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A Leading index for theA Leading index for the Colombian economic activityColombian economic activity
Luis Fernando MeloLuis Fernando MeloFabio NietoFabio Nieto
Mario RamosMario Ramos
Luis Fernando MeloLuis Fernando MeloFabio NietoFabio Nieto
Mario RamosMario Ramos
It permits to lead the turning points of the economy or, in a global manner, the dynamics of the economic activity. This information is very useful for economic policy and decision making.
The problem: Design of a leading index
In previous solutions:
Usually, the design is accomplished by means of a weighted average of a group of variables.
The weights are selected in a heuristic way
In Colombia: Melo et al. (1988), Ripoll et al. (1995), Maurer and Uribe (1996) and Maurer et al. (1996)]
The statistical problem (Stock and Watson’s approach):
Find a stochastic process that leads, in some sense, the turning points of the so-called state of the economy.
• Basic step: find an optimal estimate of the state of the economy which is called a coincident index.
• Nieto and Melo (2001) have proposed an appropriate methodology for computing a coincident index for the economic activity, which is based on a modification to Stock and Watson’s (1989, 1991, 1992) procedures.
Coincident Index Model
• : state of the economy (not observable). tC• : coincident variables, which are integrated of order 1.
ntt XX ,...,1
nt
t
t
nnt
t
nt
t
u
u
C
X
X
1111
1)
tptpttCCC
112)
nt
t
knt
kt
k
nt
t
nt
t
u
u
D
u
u
D
u
u
11
1
11
1
1
3)
Ntnniidtiiidit
,,2,1;,0~;,0~ 22
In matrix form:
ttttC uγβX
tt
CB
tt
BD εu
1)
2)
3)
Model estimationModel estimation
Maximum likelihood approach via state space models(Kalman filter).
State Space representation of the Coincident Index Model:
ttt ZW
tttt RT 1c
• Observation equation: (eq. 1)
• System equation: (eq. 2 , 3)
t: state vector
Stock and Watson coincident index
-25-20-15-10
-505
1015202530
1959 1963 1967 1971 1975 1979 1983 1987
-0.15
-0.10
-0.05
0.00
0.05
0.10
0.15
1959 1963 1967 1971 1975 1979 1983 1987
-0.15
0.00
0.15
0.30
0.45
0.60
0.75
0.90
1.05
1959 1963 1967 1971 1975 1979 1983 1987
0.8
1.0
1.2
1.4
1.6
1.8
2.0
2.2
2.4
1959 1963 1967 1971 1975 1979 1983 1987
50
70
90
110
130
150
170
190
1959 1963 1967 1971 1975 1979 1983 1987
Ct Ct(1) = Ct / 199.79
Ct(2)= Ct
(1) + 0.88 t / N Ct
(3) = exp(Ct(2)
)
Ct(4) = 100Ct
(3) / C3
(3)
Simulations of the Stock and Watson coincident index model
2400
2800
3200
3600
4000
4400
4800
5200
5600
25 50 75 100
MSE of Ct|t
Then, the state space model used by S-W does not exhibit the steady-state property.
Likelihood surface for simulated models
OurOur modifications modifications
Coincident equation. (eq. 1)
Identifiability of the model. Restriction over some parameters of the model.
State space model representation - Our model has the steady-state property. - We include seasonal effects (do not use adjusted variables). - A strategy for providing the initial values is proposed.
1
0||0|
t
jtjtttt
CCC
- Coincident index:
Leading Index Model
ttt C uγX 1)
2)
tt
BD εu 4)
ty
tc
t
t
yyyc
cycc
y
c
t
t
v
v
Y
C
LL
LL
Y
C
,
,
1
1
3)
In matrix form:
• : state of the economy (not observable). tC• : Coincident variables.ntt XX ,...,1
• : Leading variables. qtt YY ,...,1
Where:
Model estimationModel estimation
Maximum likelihood approach via state space models(Kalman filter).
State Space representation of the Leading IndexModel:
***tt
ZW
******
1 ttttRT
c
• Observation equation: (eq. 1)
• System equation: (eq. 2 , 3, 4)
t*: state vector
Leading index (Lt)
ttttt CCL ||6
,...1,0j jtC where , , denotes the prediction of given given the information up to time t.Note that the information used in the context of the leading index is given by both the coincident and leading variables.
tjtC |
where denotes the coincident index for .
}{ tL }{ tC
ttttt CCL 6ctt
ctt CC |66
}{ /cttC
Stock and Watson’s idea was:
leads
if and are very close,
}{ tC
The leading index model includes two kind of observed variables.
Coincident (Xt): Melo et al. (2002)
Leading (Yt): We consider 83 series (Appendix B) based
on the following criteria:• Monthly periodicity
• Opportunity (lag information less than 2 ½ months)
• Availability (since January of 1980)
An empirical application of the leading index methodology
Unit root test
Co-movement statistics w.r.t. IPR and Ct
• Cross-Correlation function with double prewhitening
Selection of the leading series
Seasonal unit root test
• Spectral Analysis: Coherence Canova’s statistics
• Predictive Content
6
0
*5
00 )ln()ln()ln()ln(
ititi
jjtjtkt WRRR
Predictive power w.r.t. IPR and Ct
for k=1,6,12
12
1 10 )ln()ln()ln(
j
k
ititijtjt WRR
• Marginal predictive content
for k=6,12
where Rt is the reference series and Wt is a candidate for a leading variable.
