SUBSECRETARÍA DE INDUSTRIA,
ENERGÍA Y TURISMO
SECRETARÍA GENERAL TÉCNICA
Subdirección General de Estudios,
Análisis y Planes de Actuación
A dynamic factor model to assess the real time
state of the Spanish industry using confidence
indicators
Ángel Cuevas
Research and Analysis Unit
Ministry of Industry, Energy and Tourism of Spain (MINETURprevMITYC)
[email protected]
EU workshop on business and consumer surveys (BCS)
Brussels, 15th-16th November 2012
BACKGROUND
 Interest in improving the measurement of the state of the





industrial business cycle for purposes of:
 Anticipation of adverse situations.
 Evaluation and implementation of economic and industrial
policies.
Improvement in databases of economic indicators.
Advances in econometric methods for time series.
Development of computer tools.
Stock and Watson (1991, 2002), Gayer and Genet (2006), Angelini
et al. (2008) Camacho and Perez-Quirós (2009), Cuevas and
Quilis (2011).
Objective: Multivariate modeling of a broad and representative set
of monthly indicators of industrial activity, with the purpose of
prediction, analysis and monitoring and forecasting of
macroeconomic aggregates (industrial GVA).
2
Inputs
Preprocessing
Dynamic factor model
{Treatment
unbalanced
panel}
Applications
3
Selection of indicators
• High frequency indicators (monthly).
• Must provide a synthetic measure of the Spanish
industrial activity.
• They must be available promptly.
• They must be correlated with the reference series:
Industrial Production Index (IPI)
4
Selection of indicators
• Prove the correlation with the IPI:
 Cross-correlation with the growth signal of SAC
series.
 Cyclical Analysis: Butterworth (band-pass) +
classification of the turning points (Bry-Boschan).
5
Selection of indicators
Ministry of Industry / EC
Markit Economics
General Directorate of Traffic
Spanish Electricity Network
Ministry of Industry
Start
date
1990 01
1998 05
1990 01
1990 01
1994 01
Release
date
t-2 days
t+1 day
t+1 day
t+1 day
t+25 days
balance of replies
balance of replies
units
million Kw/h
units
Ministry of Industry
1994 01
t+25 days
units
Petroleum Products
Corporation
1990 01
t+30 days
thousand of metric tons
Variable
Source
Industrial Confidence Indicator
PMI Industry
Car Registrations
Electricity Consumption
Manufacture of cars
Manufacture of commercial and industrial
vehicles
Consumption of diesel
Industrial Production Index
Large Companies Sales. Industry
Turnover Index in Industry
New Orders Index in Industry
National Statistical Institute 1990 01 t+35 days
Tax State Agency
National Statistical Institute
National Statistical Institute
