Description
This mini equilibrium model of Korea for the year 1963 is used to illustrate the basic use of CGE models. This version follows closely Chapter 11 of the reference. The original model (KORCGE,SEQ=100) is formulated as an optimization model, but it is really a square system of nonlinear equations. In this version, we formulate the model directly as a square system using the model type CNS = Constrained Nonlinear System. An MCP version exist under the name (KORMCP,SEQ=130).
Small Model of Type : CNS
Category : GAMS Model library
Main file : korcns.gms
$title General Equilibrium Model for Korea (KORCNS,SEQ=212)
$onText
This mini equilibrium model of Korea for the year 1963 is used to
illustrate the basic use of CGE models. This version follows closely
Chapter 11 of the reference.
The original model (KORCGE,SEQ=100) is formulated as an optimization
model, but it is really a square system of nonlinear equations.
In this version, we formulate the model directly as a square system
using the model type CNS = Constrained Nonlinear System.
An MCP version exist under the name (KORMCP,SEQ=130).
Lewis, J, and Robinson, S, Chapter 11. In Chenery, H B, Robinson, S,
and Syrquin, S, Eds, Industrialization and Growth: A Comparative
Study. Oxford University Press, London, 1986.
Keywords: constrained nonlinear system, general equilibrium model, economic growth,
industrialization, economic policy, Korean economy
$offText
Set
i 'sectors' / agricult 'agriculture'
industry 'industrial sectors'
services 'infra. & services' /
hh 'household type' / lab-hh 'labor households'
cap-hh 'capitalist household' /
lc 'labor categories' / labor1 'agricultural labor'
labor2 'industrial labor'
labor3 'service labor' /
it(i) 'traded sectors'
in(i) 'nontraded sectors';
Alias (i,j);
Parameter
delta(i) 'Armington function share parameter'
ac(i) 'Armington function shift parameter'
rhoc(i) 'Armington function exponent'
rhot(i) 'cet function exponent'
at(i) 'cet function shift parameter'
gamma(i) 'cet function share parameter'
ad(i) 'production function shift parameter'
gles(i) 'government consumption shares'
depr(i) 'depreciation rates'
dstr(i) 'ratio of inventory investment to gross output'
kio(i) 'shares of investment by sector of destination'
te(i) 'export duty rates'
itax(i) 'indirect tax rates'
htax(hh) 'income tax rate by household type'
pwm(i) 'world market price of imports (in dollars)'
pwe(i) 'world market price of exports (in dollars)'
tm(i) 'tariff rates on imports'
pwts(i) 'cpi weights';
htax("lab-hh ") = 0.08910;
htax("cap-hh ") = 0.08910;
Table alphl(i,lc) 'labor share parameter in production function'
labor1 labor2 labor3
agricult 0.38258 0.06740 0.00000
industry 0.00000 0.53476 0.00000
services 0.00000 0.16234 0.42326;
Table io(i,j) 'input-output coefficients'
agricult industry services
agricult 0.12591 0.19834 0.01407
industry 0.10353 0.35524 0.18954
services 0.02358 0.11608 0.08390;
Table imat(i,j) 'capital composition matrix'
agricult industry services
agricult 0.00000 0.00000 0.00000
industry 0.93076 0.93774 0.93080
services 0.06924 0.06226 0.06920;
Table wdist(i,lc) 'wage proportionality factors'
labor1 labor2 labor3
agricult 1.00000 0.52780 0.00000
industry 0.00000 1.21879 0.00000
services 0.00000 1.11541 1.00000;
Table cles(i,hh) 'private consumption shares'
lab-hh cap-hh
agricult 0.47000 0.47000
industry 0.31999 0.31999
services 0.21001 0.21001;
Table zz(*,i) 'miscellaneous parameters'
agricult industry services
depr 0.00000 0.00000 0.00000
itax 0.01000 0.03920 0.05000
gles 0.02000 0.07000 0.91000
kio 0.13000 0.29000 0.58000
dstr 0.00000 0.00000 0.00000
te 0.00000 0.00000 0.00000
tm 0.10000 0.22751 0.08084
ad 0.61447 1.60111 0.52019
