cammcp.gms : Cameroon General Equilibrium Model Using MCP

Description

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 Dervis, de Melo and Robinson in the late 1970.

In this version, we reformulate the model as a nonlinear
complementarity problem to be solved as an MCP. The original
model can be found under the CAMCGE.


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 : MCP


Category : GAMS Model library


Main file : cammcp.gms

$title Cameroon General Equilibrium Model as MCP (CAMMCP,SEQ=129)

$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 Dervis, de Melo and Robinson in the late 1970.

In this version, we reformulate the model as a nonlinear
complementarity problem to be solved as an MCP. The original
model can be found under the CAMCGE.


Condon, T, Dahl, H, and Devarajan, S, Implementing a Computable
General equilibrium Model on GAMS - The Cameroon Model. Tech. rep.,
The World Bank, 1987.

Keywords: mixed complementarity problem, general equilibrium model
$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'        /
   lc    'labor categories' / rural, urban-unsk, urban-skil /
   it(i) 'traded sectors'
   in(i) 'nontraded sectors'

Alias (i,j)

Parameter
   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 per 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;

Scalar
   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));

Positive Variable
* Market prices:
   p(i)      'price of composite goods                                 (unity)'
   wa(lc)    'average wage rate by labor category (curr mill. cfaf per person)'
   rexr      'real exchange rate'

* Shadow prices:
   pva(i)    'value added price by sector                              (unity)'
   px(i)     'average output price by sector                           (unity)'
   pd(i)     'domestic prices                                          (unity)'

* Production indices:
   xd(i)     "domestic output by sector                     ('79-80 bill cfaf)"
   x(i)      "composite goods supply                        ('79-80 bill cfaf)"
   xxd(i)    "domestic sales                                ('79-80 bill cfaf)"

* Price definitions:
   pm(i)     'domestic price of imports                                (unity)'
   pe(i)     'domestic price of exports                                (unity)'
   pk(i)     'rate of capital rent by sector                           (unity)'

* Sectoral supply and demand functions:
   pwe(i)    "world market price of exports                            (unity)"
   e(i)      "exports by sector                             ('79-80 bill cfaf)"
   m(i)      "imports                                       ('79-80 bill cfaf)"
   l(i,lc)   "employment by sector and labor category           (1000 persons)"

* Intermediate demand quantities:
   int(i)    "intermediates uses                            ('79-80 bill cfaf)"
   dst(i)    "inventory investment by sector                ('79-80 bill cfaf)"
   id(i)     "final demand for productive investment        ('79-80 bill cfaf)"
   dk(i)     "volume of investment by sector of destination ('79-80 bill cfaf)"

* Household income and final demand:
   deprecia  "total depreciation expenditure                  (curr bill cfaf)"
   y         "private gdp                                     (curr bill cfaf)"
   hhsav     "total household savings                         (curr bill cfaf)"
   cd(i)     "final demand for private consumption          ('79-80 bill cfaf)"

* Government demand:
   tariff    "tariff revenue                                  (curr bill cfaf)"
   indtax    "indirect tax revenue                            (curr bill cfaf)"
   duty      "export duty revenue                             (curr bill cfaf)"
   gr        "government revenue                              (curr bill cfaf)"
   gd(i)     "final demand for government consumption       ('79-80 bill cfaf)"
   govsav    "government savings                              (curr bill cfaf)"
   savings   "total savings                                   (curr bill cfaf)"

* Exogenous parameters (for this closure):
   pwm(i)    "world market price of imports                            (unity)"
   tm(i)     "tariff rates                                             (unity)"
   k(i)      "capital stock by sector                       ('79-80 bill cfaf)"
   ls(lc)    "labor supply by labor category                    (1000 persons)"
   gdtot     "total volume of government consumption        ('79-80 bill cfaf)"
   mps       "marginal propensity to save                              (unity)"
   fsav      "foreign savings                              (curr bill dollars)";

Variable omega 'dummy objective';

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;

Equation
* Markets:
   equil(i)        "goods market equilibrium             ('79-80 bill cfaf)"
   lmequil(lc)     "labor market equilibrium                 (1000 persons)"
   caeq            "current account balance              (curr bill dollar)"

* Exhaustion of product:
   absorption(i)   'value of domestic sales                (curr bill cfaf)'
   sales(i)        'value of domestic output               (curr bill cfaf)'

* Intermediate prices:
   pmdef(i)        'definition of domestic import prices            (unity)'
   pedef(i)        'definition of domestic export prices            (unity)'
   pkdef(i)        'definition of capital goods price               (unity)'
   actp(i)         'definition of activity prices                   (unity)'

* Primal forms:
   activity(i)     "production function                  ('79-80 bill cfaf)"
   armington(i)    "composite good aggregation function  ('79-80 bill cfaf)"
   cet(i)          "cet function                         ('79-80 bill cfaf)"

* Supply and demand functions:
   esupply(i)      'export supply                                   (unity)'
   edemand(i)      'export demand                                   (unity)'
   costmin(i)      'first order condition for cost minimization     (unity)'
   profitmax(i,lc) 'first order condition for profit maximum (1000 persons)'

* Demand definitions:
   inteq(j)        "total intermediate uses              ('79-80 bill cfaf)"
   dsteq(i)        "inventory investment                 ('79-80 bill cfaf)"
   ieq(i)          "investment by sector of origin       ('79-80 bill cfaf)"
   prodinv(i)      "investment by sector of destination    (curr bill cfaf)"

* Household income:
   depreq          'depreciation expenditure               (curr bill cfaf)'
   gdp             'private gdp                            (curr bill cfaf)'

