camcns.gms : Cameroon General Equilibrium Model Using CNS
This general equilibrium model is widely used as a blueprint
for new model developments. It follows closely the style and type
of model pioneered by Devis, De Melo and Robinson in the late 1970.
The original model (CAMCGE,SEQ=81) 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 (CAMMCP,SEQ=129) and an MPSGE
version exist under the name (CAMMGE,SEQ=140).
Reference:
- Condon, T, Dahl, H, and Devarajan, S, Implementing a Computable General equilibrium Model on GAMS - The Cameroon Model. Tech. rep., The World Bank, 1987.
Small Model of Type: CNS
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$Title Cameroon General Equilibrium Model (CAMCNS,SEQ=209)
$Ontext
This general equilibrium model is widely used as a blueprint
for new model developments. It follows closely the style and type
of model pioneered by Devis, De Melo and Robinson in the late 1970.
The original model (CAMCGE,SEQ=81) 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 (CAMMCP,SEQ=129) and an MPSGE
version exist under the name (CAMMGE,SEQ=140).
Condon, T, Dahl, H, and Devarajan, S, Implementing a Computable General
Equilibrium Model on GAMS - The Cameroon Model. Tech. rep., The World
Bank, 1987.
$Offtext
Set i sectors / ag-subsist food crops
ag-exp+ind cash crops
sylvicult forestry
ind-alim food processing
biens-cons consumer goods
biens-int intermediate goods
cim-int construction materials
biens-cap capital goods
construct construction
services private services
publiques public services /
it(i) traded sectors
in(i) nontraded sectors
lc labor categories / rural , urban-unsk , urban-skil /
Alias (i,j)
Parameters delta(i) armington function share parameter (unity)
ac(i) armington function shift parameter (unity)
rhoc(i) armington function exponent (unity)
rhot(i) cet function exponent (unity)
at(i) cet function shift parameter (unity)
gamma(i) cet function share parameter (unity)
eta(i) export demand elasticity (unity)
ad(i) production function shift parameter (unity)
cles(i) private consumption shares (unity)
gles(i) government consumption shares (unity)
depr(i) depreciation rates (unity)
dstr(i) ratio of inventory investment to gross output (unity)
kio(i) shares of investment by sector of destination (unity)
tm0(i) tariff rates (unity)
te(i) export duty rates (unity)
itax(i) indirect tax rates (unity)
alphl(lc,i) labor share parameter in production function (unity)
*dummies to hold initial data
m0(i) volume of imports ('79-80 bill cfaf)
e0(i) volume of exports ('79-80 bill cfaf)
xd0(i) volume of domestic output by sector ('79-80 bill cfaf)
k0(i) volume of capital stocks by sector ('79-80 bill cfaf)
id0(i) volume of investment by sector of origin ('79-80 bill cfaf)
dst0(i) volume of inventory investment by sector ('79-80 bill cfaf)
int0(i) volume of intermediate input demands ('79-80 bill cfaf)
xxd0(i) volume of domestic sales by sector ('79-80 bill cfaf)
x0(i) volume of composite good supply ('79-80 bill cfaf)
pwe0(i) world market price of exports (unity)
pwm0(i) world market price of imports (unity)
pd0(i) domestic good price (unity)
pe0(i) domestic price of exports (unity)
pm0(i) domestic price of imports (unity)
