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CoPSJohansen’s contribution to CGE modelling: Johansen’s contribution to CGE modelling: originator and guiding light for 50 yearsoriginator and guiding light for 50 years
by
Peter Dixon and Maureen Rimmer
paper presented at the 2013 National CGE Workshop
Melbourne, October 7, 2013
Previously presented at the Symposium in memory of Professor Leif Johansen
and to celebrate the fiftieth anniversary of the publication of his“A Multi-Sectoral Study of Economic Growth”
(North Holland 1960)The Norwegian Academy of Science and Letters
May 20-21, 2010
http://www.monash.edu.au/policy/ftp/workpapr/g-203.pdf
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CoPSPaper has six partsPaper has six parts
I. Introduction - Johansen originator of CGE: individual agents
II. Johansen’s approach to CGE modelling
III. Other starting points
- Scarf, Jorgenson, Adelman & Robinson, Taylor
- But Johansen’s style remains distinctive
IV. Extending Johansen-style CGE modelling in Australia
V. Taking Johansen from Australia to the rest of the world
VI. Validation
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CoPS
II. Johansen’s approach to CGE modelling
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CoPSDefining features of Johansen Defining features of Johansen style style
Presentation of model as a rectangular system of linear equations in change and percentage-change variables
Solution by matrix inversion
Use of linear representation and the linear solution:
to clarify properties of the model;
to elucidate real world issues; and
to validate of the model.
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CoPSLinear representation and Linear representation and solutionsolution
B* L*
T* where 1T B * L
j j j*tj j j jX A * N * K *exp
j jj j j jx * n * k
in linear form
86 endogenous variables 46 exogenous variables
(86,46)
{aggregate capital (1), aggregate employment (1), population (1), exog. demands (22), tech. change (20), price non-comp imports (1)}
{employment (20), capital (20), outputs (22), prices (22), rate of return (1), consumption (1) }
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CoPSJohansen’s fascination with the T Johansen’s fascination with the T matrix:matrix:
clarifying properties of the modelclarifying properties of the model
0 1 jT x ,k
Johansen uses BOTE model to guide analysis of his T matrix
1. He inspected individual columns
0 1 jT x ,n
Exception: 0equipT x ,n
BOTE predicts
86 x 46 = 3956 results
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CoPS
Leontief: X=(I-A)-1*C Johansen: v1 = T*v2
1(I A)
submatrix of T
all 1
all 0 but mainly <1mainly < 0
all 0mainly > 0
all 0mainly > 0
mainly < 0
2. He looked at T(x,z), 22 by 22 matrix showing elasticities of outputs with respect to exogenous demands
complementary 1930s
Competition 1950s
Johansen’s fascination with T : clarifying properties of the modelJohansen’s fascination with T : clarifying properties of the model
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CoPSJohansen’s fascination with the T Johansen’s fascination with the T matrix:matrix:
elucidating real world issueselucidating real world issues3. He decomposed growth around 1950
1 2 6 j T(j)* (j), j , , ...,
Six sets of exogenous variables: capital, employment, population, exogenous demands (22), technology (20), price of non-competing imports
• determinants of agricultural employment• capital growth as source of wage growth
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CoPSJohansen’s fascination with the T Johansen’s fascination with the T matrix:matrix:
validating the modelvalidating the model
4. He compared computed growth rates 6
1
jj with
actual growth rates from 1948 to 1953
• computed agricultural employment too high• computed forestry outputs and inputs too high• computed communication and transport outputs and inputs too high
Sets up agenda for model improvements
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CoPS
IV. Extending Johansen-style CGE modelling in Australia
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CoPSExtending Johansen-style CGE modelling in Australia
Little development of Johansen’s approach until the 1970s.Why the pause ?IMPACT Project 1975 (ORANI model, DPRS 1977, DPSV1982)
1. Introduction of Armington specification into CGE
2. Large dimensions allowing policy-relevant detail
3. Flexible closures
4. Complex functional forms
5. Multi-step solutions, free from linearization errors
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CoPSExtending Johansen in AustraliaExtending Johansen in Australia
1. The Armington specification
The Armington elasticities in ORANI were econometrically estimated for about 50 commodities by Alaouze, Marsden & Zeitsch (1977)
