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hosoe_recursive_model.gms
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$title A Recursive-Dynamic Standard CGE Model (DYNCGE,SEQ=410)
$onText
This model is featured in the following book.
Hosoe, N., Gasawa, K., Hashimoto, H. Textbook of Computable General
Equilibrium Modeling: Programming and Simulations, 2nd Edition,
University of Tokyo Press. (in Japanese)
Keywords: nonlinear programming, general equilibrium model, social accounting
matrix
$offText
option limRow = 0, limCol = 0;
$offSymXRef offSymList
* ===============================================================
* Definition of sets for suffix ---------------------------------
* ===============================================================
Set
u 'SAM entry' / AGR, LMN, HMN, SRV, CAP, LAB, HOH, GOV, INV, EXT, IDT, TRF /
i(u) 'goods' / AGR, LMN, HMN, SRV /
h(u) 'factor' / CAP, LAB /
h_mob(h) 'mobile factor' / LAB /
h_imm(h) 'immobile factor' / CAP /
t 'time' / 0*30 /;
Alias (u,v), (i,j), (h,k);
* ===============================================================
* Data for Dynamics ---------------------------------------------
* ===============================================================
Scalar
ror 'rate of return of capital'
dep 'depreciation rate'
pop 'population growth rate'
zeta 'elasticity parameter for investment allocation';
ror = 0.05;
dep = 0.04;
pop = 0.02;
zeta = 1;
* ===============================================================
* SAM Data
* ===============================================================
Table SAM(u,v) 'social accounting matrix for 2005 [bil. JPY]'
AGR LMN HMN SRV
AGR 1643.017 7560.896 237.841 1409.202
LMN 1485.854 10803.527 15330.764 18597.270
HMN 1071.954 4277.721 113390.269 48734.424
SRV 2002.380 11406.260 50513.476 177675.714
IDT 433.854 4068.616 9418.058 20103.917
TRF 149.278 2866.853 1749.385 8.575
CAP 5082.506 7042.697 21058.821 163045.396
LAB 1435.010 8942.365 42510.123 222732.700
EXT 2092.569 23796.669 30982.559 10837.256
+ IDT TRF CAP LAB
HOH 196229.420 275620.198
GOV 34024.445 4774.091
+ HOH GOV INV EXT
AGR 3563.257 0.000 919.745 62.464
LMN 32220.169 329.469 802.026 1196.525
HMN 27648.678 4.931 34979.803 55083.516
SRV 234243.865 90707.177 79169.426 17426.156
GOV 52243.041
INV 121930.608 0.000 -6059.608;
* Source: compiled by N. Hosoe, based on the I/O table for 2005
Parameter SAMGAP(u) 'gaps between row sums and column sums';
SAMGAP(u) = sum(v, SAM(u,v) - SAM(v,u));
display SAMGAP;
* ===============================================================
* Loading the initial values ------------------------------------
* ===============================================================
Parameter
* Base year values
Y00(j) 'composite factor'
F00(h,j) 'factor input'
X00(i,j) 'intermediate input'
Z00(j) 'gross output'
Xp00(i) 'household consumption'
Xg00(i) 'government consumption'
Xv00(i) 'investment demand'
E00(i) 'exports'
M00(i) 'imports'
Q00(i) "Armington's composite good"
D00(i) 'domestic good'
Sp00 'private savings'
Td00 'direct tax'
Tz00(j) 'production tax'
Tm00(j) 'import tariff'
III00 'composite investment'
II00(j) 'sectoral investment'
KK00(j) 'capital stock'
