$title Cameroon General Equilibrium Model (CAMCGE,SEQ=81) $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. 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: nonlinear programming, general equilibrium model, economic policy, Cameroonian economy, market equilibrium $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 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; 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)); Variable * 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 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 ('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; pk.lo(i) = .01; px.lo(i) = .01; x.lo(i) = .01; m.lo(it) = .01; xxd.lo(it) = .01; wa.lo(lc) = .01; e.lo(it) = .01; l.lo(i,lc) = .01; y.lo = .01; xd.lo(i) = .01; pwe.lo(it) = .01; int.lo(i) = .01; Equation * 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)"; * 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; * Note: caeq is not part in the current model definition. * However, camcge.gms is a template for equilibrium models in general. Model camcge 'square base model' / all - caeq /; solve camcge maximizing omega using nlp;