With its Armington specification, the ORANI model avoided
flip-flop on the import side
On the export side, ORANI avoided flip-flop by the introduction of downward-sloping export demand curves
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CoPSExtending Johansen in AustraliaExtending Johansen in Australia
2. Coping with large dimensions, facilitates policy-relevant detail100+ industries, margins, technical change, sales taxes, regions
Initial specification: 600,000 simple equations, 1.2 million variablesx(i,s,j,k,m) = x(i,s,j,k) + a(i,s,j,k,m)
(100x2x100x2x10)
Dimensions reduced by substitution (condensation)
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CoPSExtending Johansen in AustraliaExtending Johansen in Australia
Johansen : fixed allocation of variables between and in giving a single T matrix
B* L*
3. Closure flexibility: reallocation of variables between and In ORANI, short-run versus long-run neo-classical versus neo-Keynesian pricing employment exogenous versus wages exogenous
In MONASH, the 4 closure approach to policy analysis historical (Update, deduce unobservable variables) decomposition (Explains history, effects of policy in historical context)
forecast (Incorporates detailed trends & specialist info. Motivation: meets a demand, matters for policy, adjustment costs, validation)
policy (Deviations from baseline)
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CoPSExtending Johansen in AustraliaExtending Johansen in Australia
4. Coping with complex functional forms, e.g. CRESH demand functions
i i ix z * p p
1
n #k k
kp S *p
1
# k kk n
i ii
S *S
S *
i= 1, 2, …n
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CoPSExtending Johansen in AustraliaExtending Johansen in Australia5. Computing multi-step solutions: eliminating linearization errors while retaining Johansen’s simplicity & interpretability
VI1
+(dV )1 (1,2)
VI1
+(dV )1 (.,2)
VI1
VI1
+(dV )1 true
VI1
+(dV )1 (.,1)
V2
+(dV )2
IIV2
+ (dV )2
I 12
VI2
a
b
c
V1=G(V )
2
Slope = T (2,2)
ISlope = T(V ) = T (1,2)
V2
V1
Error in one-step computation
Error in two-step computation
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CoPSJohansen-style ORANI model achieves Johansen-style ORANI model achieves acceptance in Australiaacceptance in Australia
(200 published applications 1977-86; only 25% by ORANI-group)
5 reasons (2 to 5 made possible by Johansen’s modelling strategy) :
1. favourable policy and institutional environment sharp issue – protection Industries Assistance Commission – Rattigan
IMPACT Project – Powell
2. credibility-enhancing detail
3. flexibility in application - closures, sectors
4. transferability - documentation, training courses from 1978
5. interpretability - overcoming sceptics
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CoPSIMPACT ProjectIMPACT Project
Alan A. Powell Peter B. Dixon Brian R. Parmenter
IMPACT was set up in 1975 in the Industries Assistance Commission
Alan A. Powell was the Director
Other principals were Peter B. Dixon and Brian R. Parmenter
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CoPSJohansen-style ORANI model achieves Johansen-style ORANI model achieves acceptance in Australiaacceptance in Australia
(200 published applications 1977-86; only 25% by ORANI-group)
5 reasons (2 to 5 made possible by Johansen’s modelling strategy) :
1. favourable policy and institutional environment sharp issue – protection Industries Assistance Commission – Rattigan
IMPACT Project – Powell
2. credibility-enhancing detail
3. flexibility in application - closures, sectors
4. transferability - documentation, training courses from 1978
5. interpretability - overcoming sceptics
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CoPSJohansen-style ORANI model achieves Johansen-style ORANI model achieves acceptance in Australiaacceptance in Australia
(200 published applications 1977-86; only 25% by ORANI-group)
5 reasons (2 to 5 made possible by Johansen’s modelling strategy) :
1. favourable policy and institutional environment sharp issue – protection Industries Assistance Commission – Rattigan, Powell IMPACT Project –Powell
2. credibility-enhancing detail
3. flexibility in application - closures, sectors
4. transferability - training courses starting late 1970s
5. interpretability
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CoPS
InterpretabilityInterpretability
(a)Qualitative explanations: Johnson (1985), Adams and Parmenter (1993)
(b)Quantitative explanations:
BOTE models: diagrammatic, algebraic, statistical
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Interpretability: diagrammaticInterpretability: diagrammatic
Demand for the right to emit CO2
CO -equivalent tons2
6 billion5 billion
Price
$20
..