CC00 'composite consumption or felicity'
FF00(h) 'factor endowment'
Sf00 'foreign savings in US dollars'
tauz00(i) 'production tax rate'
taum00(i) 'import tariff rate'
* Base run value
Y0(j,t) 'composite factor'
F0(h,j,t) 'factor input'
X0(i,j,t) 'intermediate input'
Z0(j,t) 'gross output'
Xp0(i,t) 'household consumption'
Xv0(i,t) 'investment demand'
E0(i,t) 'exports'
M0(i,t) 'imports'
Q0(i,t) "Armington's composite good"
D0(i,t) 'domestic good'
Sp0(t) 'private savings'
Td0(t) 'direct tax'
Tz0(j,t) 'production tax'
Tm0(j,t) 'import tariff'
III0(t) 'composite investment'
II0(j,t) 'sectoral investment'
KK0(j,t) 'capital stock'
CC0(t) 'composite consumption or felicity'
FF0(h,t) 'factor endowment'
pf0(h,j,t) 'factor price'
py0(j,t) 'composite factor price'
pz0(j,t) 'gross output price'
pq0(i,t) "Armington's composite good price"
pe0(i,t) 'export price in local currency'
pm0(i,t) 'import price in local currency'
pd0(i,t) 'domestic good price'
pk0(t) 'composite investment goods price'
epsilon0(t) 'exchange rate'
PRICE0(t) 'numeraire price'
* Exogenous variables
Xg0(i,t) 'government consumption'
Sf0(t) 'foreign savings in US dollars'
pWe(i) 'export price in US dollars'
pWm(i) 'import price in US dollars'
tauz(i) 'production tax rate'
taum(i) 'import tariff rate'
* for result reporting
Y1(j,t) 'composite factor'
F1(h,j,t) 'factor input'
X1(i,j,t) 'intermediate input'
Z1(j,t) 'gross output'
Xp1(i,t) 'household consumption'
Xv1(i,t) 'investment demand'
E1(i,t) 'exports'
M1(i,t) 'imports'
Q1(i,t) "Armington's composite good"
D1(i,t) 'domestic good'
Sp1(t) 'private saving'
Td1(t) 'direct tax'
Tz1(j,t) 'production tax'
Tm1(i,t) 'import tariff'
FF1(h,t) 'initial sectoral factor uses'
II1(j,t) 'sectoral investment'
III1(t) 'composite investment'
KK1(j,t) 'sectoral capital stock'
CC1(t) 'utility'
tauz1(i,t) 'production tax rates'
taum1(i,t) 'import tariff rates'
pz1(j,t) 'gross output price'
pd1(j,t) 'domestic good price'
pm1(j,t) 'import price'
pe1(j,t) 'export price'
pq1(j,t) "Armington's composite good price"
pf1(h,j,t) 'factor price'
py1(j,t) 'composite factor price'
epsilon1(t) 'foreign exchange rate'
pk1(t) 'capital good price'
PRICE1(t) 'numeraire price';
Td00 = SAM("GOV","HOH");
Tz00(j) = SAM("IDT",j);
Tm00(j) = SAM("TRF",j);
F00(h,j) = SAM(h,j);
Y00(j) = sum(h, F00(h,j));
X00(i,j) = SAM(i,j);
Z00(j) = Y00(j) + sum(i, X00(i,j));
M00(i) = SAM("EXT",i);
tauz00(j) = Tz00(j)/Z00(j);
taum00(j) = Tm00(j)/M00(j);
Xp00(i) = SAM(i,"HOH");
CC00 = sum(i, Xp00(i));
FF00(h) = SAM("HOH",h);
E00(i) = SAM(i,"EXT");
D00(i) = (1 + tauz00(i))*Z00(i) - E00(i);
Q00(i) = (1 + taum00(i))*M00(i) + D00(i);
Sf00 = SAM("INV","EXT");
* ===============================================================
* Adjusting Investment in the SAM for the Assumed BAU Growth Path
* ===============================================================
Scalar
III_ASS 'required investment for the assumed growth'
III_SAM 'observed investment in the SAM'
adj 'III_ASS vs. III_SAM [>1:more than actual]';
III_ASS = (pop + dep)/ror*FF00("CAP");
III_SAM = sum(i, SAM(i,"INV"));
adj = III_ASS/III_SAM;
* Adjusting investment level
Xv00(i) = SAM(i,"INV")*adj;
* Reallocating the gap made by the inv. adjustment to gov. cons.
