kormcp.gms

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kormcp.gms : General Equilibrium Model for Korea - MCP

This mini equilibrium model of Korea for the year 1963 is used to
illustrate the basic use of cge models. This version follows closely
chapter 11 of the reference.

This version of 'KORCGE' uses nonlinear complementarity solvers
instead of nonlinear solvers to get solutions to the system of
equations.

Reference:

Lewis, J, and Robinson, S, Chapter 11. In Chenery, H B, Robinson, S, and Syrquin, M, Eds, Industrialization and Growth: A Comparative Study. Oxford University Press, London, 1986.

Small Model of Type: MCP

$title General Equilibrium Model for Korea as MCP (KORMCP,SEQ=130) $Ontext This mini equilibrium model of Korea for the year 1963 is used to illustrate the basic use of cge models. This version follows closely chapter 11 of the reference. This version of 'KORCGE' uses nonlinear complementarity solvers instead of nonlinear solvers to get solutions to the system of equations. Lewis, J, and Robinson, S, Chapter 11. In Chenery, H B, Robinson, S, and Syrquin, S, Eds, Industrialization and Growth: A Comparative Study. Oxford University Press, London, 1986. $Offtext sets i sectors /agricult agriculture industry industrial sectors services infra. & services / hh household type /lab-hh labor households cap-hh capitalist household/ lc labor categories /labor1 agricultural labor labor2 industrial labor labor3 service labor / it(i) traded sectors in(i) nontraded sectors alias (i,j); parameters delta(i) armington function share parameter ac(i) armington function shift parameter rhoc(i) armington function exponent rhot(i) cet function exponent at(i) cet function shift parameter gamma(i) cet function share parameter ad(i) production function shift parameter gles(i) government consumption shares depr(i) depreciation rates dstr(i) ratio of inventory investment to gross output kio(i) shares of investment by sector of destination te(i) export duty rates itax(i) indirect tax rates htax(hh) income tax rate by household type pwm(i) world market price of imports (in dollars) pwe(i) world market price of exports (in dollars) tm(i) tariff rates on imports pwts(i) cpi weights ; htax("lab-hh ") = 0.08910; htax("cap-hh ") = 0.08910; table alphl(i,lc) labor share parameter in production function labor1 labor2 labor3 agricult 0.38258 0.06740 0.00000 industry 0.00000 0.53476 0.00000 services 0.00000 0.16234 0.42326 table io(i,j) input-output coefficients agricult industry services agricult 0.12591 0.19834 0.01407 industry 0.10353 0.35524 0.18954 services 0.02358 0.11608 0.08390 table imat(i,j) capital composition matrix agricult industry services agricult 0.00000 0.00000 0.00000 industry 0.93076 0.93774 0.93080 services 0.06924 0.06226 0.06920 table wdist(i,lc) wage proportionality factors labor1 labor2 labor3 agricult 1.00000 0.52780 0.00000 industry 0.00000 1.21879 0.00000 services 0.00000 1.11541 1.00000 table cles(i,hh) private consumption shares lab-hh cap-hh agricult 0.47000 0.47000 industry 0.31999 0.31999 services 0.21001 0.21001 table zz(*,i) miscellaneous parameters agricult industry services depr 0.00000 0.00000 0.00000 