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CoPSInterpretability: algebraicInterpretability: algebraicIntroduction of the GSTIntroduction of the GST
-1.4
-1.2
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
2000 2001 2002 2003 2004 2005 2006 2007 2008
Employment with sticky after-tax wages
Employment with sticky before-tax wages
Employment with sticky after-tax wages
Employment with sticky before-tax wages Powers of taxes
Production gT : 1.036 1.022
Wages wT : 1.250 1.215
Consumption cT : 1.070 1.105
l realA w g cM W *(T *T *T )
1.0%
l realB g cM W *(T *T )
1.9%
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CoPSInterpretability: statistical Interpretability: statistical
-0.6
-0.5
-0.4
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
12 Idah
o33 N
orthC
arolin34 N
orthD
akota
40 Sou
thC
arolin39 R
hod
eIsland
23 Min
nesota
1 Alab
ama
49 Wiscon
sin50 W
yomin
g29 18 L
ouisian
a42 T
enn
essee41 S
outh
Dak
ota10 G
eorgia26 M
ontan
a8 D
elaware
17 Ken
tuck
y19 M
aine
45 Verm
ont
21 Massach
usett
27 Neb
raska
2 Alask
a6 C
olorado
46 Virgin
ia38 P
enn
sylvania
32 New
York
30 New
Jersey25 M
issouri
24 Mississip
pi
15 Iowa
44 Utah
13 Illinois
51 DistC
olum
bia
48 WestV
irgini
7 Con
necticu
t43 T
exas36 O
klah
oma
31 New
Mexico
4 Ark
ansas
11 Haw
aii35 O
hio
20 Marylan
d9 F
lorida
5 Californ
ia22 M
ichigan
37 Oregon
3 Arizon
a16 K
ansas
14 Ind
iana
28 Nevad
a47 W
ashin
gton
States employment effects of removing import restraints (per cent)
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CoPSState employment effects explained by State employment effects explained by
1-variable regression1-variable regression
-0.6
-0.5
-0.4
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
12 Idah
o33 N
orthC
arolin34 N
orthD
akota
40 Sou
thC
arolin39 R
hod
eIsland
23 Min
nesota
1 Alab
ama
49 Wiscon
sin50 W
yomin
g29 18 L
ouisian
a42 T
enn
essee41 S
outh
Dak
ota10 G
eorgia26 M
ontan
a8 D
elaware
17 Ken
tuck
y19 M
aine
45 Verm
ont
21 Massach
usett
27 Neb
raska
2 Alask
a6 C
olorado
46 Virgin
ia38 P
enn
sylvania
32 New
York
30 New
Jersey25 M
issouri
24 Mississip
pi
15 Iowa
44 Utah
13 Illinois
51 DistC
olum
bia
48 WestV
irgini
7 Con
necticu
t43 T
exas36 O
klah
oma
31 New
Mexico
4 Ark
ansas
11 Haw
aii35 O
hio
20 Marylan
d9 F
lorida
5 Californ
ia22 M
ichigan
37 Oregon
3 Arizon
a16 K
ansas
14 Ind
iana
28 Nevad
a47 W
ashin
gton
Emp(r) = -0.023 + 2.755*NationalIndex(r)
R-squared = 0.73
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CoPSState employment effects explained by State employment effects explained by
2-variable regression 2-variable regression
-0.6
-0.5
-0.4
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
0.4
12 Idaho
33 NorthC
arolin
34 NorthD
akota
40 SouthCarolin
39 RhodeIsland
23 Minnesota
1 Alabam
a
49 Wisconsin
50 Wyom
ing
29 New
Ham
pshire
18 Louisiana
42 Tennessee
41 SouthDakota
10 Georgia
26 Montana
8 Delaw
are
17 Kentucky
19 Maine
45 Verm
ont
21 Massachusett
27 Nebraska
2 Alaska
6 Colorado
46 Virginia
38 Pennsylvania
32 New
York
30 New
Jersey
25 Missouri
24 Mississippi
15 Iowa
44 Utah
13 Illinois
51 DistC
olumbia
48 WestV
irgini
7 Connecticut
43 Texas
36 Oklahom
a
31 New
Mexico
4 Arkansas
11 Haw
aii
35 Ohio
20 Maryland
9 Florida
5 California
22 Michigan
37 Oregon
3 Arizona
16 Kansas
14 Indiana
28 Nevada
47 Washington
Emp(r) = -0.050 + 3.164*NationalIndex(r) + 0.056*PortIndex(r)
R-squared = 0.88
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CoPSState employment effects explained by State employment effects explained by