Xg00(i) = SAM(i,"GOV") - (Xv00(i) - SAM(i,"INV"));
* Computing the direct tax revenue that balances the gov. budget
Td00 = sum(i, Xg00(i)) - sum(i, Tz00(i) + Tm00(i));
* Computing the household sav. that balances the household budget
Sp00 = sum(h, FF00(h)) - (sum(i, Xp00(i)) + Td00);
III00 = sum(i, Xv00(i));
II00(j) = (Sp00 + Sf00)*F00("CAP",j)/sum(i, F00("CAP",i));
KK00(j) = F00("CAP",j)/ror;
* ===============================================================
* Computing the BAU path
* ===============================================================
Y0(j,t) = Y00(j) *(1 + pop)**(ord(t) - 1);
F0(h,j,t) = F00(h,j)*(1 + pop)**(ord(t) - 1);
X0(i,j,t) = X00(i,j)*(1 + pop)**(ord(t) - 1);
Z0(j,t) = Z00(j) *(1 + pop)**(ord(t) - 1);
Xp0(i,t) = Xp00(i) *(1 + pop)**(ord(t) - 1);
Xv0(i,t) = Xv00(i) *(1 + pop)**(ord(t) - 1);
E0(i,t) = E00(i) *(1 + pop)**(ord(t) - 1);
M0(i,t) = M00(i) *(1 + pop)**(ord(t) - 1);
Q0(i,t) = Q00(i) *(1 + pop)**(ord(t) - 1);
D0(i,t) = D00(i) *(1 + pop)**(ord(t) - 1);
FF0(h,t) = FF00(h) *(1 + pop)**(ord(t) - 1);
III0(t) = III00 *(1 + pop)**(ord(t) - 1);
II0(j,t) = II00(j) *(1 + pop)**(ord(t) - 1);
KK0(j,t) = KK00(j) *(1 + pop)**(ord(t) - 1);
CC0(t) = CC00 *(1 + pop)**(ord(t) - 1);
Sp0(t) = Sp00 *(1 + pop)**(ord(t) - 1);
Td0(t) = Td00 *(1 + pop)**(ord(t) - 1);
Tz0(j,t) = Tz00(j) *(1 + pop)**(ord(t) - 1);
Tm0(i,t) = Tm00(i) *(1 + pop)**(ord(t) - 1);
pf0(h,j,t) = 1;
py0(j,t) = 1;
pz0(j,t) = 1;
pq0(i,t) = 1;
pe0(i,t) = 1;
pm0(i,t) = 1;
pd0(i,t) = 1;
pk0(t) = 1;
epsilon0(t) = 1;
PRICE0(t) = 1;
* Setting exogenous variables
Xg0(i,t) = Xg00(i)*(1 + pop)**(ord(t) - 1);
Sf0(t) = Sf00 *(1 + pop)**(ord(t) - 1);
pWe(i) = 1;
pWm(i) = 1;
tauz(i) = tauz00(i);
taum(i) = taum00(i);
display Y0, F0, X0, Z0, Xp0, Xv0, E0, M0, Q0, D0, Sp0, Td0, Tz0, Tm0, FF0, Sf0, tauz, taum;
* ===============================================================
* Calibration ---------------------------------------------------
* ===============================================================
Parameter
sigma(i) 'elasticity of substitution'
psi(i) 'elasticity of transformation'
eta(i) 'substitution elasticity parameter'
phi(i) 'transformation elasticity parameter';
sigma(i) = 2;
psi(i) = 2;
eta(i) = (sigma(i) - 1)/sigma(i);
phi(i) = (psi(i) + 1)/psi(i);
Parameter
alpha(i) 'share par. in composite cons. func.'
a 'scale par. in composite cons. func.'
beta(h,j) 'share par. in production func.'
b(j) 'scale par. in production func.'
ax(i,j) 'intermediate input requirement coeff.'
ay(j) 'composite fact. input req. coeff.'
lambda(i) 'investment demand share'
iota 'scale par. in comp. inv. prod. func.'
deltam(i) 'share par. in Armington func.'
deltad(i) 'share par. in Armington func.'
gamma(i) 'scale par. in Armington func.'
xid(i) 'share par. in transformation func.'
xie(i) 'share par. in transformation func.'
theta(i) 'scale par. in transformation func.'
ssp 'propensity to save';
alpha(i) = Xp00(i)/sum(j, Xp00(j));
a = CC00/prod(j, Xp00(j)**alpha(j));
beta(h,j) = F00(h,j)/sum(k, F00(k,j));
b(j) = Y00(j)/prod(h, F00(h,j)**beta(h,j));
ax(i,j) = X00(i,j)/Z00(j);
ay(j) = Y00(j) /Z00(j);
