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Analysing shock transmission in a
data-rich environment: A large BVAR
for New Zealand
Chris Bloor and Troy Matheson
Reserve Bank of New Zealand Discussion Paper DP2008/09
Motivation
• Estimate the sectoral responses to a
monetary policy shock.
Why use a Bayesian VAR
• We need a large model to tell a rich sectoral
story about the effects of monetary policy.
• Conventional VARs quickly run out of degree’s
of freedom, while DSGE theory is not yet rich
enough to tell a sufficiently disaggregated
story.
• In contrast to factor models, Bayesian VARs
can be estimated in non-stationary levels.
Previous Literature
• De Mol et al (2008) analyse the Bayesian
regression empirically and asymptotically.
• Find that Bayesian forecasts are as accurate
as those based on principal components.
• The Bayesian forecast converges to the
optimal forecast as long as the prior is
imposed more tightly as the number of
variables increases.
Previous literature
• Banbura et al (2008) extend the work of De Mol
et al (2008) by considering a Bayesian VAR
with 130 variables using Litterman priors.
• They show that a Bayesian VAR can be
estimated with more parameters than time
series observations.
• Find that a large BVAR outperforms smaller
VARs and FAVARs in an out of sample
forecasting exercise.
Contributions of this paper
• Extend the work of Banbura et al along a
number of dimensions.
– Add a co-persistence prior
– Impose restrictions on lags
– Consider a wider range of shocks
The BVAR methodology
• Augments the standard VAR model:
Yt  c  A1Yt 1  ...  ApYt  p  u t
With prior beliefs on the relationships
between variables.
• We use a modified Litterman prior.
The Litterman prior
• Standard Litterman prior assumes that all
variables follow a random walk with drift.
• We also allow for stationary variables to
follow a white noise process.
• Nearer lags are assumed to have more
influence than distant lags, and own lags
are assumed to have more influence than
lags of other variables.
BVAR priors

