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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.