lambda(i) = Xv00(i)/sum(j, Xv00(j));
iota = III00/prod(i, Xv00(i)**lambda(i));
deltam(i) = (1 + taum00(i))*M00(i)**(1 - eta(i))/((1 + taum00(i))*M00(i)**(1 - eta(i))+D00(i)**(1 - eta(i)));
deltad(i) = D00(i)**(1 - eta(i))/((1 + taum00(i))*M00(i)**(1 - eta(i)) + D00(i)**(1 - eta(i)));
gamma(i) = Q00(i)/(deltam(i)*M00(i)**eta(i)+ deltad(i)*D00(i)**eta(i))**(1/eta(i));
xie(i) = E00(i)**(1 - phi(i))/(E00(i)**(1 - phi(i)) + D00(i)**(1 - phi(i)));
xid(i) = D00(i)**(1 - phi(i))/(E00(i)**(1 - phi(i)) + D00(i)**(1 - phi(i)));
theta(i) = Z00(i)/(xie(i)*E00(i)**phi(i)+ xid(i)*D00(i)**phi(i))**(1/phi(i));
ssp = Sp00/(sum((h,j), F00(h,j)) - Td00);
display alpha, a, beta, b, ax, ay, lambda, deltam, deltad, gamma, xie, xid, theta, iota, ssp;
* ===============================================================
* Defining model system -----------------------------------------
* ===============================================================
Variable
Y(j) 'composite factor'
F(h,j) 'factor input'
X(i,j) 'intermediate input'
Z(j) 'gross domestic output'
Xp(i) 'household consumption'
Xg(i) 'government consumption'
Xv(i) 'investment demand'
E(i) 'exports'
M(i) 'imports'
Q(i) "Armington's composite good"
D(i) 'domestic good'
FF(h) 'factor endowments'
pf(h,j) 'factor price'
py(j) 'composite factor price'
pz(j) 'supply price of gross domestic output'
pq(i) "Armington's composite good price"
pe(i) 'export price in local currency'
pm(i) 'import price in local currency'
pd(i) 'domestic good price'
pk 'composite investment goods price'
epsilon 'exchange rate'
Sp 'private savings'
Sf 'foreign savings'
Td 'direct tax'
Tz(j) 'production tax'
Tm(i) 'import tariff'
KK(j) 'capital stock'
II(j) 'sectoral investment'
III 'composite investment'
PRICE 'numeraire price'
CC 'composite consumption';
Equation
eqpy(j) 'composite factor prod. func.'
eqF(h,j) 'factor demand function'
eqX(i,j) 'intermediate demand function'
eqY(j) 'composite factor demand function'
eqpzs(j) 'unit cost function'
eqTd 'direct tax revenue function'
eqTz(j) 'production tax revenue function'
eqTm(i) 'import tariff revenue function'
eqXv(i) 'investment demand function'
eqSp 'private saving function'
eqXp(i) 'household demand function'
eqpe(i) 'world export price equation'
eqpm(i) 'world import price equation'
eqepsilon 'balance of payments'
eqpqs(i) 'Armington function'
eqM(i) 'import demand function'
eqD(i) 'domestic good demand function'
eqpzd(i) 'transformation function'
eqE(i) 'export supply function'
eqDs(i) 'domestic good supply function'
eqpqd(i) 'market clearing cond. for comp. good'
eqpf1(h_mob) 'mobile factor market clearing cond.'
eqpf2(h_mob,i,j) 'mobile factor market clearing cond.'
eqpf3(j) 'immobile factor market clearing cond.'
eqpk 'composite inv. goods mar. clear. cond.'
eqIII 'composite inv. goods production func.'
eqII(j) 'evolution of target capital stocks'
eqCC 'composite consumption production func.'
eqPRICE 'numeraire price';
* ===============================================================
* Model equations
* ===============================================================
