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© 2015 Alan Mehlenbacher Associates Ltd. 1
How SAM-based parameters and results from CGE models vary across time
December, 2014 (Unfinished)
Author Information:
Alan Mehlenbacher, PhD Adjunct Assistant Professor Department of Economics University of Victoria Room 360, Business & Economics Building PO Box 1700, Stn CSC Victoria, BC, Canada, V8W 2Y2 email: [email protected]
Abstract
I create a panel of social accounting matrices (SAMS) consisting of seven countries across
11 years (1997-2007).
I am interested in whether or not the SAM structures vary across time for a given country or
vary across countries; whether or not the CGE model parameters based on the SAMS vary across
time for a given country or vary across countries; and whether or not the CGE simulation results
vary across time for a given country.
Keywords: social accounting matrix, computable general equilibrium, structure of economies
JEL code: A22
© 2015 Alan Mehlenbacher Associates Ltd. 2
1. Introduction
There are two methods of deriving parameter values for CGE models: calibration using a
social accounting matrix and using results from econometric analysis. The pros and cons of
these two methods have been debated since 1984 (Jorgenson et al, 1984) and a good summary is
McKitrick (1998). Although there have been several econometric CGE studies, the vast
majority are still SAM based.
The main advantage of using SAM-calibration is that most of the data for SAMs is available
from input-output-demand tables that are produced by many countries. The main advantage of
using econometric methods is that it provides an opportunity to use functional forms that are
other than CES-based.
The main disadvantage of using SAM-calibration is that the parameter values are single-year
snapshots that may reflect an anomalous year. The counter advantage of using econometric
methods is that it provides a parameter value that allegedly is more representative of the
economic structure, as well as a confidence interval that reflects the variation in time. This
assumes that the appropriate parameter value is a time-invariant one that is an intrinsic part of a
time-invariant economic structure.
The claims that SAM-calibration parameter values vary perhaps drastically across time has
not previously been addressed, nor has the implicit claim that the economies have a relatively
time-invariant structure that should be represented by time-invariant parameter values.
Therefore, in this paper I am interested answering the following four questions:
Q1: Do economic structures derived from national accounts vary across time for a given
country more or less than they vary across countries?
Q2: Do SAM-calibration parameters vary across time for a given country more or less than
they vary across countries?
Q3: Do the impacts of a tax policy vary a lot depending on the chosen year?
Q4: Do the impacts of a tax policy vary between simulations using a WIOD SAM and a
GTAP SAM?
© 2015 Alan Mehlenbacher Associates Ltd. 3
2. Data
I use the national input output tables and the socio-economic accounts that are provided by
the World Input-Output Database (WIOD). I use data for countries for which WIOD is based on
annual national supply-use and national input-output tables since I do not want interpolated
values. Unfortunately, this means that countries like China, India, Japan, Korea, and Turkey are
not included. As reported in Timmer et al (2012), the WIOD National Input Output (NIOT)
database uses country national accounts data that is mostly annual between 1997 and 2007.
China, India, Indonesia, Japan, Korea, and Taiwan produce national accounts data every five
years and the intermediate years are interpolated by WIOD; these countries are excluded. To
create the SAM for each country-year combination I also use the Capital and Labour accounts in
the WIOD Socio-Economic Accounts databases and Direct Tax data from OECD. Since national
accounts data is irregularly sparse for Australia, Bulgaria, Latvia, Lithuania, Mexico, Russia,
Turkey, these countries also must be excluded. Data for the USA is excluded because there is no
data on indirect taxes and Austria, Poland, Portugal, Slovenia are excluded because of negative
capital accounta. Belgium and Luxembourg are excluded because transshipment makes exports
greater than production. The Czech Republic is infeasible. This leaves us with the following
countries with WIOD data that is supported by national accounts data for 1997-2007.
Countries with infeasible CGE’s include Chech, Estonia, Slovak, Spain, UK. This further
restricts the sample size to OECD countries, resulting in the selection shown in Table 1.
Table 1: Countries in Study
# Country 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007
Canada X X X X X X X X X X X
Denmark X X X X X X X X X
Finland X X X X X X X X X X X
France X X X X X X X X X X X
Hungary X X X X X X X X
Italy X X X X X X X X X X X
Sweden X X X X X X X X X X X
© 2015 Alan Mehlenbacher Associates Ltd. 4
3. CGE equations
I use a model similar to the standard CGE model in Hosoe (2010). Table X shows the equation
parameters that are derived from the SAM and for which I study the country and year effects.