The optimum group was select according to :
Selection of the leading index model
Coincident series: Melo et al. (2002)
Leading series: different sub-groups of the selected leading variables
• Economic criteria
• AIC
• Residual diagnostics
• Model stability
• Leading performance of the resulting index
Leading performance
Cross-correlation between Lt and Mt
where Lt is the resulting leading index:
ttttt CCL ||6
andCtt
Cttt CCM |6|6
with the super-index C denoting the estimations from N-M.
Then, if Lt and Mt are very close Lt can be considered as a leading index for {Ct}.
The final leading index model includes the following leading series:
• Approved building area (areacon)
• Real money supply M1 (m1r)
• Real Interest rate of 90-day certificate of deposit for banks and corporations (cdttr)
• Consumption good imports in real terms (impr_bco)
• Business conditions (clineg)
• Confidence indicator (incon)
Lt vs. Mt
-60
-40
-20
0
20
40
60
80 82 84 86 88 90 92 94 96 98 00
Lt Mt
ttttt CCL ||6 ctt
cttt CCM |6|6
-60
-40
-20
0
20
40
60
En
e-9
3
Ju
l-9
3
En
e-9
4
Ju
l-9
4
En
e-9
5
Ju
l-9
5
En
e-9
6
Ju
l-9
6
En
e-9
7
Ju
l-9
7
En
e-9
8
Ju
l-9
8
En
e-9
9
Ju
l-9
9
En
e-0
0
Ju
l-0
0
En
e-0
1
Ju
l-0
1
ttttt CCL /6/6
-60
-40
-20
0
20
40E
ne-9
3
Ju
l-9
3
En
e-9
4
Ju
l-9
4
En
e-9
5
Ju
l-9
5
En
e-9
6
Ju
l-9
6
En
e-9
7
Ju
l-9
7
En
e-9
8
Ju
l-9
8
En
e-9
9
Ju
l-9
9
En
e-0
0
Ju
l-0
0
En
e-0
1
Ju
l-0
1
ctt
cttt CCM /6/6
-0.20
-0.15
-0.10
-0.05
0.00
0.05
0.10
0.15
En
e-9
3
Ju
l-9
3
En
e-9
4
Ju
l-9
4
En
e-9
5
Ju
l-9
5
En
e-9
6
Ju
l-9
6
En
e-9
7
Ju
l-9
7
En
e-9
8
Ju
l-9
8
En
e-9
9
Ju
l-9
9
En
e-0
0
Ju
l-0
0
En
e-0
1
Ju
l-0
1
tt LIPRLIPR 6
-0.06
-0.04
-0.02
0.00
0.02
0.04
0.06
Ma
r-9
3
Sep
-9
3
Ma
r-9
4
Sep
-9
4
Ma
r-9
5
Sep
-9
5
Ma
r-9
6
Sep
-9
6
Ma
r-9
7
Sep
-9
7
Ma
r-9
8
Sep
-9
8
Ma
r-9
9
Sep
-9
9
Ma
r-0
0
Sep
-0
0
Ma
r-0
1
Sep
-0
1
tt LGDPLGDP 2
Lt vs. reference series
ttttt CCL ||6
ctt
cttt CCM |6|6
tt LIPRLIPR 6
tt LGDPLGDP 2
.
-40
-20
0
20
40
1991 1992 1993 1994 1995 1996 1997 1998.
-40
-20
0
20
40
1991 1992 1993 1994 1995 1996 1997 1998.
-40
-20
0
20
40
1991 1992 1993 1994 1995 1996 1997 1998.
-40
-20
0
20
40
1991 1992 1993 1994 1995 1996 1997 1998
September 1997
November 1997
January 1998
March 1998
Recession exercise for Lt
Indicador Coincidente de Actividad Económica
170
190
210
230
250
270
290M
ay-9
4
Nov
-94
May
-95
Nov
-95
May
-96
Nov
-96
May
-97
Nov
-97
May
-98
Nov
-98
May
-99
Nov
-99
May
-00
Nov
-00
May
-01
Nov
-01
May
-02
Nov
-02
May
-03
Fuente: SGEE - Banco de la República
Coincident Index (up to May 2003)
Indicador Líder de Actividad Económica
-60
-50
-40
-30
-20
-10
0
10
20
30
40
50N
ov-9
7
May
-98
Nov
-98
May
-99
Nov
-99
May
-00
Nov
-00
May
-01
Nov
-01
May
-02
Nov
-02
May
-03
Nov
-03
Fuente: SGEE - Banco de la República
IndicadorII TrimIII TrimIV Trim
Leading Indicator (up to May 2003)
