Real-time conditional forecasting with Bayesian VARs. VARs: An application to New Zealand

Transcription

1 Real-time conditional forecasting with Bayesian VARs: An application to New Zealand Economics Department - Reserve Bank of New Zealand 9 CEF Conference

2 Overview Methodology Data VAR Large Large structural Large structural (conditional forecasts) Real time forecasting Tools for analysing the forecasts

3 Reserve Bank s forecasting process First-pass forecasts Monitoring quarter forecasts (incl. judgement) Model-based forecasts (incl. judgement) Alternative forecasts and scenarios to highlight risks Published forecasts (incl. judgement)

4 VAR Y t = (y,t, y,t,..., y N,t ) is a set of time series with a reduced-form VAR(p) representation: Y t = c + p B k Y t k + u t k=

5 The moments for the prior distribution of the coefficients are: { δi, j = i, k = E[(B k ) ij ] =, otherwise and V[(B k ) ij ] = λ k σ i σ j

6 Additional priors: Sums of coefficients and co-persistence In addition to these priors, we also add a couple more priors that favour unit roots and conintegration. The sums of coefficients prior of Doan, Litterman and Sims (98) and the co-persistence prior of Sims (99).

7 Large In a Bayesian regression, De Mol, Gianonne and Reichlin (8) show that a forecast based on point estimates converges to the optimal forecast as long as the tightness of the prior increases as the number of time series N becomes larger. Banbura, Gianonne and Reichlin (8) apply this result to a large.

8 Increasing tightness with N Select N (where N < N) benchmark variables for which in-sample fit will be evaluated; Evaluate the in-sample fit of a VAR estimated with OLS on the N benchmark variables; Set the sums of coefficients hyperparameter τ and the co-persistence hyperparameter θ to be proportionate to the overall tightness hyperparameter λ (τ = φ λ and θ = φ λ, where φ and φ ); Choose the overall tightness hyperparameter λ to have the same in-sample fit as the benchmark VAR.

9 Lag restrictions New Zealand is a small open economy where the foreign sector can be assumed exogenous. We estimate the model with strong recursive blocks (Zha 999), and assume that the world is block exogenous to the domestic economy.

10 Conditional forecasting We use Waggoner and Zha s (999) conditional forecasting algorithm. This allows us to forecast using an unbalanced panel, and to impose exogenous paths for some variables.

11 So, what have we got? A (potentially) large structural, capable of producing conditional forecasts. Estimation using Zha s block-by-block approach and Wagonner and Zha s conditional forecasting approach. Estimated parameters are conditional on structural assumptions (recursive ordering of blocks) and on assumed future paths for variables.

12 Real-time forecasting problem Data is released incrementally throughout the quarter. Data is subject to revision over time. At the same time the forecaster may have information available to them which is not captured by the model. We want to test the forecasting performance of our methodology, taking into account these features of the data.

13 Real time data Baseline variables: real GDP, non-tradable CPI, tradable CPI, 9-day rate, TWI other macroeconomic indicators (both domestic and foreign) Quarterly data ranging from 99Q to 8Q Real time panels run from Q to 8Q All data in levels or log levels

14 Conditioning information for real-time forecasts Time Activity Prices Financial Foreign t X X X X t FP X X X t FP FP FP FP t + h O O O FP

15 MSFE relative to FP MSFE Univariate Multivariate h AR SBC Priors BL BL SBC BL M ML LG LG GDP day TR CPI NT CPI TWI

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51 Useful tools Alternative scenarios Shock decompositions

52 Alternative Scenarios

53 Useful tools: Shock decompositions Recall, we have: Foreign Domestic We can further decompose the domestic sector: Foreign Real activity Prices Financial

54 Useful tools: Shock decomposition

55 Useful tools: Shock decomposition

56 Summary Large produces reliable forecasts for most variables considered. The ability to present alternative scenarios and shock decompositions make s more useful to policy makers than many competing methodologies.