pva0(i) value added price by sector (unity)
qd(i) dummy variable for computing ad(i) (unity)
xllb(i,lc) dummy variable (l matrix with no zeros) (unity)
wa0(lc) average wage rate by labor category ('79-80 mill cfaf pr worker)
ld(lc) employment (1000 persons)
ls0(lc) labor supplies by category (1000 persons) ;
*base data
wa0("rural") = .11 ;
wa0("urban-unsk") = .15678 ;
wa0("urban-skil") = 1.8657 ;
Scalars
er real exchange rate (unity) / .21 /
gr0 government revenue ('79-80 bill cfaf) / 179.00 /
gdtot0 government consumption ('79-80 bill cfaf) / 135.03 /
cdtot0 private consumption ('79-80 bill cfaf) / 947.98 /
fsav0 foreign saving ('79-80 bill dollars) / 36.841 /
;
Table io(i,j) input-output coefficients (unity)
ag-subsist ag-exp+ind sylvicult ind-alim biens-cons biens-int cim-int biens-cap construct services publiques
ag-subsist .03046 .30266 .00206 .04120
ag-exp+ind .01518 .02043 .01123 .00669
sylvicult .00243 .02106
ind-alim .00341 .00629 .03241 .01234 .00503 .00092 .01532
biens-cons .00105 .05385 .00435 .00103 .00338
biens-int .00676 .12385 .02095 .03794 .08309 .23461 .18289 .01567 .14665 .00929 .08466
cim-int .00002 .00025 .00017 .11238 .05095 .05593 .27608 .11722 .18643 .00018
biens-cap .00041 .00971 .02427 .00931 .01229 .05259 .02053 .05013 .02622 .00389
construct .00472 .00113 .00318 .10456 .01831 .05302 .00172 .00031 .01457 .00385 .00394
services .00375 .30649 .26666 .10100 .26072 .23006 .11793 .09922 .13692 .13728 .24145
publiques .00022 .00293 .00327 .00536 .00539 .00957 .00486 .00081 .00447 .00219
Table imat(i,j) capital composition matrix (unity)
ag-subsist ag-exp+ind sylvicult ind-alim biens-cons biens-int cim-int biens-cap construct services publiques
ag-subsist .23637
biens-cap .59530 .60608 .63876 .60608 .78723 .63876 .63876 .60608 .71728 .17610 .17610
construct .16833 .39392 .36124 .39392 .21277 .36124 .36124 .39392 .28272 .82390 .82390
Table wdist(i,lc) wage proportionality factors (unity)
rural urban-unsk urban-skil
ag-subsist 1.01890 .71491
ag-exp+ind .49556 .34774 .29222
sylvicult 3.26280 2.28900 1.92320
ind-alim 1.45710 1.02230 .85902
biens-cons 1.13350 .79531 .66829
biens-int 3.10740 2.18060 1.83230
cim-int 6.32240 4.43640 3.72770
biens-cap 2.50350 1.75520 1.47580
construct 2.92040 2.04920 1.72200
services 1.40390 .98502 .82776
publiques 1.32630 1.11460
Table xle(i,lc) employment by sector and labor category (1000 persons)
rural urban-unsk urban-skil
ag-subsist 1654.43 162.89
ag-exp+ind 399.93 45.50800 5.05700
sylvicult 7.66200 1.78900 .59700
ind-alim 12.98900 9.43400 2.35800
biens-cons 28.34400 37.46200 12.48800
biens-int 18.33100 16.55300 8.30000
cim-int 1.45800 1.31700 .66000
biens-cap 3.11200 2.82000 1.20800
construct 22.58400 28.46200 7.11600
services 121.20 125.8 61.96000
publiques 83.029 32.77100
Table zz(*,i) miscellaneous parameters and initial data
ag-subsist ag-exp+ind sylvicult ind-alim biens-cons biens-int cim-int biens-cap construct services publiques
m0 2.461 8.039 .023 17.961 37.062 138.57 49.616 134.72 74.439
e0 4.594 125.07 22.337 23.451 5.864 101.33 10.501 3.838 81.626
xd0 330.480 131.45 29.503 72.024 118.430 284.38 34.169 10.298 174.12 615.79 163.98
k 495.730 170.89 73.760 .14e+03 236.870 853.13 102.51 20.600 435.29 769.73 180.36