itax 0.01000 0.03920 0.05000 gles 0.02000 0.07000 0.91000 kio 0.13000 0.29000 0.58000 dstr 0.00000 0.00000 0.00000 te 0.00000 0.00000 0.00000 tm 0.10000 0.22751 0.08084 ad 0.61447 1.60111 0.52019 pwts 0.33263 0.43486 0.23251 pwm 0.90909 0.81466 0.92521 pwe 1.00000 1.00000 1.00000 sigc 2.00000 0.66000 0.40000 delta 0.24820 0.05111 0.00001 ac 1.59539 1.34652 1.01839 sigt 2.00000 2.00000 2.00000 gamma 0.86628 0.84602 0.82436 at 3.85424 3.51886 3.23592 ; depr(i) = zz("depr",i); itax(i) = zz("itax",i); gles(i) = zz("gles",i); kio(i) = zz("kio",i); dstr(i) = zz("dstr",i); te(i) = zz("te",i); tm(i) = zz("tm",i); ad(i) = zz("ad",i); pwts(i) = zz("pwts",i); pwm(i) = zz("pwm",i); pwe(i) = zz("pwe",i); rhoc(i) = (1/zz("sigc",i)) - 1 ; delta(i) = zz("delta",i); ac(i) = zz("ac",i); rhot(i) = (1/zz("sigt",i)) + 1; gamma(i) = zz("gamma",i); at(i) = zz("at",i); $stitle model definition variables *prices block er real exchange rate (won per dollar) pd(i) domestic prices pm(i) domestic price of imports pe(i) domestic price of exports pk(i) rate of capital rent by sector px(i) average output price by sector p(i) price of composite goods pva(i) value added price by sector pr import premium pindex general price level *production block x(i) composite goods supply ('68 bill won) xd(i) domestic output by sector ('68 bill won) xxd(i) domestic sales ('68 bill won) e(i) exports by sector ('68 bill won) m(i) imports ('68 bill won) * factors block k(i) capital stock by sector ('68 bill won) wa(lc) average wage rate by labor category (mill won 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 ('68 bill won) cd(i) final demand for private consumption ('68 bill won) gd(i) final demand for government consumption ('68 bill won) id(i) final demand for productive investment ('68 bill won) dst(i) inventory investment by sector ('68 bill won) y private gdp (bill won) gr government revenue (bill won) tariff tariff revenue (bill won) indtax indirect tax revenue (bill won) netsub export duty revenue (bill won) gdtot total volume of government consumption ('68 bill won) hhsav total household savings (bill won) govsav government savings (bill won) deprecia total depreciation expenditure (bill won) invest total investment (bill won) savings total savings (bill won) mps(hh) marginal propensity to save by household type fsav foreign savings (bill dollars) dk(i) volume of investment by sector of destination ('68 bill won) ypr total premium income accruing to capitalists (bill won) remit net remittances from abroad (bill dollars) fbor net flow of foreign borrowing (bill dollars) yh(hh) total income by household type (bill won) tothhtax household tax revenue (bill won) *welfare indicator for objective function omega objective function variable ('68 bill won); er.l = 1.0000 ; pr.l = 0.0000 ; pindex.l = 1.0000 ; gr.l = 194.0449 ; tariff.l = 28.6572 ; indtax.l = 65.2754 ; netsub.l = 0.0000 ; gdtot.l = 141.1519 ; hhsav.l = 61.4089 ; govsav.l = 52.8930 ; deprecia.l = 0.0000 ; savings.l = 159.1419 ; invest.l = 159.1419 ; fsav.l = 39.1744 ; fbor.l = 58.7590 ; remit.l = 0.0000 ; tothhtax.l = 100.1122 ; y.l = 1123.5941 ; table labres1(i,lc) summary matrix with sectoral employment results