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.

$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 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 ;

 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

 positive
 variables

*       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 ;

*       model definition - equations

 equations

*       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) ;
 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;

*       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;