*[domestic production] -
* composite factor production func. (Cobb-Douglas)
eqpy(j).. Y(j) =e= b(j)*prod(h, F(h,j)**beta(h,j));
* factor demand function (Cobb-Douglas)
eqF(h,j).. F(h,j) =e= beta(h,j)*py(j)*Y(j)/pf(h,j);
* intermediate input demand function (Leontief)
eqX(i,j).. X(i,j) =e= ax(i,j)*Z(j);
* composite factor demand function (Leontief)
eqY(j).. Y(j) =e= ay(j)*Z(j);
* unit price of gross output (Leontief)
eqpzs(j).. pz(j) =e= ay(j)*py(j) + sum(i, ax(i,j)*pq(i));
*[government behavior] -
* lump sum direct tax revenue
eqTd.. Td =e= sum(i, pq(i)*Xg(i)) - sum(i, Tm(i) + Tz(i));
* production tax revenue
eqTz(j).. Tz(j) =e= tauz(j)*pz(j)*Z(j);
* import tariff revenue
eqTm(i).. Tm(i) =e= taum(i)*pm(i)*M(i);
*[investment behavior] -
* composite investment production function
eqXv(i).. Xv(i) =e= lambda(i)*pk*sum(j, II(j))/pq(i);
*[savings] ----------
* savings function
eqSp.. Sp =e= ssp*(sum((h,j), pf(h,j)*F(h,j)) - Td);
*[household consumption] -- (Cobb-Douglas)
eqXp(i).. Xp(i) =e= alpha(i)*(sum((h,j), pf(h,j)*F(h,j)) - Sp - Td)/pq(i);
*[international trade] --
eqpe(i).. pe(i) =e= epsilon*pWe(i);
eqpm(i).. pm(i) =e= epsilon*pWm(i);
* BOP constraint
eqepsilon.. sum(i, pWe(i)*E(i)) + Sf =e= sum(i, pWm(i)*M(i));
*[Armington function] --
* Armington's composite good production function (CES)
eqpqs(i).. Q(i) =e= gamma(i)*(deltam(i)*M(i)**eta(i) + deltad(i)*D(i)**eta(i))**(1/eta(i));
* import demand function (CES)
eqM(i).. M(i) =e= (gamma(i)**eta(i)*deltam(i)*pq(i)/((1 + taum(i))*pm(i)))**(1/(1 - eta(i)))*Q(i);
* domestic good demand function (CES)
eqD(i).. D(i) =e= (gamma(i)**eta(i)*deltad(i)*pq(i)/pd(i))**(1/(1 - eta(i)))*Q(i);
*[transformation function] --
* gross domestic output disaggregation function (CET)
eqpzd(i).. Z(i) =e= theta(i)*(xie(i)*E(i)**phi(i) + xid(i)*D(i)**phi(i))**(1/phi(i));
*export supply function (CET)
eqE(i).. E(i) =e= (theta(i)**phi(i)*xie(i)*(1 + tauz(i))*pz(i)/pe(i))**(1/(1 - phi(i)))*Z(i);
*domestic good supply function (CET)
eqDs(i).. D(i) =e= (theta(i)**phi(i)*xid(i)*(1 + tauz(i))*pz(i)/pd(i))**(1/(1 - phi(i)))*Z(i);
*[market clearing condition]
*Arminton's composite good market
eqpqd(i).. Q(i) =e= Xp(i) + Xg(i) + Xv(i) + sum(j, X(i,j));
*labor market: quantity
eqpf1(h_mob).. sum(j, F(h_mob,j)) =e= FF(h_mob);
*labor market: price
eqpf2(h_mob,i,j).. pf(h_mob,j) =e= pf(h_mob,i);
*capital market
eqpf3(j).. F("CAP",j) =e= ror*KK(j);
*investment goods market
eqpk.. sum(j, II(j)) =e= III;
*[dynamic equations]
*composite investment good market clearing condition
eqIII.. III =e= iota*prod(i, Xv(i)**lambda(i));
*sectoral investment allocation
eqII(j).. pk*II(j) =e= pf("CAP",j)**zeta*F("CAP",j)/sum(i, pf("CAP",i)**zeta*F("CAP",i))*(Sp + epsilon*Sf);
*felicity function
eqCC.. CC =e= a*prod(i, Xp(i)**alpha(i));
* Price level [numeraire]
eqPRICE.. PRICE =e= sum(j, pq(j)*Q00(j)/sum(i,Q00(i)));
* ===============================================================
* Initializing variables ----------------------------------------
* ===============================================================
Y.l(j) = Y00(j);
F.l(h,j) = F00(h,j);
X.l(i,j) = X00(i,j);