pwts 0.33263 0.43486 0.23251
pwm 0.90909 0.81466 0.92521
pwe 1.00000 1.00000 1.00000
sigc 2.00000 0.66000 0.40000
delta 0.24820 0.05111 0.00001
ac 1.59539 1.34652 1.01839
sigt 2.00000 2.00000 2.00000
gamma 0.86628 0.84602 0.82436
at 3.85424 3.51886 3.23592;
depr(i) = zz("depr",i);
itax(i) = zz("itax",i);
gles(i) = zz("gles",i);
kio(i) = zz("kio",i);
dstr(i) = zz("dstr",i);
te(i) = zz("te",i);
tm(i) = zz("tm",i);
ad(i) = zz("ad",i);
pwts(i) = zz("pwts",i);
pwm(i) = zz("pwm",i);
pwe(i) = zz("pwe",i);
rhoc(i) = (1/zz("sigc",i)) - 1 ;
delta(i) = zz("delta",i);
ac(i) = zz("ac",i);
rhot(i) = (1/zz("sigt",i)) + 1;
gamma(i) = zz("gamma",i);
at(i) = zz("at",i);
$sTitle Model Definition
Variable
* prices block
er 'real exchange rate (won per dollar)'
pd(i) 'domestic prices'
pm(i) 'domestic price of imports'
pe(i) 'domestic price of exports'
pk(i) 'rate of capital rent by sector'
px(i) 'average output price by sector'
p(i) 'price of composite goods'
pva(i) 'value added price by sector'
pr 'import premium'
pindex 'general price level'
* production block
x(i) "composite goods supply ('68 bill won)"
xd(i) "domestic output by sector ('68 bill won)"
xxd(i) "domestic sales ('68 bill won)"
e(i) "exports by sector ('68 bill won)"
m(i) "imports ('68 bill won)"
* factors block
k(i) "capital stock by sector ('68 bill won)"
wa(lc) "average wage rate by labor category (mill won pr person)"
ls(lc) "labor supply by labor category (1000 persons)"
l(i,lc) "employment by sector and labor category (1000 persons)"
* demand block
int(i) "intermediates uses ('68 bill won)"
cd(i) "final demand for private consumption ('68 bill won)"
gd(i) "final demand for government consumption ('68 bill won)"
id(i) "final demand for productive investment ('68 bill won)"
dst(i) "inventory investment by sector ('68 bill won)"
y "private gdp (bill won)"
gr "government revenue (bill won)"
tariff "tariff revenue (bill won)"
indtax "indirect tax revenue (bill won)"
netsub "export duty revenue (bill won)"
gdtot "total volume of government consumption ('68 bill won)"
hhsav "total household savings (bill won)"
govsav "government savings (bill won)"
deprecia "total depreciation expenditure (bill won)"
invest "total investment (bill won)"
savings "total savings (bill won)"
mps(hh) "marginal propensity to save by household type"
fsav "foreign savings (bill dollars)"
dk(i) "volume of investment by sector of destination ('68 bill won)"
ypr "total premium income accruing to capitalists (bill won)"
remit "net remittances from abroad (bill dollars)"
fbor "net flow of foreign borrowing (bill dollars)"
yh(hh) "total income by household type (bill won)"
tothhtax "household tax revenue (bill won)"
* welfare indicator for objective function
omega "objective function variable ('68 bill won)";
er.l = 1.0000;
pr.l = 0.0000;
pindex.l = 1.0000;
gr.l = 194.0449;
tariff.l = 28.6572;
indtax.l = 65.2754;
netsub.l = 0.0000;
gdtot.l = 141.1519;
hhsav.l = 61.4089;
govsav.l = 52.8930;
deprecia.l = 0.0000;
savings.l = 159.1419;
invest.l = 159.1419;
fsav.l = 39.1744;
fbor.l = 58.7590;
remit.l = 0.0000;
tothhtax.l = 100.1122;
y.l = 1123.5941;
Table labres1(i,lc) 'summary matrix with sectoral employment results'
labor1 labor2 labor3
agricult 2515.900 442.643 0.000
industry 0.000 767.776 0.000
services 0.000 355.568 948.100;
Table labres2(*,lc) 'summary matrix with aggregate employment results'
labor1 labor2 labor3
wa 0.074 0.140 0.152
ls 2515.900 1565.987 948.100;
Table hhres(*,hh) 'summary matrix with household results'
lab-hh cap-hh
yh 548.7478 574.8463
mps 0.0600 0.0600;
l.l(i,lc) = labres1(i,lc);
ls.l(lc) = labres2("ls",lc);
wa.l(lc) = labres2("wa",lc);
mps.l(hh) = hhres("mps",hh);
yh.l(hh) = hhres("yh",hh);
