Post on 12-Jan-2016
description
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:
With prior beliefs on the relationships between variables.
• We use a modified Litterman prior.
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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
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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
Horizon Variable AR RW BL BL(SBC) BL(BVAR) MED MEDL1 GDP 0.83 0.83 0.29* 0.83 0.73* 0.45* 0.64
Tradable CPI 0.81 0.53* 1.21 1.16 1.25* 0.97 1.03Non-tradable CPI 1.16 1.13 0.41* 0.65 0.67 0.32 0.47*90 day rates 0.75 0.68 0.29* 0.53* 0.74 0.32* 0.48*Real exchange rate 1.04 0.85 0.58* 1.09 1.07 0.73* 0.73*
2 GDP 0.76 0.79 0.23* 0.74 0.73* 0.36* 0.52*Tradable CPI 0.70 0.53* 1.35 1.35* 1.29 0.98 1.00Non-tradable CPI 1.21 1.12 0.41* 0.60 0.57* 0.33* 0.42*90 day rates 0.57* 0.54* 0.27* 0.52* 0.78 0.16* 0.36*Real exchange rate 1.17 0.50* 0.29* 0.76 1.02 0.47* 0.51*
3 GDP 0.65* 0.77 0.15* 0.57 0.68* 0.24* 0.41*Tradable CPI 0.67 0.61* 1.08 1.64* 1.26 0.97 0.92*Non-tradable CPI 1.41 1.44 0.67 0.75 0.66* 0.42* 0.49*90 day rates 0.43* 0.37* 0.24* 0.45 0.54 0.13* 0.19*Real exchange rate 1.20 0.45* 0.23* 0.71 1.02 0.45* 0.44*
4 GDP 0.72 1.04 0.16* 0.49* 0.83 0.23* 0.37*Tradable CPI 0.70 0.78 1.11 2.29 1.38* 1.03 1.03Non-tradable CPI 1.92 2.14 1.13 1.26 0.88 0.58* 0.65*90 day rates 0.46* 0.35* 0.30* 0.51* 0.60 0.17* 0.15*Real exchange rate 1.27 0.49* 0.23* 0.71 1.04 0.38* 0.45*
Univariate Multivariate
Table 1: RMSFE of large BVAR relative to competing specifications
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
0 12-1
-0.8
-0.6
-0.4
-0.2
0House prices
0 12-0.4
-0.3
-0.2
-0.1
0GDP
0 12-0.3
-0.2
-0.1
0
0.1Private consumption
0 12-1.5
-1
-0.5
0Private investment
0 120
0.05
0.1
0.15
0.2Unemployment rate
0 12-0.15
-0.1
-0.05
0
0.05Tradable prices
0 12-0.15
-0.1
-0.05
0
0.05Non-tradable prices
0 12-0.5
0
0.5
190-day rates
0 12-1
-0.5
0
0.5
1Real exchange rate
Migration shock
0 12-2
-1
0
1
2
3
4Ease finding skilled labour
0 12-2
-1
0
1
2
3House prices
0 12-1
-0.5
0
0.5
1Private consumption
0 12-8
-6
-4
-2
0
2
4Residential investment
0 12-1.5
-1
-0.5
0Tradable prices
0 12-0.4
-0.2
0
0.2
0.4Non-tradable prices
0 12-2000
0
2000
4000
6000
8000
10000Net migration
0 12-0.2
0
0.2
0.4
0.6
0.890-day interest rates
0 12-6
-4
-2
0
2
4Real exchange rate
Climate shock
0 12-0.2
-0.1
0
0.1
0.2
0.390-day rates
0 12-2
-1
0
1
2
3
4Real exchange rate
0 12-4
-3
-2
-1
0
1
2Primary production
0 12-3
-2
-1
0
1Manufactured production
0 12-1
-0.5
0
0.5
1GDP
0 12-4
-3
-2
-1
0
1Exports
0 12-0.5
0
0.5
1Tradable prices
0 12-0.6
-0.4
-0.2
0
0.2Non-tradable prices
0 120
5
10
15
20Southern oscillation index
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.