Z.l(j) = Z00(j);
Xp.l(i) = Xp00(i);
Xv.l(i) = Xv00(i);
E.l(i) = E00(i);
M.l(i) = M00(i);
Q.l(i) = Q00(i);
D.l(i) = D00(i);
pf.l(h,j) = 1;
py.l(j) = 1;
pz.l(j) = 1;
pq.l(i) = 1;
pe.l(i) = 1;
pm.l(i) = 1;
pd.l(i) = 1;
pk.l = 1;
epsilon.l = 1;
Sp.l = Sp00;
Td.l = Td00;
Tz.l(j) = Tz00(j);
Tm.l(i) = Tm00(i);
FF.l(h) = FF00(h);
III.l = III00;
II.l(j) = II00(j);
* ---------------------------------------------------------------
* Numeraire
PRICE.fx = 1;
* Initial factor endowments and exogenous variables
FF.fx(h_mob) = FF00(h_mob);
KK.fx(j) = KK00(j);
Xg.fx(i) = Xg00(i);
Sf.fx = Sf00;
* ===============================================================
* Defining and solving the model --------------------------------
* ===============================================================
Model dyncge / all /;
solve dyncge maximizing CC using nlp;
* Terminate before scenario runs when running under GAMS SQA Suite
$if not x%gams.jt%==x $exit
option limRow = 0, limCol = 0, solPrint = off, solveLink = %solveLink.loadlibrary%;
* ===============================================================
* Simulation Runs: Abolition of Import Tariffs
* ===============================================================
* Scenario:
taum(i) = taum00(i)*0;
loop(t,
solve dyncge maximizing CC using nlp;
* storing results -------------------------
Y1(j,t) = Y.l(j);
F1(h,j,t) = F.l(h,j);
X1(i,j,t) = X.l(i,j);
Z1(j,t) = Z.l(j);
Xp1(i,t) = Xp.l(i);
Xv1(i,t) = Xv.l(i);
E1(i,t) = E.l(i);
M1(i,t) = M.l(i);
Q1(i,t) = Q.l(i);
D1(i,t) = D.l(i);
Sp1(t) = Sp.l;
Td1(t) = Td.l;
Tz1(j,t) = Tz.l(j);
Tm1(i,t) = Tm.l(i);
FF1(h,t) = FF.l(h);
II1(j,t) = II.l(j);
III1(t) = III.l;
KK1(j,t) = KK.l(j);
CC1(t) = CC.l;
tauz1(i,t) = tauz(i);
taum1(i,t) = taum(i);
pf1(h,j,t) = pf.l(h,j);
py1(j,t) = py.l(j);
pz1(j,t) = pz.l(j);
pd1(j,t) = pd.l(j);
pe1(j,t) = pe.l(j);
pm1(j,t) = pm.l(j);
pq1(j,t) = pq.l(j);
pk1(t) = pk.l;
epsilon1(t) = epsilon.l;
PRICE1(t) = PRICE.l;
* updating the state variables --------------
FF.fx(h_mob) = FF.l(h_mob)*(1 + pop);
KK.fx(j) = (1 - dep)*KK.l(j) + II.l(j);
Xg.fx(i) = Xg0(i,t+1);
Sf.fx = Sf0(t+1);
);
* ===============================================================
* Aftermath Computation
* ===============================================================
* Display of changes --------------------------------------------
Parameter
* changes
dY(j,t) 'change of composite factor [%]'
dF(h,j,t) 'change of factor input [%]'
dX(i,j,t) 'change of intermediate input [%]'
dZ(j,t) 'change of gross output [%]'
dXp(i,t) 'change of household consumption [%]'
dXv(i,t) 'change of investment demand [%]'
dE(i,t) 'change of exports [%]'
dM(i,t) 'change of imports [%]'
dQ(i,t) "change of Armington's composite good [%]"
dD(i,t) 'change of domestic good [%]'
dSp(t) 'change of private saving [%]'
dTd(t) 'change of direct tax [%]'
dTz(j,t) 'change of production tax [%]'
dTm(i,t) 'change of import tariff [%]'
dFF(h,t) 'change of initial sectoral factor uses [%]'
dKK(j,t) 'change of sectoral capital stock [%]'
dII(j,t) 'change of sectoral investment [%]'
dIII(t) 'change of composite investment [%]'