Table sectres(*,i) 'summary matrix with sectoral results'
agricult industry services
pd 1.0000 1.0000 1.0000
pk 1.0000 1.0000 1.0000
pva 0.7370 0.2911 0.6625
x 711.6443 930.3509 497.4428
xd 657.3677 840.0500 515.4296
xxd 641.7037 812.2222 492.0307
e 15.6639 27.8278 23.3988
m 69.9406 118.1287 5.4120
k 657.5754 338.7076 1548.5192
int 256.6450 464.1656 156.2598
cd 452.1765 307.8561 202.0416
gd 2.8230 9.8806 128.4482
id 0.0000 148.4488 10.6931
dst 0.0000 0.0000 0.0000
dk 20.6884 46.1511 92.3023
pm 1.0000 1.0000 1.0000
pe 1.0000 1.0000 1.0000
px 1.0000 1.0000 1.0000
p 1.0000 1.0000 1.0000;
pd.l(i) = sectres("pd",i);
pm.l(i) = sectres("pm",i);
pe.l(i) = sectres("pe",i);
pk.l(i) = sectres("pk",i);
px.l(i) = sectres("px",i);
p.l(i) = sectres("p",i);
pva.l(i) = sectres("pva",i);
x.l(i) = sectres("x",i);
xd.l(i) = sectres("xd",i);
xxd.l(i) = sectres("xxd",i);
e.l(i) = sectres("e",i);
m.l(i) = sectres("m",i);
k.l(i) = sectres("k",i);
int.l(i) = sectres("int",i);
cd.l(i) = sectres("cd",i);
gd.l(i) = sectres("gd",i);
id.l(i) = sectres("id",i);
dst.l(i) = sectres("dst",i);
dk.l(i) = sectres("dk",i);
it(i) = yes$(e.l(i) or m.l(i));
in(i) = not it(i);
k.fx(i) = k.l(i);
m.fx(in) = 0;
e.fx(in) = 0;
l.fx(i,lc)$( l.l(i,lc) = 0) = 0;
p.lo(i) = .01; pd.lo(i) = .01; pm.lo(it) = .01;
pk.lo(i) = .01; px.lo(i) = .01; x.lo(i) = .01;
xd.lo(i) = .01; m.lo(it) = .01; xxd.lo(it) = .01;
wa.lo(lc) = .01; int.lo(i) = .01; y.lo = .01;
e.lo(it) = .01; l.lo(i,lc)$(l.l(i,lc) <> 0) = .01;
$sTitle Equation Definitions
Equation
* price block
pmdef(i) 'definition of domestic import prices'
pedef(i) 'definition of domestic export prices'
absorption(i) 'value of domestic sales'
sales(i) 'value of domestic output'
actp(i) 'definition of activity prices'
pkdef(i) 'definition of capital goods price'
pindexdef 'definition of general price level'
* output block
activity(i) 'production function'
profitmax(i,lc) 'first order condition for profit maximum'
lmequil(lc) 'labor market equilibrium'
cet(i) 'cet function'
esupply(i) 'export supply'
armington(i) 'composite good aggregation function'
costmin(i) 'f.o.c. for cost minimization of composite good'
xxdsn(i) 'domestic sales for nontraded sectors'
xsn(i) 'composite good agg. for nontraded sectors'
* demand block
inteq(i) 'total intermediate uses'
cdeq(i) 'private consumption behavior'
dsteq(i) 'inventory investment'
gdp 'private gdp'
labory 'total income accruing to labor'
capitaly 'total income accruing to capital'
hhtaxdef 'total household taxes collected by govt.'
gdeq 'government consumption shares'
greq 'government revenue'
tariffdef 'tariff revenue'
premium 'total import premium income'
indtaxdef 'indirect taxes on domestic production'
netsubdef 'export duties'
* savings-investment block
hhsaveq 'household savings'
gruse 'government savings'
depreq 'depreciation expenditure'
totsav 'total savings'
prodinv(i) 'investment by sector of destination'
ieq(i) 'investment by sector of origin'
* balance of payments
caeq 'current account balance (bill dollars)'
* market clearing
equil(i) 'goods market equilibrium'
* objective function
obj 'objective function';
* price block
pmdef(it).. pm(it) =e= pwm(it)*er*(1 + tm(it) + pr);
pedef(it).. pe(it) =e= pwe(it)*(1 + te(it))*er;
absorption(i).. p(i)*x(i) =e= pd(i)*xxd(i) + (pm(i)*m(i))$it(i);
sales(i).. px(i)*xd(i) =e= pd(i)*xxd(i) + (pe(i)*e(i))$it(i);
actp(i).. px(i)*(1-itax(i)) =e= pva(i) + sum(j, io(j,i)*p(j));
pkdef(i).. pk(i) =e= sum(j, p(j)*imat(j,i));
pindexdef.. pindex =e= sum(i, pwts(i)*p(i));
* output and factors of production block
activity(i).. xd(i) =e= ad(i)*prod(lc$wdist(i,lc), l(i,lc)**alphl(i,lc))
* k(i)**(1 - sum(lc, alphl(i,lc)));
profitmax(i,lc)$wdist(i,lc)..