labor1 labor2 labor3 agricult 2515.900 442.643 0.000 industry 0.000 767.776 0.000 services 0.000 355.568 948.100 table labres2(*,lc) summary matrix with aggregate employment results labor1 labor2 labor3 wa 0.074 0.140 0.152 ls 2515.900 1565.987 948.100 table hhres(*,hh) summary matrix with household results lab-hh cap-hh yh 548.7478 574.8463 mps 0.0600 0.0600 ; l.l(i,lc) = labres1(i,lc); ls.l(lc) = labres2("ls",lc); wa.l(lc) = labres2("wa",lc); mps.l(hh) = hhres("mps",hh) ; yh.l(hh) = hhres("yh",hh) ; table sectres(*,i) summary matrix with sectoral results agricult industry services pd 1.0000 1.0000 1.0000 pk 1.0000 1.0000 1.0000 pva 0.7370 0.2911 0.6625 x 711.6443 930.3509 497.4428 xd 657.3677 840.0500 515.4296 xxd 641.7037 812.2222 492.0307 e 15.6639 27.8278 23.3988 m 69.9406 118.1287 5.4120 k 657.5754 338.7076 1548.5192 int 256.6450 464.1656 156.2598 cd 452.1765 307.8561 202.0416 gd 2.8230 9.8806 128.4482 id 0.0000 148.4488 10.6931 dst 0.0000 0.0000 0.0000 dk 20.6884 46.1511 92.3023 pm 1.0000 1.0000 1.0000 pe 1.0000 1.0000 1.0000 px 1.0000 1.0000 1.0000 p 1.0000 1.0000 1.0000 ; pd.l(i) = sectres("pd",i) ; pm.l(i) = sectres("pm",i) ; pe.l(i) = sectres("pe",i) ; pk.l(i) = sectres("pk",i) ; px.l(i) = sectres("px",i) ; p.l(i) = sectres("p",i) ; pva.l(i) = sectres("pva",i) ; x.l(i) = sectres("x",i) ; xd.l(i) = sectres("xd",i) ; xxd.l(i) = sectres("xxd",i) ; e.l(i) = sectres("e",i) ; m.l(i) = sectres("m",i) ; k.l(i) = sectres("k",i) ; int.l(i) = sectres("int",i) ; cd.l(i) = sectres("cd",i) ; gd.l(i) = sectres("gd",i) ; id.l(i) = sectres("id",i) ; dst.l(i) = sectres("dst",i) ; dk.l(i) = sectres("dk",i) ; it(i) = yes$( e.l(i) or m.l(i) ) ; in(i) = not it(i) ; k.fx(i) = k.l(i) ; m.fx(in) = 0; e.fx(in) = 0; l.fx(i,lc)$( l.l(i,lc) eq 0 ) = 0 ; * for mcp version, need to avoid lower bounds: *. p.lo(i) = .01 ; pd.lo(i) = .01 ; pm.lo(it) = .01 ; *. pk.lo(i) = .01 ; px.lo(i) = .01 ; x.lo(i) = .01 ; *. xd.lo(i) = .01 ; m.lo(it) = .01 ; xxd.lo(it) = .01 ; wa.lo(lc) = .01 ; *. int.lo(i) = .01 ; y.lo = .01 ; e.lo(it) = .01 ; *. l.lo(i,lc)$( l.l(i,lc) ne 0 ) = .01 ; $stitle equation definitions equations *price block pmdef(i) definition of domestic import prices pedef(i) definition of domestic export prices absorption(i) value of domestic sales sales(i) value of domestic output actp(i) definition of activity prices pkdef(i) definition of capital goods price pindexdef definition of general price level *output block activity(i) production function profitmax(i,lc) first order condition for profit maximum lmequil(lc) labor market equilibrium cet(i) cet function esupply(i) export supply armington(i) composite good aggregation function costmin(i) f.o.c. for cost minimization of composite good xxdsn(i) domestic sales for nontraded sectors xsn(i) composite good agg. for nontraded sectors *demand block inteq(i) total intermediate uses cdeq(i) private consumption behavior dsteq(i) inventory investment gdp private gdp labory total income accruing to labor capitaly total income accruing to capital hhtaxdef total household taxes collected by govt. gdeq government consumption shares greq government revenue tariffdef tariff revenue premium total import premium income