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BRICS: Testing for Commonalities using Common
Features
Bruno Delalibera (FGV), Roberto Castello Branco (FGV), Jo˜ao V.
Issler (FGV)
June, 2015
B. Delalibera, R. Castello Branco, J.V. Issler
BRICS: Testing for Commonalities
June, 2015
1 / 16
Common Features – Basic Ideas
1
Series y1t has property A.
B. Delalibera, R. Castello Branco, J.V. Issler
BRICS: Testing for Commonalities
June, 2015
2 / 16
Common Features – Basic Ideas
1
Series y1t has property A.
2
Series y2t has property A.
B. Delalibera, R. Castello Branco, J.V. Issler
BRICS: Testing for Commonalities
June, 2015
2 / 16
Common Features – Basic Ideas
1
Series y1t has property A.
2
Series y2t has property A.
3
There exists a linear combination of them, y1t − e
αy2t , that does not
have property A.
B. Delalibera, R. Castello Branco, J.V. Issler
BRICS: Testing for Commonalities
June, 2015
2 / 16
Common Features – Basic Ideas
1
Series y1t has property A.
2
Series y2t has property A.
3
There exists a linear combination of them, y1t − e
αy2t , that does not
have property A.
4
Cointegration is the most well-known example of common features.
B. Delalibera, R. Castello Branco, J.V. Issler
BRICS: Testing for Commonalities
June, 2015
2 / 16
Common Features – Basic Ideas
1
Series y1t has property A.
2
Series y2t has property A.
3
There exists a linear combination of them, y1t − e
αy2t , that does not
have property A.
4
Cointegration is the most well-known example of common features.
5
Serial correlation-common features (SCCF) or common cycles are also
well-known: stationary series y1t and y2t both have serial correlation
(are predictable), but there exists y1t − e
αy2t which is white noise
(unpredictable).
B. Delalibera, R. Castello Branco, J.V. Issler
BRICS: Testing for Commonalities
June, 2015
2 / 16
Common Features – Basic Ideas
Engle and Kozicki (1993) main example.
1
No cointegration for log-levels of GDP for the U.S. and Canada.
Instantaneous growth rates of GDP for the U.S. and Canada have
serial correlation and there is a linear combination of growth rates
that is white noise. Cycles in U.S. and Canadian GDP growth are
synchronized.
B. Delalibera, R. Castello Branco, J.V. Issler
BRICS: Testing for Commonalities
June, 2015
3 / 16
Common Features – Basic Ideas
Engle and Kozicki (1993) main example.
1
2
No cointegration for log-levels of GDP for the U.S. and Canada.
Instantaneous growth rates of GDP for the U.S. and Canada have
serial correlation and there is a linear combination of growth rates
that is white noise. Cycles in U.S. and Canadian GDP growth are
synchronized.
This is our main finding between the growth rates of GDP for BRICS
countries (also for Industrial Production).
B. Delalibera, R. Castello Branco, J.V. Issler
BRICS: Testing for Commonalities
June, 2015
3 / 16
Common Features – Basic Ideas
Engle and Kozicki (1993) main example.
1
2
3
No cointegration for log-levels of GDP for the U.S. and Canada.
Instantaneous growth rates of GDP for the U.S. and Canada have
serial correlation and there is a linear combination of growth rates
that is white noise. Cycles in U.S. and Canadian GDP growth are
synchronized.
This is our main finding between the growth rates of GDP for BRICS
countries (also for Industrial Production).
Factor models and latent features:
US ∆ ln ytUS
λ
εt
=
ft +
, or,
CAN
1
∆ ln yt
εCAN
t
CAN
∆ ln ytUS − λ∆ ln ytCAN = εUS
,
t − λεt
1 −λ is the cofeature vector, eliminating the SCCF.
B. Delalibera, R. Castello Branco, J.V. Issler
BRICS: Testing for Commonalities
June, 2015
3 / 16
Common GDP Cycles – BRICS (no India)
B. Delalibera, R. Castello Branco, J.V. Issler
BRICS: Testing for Commonalities
June, 2015
4 / 16
Common Growth Cycles – BRICS (no India)
B. Delalibera, R. Castello Branco, J.V. Issler
BRICS: Testing for Commonalities
June, 2015
5 / 16
Common Features – VAR and VECM
Vahid and Engle (1993): VAR for yt , an n-vector of I (1) log GDP (or log
Industrial Production):
yt = Γ1 yt −1 + . . . + Γp yt −p + et .
(1)
∆ yt = Γ1∗ ∆ yt −1 + . . . + Γp∗ −1 ∆ yt −p +1 + γα0 yt −1 + et .
(2)
VECM:
Normalized cofeature vectors:
α˜ =
Is
α˜ ∗(n−s )×s
Quasi-structural model (restricted VECM):

"
Is
0
(n−s )×s
α˜ ∗0
In−s
#
"
∆ yt =
B. Delalibera, R. Castello Branco, J.V. Issler
#
0
s ×(np +r )
Γ1∗∗ . . . Γp∗∗−1
γ∗
BRICS: Testing for Commonalities
∆ yt −1
..
.