Parameter Description
alpha(i) share parameter in utility function
beta(h,j) share of factor h in production function
b(j) scale parameter in production function
ax(i,j) intermediate input requirement coefficient
ay(j) composite factor. input requirement coefficient
lambda(i) investment demand share
deltam(i) share parameter for imports in Armington function
deltad(i) share parameter for domestic in Armington function
gamma(i) scale parameter in Armington function
xie(i) share parameter for exports in transformation function
xid(i) share parameter for domestic in transformation function
theta(i) scale parameter in transformation function
Table X shows the percent changes in variables for which I study country and year effects
Variable Description
dTz% indirect taxes
dY% composite factor
dZ% output of the j-th good
dXp% household consumption of the i-th good
dXg% government consumption
dXv% investment demand
dE% exports
dM% imports by industries
dQ% Armington composite good
dD% domestic good
© 2015 Alan Mehlenbacher Associates Ltd. 5
4. Q1: Do SAM structures vary across time for a given country more than they vary across
countries?
Variation across time
0
0.002
0.004
0.006
0.008
0.01
0.012
0.014
0.016
AGR_AGR
AGR_MAN
AGR_SRV
AGR_HOH
AGR_INV
AGR_ROW
MAN_AGR
MAN_MAN
MAN_SRV
MAN_HOH
MAN_GOV
MAN_INV
MAN_ROW
SRV_AGR
SRV_MAN
SRV_SRV
SRV_HOH
SRV_GOV
SRV_INV
SRV_ROW
CAP_AGR
CAP_MAN
CAP_SRV
LAB_AGR
LAB_MAN
LAB_SRV
IDT_AGR
IDT_MAN
IDT_SRV
IDT_HOH
IDT_GOV
IDT_INV
HOH_CAP
HOH_LAB
GOV_IDT
GOV_HOH
INV_HOH
INV_GOV
INV_ROW
ROW_AGR
ROW_MAN
ROW_SRV
ROW_HOH
ROW_GOV
ROW_INV
CAN
DNK
FIN
FRA
HUN
ITA
SWE
Variation across countries
0
0.01
0.02
0.03
0.04
0.05
0.06
AGR_AGR
AGR_MAN
AGR_SRV
AGR_HOH
AGR_INV
AGR_ROW
MAN_AGR
MAN_MAN
MAN_SRV
MAN_HOH
MAN_GOV
MAN_INV
MAN_ROW
SRV_AGR
SRV_MAN
SRV_SRV
SRV_HOH
SRV_GOV
SRV_INV
SRV_ROW
CAP_AGR
CAP_MAN
CAP_SRV
LAB_AGR
LAB_MAN
LAB_SRV
IDT_AGR
IDT_MAN
IDT_SRV
IDT_HOH
IDT_GOV
IDT_INV
HOH_CAP
HOH_LAB
GOV_IDT
GOV_HOH
INV_HOH
INV_GOV
INV_ROW
ROW_AGR
ROW_MAN
ROW_SRV
ROW_HOH
ROW_GOV
ROW_INV
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007
© 2015 Alan Mehlenbacher Associates Ltd. 6
5. Q2: Do SAM-calibration parameters vary across time for a given country more or less
than they vary across countries?
Variation across time
First we take a visual look at Canada. The table illustrates the time series for parameters for Canada. You can see that there is variation across time.
alpha
0
0.005
0.01
0.015
0.02
1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007
AGR
0.11
0.115
0.12
0.125
0.13
0.135
0.14
1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007
MAN
0.605
0.61
0.615
0.62
0.625
0.63
0.635
0.64
0.645
0.65
1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007
SRV
ay
0.34
0.36
0.38
0.4
0.42
0.44
0.46
0.48
1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007
AGR
0.44
0.445
0.45
0.455
0.46
0.465
0.47
0.475
0.48
0.485
1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007
MAN
0.62
0.63
0.64
0.65
0.66
0.67
0.68
1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007
SRV
b
© 2015 Alan Mehlenbacher Associates Ltd. 7
The next table shows the standard deviation divided by the average as a measure of change over time.