depr .0246 .0472 .0244 .0144 .0212 .0335 .0335 .0111 .0232 .0637 .0637
rhoc 1.5 .9 .4 1.25 1.25 .5 .75 .4 .4 .4 .4
rhot 1.5 .9 .4 1.25 1.25 .5 .75 .4 .4 .4 .4
eta 1.0 1.0 1.0 4.00 4.00 4.0 4.00 4.0 4.0 4.0 4.0
pd0 1.0 1.0 1.0 1.00 1.00 1.0 1.00 1.0 1.0 1.0 1.0
tm0 .2205 .2330 .278 .3534 .3826 .1768 .2633 .268
itax .0020 .1910 .057 .038 .096 .026 .014 .029 .034 .076
cles .2744 .00445 .05599 .14099 .17738 .004 .31921 .02358
gles 1.00
kio .11 .09 .06 .01 .04 .14 .02 .01 .08 .34 .100
dstr .012203 .026694 .034742 .044291 .059958 .012287 .042047
dst 4.033 3.509 1.025 3.19 7.101 3.494 .433
id 6.710 113.36 138.13
;
*computation of parameters and coefficients for calibration
depr(i) = zz("depr",i);
rhoc(i) = (1/zz("rhoc",i)) - 1 ;
rhot(i) = (1/zz("rhot",i)) + 1;
eta(i) = zz("eta",i);
tm0(i) = zz("tm0",i);
te(i) = 0;
*te(i) = zz("te",i);
itax(i) = zz("itax",i);
cles(i) = zz("cles",i);
gles(i) = zz("gles",i);
kio(i) = zz("kio",i);
dstr(i) = zz("dstr",i);
xllb(i,lc) = xle(i,lc) + (1 - sign(xle(i,lc)));
m0(i) = zz("m0",i);
it(i) = yes$m0(i);
in(i) = not it(i);
e0(i) = zz("e0",i);
xd0(i) = zz("xd0",i);
k0(i) = zz("k",i);
pd0(i) = zz("pd0",i);
pm0(i) = pd0(i) ;
pe0(i) = pd0(i) ;
pwm0(i) = pm0(i)/((1+tm0(i))*er) ;
pwe0(i) = pe0(i)/((1+te(i))*er) ;
pva0(i) = pd0(i) - sum(j, io(j,i)*pd0(j) ) - itax(i);
xxd0(i) = xd0(i) - e0(i);
dst0(i) = zz("dst",i);
id0(i) = zz("id",i);
ls0(lc) = sum(i, xle(i,lc) );
*calibration of all shift and share parameters
* get delta from costmin, x0 from absorption , ac from armington
delta(it)$m0(it) = pm0(it)/pd0(it)*(m0(it)/xxd0(it))**(1+rhoc(it)) ;
delta(it) = delta(it)/(1+delta(it)) ;
x0(i) = pd0(i)*xxd0(i) + (pm0(i)*m0(i))$it(i) ;
ac(it) = x0(it)/(delta(it)*m0(it)**(-rhoc(it)) + (1-delta(it))*xxd0(it)**(-rhoc(it)))**(-1/rhoc(it)) ;
* get int0 from inteq, gamma from esupply, alphl from profitmax
int0(i) = sum(j, io(i,j)*xd0(j) );
gamma(it) = 1/(1 + pd0(it)/pe0(it)*(e0(it)/xxd0(it))**(rhot(it) - 1) ) ;
gamma(in) = 0;
alphl(lc,i) = (wdist(i,lc) * wa0(lc) * xle(i,lc)) /(pva0(i)*xd0(i));
* get ad from output, ld from profitmax, at from cet
qd(i) = (xllb(i,"rural")**alphl("rural",i))*(xllb(i,"urban-unsk")**alphl("urban-unsk",i))
*(xllb(i,"urban-skil")**alphl("urban-skil",i))*(k0(i)**(1 - sum(lc, alphl(lc,i))) ) ;
ad(i) = xd0(i)/qd(i);
ld(lc) = sum(i, (xd0(i)*pva0(i)*alphl(lc,i)/(wdist(i,lc)*wa0(lc)))$wdist(i,lc));
at(it) = xd0(it)/( gamma(it)*e0(it)**rhot(it) + ( 1-gamma(it) )*xxd0(it)**rhot(it) )**(1/rhot(it)) ;
*model definition - variables
Variables
*prices block
pd(i) domestic prices (unity)
pm(i) domestic price of imports (unity)
pe(i) domestic price of exports (unity)
pk(i) rate of capital rent by sector (unity)
px(i) average output price by sector (unity)
p(i) price of composite goods (unity)
pva(i) value added price by sector (unity)
pwm(i) world market price of imports (unity)
pwe(i) world market price of exports (unity)
tm(i) xxxxxxxxxxxxxxx
* tm(it) tariff rates (unity)
*production block
x(i) composite goods supply ('79-80 bill cfaf)
xd(i) domestic output by sector ('79-80 bill cfaf)
xxd(i) domestic sales ('79-80 bill cfaf)
e(i) exports by sector ('79-80 bill cfaf)
m(i) imports ('79-80 bill cfaf)