* Household expenditure:
   hhsaveq         'household savings                      (curr bill cfaf)'
   cdeq(i)         'private consumption behavior           (curr bill cfaf)'

* Government income:
   tariffdef       'tariff revenue                         (curr bill cfaf)'
   indtaxdef       'indirect taxes on domestic production  (curr bill cfaf)'
   dutydef         'export duties                          (curr bill cfaf)'
   greq            'government revenue                     (curr bill cfaf)'

* Government expenditure:
   gdeq            "government consumption behavior      ('79-80 bill cfaf)"
   gruse           "government savings                     (curr bill cfaf)"

* Closure:
   totsav          'total savings                          (curr bill cfaf)'
   obj             'dummy objective';


* Market clearing conditions
equil(i)..        x(i)   =e= int(i) + cd(i) + gd(i) + id(i) + dst(i);

lmequil(lc)..     ls(lc) =e= sum(i, l(i,lc));

caeq..            sum(it, pwe(it)*e(it)) + fsav =e= sum(it, pwm(it)*m(it));

* Zero profit:
actp(i)..         pva(i) + sum(j, io(j,i)*p(j))     =e= px(i)*(1-itax(i));

absorption(i)..   pd(i)*xxd(i) + (pm(i)*m(i))$it(i) =e= p(i)*x(i);

sales(i)..        px(i)*xd(i) =e= pd(i)*xxd(i) + (pe(i)*e(i))$it(i);

* Household income:
depreq..          deprecia =e= sum(i, depr(i)*pk(i)*k(i));

gdp..             y        =e= sum(i, pva(i)*xd(i)) - deprecia;

* Household expenditure:
hhsaveq..         hhsav      =e= mps*y;

cdeq(i)..         p(i)*cd(i) =e= cles(i)*(1-mps)*y;

* Government income:
tariffdef..       tariff =e= sum(it, tm(it)*m(it)*pwm(it))*er*rexr;

indtaxdef..       indtax =e= sum(i, itax(i)*px(i)*xd(i));

dutydef..         duty   =e= sum(it, te(it)*e(it)*pe(it));

greq..            tariff + duty + indtax =e= gr;

* Government expenditure:
gdeq(i)..         gd(i) =e= gles(i)*gdtot;

gruse..           sum(i, p(i)*gd(i)) + govsav =e= gr;

* Closure:
totsav..          savings =e= hhsav + govsav + deprecia + fsav*er*rexr;

* Primal forms:
activity(i)..     ad(i) * prod(lc$wdist(i,lc), l(i,lc)**alphl(lc,i))
                  * k(i)**(1 - sum(lc, alphl(lc,i))) =e= xd(i);

armington(i)..    (ac(i)*(delta(i)*m(i)**(-rhoc(i))
                  + (1-delta(i))*xxd(i)**(-rhoc(i))) **(-1/rhoc(i)))$it(i)
                  + xxd(i)$in(i) =e= x(i);

cet(i)..          xd(i) =e= (at(i)*(gamma(i)*e(i)**rhot(i)
                            + (1-gamma(i))*xxd(i)**rhot(i) )**(1/rhot(i)))$it(i)
                            + xxd(i)$in(i);

* Price definitions (could be replaced):
pmdef(it)..       pm(it) =e= pwm(it)*er*rexr*(1 + tm(it));

pedef(it)..       pe(it)*(1 + te(it)) =e= pwe(it)*er*rexr;

pkdef(i)..        pk(i)  =e= sum(j, p(j)*imat(j,i));

* Demand and supply functions (could be replaced):
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));

costmin(it)..     m(it)/xxd(it) =e= (pd(it)/pm(it)*delta(it)/(1-delta(it)))
                                    ** (1/(1 + rhoc(it)));

profitmax(i,lc)$wdist(i,lc).. wa(lc)*wdist(i,lc)*l(i,lc) =e= xd(i)*pva(i)*alphl(lc,i);

obj..             omega =e= prod(i$cles(i), cd(i)**cles(i));

* Intermediate demand definitions (could be replaced):
inteq(j)..        int(j)      =e= sum(i, io(j,i)*xd(i) );

dsteq(i)..        dst(i)      =e= dstr(i)*xd(i);

ieq(i)..          id(i)       =e= sum(j, imat(i,j)*dk(j));

prodinv(i)..      pk(i)*dk(i) =e= kio(i)*savings - kio(i)*sum(j, dst(j)*p(j));

* Model setup - initialization
rexr.l    = 1;
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;
fsav.l    = fsav0;
tm.l(it)  = tm0(it);
tariff.l  = 76.548;
indtax.l  = 102.45;
savings.l = 280.98;
gd.l("publiques") = 135.03;

* 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;
e.fx(in)  = 0;
l.fx("publiques","rural")       = 0;
l.fx("ag-subsist","urban-skil") = 0;


* fix price level using income:
y.fx = sum(i, pva0(i)*xd0(i) - depr(i)*k0(i));

Model cammcp 'mcp model structure'
             / equil.p         , lmequil.wa  , caeq.rexr    , activity.pva, cet.px
               armington.pd    , actp.xd     , absorption.x , sales.xxd   , pmdef.pm
               pedef.pe        , pkdef.pk    , edemand.pwe  , esupply.e   , costmin.m
               profitmax.l     , inteq.int   , dsteq.dst    , ieq.id      , prodinv.dk
               depreq.deprecia , gdp.y       , hhsaveq.hhsav, cdeq.cd     , tariffdef.tariff
               indtaxdef.indtax, dutydef.duty, greq.gr      , gdeq.gd     , gruse.govsav
               totsav.savings                                                                /;

Model camcge / all /;

solve cammcp using mcp;