Canada Denmark Finland France Hungary Italy Sweden
alphaAGR 0.0608 0.2307 0.0987 0.1127 0.2021 0.0664 0.0965
alphaMAN 0.0608 0.2307 0.0987 0.1127 0.2021 0.0664 0.0965
alphaSRV 0.0608 0.2307 0.0987 0.1127 0.2021 0.0664 0.0965
bAGR 0.0055 0.1786 0.1060 0.0088 0.0690 0.0542 0.0389
bMAN 0.0055 0.1786 0.1060 0.0088 0.0690 0.0542 0.0389
bSRV 0.0055 0.1786 0.1060 0.0088 0.0690 0.0542 0.0389
betaCAPAGR 0.0314 0.5629 0.4878 0.1177 0.2618 0.1866 0.1360
betaCAPMAN 0.0314 0.5629 0.4878 0.1177 0.2618 0.1866 0.1360
betaCAPSRV 0.0314 0.5629 0.4878 0.1177 0.2618 0.1866 0.1360
betaLABAGR 0.0431 0.2022 0.0601 0.1062 0.0691 0.0604 0.0444
betaLABMAN 0.0431 0.2022 0.0601 0.1062 0.0691 0.0604 0.0444
betaLABSRV 0.0431 0.2022 0.0601 0.1062 0.0691 0.0604 0.0444
axAGRAGR 0.0819 0.0970 0.0745 0.0320 0.0954 0.0422 0.2217
axAGRMAN 0.0819 0.0970 0.0745 0.0320 0.0954 0.0422 0.2217
axAGRSRV 0.0819 0.0970 0.0745 0.0320 0.0954 0.0422 0.2217
axMANAGR 0.0932 0.2556 0.0979 0.1018 0.0641 0.0620 0.0786
axMANMAN 0.0932 0.2556 0.0979 0.1018 0.0641 0.0620 0.0786
axMANSRV 0.0932 0.2556 0.0979 0.1018 0.0641 0.0620 0.0786
axSRVAGR 0.0723 0.1284 0.1248 0.0674 0.0570 0.0979 0.0692
axSRVMAN 0.0723 0.1284 0.1248 0.0674 0.0570 0.0979 0.0692
axSRVSRV 0.0723 0.1284 0.1248 0.0674 0.0570 0.0979 0.0692
ayAGR 0.0508 0.1318 0.0265 0.0314 0.0407 0.0308 0.0302
ayMAN 0.0508 0.1318 0.0265 0.0314 0.0407 0.0308 0.0302
aySRV 0.0508 0.1318 0.0265 0.0314 0.0407 0.0308 0.0302
lambdaAGR 3.4895 4.2384 1.6897 0.3040 0.3884 0.7229 0.3444
lambdaMAN 3.4895 4.2384 1.6897 0.3040 0.3884 0.7229 0.3444
lambdaSRV 3.4895 4.2384 1.6897 0.3040 0.3884 0.7229 0.3444
deltamAGR 0.0263 0.0797 0.0400 0.0301 0.0441 0.0505 0.0507
deltamMAN 0.0263 0.0797 0.0400 0.0301 0.0441 0.0505 0.0507
deltamSRV 0.0263 0.0797 0.0400 0.0301 0.0441 0.0505 0.0507
deltadAGR 0.0094 0.0374 0.0112 0.0099 0.0177 0.0112 0.0178
deltadMAN 0.0094 0.0374 0.0112 0.0099 0.0177 0.0112 0.0178
deltadSRV 0.0094 0.0374 0.0112 0.0099 0.0177 0.0112 0.0178
gammaAGR 0.0107 0.0315 0.0149 0.0119 0.0184 0.0167 0.0204
© 2015 Alan Mehlenbacher Associates Ltd. 8
gammaMAN 0.0107 0.0315 0.0149 0.0119 0.0184 0.0167 0.0204
gammaSRV 0.0107 0.0315 0.0149 0.0119 0.0184 0.0167 0.0204
xieAGR 0.0232 0.0417 0.0133 0.0052 0.0208 0.0144 0.0180
xieMAN 0.0232 0.0417 0.0133 0.0052 0.0208 0.0144 0.0180
xieSRV 0.0232 0.0417 0.0133 0.0052 0.0208 0.0144 0.0180
xidAGR 0.0439 0.0664 0.0515 0.0113 0.0475 0.0459 0.0600
xidMAN 0.0439 0.0664 0.0515 0.0113 0.0475 0.0459 0.0600
xidSRV 0.0439 0.0664 0.0515 0.0113 0.0475 0.0459 0.0600
thetaAGR 0.0215 0.0374 0.0323 0.0111 0.0233 0.0283 0.0394
thetaMAN 0.0215 0.0374 0.0323 0.0111 0.0233 0.0283 0.0394
thetaSRV 0.0215 0.0374 0.0323 0.0111 0.0233 0.0283 0.0394
The next table shows the occurrences of the variation measure when it is greater that 0.05
Threshold 0.05 Canada Denmark Finland France Hungary Italy Sweden
alphaAGR 0.0608 0.2307 0.0987 0.1127 0.2021 0.0664 0.0965
