A look into the factor model black box Publication lags and the role of hard and soft data in forecasting GDP

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1 A look into the factor model black box Publication lags and the role of hard and soft data in forecasting GDP Marta Bańbura and Gerhard Rünstler Directorate General Research European Central Bank November 2006

2 PRESENTATION OUTLINE ECB uses DFM by Doz et al. (2005) Forecasting from unbalanced monthly data Integration of interpolation and forecasting Good forecasting performance Statistics to assess role of individual series

3 PRESENTATION OUTLINE Unbalanced data & dynamic model Kalman filter weights Uncertainty measures Application: hard & soft data in forecasting euro area GDP Publication lags matter a lot

4 MODEL: DFM x t = Λf t + ξ t, ξ t N(0, Σ ξ ), px f t = A i f t i + ζ t, i=1 ζ t = Bη t, η t N(0,I q ).

5 MODEL: interpolation Forecast for 3-month growth in GDP by (3) t y Q t = 1 3 (y(3) t + y (3) t 1 + y(3) t 2 ) y (3) t = y t + y t 1 + y t 2 Evaluated only in 3 rd month of the quarter Fcst equation for monthly growth rates y t y (3) t+1 = µ + λ0 f t+1 + ε (3) t+1, ε(3) t+1 N(0, Σ(3) ε )

6 MODEL: State space form xt y Q t = Λ f t y (3) t Q t ξt + 0 I r 0 0 λ f t+1 by (3) t+1 Q t+1 = A Ξ t+1 f t y (3) t Q t + ζ t+1 ε (3) t 0

7 MODEL: interpolation Forecast for monthly GDP by t y Q t = 1 3 (y(3) t + y (3) t 1 + y(3) t 2 ) y (3) t = y t + y t 1 + y t 2 Evaluated only in 3 rd month of the quarter Fcst equation for monthly growth rates y t y t+1 = µ + λ 0 f t+1 + ε t+1, ε t+1 N(0, Σ ε )

8 MODEL: Kalman filter & smoother For state space form z t = Wα t + u t, u t N(0, Σ u ) α t+1 = T t α t + v t, v t N(0, Σ v ), and any unbalanced data Z t the KF provides a j t+h t = E [α t+h Z t ] P j t+h t = E a t+h t α t+h at+h t α t+h 0,

9 Euro area data set Real activity 32 Industrial production 6 weeks Retail sales 6 weeks Labour market 6-8 weeks Surveys (EC) 22 0 weeks Business Consumer Retail & construction Financial data 22 0 weeks Exchange & interest rates Stock price indices Other

10 FORECAST EVALUATION Example Real activity Surveys Financial Q2 (Oct) (Nov) (Dec) 1 Jan 2 Feb 3 Mar 4 Apr 5 May 6 Jun 7 Jul

11 FORECAST EVALUATION Example Real data Surveys Financial Q2 (Oct) (Nov) (Dec) 1 Jan 2 Feb 3 Mar 4 Apr 5 May 6 Jun 7 Jul

12 FORECAST EVALUATION Example Real data Surveys Financial Q2 (Oct) (Nov) (Dec) 1 Jan 2 Feb 3 Mar 4 Apr 5 May 6 Jun 7 Jul

13 FORECAST EVALUATION Example Real data Surveys Financial Q2 (Oct) (Nov) (Dec) 1 Jan 2 Feb 3 Mar 4 Apr 5 May 6 Jun 7 Jul

14 FORECAST EVALUATION Forecast performance (2000 Q Q2) Fcst Example Nr Q2 AR(1) QVAR Bridge DFM eqs 1 Jan Feb Mar Apr Jun Jul Aug

15 INDIVIDUAL SERIES: Forecast weights Express by Q t+h t as the weighted sum of observations in Z t (Harvey and Koopman, 2003) t 1 by Q t+h t = X ω k,t (h)z t k, k=0 Weights are time-invariant for our definition of Z t. Cumulative forecast weights P t 1 k=0 ω k,i(h) for series i, Historical contributions of series i to the forecast

16 INDIVIDUAL SERIES: Uncertainty measures Define subsets of indicators x t =(x 1 t 0,x 2 t 0,x 3 t 0 ) 0 Form data Z j t : all observations of x j t eliminated Consider difference in precision from data Z t and Z j t Advantage: no re-estimation (maintain original factor loadings)!

17 INDIVIDUAL SERIES: Uncertainty measures Example Real data Surveys Financial Q2 (Oct) (Nov) (Dec) 1 Jan 2 Feb 3 Mar 4 Apr 5 May 6 Jun 7 Jul

18 INDIVIDUAL SERIES: Uncertainty measures a) Filter uncertainty (Giannone et al., 2005) var(by Q, j t+h t yq t+h )=π j t+h t + σ2 ε, σ 2 ε is residual uncertainty π j j j t+h t is uncertainty from ft+h t.(from Pt+h t ) b) RMSE from recursive forecasts

19 APPLICATION Data downloaded on 30, June 2006 Pseudo real-time design 2datasets Main (original publication lags) Balanced (w/o publication lags in real data)

20 Cumulative forecast weights R e a l a c t v i t y S u r v e y s F i n a n c i a l M ai n B al a n ce d

21 Cumulative forecast weights 1.0 Main data Forecast Balanced data Forecast Forecast Forecast Forecast Forecast

22 Mean absolute contributions of data groups (1998 Q1-2005Q4) Data Main Balanced Fcst Contributions (%) Fcst Contributions (%) Z S F R Z S F R % 57 % 14 % % 46 % 46 % % 57 % 15 % % 46 % 44 % % 56 % 16 % % 42 % 49 % % 50 % 16 % % 40 % 48 % % 42 % 17 % % 35 % 47 % % 37 % 25 % % 29 % 52 % % 35 % 32 % % 29 % 50 %

23 Filter uncertainty ALL w/o Financial w/o Surveys w/o RA ALL w/o Financial w/o Surveys w/o RA w/o Financial w/o Surveys w/o RA w/o Financial w/o Surveys w/o RA

24 Filter uncertainty (Full-sample parameter estimates) Main Balanced Z RS RF SF Z RS RF SF

25 Table 3: RMSE from recursive forecasts (1998 Q1-2005Q4) AR Main Balanced Z RS RF SF Z RS RF SF

26 CONCLUSIONS Investigating the role of individual series in a DFM Based on Kalman filter Deal with unbalanced data sets Avoid re-estimation of parameters Usage for selection of series

27 CONCLUSIONS Hard & soft data: differences in publication lags matter a lot! Surveys are close substitutes to real data Financial data provide complementary information Balanced data give a grossly wrong picture