Short-term forecasts of GDP from dynamic factor models · Angelini et al. (EJ, 2010): DFM vs ECB...

Short-term forecasts of GDPfrom dynamic factor models

Gerhard Rünstler

[email protected] Institute for Economic Research

November 16, 2011

1

1 Introduction

Forecasting GDP from large unbalanced monthly data sets

Dynamic factor models (DFMs) have become a common tool

Latest development: Giannone, Reichlin and Small (JME, 2010)

�Explicit modelling of factor dynamics

� Implemented with Kalman �lter

�Nowadays widely used in CB world

2

DFM (Giannone et al., 2010)

xt = �ft + �t; �t � N(0;��),

ft =

pXi=1

Aift�i + �t,

�t = B�t; �t � N(0; Iq)

3

Introducing monthly GDP growth

byt = �0ft

by(3)t = byt + byt�1 + byt�2yQ3k =

1

3(y(3)3k + y

(3)3k�1 + y

(3)3k�2)

4

State space form

�xtyQt

�=

�� 0 00 0 1

�24 ft

y(3)t

Qt

35+ � �t0

�

24 Ir 0 0��0 1 00 �1

3 1

3524 ft+1

y(3)t+1

Qt+1

35 =

24 A1 0 00 0 00 0 �t

3524 ft

y(3)t

Qt

35+24 B�t"t+10

35

5

2 Features

E¢ cient handling of unbalanced data

Good forecasting performance

Integration of interpolation and forecasting

Contributions for forecast can be obtained

Weights may be used for series selection

6

3 Forecast performance 1

Angelini et al. (EJ, 2010): DFM vs ECB BEQs for euro area

Data set: 85 series from 1991 Q1

Fcst evaluation: 1999 Q1 - 2007 Q2

Pseudo-real time forecast design

� recursive estimates

� replicate real-time data availability

� but �nal data vintages

7

C30 E. Angelini et al.

Table 1. Bridge equations for euro area GDP growth (BES model).

Equation

Explanatory variables 1 2 3 4 5 6 7 8 9 10 11 12

Industrial production (total) ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗

Ind. production construction ∗ ∗ ∗ ∗ ∗ ∗ ∗

Retail sales ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗

New car registrations ∗ ∗ ∗ ∗ ∗

Service confidence ∗ ∗ ∗ ∗

Unemployment rate ∗ ∗

Money M1 ∗ ∗

Business confidence ∗

EuroCoin (CEPR) ∗

OECD leading indicator ∗

Note: With the exception of EuroCoin and the service confidence index, the data have been transformed to representmonthly differences when expressed in rates (unemployment and business survey) and monthly growth rates otherwise.All series appear at lag 0 in the equations, i.e. β

ji (L) = β

ji0 with the exception of EuroCoin, which appears at lag 1, i.e.

βji (L) = β

ji1L, and real money, which appears at lag 2, i.e. β

ji (L) = β

ji2L

2.

the CEPR–Bank of Italy coincident indicator for the euro area ‘EuroCoin’. The models used ineach of the 12 individual equations are listed in Table 1. The GDP forecast is derived as thesimple average of the predictions from such equations. In what follows we refer to the method asthe BES model, standing for Bridge Equations based on Selected predictors.

These indicators are regularly monitored not only by the ECB in its Monthly Bulletin, butalso by a majority of euro area market analysts. Some equations are based on simple accountingreasoning. This is the case for the equations based on hard monthly indicators, like industrialproduction, construction production, retail sales and new car registrations, which are componentsof GDP. Other equations are instead based on soft/indirect indicators such as surveys andfinancial variables, whose relationship with GDP is looser but they convey useful informationsince they cover some areas of activity for which there are no hard indicators and they are releasedearlier. For further details, see Runstler and Sedillot (2003) and Diron (2006).

The factor model is based on a larger information set incorporating a wide range of monthlyindicators. We consider n = 85 monthly predictors. Among the official data on the euro areaeconomic activity we include 19 series, i.e. components of industrial production (17), retailsales, new passenger car registrations. As for survey data, we use 24 series from the EuropeanCommission business, consumer, retail and construction surveys. Financial data comprise 22series including exchange rates (6), interest rates (7), equity price indices (4) and raw materialprices (5). For the international economy we consider 11 series, including key macroeconomicindicators for the United States (7) and extra area trade volumes from the balance of paymentsstatistics (4). In addition, the data set includes five series related to employment and four serieson monetary aggregates and loans. We have transformed series to obtain stationarity. The seriesand their transformations are described in the Appendix.