dKK(j,t) 'change of sectoral capital stock [%]'
dKK(j,t) 'change of changes of KK from the BAU [%]'
dKK(j,t) 'change of growth rate of KK [%]'
dCC(t) 'change of utility [%]'
dCC(t) 'change of changes of CC from the BAU [%]'
dCC(t) 'change of growth rate of CC [%]'
dpz(j,t) 'change of gross output price [%]'
dpd(j,t) 'change of domestic good price [%]'
dpm(j,t) 'change of import price [%]'
dpe(j,t) 'change of export price [%]'
dpq(j,t) "change of Armington's comp. good price [%]"
dpf(h,j,t) 'change of factor price [%]'
dpy(j,t) 'change of composite factor price [%]'
depsilon(t) 'change of foreign exchange rate [%]'
dpk(t) 'change of capital good price [%]'
* BAU growth rate
gY0(j,t) 'growth of composite factor [%]'
gF0(h,j,t) 'growth of factor input [%]'
gX0(i,j,t) 'growth of intermediate input [%]'
gZ0(j,t) 'growth of gross output [%]'
gXp0(i,t) 'growth of household consumption [%]'
gXv0(i,t) 'growth of investment demand [%]'
gE0(i,t) 'growth of exports [%]'
gM0(i,t) 'growth of imports [%]'
gQ0(i,t) "growth of Armington's composite good [%]"
gD0(i,t) 'growth of domestic good [%]'
gSp0(t) 'growth of private saving [%]'
gTd0(t) 'growth of direct tax [%]'
gTz0(j,t) 'growth of production tax [%]'
gTm0(i,t) 'growth of import tariff [%]'
gFF0(h,t) 'growth of initial sectoral factor uses [%]'
gKK0(j,t) 'growth of sectoral capital stock [%]'
gII0(j,t) 'growth of sectoral investment [%]'
gIII0(t) 'growth of composite investment [%]'
gCC0(t) 'growth of growth rate of CC [%]'
* C/F growth rate
gY1(j,t) 'growth of composite factor [%]'
gF1(h,j,t) 'growth of factor input [%]'
gX1(i,j,t) 'growth of intermediate input [%]'
gZ1(j,t) 'growth of gross output [%]'
gXp1(i,t) 'growth of household consumption [%]'
gXv1(i,t) 'growth of investment demand [%]'
gE1(i,t) 'growth of exports [%]'
gM1(i,t) 'growth of imports [%]'
gQ1(i,t) "growth of Armington's composite good [%]"
gD1(i,t) 'growth of domestic good [%]'
gSp1(t) 'growth of private saving [%]'
gTd1(t) 'growth of direct tax [%]'
gTz1(j,t) 'growth of production tax [%]'
gTm1(i,t) 'growth of import tariff [%]'
gFF1(h,t) 'growth of initial sectoral factor uses [%]'
gKK1(j,t) 'growth of sectoral capital stock [%]'
gII1(j,t) 'growth of sectoral investment [%]'
gIII1(t) 'growth of composite investment [%]'
gCC1(t) 'growth of growth rate of CC [%]'
* welfare
EV(t) 'equivalent variations [current]'
EV_TTL 'total EV [discounted sum]';
dY(j,t) $Y0(j,t) = (Y1(j,t) /Y0(j,t) - 1)*100;
dF(h,j,t) $F0(h,j,t) = (F1(h,j,t) /F0(h,j,t) - 1)*100;
dX(i,j,t) $X0(i,j,t) = (X1(i,j,t) /X0(i,j,t) - 1)*100;
dZ(j,t) $Z0(j,t) = (Z1(j,t) /Z0(j,t) - 1)*100;
dXp(i,t) $Xp0(i,t) = (Xp1(i,t) /Xp0(i,t) - 1)*100;
dXv(i,t) $Xv0(i,t) = (Xv1(i,t) /Xv0(i,t) - 1)*100;
dE(i,t) $E0(i,t) = (E1(i,t) /E0(i,t) - 1)*100;
dM(i,t) $M0(i,t) = (M1(i,t) /M0(i,t) - 1)*100;
dQ(i,t) $Q0(i,t) = (Q1(i,t) /Q0(i,t) - 1)*100;
dD(i,t) $D0(i,t) = (D1(i,t) /D0(i,t) - 1)*100;
dSp(t) $Sp0(t) = (Sp1(t) /Sp0(t) - 1)*100;
dTd(t) $Td0(t) = (Td1(t) /Td0(t) - 1)*100;
dTz(j,t) $Tz0(j,t) = (Tz1(j,t) /Tz0(j,t) - 1)*100;
dTm(i,t) $Tm0(i,t) = (Tm1(i,t) /Tm0(i,t) - 1)*100;
