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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ijk ,0

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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.