1995 01
2002 01
2002 01
t+35 days
t+50 days
t+50 days
Unit
volume index
deflated value index
deflated value index
deflated value index
Leading indicators are highlighted in yellow
6
Leading indicators
0.90
0.80
Cross-correlation:
y-o-y rates/differences
0.72
0.77
0.79 0.81 0.80 0.78
0.75
Industrial Confidence
Indicator
0.68
0.70
0.60
0.60
0.52
0.50
0.43
0.40
0.31
0.30
0.22
0.20
0.10
0.00
6
0.70
0.65 0.65 0.64 0.62
0.60
0.70
0.58
PMI Industry
0.52
0.50
5
4
3
0.65 0.65 0.64 0.65
2
0.62
0.60
1
0.30
0.20
-3
-4
-5
-6
0.54
0.45
0.39
0.40
0.21
-2
Car registrations
0.50
0.34
-1
0.58
0.44
0.40
0
0.31
0.10
0.30
0.10
0.22
0.00
0.20
0.13
-0.02
-0.10
0.10
-0.13
-0.20
-0.22
-0.30
6
5
4
3
2
1
0
-1
-2
-3
-4
-5
-6
0.04
0.00
6
5
4
3
2
1
0
-1
-2
-3
-4
-5
-6
7
Leading indicators
0.40
Cross-correlation:
m-o-m rates/differences
0.35
0.30
0.20
Industrial Confidence
Indicator
0.24
0.10
0.10
0.20
0.18 0.17
0.17
0.12 0.13 0.11
0.09
0.04
0.00
-0.10
-0.20
-0.19
-0.30
6
4
3
2
1
0
-1
-2
-3
-4
-5
-6
0.40
0.40
PMI Industry
0.30
0.20
5
0.10
0.18 0.16
0.20
0.11
0.10
0.05
0.14
0.10
0.05
0.08 0.08
0.07
0.06
0.08
0.01
0.00
0.00
-0.10
-0.10
-0.08
-0.13
-0.20
Car registrations
0.22
0.23
0.22
0.19
0.27
0.30
-0.02 -0.03
-0.05
-0.07
-0.08
-0.20
-0.18
-0.30
-0.30
6
5
4
3
2
1
0
-1
-2
-3
-4
-5
-6
6
5
4
3
2
1
0
-1
-2
-3
-4
-5
-6
8
Leading indicators
0.80
0.69
0.39
0.37
0.40
0.20
Industrial Confidence
Indicator
0.54
0.60
Cross-correlation:
q-o-q rates/differences
(quarterly frequency)
0.68
0.18
0.11
0.00
-0.20
-0.16
-0.28
-0.40
4
2
1
0
0.44
0.43
-1
-2
-3
-4
0.80
0.80
PMI Industry
0.60
0.39
0.40
0.45
0.60
0.45
0.38
0.40
0.22
0.20
3
0.20
0.09
0.19
Car registrations
0.24
0.16
0.00
0.00
-0.04
-0.05
-0.20
-0.20
-0.25
-0.40
4
3
2
1
0
-1
-2
-0.22
-0.31
-3
-0.35
-4
-0.17
-0.40
4
3
2
1
0
-1
-2
-3
-4
9
Leading indicators
Cyclical Analysis: ICI
10
Leading indicators
Cyclical Analysis: Car registrations
11
Leading indicators
Cyclical Analysis: PMI
12
Inputs
Preprocessing
Dynamic factor model
{Treatment
unbalanced
panel}
Applications
13
Preprocessing
• The series are adjusted for seasonal and calendar effects (if such
effects are significant).
• Logarithmically transformed.
• Regular differences.
s ac
i,t
zi,t  (1  B) log(x
)
s ac
i,t
x
s ac
i,t 1
x
s ac
i,t 1
x
s ac
i,t (Soft)
zi,t  (1  B)x
• The above variables are standardized.
14
Inputs
Preprocessing
Dynamic factor model
{Treatment
unbalanced
panel}
Applications
15
at
Common dynamic
(B)
ft
Idiosyncratic
dynamics
z1,t
z2,t
z3,t
u1,t
u2,t
u3,t
1(B)
2(B)
e1,t
e2,t
Static factor model
3(B)
e3,t
16
Dynamic factor model: complete representation
Zt  Lft  Ut
0   ft  at 
 f (B)
 