indtaxdef indirect taxes on domestic production netsubdef export duties *savings-investment block hhsaveq household savings gruse government savings depreq depreciation expenditure totsav total savings prodinv(i) investment by sector of destination ieq(i) investment by sector of origin *balance of payments caeq current account balance (bill dollars) *market clearing equil(i) goods market equilibrium *objective function obj objective function ; *price block pmdef(it).. pm(it) =e= pwm(it)*er*(1 + tm(it) + pr) ; pedef(it).. pe(it) =e= pwe(it)*(1 + te(it))*er ; absorption(i).. p(i)*x(i) =e= pd(i)*xxd(i) + (pm(i)*m(i))$it(i) ; sales(i).. px(i)*xd(i) =e= pd(i)*xxd(i) + (pe(i)*e(i))$it(i) ; actp(i).. px(i)*(1-itax(i)) =e= pva(i) + sum(j, io(j,i)*p(j) ) ; pkdef(i).. pk(i) =e= sum(j, p(j)*imat(j,i) ); pindexdef.. pindex =e= sum(i, pwts(i)*p(i) ) ; *output and factors of production block activity(i).. xd(i) =e= ad(i) * prod(lc$wdist(i,lc), l(i,lc)**alphl(i,lc) ) *k(i)**(1 - sum(lc, alphl(i,lc)) ) ; profitmax(i,lc)$wdist(i,lc).. wa(lc)*wdist(i,lc)*l(i,lc) =e= xd(i)*pva(i)*alphl(i,lc) ; lmequil(lc).. sum(i, l(i,lc)) =e= ls(lc) ; cet(it).. xd(it) =e= at(it)*( gamma(it)*e(it)**rhot(it) + ( 1-gamma(it) )*xxd(it)**rhot(it) )**(1/rhot(it)) ; esupply(it).. e(it)/xxd(it) =e= ( pe(it)/pd(it)*(1 - gamma(it))/gamma(it) ) **(1/(rhot(it)-1) ) ; armington(it).. x(it) =e= ac(it)*(delta(it)*m(it)**(-rhoc(it)) + (1-delta(it))*xxd(it)**(-rhoc(it)))**(-1/rhoc(it)) ; costmin(it).. m(it)/xxd(it) =e= ( pd(it)/pm(it)*delta(it)/(1-delta(it)) )** (1/(1 + rhoc(it))) ; xxdsn(in).. xxd(in) =e= xd(in) ; xsn(in).. x(in) =e= xxd(in) ; *demand block inteq(i).. int(i) =e= sum(j, io(i,j)*xd(j) ); dsteq(i).. dst(i) =e= dstr(i)*xd(i) ; cdeq(i).. p(i)*cd(i) =e= sum(hh, cles(i,hh)*(1-mps(hh))*yh(hh) *(1-htax(hh)) ) ; gdp.. y =e= sum(hh, yh(hh) ) ; labory.. yh("lab-hh") =e= sum(lc, wa(lc)*ls(lc) ) + remit*er ; capitaly.. yh("cap-hh") =e= sum(i, pva(i)*xd(i) ) - deprecia - sum(lc, wa(lc)*ls(lc) ) + fbor*er + ypr ; hhsaveq.. hhsav =e= sum(hh, mps(hh)*yh(hh)*(1 - htax(hh))) ; greq.. gr =e= tariff - netsub + indtax +tothhtax ; gruse.. gr =e= sum(i, p(i)*gd(i)) + govsav ; gdeq(i).. gd(i) =e= gles(i)*gdtot ; tariffdef.. tariff =e= sum(it, tm(it)*m(it)*pwm(it) )*er ; indtaxdef.. indtax =e= sum(i, itax(i)*px(i)*xd(i) ); netsubdef.. netsub =e= sum(it, te(it)*e(it)*pwe(it) )*er ; premium.. ypr =e= sum(it, pwm(it)*m(it) )*er*pr ; hhtaxdef.. tothhtax =e= sum(hh, htax(hh)*yh(hh) ) ; depreq.. deprecia =e= sum(i, depr(i)*pk(i)*k(i) ) ; totsav.. savings =e= hhsav + govsav + deprecia + fsav*er ; prodinv(i).. pk(i)*dk(i) =e= kio(i)*invest - kio(i)*sum(j, dst(j)*p(j)) ; ieq(i).. id(i) =e= sum(j, imat(i,j)*dk(j)); *balance of payments caeq.. sum(it, pwm(it)*m(it)) =e= sum(it, pwe(it)*e(it)) + fsav + remit + fbor ; *market clearing equil(i).. x(i) =e= int(i) + cd(i) + gd(i) + id(i) + dst(i) ; *objective function obj.. omega =e= prod(i$cles(i,"lab-hh"), cd(i)**cles(i,"lab-hh")) ; er.fx = er.l ; fsav.fx = fsav.l ; remit.fx = remit.l ; fbor.fx = fbor.l ; pindex.fx = pindex.l ; mps.fx(hh) = mps.l(hh) ; gdtot.fx = gdtot.l ; ls.fx(lc) = ls.l(lc) ; model model1 square base model / all / ; solve model1 using mcp;