alphaMAN 0.0608 0.2307 0.0987 0.1127 0.2021 0.0664 0.0965
alphaSRV 0.0608 0.2307 0.0987 0.1127 0.2021 0.0664 0.0965
bAGR 0.1786 0.1060 0.0690 0.0542
bMAN 0.1786 0.1060 0.0690 0.0542
bSRV 0.1786 0.1060 0.0690 0.0542
betaCAPAGR 0.5629 0.4878 0.1177 0.2618 0.1866 0.1360
betaCAPMAN 0.5629 0.4878 0.1177 0.2618 0.1866 0.1360
betaCAPSRV 0.5629 0.4878 0.1177 0.2618 0.1866 0.1360
betaLABAGR 0.2022 0.0601 0.1062 0.0691 0.0604
betaLABMAN 0.2022 0.0601 0.1062 0.0691 0.0604
betaLABSRV 0.2022 0.0601 0.1062 0.0691 0.0604
axAGRAGR 0.0819 0.0970 0.0745 0.0954 0.2217
axAGRMAN 0.0819 0.0970 0.0745 0.0954 0.2217
axAGRSRV 0.0819 0.0970 0.0745 0.0954 0.2217
axMANAGR 0.0932 0.2556 0.0979 0.1018 0.0641 0.0620 0.0786
axMANMAN 0.0932 0.2556 0.0979 0.1018 0.0641 0.0620 0.0786
axMANSRV 0.0932 0.2556 0.0979 0.1018 0.0641 0.0620 0.0786
axSRVAGR 0.0723 0.1284 0.1248 0.0674 0.0570 0.0979 0.0692
axSRVMAN 0.0723 0.1284 0.1248 0.0674 0.0570 0.0979 0.0692
axSRVSRV 0.0723 0.1284 0.1248 0.0674 0.0570 0.0979 0.0692
ayAGR 0.0508 0.1318
ayMAN 0.0508 0.1318
© 2015 Alan Mehlenbacher Associates Ltd. 9
aySRV 0.0508 0.1318
lambdaAGR 3.4895 4.2384 1.6897 0.3040 0.3884 0.7229 0.3444
lambdaMAN 3.4895 4.2384 1.6897 0.3040 0.3884 0.7229 0.3444
lambdaSRV 3.4895 4.2384 1.6897 0.3040 0.3884 0.7229 0.3444
deltamAGR 0.0797 0.0505 0.0507
deltamMAN 0.0797 0.0505 0.0507
deltamSRV 0.0797 0.0505 0.0507
deltadAGR
deltadMAN
deltadSRV
gammaAGR
gammaMAN
gammaSRV
xieAGR
xieMAN
xieSRV
xidAGR 0.0664 0.0515 0.0600
xidMAN 0.0664 0.0515 0.0600
xidSRV 0.0664 0.0515 0.0600
thetaAGR
thetaMAN
The next table uses a threshold of 0.1
Canada Denmark Finland France Hungary Italy Sweden
alphaAGR 0.2307 0.1127 0.2021
alphaMAN 0.2307 0.1127 0.2021
alphaSRV 0.2307 0.1127 0.2021
bAGR 0.1786 0.1060
bMAN 0.1786 0.1060
bSRV 0.1786 0.1060
betaCAPAGR 0.5629 0.4878 0.1177 0.2618 0.1866 0.1360
betaCAPMAN 0.5629 0.4878 0.1177 0.2618 0.1866 0.1360
betaCAPSRV 0.5629 0.4878 0.1177 0.2618 0.1866 0.1360
betaLABAGR 0.2022 0.1062
betaLABMAN 0.2022 0.1062
betaLABSRV 0.2022 0.1062
axAGRAGR 0.2217
© 2015 Alan Mehlenbacher Associates Ltd. 10
axAGRMAN 0.2217
axAGRSRV 0.2217
axMANAGR 0.2556 0.1018
axMANMAN 0.2556 0.1018
axMANSRV 0.2556 0.1018
axSRVAGR 0.1284 0.1248
axSRVMAN 0.1284 0.1248
axSRVSRV 0.1284 0.1248
ayAGR 0.1318
ayMAN 0.1318
aySRV 0.1318
lambdaAGR 3.4895 4.2384 1.6897 0.3040 0.3884 0.7229 0.3444
lambdaMAN 3.4895 4.2384 1.6897 0.3040 0.3884 0.7229 0.3444
lambdaSRV 3.4895 4.2384 1.6897 0.3040 0.3884 0.7229 0.3444
deltamAGR
deltamMAN
deltamSRV
deltadAGR
deltadMAN
deltadSRV
gammaAGR
gammaMAN
gammaSRV
xieAGR
xieMAN
xieSRV
xidAGR
xidMAN
xidSRV
thetaAGR
thetaMAN
thetaSRV
© 2015 Alan Mehlenbacher Associates Ltd. 11
Variation across countries
The figure shows the cross-country comparison for alpha(AGR). You can see that there appear
to be two or three groups (Canada, Denmark, Sweden), (Finland, France, Italy), and Hungary.
