$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, 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 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;