Naïve No-Change; Rolling from 1992Q1, T=24)

Model	Avg Theil U 1–4Q	Avg Theil U 5–8Q
AR(5)	0.90	0.77
LVAR1 (OLS, 3-var)	0.90	0.60
BVAR1 (SOE)	0.71	0.55
LVAR2 (OLS, 5-var)	1.21	0.92
BVAR2 (Augmented)	0.74	0.58
LVAR3 (OLS, monetary)	1.54	1.31
BVAR3 (Monetary)	0.85	0.59

At 5–8Q, LVAR1 (Theil $U = 0.60$ ) is not significantly worse than BVAR1 ( $0.55$ ), suggesting Bayesian shrinkage matters most at short horizons.

Concepts Introduced or Extended

Entities Mentioned

Quotes

"The results suggest that the optimal amount of prior information differs substantially across model specifications. The monetary BVAR requires the most shrinkage ( $\gamma=0.2$ ) while the SOE model is most data-tolerant ( $\gamma=0.4$ )."

"The best 95 per cent confidence interval achievable ... is approximately ±1.6 per cent per quarter — this should be borne in mind when utilising these models for policy purposes."

My Take

The paper's main value is empirical: it documents the dominance of external prices over monetary aggregates for a small open economy in a transparent, replicable framework. The Cecchetti pre-screening is sensible and honest about sub-sample instability. The claim that the general prior (forcing P* and E to univariate ARs) fails is notable — it contradicts the prior expectation that treating small-open-economy drivers as weakly exogenous would help.

Weaknesses: T=24 evaluation periods is too small for robust statistical comparison; Theil U confidence intervals would overlap substantially. The choice of Theil mixed estimation rather than full Bayesian Markov chain Monte Carlo (MCMC) means posterior distributions are not characterised, only point forecasts. The Minnesota prior is calibrated by grid search over a coarse two-parameter space $(\gamma, w)$ , which could overfit the evaluation sample. The paper would benefit from Diebold-Mariano tests to formalise the pairwise comparisons.