 ∆ yt −p +1
α0 yt −1



 + vt . (3)

June, 2015
6 / 16
A GMM Test for Common Cycles
GMM approach: exploits the following moment restriction and test
H0 :existence of s linearly independent SCCF:
"
#



Is
α˜ ∗0



0
In − s ∆ y t −



n
−
s
s
(
)×








∆ yt −1



"
#
⊗ Zt − 1 
0 = E 
,



.
0
..



 
s
×(
np
+
r
)



 


Γ1∗∗ . . . Γp∗∗−1 γ∗  ∆ yt −p +1  
0
α yt −1
where the elements of Zt −1 are the instruments comprising past series:
α0 yt −1 , ∆ yt −1 , ∆ yt −2 , · · · , ∆ yt −p +1 . The test for common cycles is an
over-identifying restriction test – the J test proposed by Hansen (1982).
This test is robust to HSK of unknown form if it uses a White-correction
in its several forms.
B. Delalibera, R. Castello Branco, J.V. Issler
BRICS: Testing for Commonalities
June, 2015
7 / 16
Common-Cycle Tests (GDP)
Country
Brazil
China
Russia
South Africa
Brazil
0.70
0.50
0.37
GDP
China
Russia
South Africa
0.48
0.62
0.17
-
Table: Real GDP: P-Values of Common-cycle tests – GMM based
B. Delalibera, R. Castello Branco, J.V. Issler
BRICS: Testing for Commonalities
June, 2015
8 / 16
Common Cycles in Industrial Production
B. Delalibera, R. Castello Branco, J.V. Issler
BRICS: Testing for Commonalities
June, 2015
9 / 16
Common Cycles in Industrial Production
B. Delalibera, R. Castello Branco, J.V. Issler
BRICS: Testing for Commonalities
June, 2015
10 / 16
Common Cycles in Industrial Production
B. Delalibera, R. Castello Branco, J.V. Issler
BRICS: Testing for Commonalities
June, 2015
11 / 16
Common-Cycle Tests (Ind. Production)
Country
Brazil
China
India
Russia
South Africa
Industrial Production
Brazil China India Russia
0.050
0.022 0.066
0.410 0.180 0.015
0.390 0.062 0.012 0.030
South Africa
-
Table: Industrial Production: P-Values of Common-cycle tests – GMM based
B. Delalibera, R. Castello Branco, J.V. Issler
BRICS: Testing for Commonalities
June, 2015
12 / 16
Common-Cycle Tests (Exports)
Country
Brazil
China
India
Russia
South Africa
Brazil
0.004
0.013
0.002
0.002
Exports
China India
Russia
South Africa
0.001
0.005
0.001
0.000
-
0.000
0.002
Table: Exports: P-Values in Common-cycle tests – GMM based
B. Delalibera, R. Castello Branco, J.V. Issler
BRICS: Testing for Commonalities
June, 2015
13 / 16
Common-Cycle Tests (Imports)
Country
Brazil
China
India
Russia
South Africa
Brazil
0.002
0.015
0.210
0.001
Imports
China India
Russia
South Africa
0.002
0.019
0.001
0.003
-
0.003
0.370
Table: Imports: P-Values in Common-cycle tests – GMM based
B. Delalibera, R. Castello Branco, J.V. Issler
BRICS: Testing for Commonalities
June, 2015
14 / 16
Common-Cycle Tests (BRICS and US)
BRICS and US
Country
Industrial Production
Brazil
0.09
China
0.54
India
0.62
Russia
0.21
South Africa
0.48
GDP
0.22
0.69
0.14
0.23
Table: BRICS and US: P-Values of Common-cycle tests – GMM based
B. Delalibera, R. Castello Branco, J.V. Issler
BRICS: Testing for Commonalities
June, 2015
15 / 16
Common-Cycle Tests (BRICS and Euro)
BRICS and Euro zone
Country
Industrial Production
Brazil
0.057
China
0.050
India
0.011
Russia
0.021
South Africa
0.024
GDP
0.293
0.420
0.270
0.210
Table: BRICS and Euro zone: P-Values of Common-cycle tests – GMM based
B. Delalibera, R. Castello Branco, J.V. Issler
BRICS: Testing for Commonalities
June, 2015
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