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.

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

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

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

Migration shock

Climate shock

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.