* factors block
k(i) capital stock by sector ('79-80 bill cfaf)
wa(lc) average wage rate by labor category (curr mill. cfaf per 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 ('79-80 bill cfaf)
cd(i) final demand for private consumption ('79-80 bill cfaf)
gd(i) final demand for government consumption ('79-80 bill cfaf)
id(i) final demand for productive investment ('79-80 bill cfaf)
dst(i) inventory investment by sector ('79-80 bill cfaf)
y private gdp (curr bill cfaf)
gr government revenue (curr bill cfaf)
tariff tariff revenue (curr bill cfaf)
indtax indirect tax revenue (curr bill cfaf)
duty export duty revenue (curr bill cfaf)
gdtot total volume of government consumption ('79-80 bill cfaf)
mps marginal propensity to save (unity)
hhsav total household savings (curr bill cfaf)
govsav government savings (curr bill cfaf)
deprecia total depreciation expenditure (curr bill cfaf)
savings total savings (curr bill cfaf)
fsav foreign savings (curr bill dollars)
dk(i) volume of investment by sector of destination ('79-80 bill cfaf)
*welfare indicator for objective function
omega objective function variable ('79-80 bill cfaf)
;
p.lo(i) = .01 ;pd.lo(i) = .01 ; pm.lo(it) =.01; pwe.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) = .01 ;
*model definition - equations
Equations
*price block
pmdef(i) definition of domestic import prices (unity)
pedef(i) definition of domestic export prices (unity)
absorption(i) value of domestic sales (curr bill cfaf)
sales(i) value of domestic output (curr bill cfaf)
actp(i) definition of activity prices (unity)
pkdef(i) definition of capital goods price (unity)
*output block
activity(i) production function ('79-80 bill cfaf)
profitmax(i,lc) first order condition for profit maximum (1000 persons)
lmequil(lc) labor market equilibrium (1000 persons)
cet(i) cet function ('79-80 bill cfaf)
edemand(i) export demand (unity)
esupply(i) export supply (unity)
armington(i) composite good aggregation function ('79-80 bill cfaf)
costmin(i) first order condition for cost minimization of composite good (unity)
xxdsn(i) domestic sales for nontraded sectors ('79-80 bill cfaf)
xsn(i) composite good aggregation for nontraded sectors ('79-80 bill cfaf)
*demand block
inteq(j) total intermediate uses ('79-80 bill cfaf)
cdeq(i) private consumption behavior (curr bill cfaf)
dsteq(i) inventory investment ('79-80 bill cfaf)
gdp private gdp (curr bill cfaf)
gdeq government consumption behavior ('79-80 bill cfaf)
greq government revenue (curr bill cfaf)
tariffdef tariff revenue (curr bill cfaf)
indtaxdef indirect taxes on domestic production (curr bill cfaf)
dutydef export duties (curr bill cfaf)
*savings-investment block
hhsaveq household savings (curr bill cfaf)
gruse government savings (curr bill cfaf)
depreq depreciation expenditure (curr bill cfaf)
totsav total savings (curr bill cfaf)
prodinv(i) investment by sector of destination (curr bill cfaf)
ieq(i) investment by sector of origin ('79-80 bill cfaf)
*balance of payments
caeq current account balance (curr bill dollar)
*market clearing
equil(i) goods market equilibrium ('79-80 bill cfaf)
*objective function
obj objective function ('79-80 bill cfaf) ;
*model definition - price block