We also produce early estimates of GDP growth averaging many bridge equations based onthe same information set used for bridging with factors. We assess the forecasting performanceof an average of the predictions obtained by the 85 univariate bridge equations. Each equation j

C© 2011 The Author(s). The Econometrics Journal C© 2011 Royal Economic Society.

Euro area data set

Real activity 32Industrial production 6 weeksRetail sales 6 weeksLabour market 6-8 weeks

Surveys (EC) 22 0 weeksBusinessConsumerRetail & construction

Financial data 22 0 weeksExchange & interest ratesStock price indicesOther

US data 10 various

9

FORECAST EVALUATION

Example Real activity Surveys FinancialQ2

(Oct)(Nov)(Dec)

1 Jan2 Feb3 Mar4 Apr5 May6 Jun7 Jul

11

FORECAST EVALUATION

Example Real data Surveys FinancialQ2

(Oct)(Nov)(Dec)


12

FORECAST EVALUATION


(Oct)(Nov)(Dec)


13

FORECAST EVALUATION


(Oct)(Nov)(Dec)


14

C34 E. Angelini et al.

Figure 1. Euro area GDP growth and model forecasts.

model exploits the information content of cross-correlations across series. The major gains occurfor the intermediate horizons, i.e. the forecasts made three to five months ahead of the releaseof the GDP flash estimate. For these forecasts, the RMSE is about 20% lower compared to theAR(1) benchmark. Differences among specification selection methods are small. This is in linewith Runstler et al. (2008) who found that information and recursive RMSE criteria perform


Short-term forecasts of euro area GDP growth C35

Figure 2. RMSE from pseudo real-time exercise 1999Q1–2005Q4.

Table 2. Root mean squared error from short-term forecasts (1999Q1–2007Q2).

BE models

Benchmarks BF model BEA

Quarter Vintage Naive AR(1) Rec Avg IC Best BES Rec Avg IC

Next −7 mid 0.35 0.35 0.34 0.33 0.33 0.32 0.35 0.35 0.35 0.34

−7 end 0.35 0.35 0.32 0.32 0.33 0.30 0.35 0.34 0.34 0.34

Next −6 mid 0.35 0.34 0.31 0.31 0.32 0.30 0.35 0.34 0.34 0.34

−6 end 0.35 0.34 0.31 0.29 0.31 0.28 0.34 0.33 0.34 0.33

Next −5 mid 0.35 0.34 0.31 0.29 0.30 0.28 0.35 0.33 0.33 0.33

−5 end 0.35 0.34 0.27 0.26 0.26 0.24 0.35 0.33 0.33 0.33

Curr. −4 mid 0.35 0.34 0.27 0.26 0.26 0.24 0.34 0.33 0.33 0.32

−4 end 0.35 0.34 0.27 0.26 0.27 0.24 0.35 0.33 0.33 0.32

Curr. −3 mid 0.34 0.29 0.26 0.26 0.26 0.23 0.32 0.32 0.32 0.32

−3 end 0.34 0.29 0.26 0.25 0.26 0.24 0.32 0.31 0.32 0.31

Curr. −2 mid 0.34 0.29 0.22 0.23 0.23 0.21 0.26 0.31 0.31 0.31

−2 end 0.34 0.29 0.21 0.22 0.22 0.20 0.25 0.31 0.31 0.31

Prev. −1 mid 0.34 0.29 0.19 0.21 0.20 0.18 0.23 0.30 0.31 0.30

−1 end 0.34 0.29 0.20 0.21 0.21 0.20 0.23 0.30 0.31 0.30

Note: The table reports root mean square forecast errors from different models computed at the end of the month (end)or in the middle of the month (mid) as explained in the main text. The number preceding these terms is used to indicatethe number of months pending prior to the release of GDP, e.g. −7 mid. The parametrizations for the BF model and theBEA model have been selected using three criteria. Namely, recursive mean square forecast error (Rec); averaging acrossall possible parameterizations (Avg); and applying recursively information criteria (IC). Best refers to the best modelex post , i.e. that which gave the lowest RMSE over the whole forecasting sample, which turn out to be the BF modelwith parameter settings r = 5, p = 3 and q = 1.