0
0.01
0.02
0.03
0.04
0.05
0.06
97
01
04
07
Canada
Denmark
Finland
France
Hungary
Italy
Sweden
Using the usual Euclidean norm, we have the following distances between these time series:
Denmark Finland France Hungary Italy Sweden
Canada 0.020 0.019 0.029 0.088 0.025 0.017
Denmark 0.024 0.031 0.081 0.029 0.023
Finland 0.022 0.070 0.021 0.033
France 0.065 0.005 0.041
Hungary 0.069 0.097
Italy 0.038
Doing a cluster analysis for K=3 and K=2:
0 0.2 0.4 0.6 0.8 1
1
2
3
Silhouette Value
Clu
ste
r
0 0.2 0.4 0.6 0.8 1
1
2
Silhouette Value
Clu
ste
r
© 2015 Alan Mehlenbacher Associates Ltd. 12
The table below presents all of the results for parameters across countries (and time). The first column is AGR, then MAN and SRV.
alpha
0
0.01
0.02
0.03
0.04
0.05
0.06
9799
02
04
06
08
0
0.1
0.2
0.3
0.4
9799
01
03
05
07
0
0.2
0.4
0.6
0.8
9799
01
03
05
07
b
0
0.5
1
1.5
2
9799
02
04
06
08
0
0.5
1
1.5
2
9799
01
03
05
07
0
0.5
1
1.5
2
9799
01
03
05
07
ay
0
0.2
0.4
0.6
0.8
97
99
02
04
06
08
0
0.2
0.4
0.6
9799
01
03
05
07
0
0.2
0.4
0.6
0.8
9799
01
03
05
07
alpha
© 2015 Alan Mehlenbacher Associates Ltd. 13
Parameter K = 2 K=3 K=4 Can Den Fin Fra Hun Ita Swe
alphaAGR .781 .723 .613 1 1 1 1 2 1 1
alphaMAN 1 1 1 1 1 1 1
alphaSRV 1 1 1 1 1 1 1
bAGR 1 1 1 1 1 1 1
bMAN 1 1 1 1 1 1 1
bSRV 1 1 1 1 1 1 1
6. Q3: Do the impacts of a tax policy vary a lot depending on the chosen year?
7. Q4: Do the impacts of a tax policy vary between simulations using a WIOD SAM and a
GTAP SAM?
© 2015 Alan Mehlenbacher Associates Ltd. 14
References
Jorgenson, D., Scarf, H., & Shoven, J. 1984. Econometric methods for applied general equilibrium analysis. Applied general equilibrium analysis. McKitrick, R. R. 1998. The econometric critique of computable general equilibrium modeling: the role of functional forms. Economic Modelling, 15(4), 543-573. Timmer, M., Erumban, A. A., Gouma, R., Los, B., Temurshoev, U., de Vries, G. J., & Streicher, G. 2012. The world input-output database (WIOD): contents, sources and methods (No. 20120401). Institue for International and Development Economics.
© 2015 Alan Mehlenbacher Associates Ltd. 15
APPENDIX: CREATING THE SAMS
After careful manual testing with several SAMs, the following process was automated using
Visual Basic for Applications:
1. Start with NIOT data (million $US)
2. Delete total row and label accounts for aggregation
3. Enter data for Capital and Labour from SEA data (in local currency)
4. Convert the SEA data using annual exchange rates data from WIOD.
5. Aggregate WIOD accounts by summing across columns and rows of the Input-Output
data, and create the SAM matrix structure for the following accounts by summing across
columns and rows: Agriculture Sector, Manufacturing Sector, Services Sector, Capital,
Labour, Indirect Tax, Households, Governments, Investments, Exports and Imports to the
rest of the world.
6. Balance CAP & LAB accounts with payment to HOH
7. Balance the ROW account with INV (Table 4.5B)
8. Balance the IDT accounts with payment to GOV (Table 4.5B)
9. Obtain data on HOH direct tax (Table 4.5C) (You will use:
10. Use the INV account to balance HOH, GOV, NP, INV (Table 4.5C)
Since I am interested in the structure of the economies and not the levels, I then divide each
cell in the SAM by the grand total resulting in what I call total ratios (in contrast to a commonly
used column ratios that are the input-output coefficients for the industry sector accounts).