3-variable regression 3-variable regressionEmp(r) = -0.063 + 3.121*NationalIndex(r) + 0.056*PortIndex(r) + 0.011*HolidayIndex(r)
R-squared = 0.90
-0.6
-0.5
-0.4
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
0.4
12 Idah
o33 N
orthC
arolin34 N
orthD
akota
40 Sou
thC
arolin39 R
hod
eIsland
23 Min
nesota
1 Alab
ama
49 Wiscon
sin50 W
yomin
g29 N
ewH
amp
18 Lou
isiana
42 Ten
nessee
41 Sou
thD
akota
10 Georgia
26 Mon
tana
8 Delaw
are17 K
entu
cky
19 Main
e45 V
ermon
t21 M
assach27 N
ebrask
a2 A
laska
6 Colorad
o46 V
irginia
38 Pen
nsylvan
ia32 N
ewY
ork30 N
ewJersey
25 Missou
ri24 M
ississipp
i15 Iow
a44 U
tah13 Illin
ois51 D
istColu
mb
ia48 W
estVirgin
i7 C
onn
ecticut
43 Texas
36 Ok
lahom
a31 N
ewM
exico4 A
rkan
sas11 H
awaii
35 Oh
io20 M
aryland
9 Florid
a5 C
alifornia
22 Mich
igan37 O
regon3 A
rizona
16 Kan
sas14 In
dian
a28 N
evada
47 Wash
ington
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V. Taking Johansen from Australia to rest of world
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CoPSTaking Johansen from AustraliaTaking Johansen from Australiato rest of the worldto rest of the world
Starting in early 1980s• foreign appointments of ORANI modellers• teaching of foreign students in Australia • international model building projects from Australia: 20 countries including South Africa, Thailand, Brazil, Indonesia, Vietnam, Finland, Netherlands, Malaysia, China and the U.S.A. (USAGE model) • GTAP network: Hertel’s visit to Australia in 1990-1
- 7500 Johansen-style modellers in 150 countriesfacilitated by Ken Pearson’s GEMPACK
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CoPSGEMPACK dominates GAMSGEMPACK dominates GAMS
Solution time versus no. of sectors: Log-log scale
1
10
100
1000
10000
100 1000sectors
seco
nds
GEMPACK exe
GEMSIM
GAMS MCP
GAMS NLP
MPSGE
MCP-PATH
500
NLP-CONOPT
MPSGE
GEMPACK EXE
GEMSIM
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CoPSConclusionsConclusions
Since Johansen (1960), CGE modellers have combined data and theory to project implications for macro, industry, regional, occupational, environmental and distributional variables of a wide range of policy and other shocks.
Johansen used a linear representation and solution method. The objection was that the solutions were approximations. This objection was overcome in Australia by 1980 through a multi-step Johansen procedure that eliminated linearization errors.
By adopting the Johansen-style, Australian CGE modellers made rapid progress.
In the 1970s they created CGE models with: price-sensitive treatments of international trade; policy-relevant levels of detail; flexible closures; andthe ability to handle complex functional forms for production and consumption
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CoPSConclusionsConclusions
By adopting the Johansen-style, Australian CGE modellers made rapid progress.
In the 1980s they: developed world-wide transferable software - GEMPACK; andexpanded the range of CGE application to encompass industry and occupational forecasting, income distribution, micro policy (e.g. ORANI-milk) and the environment (e.g. greenhouse and water modelling)
In the 1990s they developed the 4-closure approach to policy analysis:historical; decomposition; forecast; andpolicy
In the 2000s they focused on validation – checking forecasts against reality; technological realism – combining CGE with engineering models in energy, transport, water ;bottom-up regional modelling – MMRF, TERM