dFF(h,t) $FF0(h,t) = (FF1(h,t) /FF0(h,t) - 1)*100;
dII(j,t) $II0(j,t) = (II1(j,t) /II0(j,t) - 1)*100;
dIII(t) $III0(t) = (III1(t) /III0(t) - 1)*100;
dKK(j,t) $KK0(j,t) = (KK1(j,t) /KK0(j,t) - 1)*100;
dCC(t) $CC0(t) = (CC1(t) /CC0(t) - 1)*100;
dpz(j,t) $pz0(j,t) = (pz1(j,t) /pz0(j,t) - 1)*100;
dpd(j,t) $pd0(j,t) = (pd1(j,t) /pd0(j,t) - 1)*100;
dpm(j,t) $pm0(j,t) = (pm1(j,t) /pm0(j,t) - 1)*100;
dpe(j,t) $pe0(j,t) = (pe1(j,t) /pe0(j,t) - 1)*100;
dpq(j,t) $pq0(j,t) = (pq1(j,t) /pq0(j,t) - 1)*100;
dpf(h,j,t) $pf0(h,j,t) = (pf1(h,j,t) /pf0(h,j,t) - 1)*100;
dpy(j,t) $py0(j,t) = (py1(j,t) /py0(j,t) - 1)*100;
depsilon(t) $epsilon0(t) = (epsilon1(t) /epsilon0(t) - 1)*100;
dpk(t) $pk0(t) = (pk1(t) /pk0(t) - 1)*100;
gY0(j,t+1) $Y0(j,t) = (Y0(j,t+1) /Y0(j,t) - 1)*100;
gF0(h,j,t+1) $F0(h,j,t) = (F0(h,j,t+1) /F0(h,j,t) - 1)*100;
gX0(i,j,t+1) $X0(i,j,t) = (X0(i,j,t+1) /X0(i,j,t) - 1)*100;
gZ0(j,t+1) $Z0(j,t) = (Z0(j,t+1) /Z0(j,t) - 1)*100;
gXp0(i,t+1) $Xp0(i,t) = (Xp0(i,t+1) /Xp0(i,t) - 1)*100;
gXv0(i,t+1) $Xv0(i,t) = (Xv0(i,t+1) /Xv0(i,t) - 1)*100;
gE0(i,t+1) $E0(i,t) = (E0(i,t+1) /E0(i,t) - 1)*100;
gM0(i,t+1) $M0(i,t) = (M0(i,t+1) /M0(i,t) - 1)*100;
gQ0(i,t+1) $Q0(i,t) = (Q0(i,t+1) /Q0(i,t) - 1)*100;
gD0(i,t+1) $D0(i,t) = (D0(i,t+1) /D0(i,t) - 1)*100;
gSp0(t+1) $Sp0(t) = (Sp0(t+1) /Sp0(t) - 1)*100;
gTd0(t+1) $Td0(t) = (Td0(t+1) /Td0(t) - 1)*100;
gTz0(j,t+1) $Tz0(j,t) = (Tz0(j,t+1) /Tz0(j,t) - 1)*100;
gTm0(i,t+1) $Tm0(i,t) = (Tm0(i,t+1) /Tm0(i,t) - 1)*100;
gFF0(h,t+1) $FF0(h,t) = (FF0(h,t+1) /FF0(h,t) - 1)*100;
gII0(j,t+1) $II0(j,t) = (II0(j,t+1) /II0(j,t) - 1)*100;
gIII0(t+1) $III0(t) = (III0(t+1) /III0(t) - 1)*100;
gKK0(j,t+1) $KK0(j,t) = (KK0(j,t+1) /KK0(j,t) - 1)*100;
gCC0(t+1) $CC0(t) = (CC0(t+1) /CC0(t) - 1)*100;
gY1(j,t+1) $Y1(j,t) = (Y1(j,t+1) /Y1(j,t) - 1)*100;
gF1(h,j,t+1) $F1(h,j,t) = (F1(h,j,t+1) /F1(h,j,t) - 1)*100;
gX1(i,j,t+1) $X1(i,j,t) = (X1(i,j,t+1) /X1(i,j,t) - 1)*100;
gZ1(j,t+1) $Z1(j,t) = (Z1(j,t+1) /Z1(j,t) - 1)*100;
gXp1(i,t+1) $Xp1(i,t) = (Xp1(i,t+1) /Xp1(i,t) - 1)*100;
gXv1(i,t+1) $Xv1(i,t) = (Xv1(i,t+1) /Xv1(i,t) - 1)*100;
gE1(i,t+1) $E1(i,t) = (E1(i,t+1) /E1(i,t) - 1)*100;
gM1(i,t+1) $M1(i,t) = (M1(i,t+1) /M1(i,t) - 1)*100;
gQ1(i,t+1) $Q1(i,t) = (Q1(i,t+1) /Q1(i,t) - 1)*100;
gD1(i,t+1) $D1(i,t) = (D1(i,t+1) /D1(i,t) - 1)*100;
gSp1(t+1) $Sp1(t) = (Sp1(t+1) /Sp1(t) - 1)*100;
gTd1(t+1) $Td1(t) = (Td1(t+1) /Td1(t) - 1)*100;
gTz1(j,t+1) $Tz1(j,t) = (Tz1(j,t+1) /Tz1(j,t) - 1)*100;
gTm1(i,t+1) $Tm1(i,t) = (Tm1(i,t+1) /Tm1(i,t) - 1)*100;
gFF1(h,t+1) $FF1(h,t) = (FF1(h,t+1) /FF1(h,t) - 1)*100;
gII1(j,t+1) $II1(j,t) = (II1(j,t+1) /II1(j,t) - 1)*100;
gIII1(t+1) $III1(t) = (III1(t+1) /III1(t) - 1)*100;
gKK1(j,t+1) $KK1(j,t) = (KK1(j,t+1) /KK1(j,t) - 1)*100;
gCC1(t+1) $CC1(t) = (CC1(t+1) /CC1(t) - 1)*100;
* Welfare measure: Hicksian equivalent variations ---------------
EV(t) = (CC1(t) - CC0(t))/a/prod(i, (alpha(i)/1)**alpha(i));
EV_TTL = sum(t, EV(t)/(1 + ror)**(ord(t) - 1));
* ===============================================================
* GDX file output
* ===============================================================
execute_unload "result.gdx";