Analysing shock transmission in a data-rich environment: A large BVAR for New Zealand

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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
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Motivation

• Estimate the sectoral responses to a monetary
  policy shock.

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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 degrees 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.

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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.

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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.

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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

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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.

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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.

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How do we determine tightness of the priors (l)

• 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 l.
• Choose l so that the large BVAR produces the same
  in-sample fit on the n benchmark variables as
  the small VAR.

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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 Zhas (1999) block-by-block
  algorithm.

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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.

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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.

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Results
Table 1 RMSFE of large BVAR relative to
competing specifications
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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

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Monetary Policy Shock
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Migration shock
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Climate shock
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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.

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Extensions

• The model has recently been modified to produce
  conditional forecasts and fancharts using
  Waggoner and Zhas (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.