4 Forecast performance 2

Rünstler et al. (JoF, 2009): Forecast evaluation for 8 countries

Compare

�Fcst avg from bivariate quarterly VARS

�Fcst avg from bridge equations (single indicators)

�DFM by Giannone et al (2010)

�Di¤usion index (Stock and Watson, 1997)

�Generalized dynamic factor model (Forni et al, 2002)

8

Production and sales

Surveys Financial Prices Other

Euro area EA 85 25 25 24 0 11 1991Belgium BE 393 25 262 50 42 14 1991Germany DE 111 55 19 32 4 1 1991France FR 118 19 96 0 2 1 1991Italy IT 84 27 24 10 20 3 1991Netherlands NL 76 8 33 8 23 4 1991Portugal PT 141 32 78 12 10 9 1991Lithuania LT 103 35 21 12 33 1 1995Hungary HU 80 33 9 12 11 15 1998Poland PL 81 16 30 10 11 14 1997

of which

Table 1: DatasetsNo of series

Sample start

EA BE DE FR IT NL PT LT HU PL EuroA NMS

AR 5 5 5 6 3 6 6 5 2 3 5.2 3.3VAR 4 6 6 5 5 1 5 1 5 1 4.7 2.3BEQ 3 4 4 4 6 4 4 2 3 4 4.3 3.0KF 1 1 1 2 1 2 1 4 4 5 1.3 4.3PC 2 3 2 1 2 5 2 6 6 6 2.5 6.0GPC 6 2 3 3 4 3 3 3 1 2 3.0 2.0

Table 3: Results overviewForecasts 2000 Q1 – 2005 Q4 for euro area countries and 2002 Q1– 2005 Q4 for NMS

Average RMSE for preceding, current and one-quarter-ahead forecasts relative to the naive forecast

4 Forecast weights

Express forecasts as the weighted sum of observations

byQt+hjt =Pt�1k=0 !k;t(h)zt�k

Algorithm due to Harvey and Koopman (2003)

Weights are invariant for pseudo-real-time fcst

Inspect

�Cumulative forecast weightsPt�1k=0 !k;i(h) for series i,

�Historical contributions of series i to the forecast

9

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

Main

Balanced

1 2 3 4 5 6 7 1 2 3 4 5 6 71 2 3 4 5 6 7

21

Cumulative forecast weights

.

Main dataForecast 1

0.0

0.2

0.4

0.6

0.8

1.0

Forecast 4

0.0

0.2

0.4

0.6

0.8

1.0

Forecast 7

0.0

0.2

0.4

0.6

0.8

1.0

12

Balanced dataForecast 1

0.0

0.2

0.4

0.6

0.8

1.0

Forecast 4

0.0

0.2

0.4

0.6

0.8

1.0

Forecast 7

0.0

0.2

0.4

0.6

0.8

1.0

22

5 Variable selection

Bai and Ng (2007): Smaller data sets may be more e¢ cient

Use robust versions of stepwise regressions (LARS, LASSO)

Rünstler (2010) compares KF weights with LARS

Selections obtained from pre-sample

KF weights tend to be more robust

10

Euro area

0,1

0,2

0,3

7 6 5 4 3 2 1

Out-of-sample RMSEOptimal selections

All

Weights 20

LARS 30-0,3

-0,2

-0,1

0,0

0,1

0,2

0,3A

R(1) All 60 50 40 30 20 15 10

Out-of-sample RMSEGains against naive fcst Average across horizons

AR(1)KFWLars

Germany

0,3

0,4

0,5

7 6 5 4 3 2 1

Out-of-sample RMSEOptimal selections

AllWeights 20LARS 30-0,2

-0,1

0,0

0,1

0,2

AR(

1) All 60 50 40 30 20 15 10

Out-of-sample RMSEGains against naive fcst Average across horizons

AR(1)KFWLars

France

0,2

0,3

0,4

7 6 5 4 3 2 1

Out-of-sample forecastOptimal selections

AllWeights 50LARS 30

-0,3

-0,2

-0,1

0,0

0,1

0,2

0,3A

R(1) All 60 50 40 30 20 15 10

Out-of-sample RMSE Gains against naive forecastAverage across horizons

AR(1)KFWLars

Short-term forecasts of GDP from dynamic factor models · Angelini et al. (EJ, 2010): DFM vs ECB...

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