 0



 U(B) Ut  et 

 0 1 0  
at 
e  ~ iid N  , 0 Q  
e
 t
 0 
17
Factor model: dynamics
2
3
f (B)  1  1B  2B  3B  4B

 U (B)  diag 1  i,1B i  1..k
Qe  diag
4

  i  1..k 
i,i
18
Factor model: estimation (Nº. factors)
SCREE PLOT
4
3.5
3
Eigenvalue
2.5
2
1.5
1
0.5
0
0
2
4
6
Number
8
10
12
19
Dynamic factor model: estimation (f)
• The common factor and its standard deviation are
estimated by Kalman filter, adjusting the dynamic
factor model to state space representation.
Z t  HS t  Vt
S t  FS t 1  Wt
 0   R 0 
 Vt 

  ~ iidN , 
Wt 
 0   0 Q 
  [H(L), F( F ,  U ), R  0, Q()]
20
Dynamic factor model: loadings
Turnover Index in Industry
Industrial Production Index
New Orders Index in Industry
Large Companies Sales. Industry
Consumption of diesel
Manufacture of commercial and industrial
vehicles
PMI Industry
Electricity Consumption
Manufacture of cars
Industrial Confidence Indicator
Car Registrations
Loadings
0,90
0,83
0,83
0,73
0,71
Lead/Lag
0
0
0
0
0
0,43
0
0,39
0,36
0,36
0,31
0,24
3
0
0
3
3
21
Inputs
Preprocessing
Dynamic factor model
{Treatment
unbalanced
panel}
Applications
22
Estimation with an unbalanced panel
1
... ... ... ... ... ... ... ...
Observation
1
2
3
T1
T2
2
3
Indicator
4
5
6
7
8
Longitudinal panel:
initial estimate of
the common factor
Cross-section panel
Dark grey: observed
Light grey: non observed
23
Estimation with an unbalanced panel
t
1
2
3
4
5
6
7
8
9
10
11
12
13
14
1
2
3
Indicator
4
5
6
7
8
Factor
Static Dynamic
24
Estimation with an unbalanced panel
t
1
2
3
4
5
6
7
8
9
10
11
12
13
14
BALANCED PANEL: Using OLS (Stock-Watson)
Indicator
1
2
3
4
5
6
7
8
Factor
Static Dynamic
25
Estimation with an unbalanced panel
t
1
2
3
4
5
6
7
8
9
10
11
12
13
14
BALANCED PANEL: Using Kalman Filter
Indicator
1
2
3
4
5
6
7
8
Factor
Static Dynamic
26
Estimation with an unbalanced panel
t
1
2
3
4
5
6
7
8
9
10
11
12
13
14
REFINED BALANCED PANEL (KF). Repeat until convergence is achieved.
Indicator
Factor
1
2
3
4
5
6
7
8
Static Dynamic
27
Estimation with an unbalanced panel
t
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
FINAL BALANCED PANEL AND FORECASTS: Using Kalman Filter.
Indicator
Factor
1
2
3
4
5
6
7
8
Static Dynamic
28
Inputs
Preprocessing
Dynamic factor model
{Treatment
unbalanced
panel}
Applications
29
199101
199104
199203
199302
199401
199404
199503
199602
199701
199704
199803
199902
200001
200004
200103
200202
200301
200304
200403
200502
200601
200604
200703
200802
200901
200904
201003
201102
201201
Industrial GVA and dynamic factor
IGVA and Factor. y-o-y rates. Quarterly frequency
10
5
0
-5
-10
IGVA
Factor
-15
30
Industrial GVA and dynamic factor
0.90
0.80
0.80
0.78
0.70
0.70
0.62
0.60
0.54
0.50
Cross-correlation:
y-o-y rates
0.40
0.41
0.36
0.30
0.24
0.20
0.09
0.10
0.00
4
3
2
1
0
-1
-2
-3
0.08
0.07
-2
-3
-4
0.70
0.60
Cross-correlation:
q-o-q rates
0.55
0.57
0.50
0.39
0.40
0.30
0.30
0.24
0.20
0.10
0.09
0.04
0.00
4
3
2
1
0
-1
-4
31
Forecasting and interpolation of industrial GVA
Monthly IGVA y-o-y rate
6
5
4
3
2
1
0
-1
-2
-3
-4
Benchmarking method:
Chow-Lin, Fernández
Real time estimation: y-o-y rate IGVA 2012 Q-I
-2.4
-2.6
3.1
3.5
2.5 2.7 2.3
2.7
1.7
3.4
2.3
0.5
-0.9 -0.7
-2.5
-3.3 -3.1 -3.2 -3.2
Forecasting performance,
2003:Q1 – 2012:Q1
-3,101%
RMSE
-2.8
-3.0
-2.8
ARIMA
2,755
-3.4
DFM + Bench.
1,461
-3.6
ISI (MEC) + Bench.
1,707
-3.2
32
Markov swithching model
33
Conclusions
 It has developed a coincident indicator of Spanish industrial activity, trying




to exploit all possible information from various related monthly indicators.
The presence of leading indicators is critical in order to project the factor
and anticipate the evolution of industrial activity in real time.
These leading indicators are ICI, PMI and car registrations and they have a
lead of three months.
The methodology allows not only to estimate this factor, but also get
individual predictions in a multivariate context of all the indicators
included in the model.
With the estimated factor there are various options for use:
 Perform a real time prediction of IGVA
 Translate its variations into probabilities of recession
 This work can be extended in many directions: transfer functions, more
sophisticated Markov switching models, etc.
34
References
 Angelini, E., Camba-Méndez, G., Giannone, D., Reichlin, L.,




Runstler, G (2008) “Short-term forecasts of Euro area GDP growth”.
CEPR Discussion Paper n. 6746.
Camacho M, Pérez-Quirós G (2010) “Introducing the EuroSTING: Short Term Indicator of Euro Area Growth. Journal of Applied
Econometrics.
Cuevas, A. & Quilis, E.M. (2011) “A factor analysis for the Spanish
economy”. SERIEs Journal of the Spanish Economic Association.
Gayer, C. & Genet, J.(2006) “Using Factor Models to Construct
Composite Indicators from BCS Data - A Comparison with European
Commission Confidence Indicators”. Economic Papers N.240,
European Commission.
Kim, C.-J. & Nelson, C.R. (1999) “State-Space Models with Regime
Switching”, The MIT Press.
35
SUBSECRETARÍA DE INDUSTRIA,
ENERGÍA Y TURISMO
SECRETARÍA GENERAL TÉCNICA
Subdirección General de Estudios,
Análisis y Planes de Actuación
Thanks for your attention
Ángel Cuevas
Research and Analysis Unit
Ministry of Industry, Energy and Tourism of Spain (MINETUR)
[email protected]
EU workshop on business and consumer surveys (BCS)
Brussels, 15th-16th November 2012