E  Ak ij


 i , j  1, k  1

0, otherwise
V  Ak ij

 
 2
k 
2
2
i
2
j
Additional priors
• Sum of coefficients prior (Doan et al 1984).
– Restricts the sum of lagged AR coefficients to be
equal to one.
• Co-persistence prior (Sims 1993/ Sims and
Zha 1998).
– Allows for the possibility of cointegrating
relationships.
How do we determine tightness of the
priors (
• Select n* benchmark variables on which to
evaluate the in-sample fit.
• Estimate a VAR on these n* variables and
calculate the in-sample fit.
• Set the sums of coefficients and co-persistence
priors to be proportionate to .
• Choose  so that the large BVAR produces the
same in-sample fit on the n* benchmark variables
as the small VAR.
Restrictions on lags
• Foreign and climate variables are placed in
exogenous blocks.
• We apply separate hyperparameters for each of
the exogenous blocks.
• The hyperparameters in the small blocks are fairly
standard (Robertson and Tallman, 1999).
• Estimated using Zha’s (1999) block-by-block
algorithm.
Data and block structure
• 94 time-series variables spanning 1990 to
2007:
– Block exogenous oil price block.
– Block exogenous world block containing 7 foreign
variables (Haug and Smith, 2007).
– Block exogenous climate block (Buckle et al, 2007).
– Fully endogenous domestic block, containing 85
variables spanning national accounts, labour,
housing, financial market, and confidence.
Results
• Compare out of sample forecasting performance
for the large BVAR against :
–
–
–
–
–
AR forecasts
Random walk
Small VARs and BVARs
8 variable BVAR (Haug and Smith, 2007)
14 variable BVAR (Buckle et al, 2007)
• For most variables, the large BVAR performs at
least as well as other model specifications.
Results
Table 1: RMSFE of large BVAR relative to competing specifications
Horizon
1
2
3
4
Variable
GDP
Tradable CPI
Non-tradable CPI
90 day rates
Real exchange rate
GDP
Tradable CPI
Non-tradable CPI
90 day rates
Real exchange rate
GDP
Tradable CPI
Non-tradable CPI
90 day rates
Real exchange rate
GDP
Tradable CPI
Non-tradable CPI
90 day rates
Real exchange rate
Univariate
AR
RW
0.83
0.83
0.81
0.53*
1.16
1.13
0.75
0.68
1.04
0.85
0.76
0.79
0.70
0.53*
1.21
1.12
0.57*
0.54*
1.17
0.50*
0.65*
0.77
0.67
0.61*
1.41
1.44
0.43*
0.37*
1.20
0.45*
0.72
1.04
0.70
0.78
1.92
2.14
0.46*
0.35*
1.27
0.49*
BL
0.29*
1.21
0.41*
0.29*
0.58*
0.23*
1.35
0.41*
0.27*
0.29*
0.15*
1.08
0.67
0.24*
0.23*
0.16*
1.11
1.13
0.30*
0.23*
Multivariate
BL(SBC) BL(BVAR)
MED
0.83
0.73*
0.45*
1.16
1.25*
0.97
0.65
0.67
0.32
0.53*
0.74
0.32*
1.09
1.07
0.73*
0.74
0.73*
0.36*
1.35*
1.29
0.98
0.60
0.57*
0.33*
0.52*
0.78
0.16*
0.76
1.02
0.47*
0.57
0.68*
0.24*
1.64*
1.26
0.97
0.75
0.66*
0.42*
0.45
0.54
0.13*
0.71
1.02
0.45*
0.49*
0.83
0.23*
2.29
1.38*
1.03
1.26
0.88
0.58*
0.51*
0.60
0.17*
0.71
1.04
0.38*
MEDL
0.64
1.03
0.47*
0.48*
0.73*
0.52*
1.00
0.42*
0.36*
0.51*
0.41*
0.92*
0.49*
0.19*
0.44*
0.37*
1.03
0.65*
0.15*
0.45*
Impulse responses
• Apply a recursive shock specific identification
scheme.
• Variables are split into fast-moving variables
which respond contemporaneously to a shock,
and slow-moving variables which do not.
• Shocks
– Monetary policy shock
– Net migration shock
– Climate shock
Monetary Policy Shock
GDP
90-day rates
0
1
Real exchange rate
1
-0.1
0.5
0.5
-0.2
0
-0.5
0
-0.3
0
12
-0.4
-0.5
0
Non-tradable prices
12
-1
Tradable prices
0.05
0.2
0
0
0.15
-0.05
-0.05
0.1
-0.1
-0.1
0.05
0
12
-0.15
0
12
0
0
Private consumption
House prices
0
0.1
-0.2
0
12
Unemployment rate
0.05
-0.15
0
12
Private investment
0
-0.5
-0.4
-0.1
-0.6
-1
-0.2
-0.8
-1
-0.3
0
12
0
12
-1.5
0
12
Migration shock
Net migration
90-day interest rates
Real exchange rate
0.8
4
8000
0.6
2
6000
0.4
0
0.2
-2
0
-4
10000
4000
2000
0
-2000
-0.2
0
12
0
Private consumption
1
12
-6
0
12
Tradable prices
0
Non-tradable prices
0.4
0.5
0.2
-0.5
0
0
-1
-0.5
-1
-0.2
0
12
-1.5
0
12
-0.4
0
House prices
Ease finding skilled labour
Residential investment
4
3
4
3
2
2
2
12
0
1
1
-2
0
0
-4
-1
-1
-2
-2
0
12
-6
0
12
-8
0
12
Climate shock
Southern oscillation index
20
90-day rates
Real exchange rate
0.3
4
0.2
3
15
2
0.1
1
10
0
0
5
-0.1
0
-0.2
0
12
-1
0
GDP
12
Non-tradable prices
1
0.2
0.5
0
0
-0.2
-0.5
-0.4
-2
0
12
Tradable prices
1
0.5
0
-1
0
12
-0.6
-0.5
0
0
0
12
Exports
Manufactured production
1
12
Primary production
1
2
0
1
0
-1
-1
-1
-2
-2
-3
-2
-3
-4
0
12
-3
0
12
-4
0
12
Summary
• The large BVAR provides a good description of
New Zealand data, and tends to produce better
forecasts than smaller VAR specifications.
• The impulse responses produced by this model
appear very reasonable.
• Due to the large size of the model, we are able to
obtain responses down to a sectoral level.
Extensions
• The model has recently been modified to produce
conditional forecasts and fancharts using
Waggoner and Zha’s (1999) algorithms.
• This allows us to forecast with an unbalanced
panel, impose exogenous tracks for foreign
variables, and to incorporate shocks into the
forecasts.
• We have evaluated the forecasting performance in
a real-time out of sample forecasting experiment,
and found that the BVAR is competitive with other
forecasts including published RBNZ forecasts.