wa(lc)*wdist(i,lc)*l(i,lc) =e= xd(i)*pva(i)*alphl(i,lc);
lmequil(lc).. sum(i, l(i,lc)) =e= ls(lc) ;
cet(it).. xd(it) =e= at(it)*(gamma(it)*e(it)**rhot(it)
+ (1 - gamma(it))*xxd(it)**rhot(it) )**(1/rhot(it));
esupply(it).. e(it)/xxd(it) =e= (pe(it)/pd(it)*(1 - gamma(it))/gamma(it))
** (1/(rhot(it) - 1) );
armington(it).. x(it) =e= ac(it)*(delta(it)*m(it)**(-rhoc(it))
+ (1 - delta(it))*xxd(it)**(-rhoc(it)))**(-1/rhoc(it));
costmin(it).. m(it)/xxd(it) =e= (pd(it)/pm(it)*delta(it)/(1 - delta(it)))
** (1/(1 + rhoc(it)));
xxdsn(in).. xxd(in) =e= xd(in);
xsn(in).. x(in) =e= xxd(in);
* demand block
inteq(i).. int(i) =e= sum(j, io(i,j)*xd(j));
dsteq(i).. dst(i) =e= dstr(i)*xd(i);
cdeq(i).. p(i)*cd(i) =e= sum(hh, cles(i,hh)*(1 - mps(hh))*yh(hh)*(1 - htax(hh)));
gdp.. y =e= sum(hh, yh(hh));
labory.. yh("lab-hh") =e= sum(lc, wa(lc)*ls(lc)) + remit*er;
capitaly.. yh("cap-hh") =e= sum(i, pva(i)*xd(i)) - deprecia
- sum(lc, wa(lc)*ls(lc)) + fbor*er + ypr;
hhsaveq.. hhsav =e= sum(hh, mps(hh)*yh(hh)*(1 - htax(hh)));
greq.. gr =e= tariff - netsub + indtax +tothhtax;
gruse.. gr =e= sum(i, p(i)*gd(i)) + govsav;
gdeq(i).. gd(i) =e= gles(i)*gdtot;
tariffdef.. tariff =e= sum(it, tm(it)*m(it)*pwm(it))*er;
indtaxdef.. indtax =e= sum(i, itax(i)*px(i)*xd(i));
netsubdef.. netsub =e= sum(it, te(it)*e(it)*pwe(it))*er;
premium.. ypr =e= sum(it, pwm(it)*m(it))*er*pr;
hhtaxdef.. tothhtax =e= sum(hh, htax(hh)*yh(hh));
depreq.. deprecia =e= sum(i, depr(i)*pk(i)*k(i));
totsav.. savings =e= hhsav + govsav + deprecia + fsav*er;
prodinv(i).. pk(i)*dk(i) =e= kio(i)*invest - kio(i)*sum(j, dst(j)*p(j));
ieq(i).. id(i) =e= sum(j, imat(i,j)*dk(j));
* balance of payments
caeq.. sum(it, pwm(it)*m(it)) =e= sum(it, pwe(it)*e(it))
+ fsav + remit + fbor;
* market clearing
equil(i).. x(i) =e= int(i) + cd(i) + gd(i) + id(i) + dst(i);
* objective function
obj.. omega =e= prod(i$cles(i,"lab-hh"), cd(i)**cles(i,"lab-hh"));
er.fx = er.l;
fsav.fx = fsav.l;
remit.fx = remit.l;
fbor.fx = fbor.l;
pindex.fx = pindex.l;
mps.fx(hh) = mps.l(hh);
gdtot.fx = gdtot.l;
ls.fx(lc) = ls.l(lc);
Model model1 'square base model' / all /;
solve model1 using cns;