pmdef(it).. pm(it) =e= pwm(it)*er*(1 + tm(it)) ;
pedef(it).. pe(it)*(1 + te(it)) =e= pwe(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))$it(i) ;
actp(i).. px(i)*(1-itax(i)) =e= pva(i) + sum(j, io(j,i)*p(j) ) ;
pkdef(i).. pk(i) =e= sum(j, p(j)*imat(j,i) );
*output and factors of production block
activity(i).. xd(i) =e= ad(i) * prod(lc$wdist(i,lc), l(i,lc)**alphl(lc,i) )*k(i)**(1 - sum(lc, alphl(lc,i)) ) ;
profitmax(i,lc)$wdist(i,lc).. wa(lc)*wdist(i,lc)*l(i,lc) =e= xd(i)*pva(i)*alphl(lc,i) ;
lmequil(lc).. sum(i, l(i,lc)) =e= ls(lc) ;
cet(it).. xd(it) =e= at(it)*( gamma(it)*e(it)**rhot(it) + ( 1-gamma(it) )*xxd(it)**rhot(it) )**(1/rhot(it)) ;
edemand(it).. e(it)/e0(it) =e= ( pwe0(it)/pwe(it) )**eta(it) ;
esupply(it).. e(it)/xxd(it) =e= ( pe(it)/pd(it)*(1 - gamma(it))/gamma(it) )**(1/(rhot(it)-1) ) ;
armington(it).. x(it) =e= ac(it)*(delta(it)*m(it)**(-rhoc(it)) + (1-delta(it))*xxd(it)**(-rhoc(it)))**(-1/rhoc(it)) ;
costmin(it).. m(it)/xxd(it) =e= ( pd(it)/pm(it)*delta(it)/(1-delta(it)) )**(1/(1 + rhoc(it))) ;
xxdsn(in).. xxd(in) =e= xd(in) ;
xsn(in).. x(in) =e= xxd(in) ;
*demand block
inteq(j).. int(j) =e= sum(i, io(j,i)*xd(i) );
dsteq(i).. dst(i) =e= dstr(i)*xd(i) ;
cdeq(i).. p(i)*cd(i) =e= cles(i)*(1-mps)*y ;
gdp.. y =e= sum(i, pva(i)*xd(i) ) - deprecia ;
hhsaveq.. hhsav =e= mps*y ;
greq.. gr =e= tariff + duty + indtax ;
gruse.. gr =e= sum(i, p(i)*gd(i)) + govsav ;
gdeq(i).. gd(i) =e= gles(i)*gdtot ;
tariffdef.. tariff =e= sum(it, tm(it)*m(it)*pwm(it) )*er ;
indtaxdef.. indtax =e= sum(i, itax(i)*px(i)*xd(i) );
dutydef.. duty =e= sum(it, te(it)*e(it)*pe(it) ) ;
depreq.. deprecia =e= sum(i, depr(i)*pk(i)*k(i) ) ;
totsav.. savings =e= hhsav + govsav + deprecia + fsav*er ;
prodinv(i).. pk(i)*dk(i) =e= kio(i)*savings - kio(i)*sum(j, dst(j)*p(j)) ;
ieq(i).. id(i) =e= sum(j, imat(i,j)*dk(j));
caeq.. sum(it, pwm(it)*m(it)) =e= sum(it, pwe(it)*e(it)) + fsav ;
*market clearing
equil(i).. x(i) =e= int(i) + cd(i) + gd(i) + id(i) + dst(i) ;
obj.. omega =e= prod(i$cles(i), cd(i)**cles(i)) ;
*model setup - initialization
x.l(i) = x0(i) ; xd.l(i) = xd0(i); xxd.l(i) = xxd0(i); cd.l(i) = cles(i)*cdtot0; m.l(i) = m0(i);
e.l(i) = e0(i); id.l(i) = id0(i); dst.l(i) = dst0(i); int.l(i) = int0(i); pd.l(i) = pd0(i);
pm.l(i) = pm0(i); pe.l(i) = pe0(i); p.l(i) = pd0(i); px.l(i) = pd0(i); pk.l(i) = pd0(i);
pva.l(i) = pva0(i); pwe.l(i) = pwe0(i); wa.l(lc) = wa0(lc); l.l(i,lc)= xle(i,lc); gr.l = gr0;
y.l = sum(i, pva0(i)*xd0(i) - depr(i)*k0(i)); fsav.l = fsav0 ; tm.l(it) = tm0(it) ;
gd.l("publiques") = 135.03;
tariff.l = 76.548;
indtax.l = 102.45;
savings.l= 280.98;
*closure
k.fx(i) = k0(i);
pwm.fx(i) = pwm0(i);
ls.fx(lc) = ls0(lc);
tm.fx(it) = tm0(it);
fsav.fx = fsav0 ;
mps.fx = .09305;
gdtot.fx = gdtot0;
m.fx(in) = 0;
l.fx("publiques","rural") = 0;
l.fx("ag-subsist","urban-skil") = 0;
e.fx(in) = 0;
Model camcns square base model /
pmdef, pedef, absorption, sales, actp, pkdef, activity, profitmax, lmequil, cet
edemand, esupply, armington, costmin, xxdsn, xsn, inteq, cdeq, dsteq, gdp, gdeq
greq, tariffdef, indtaxdef, dutydef, hhsaveq, gruse, depreq, totsav, prodinv
ieq, equil, obj / ;
Solve camcns using cns;
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