dyncge.gms : A Recursive-Dynamic Standard CGE Model

Description

This model is featured in the following book.


Reference

  • Hosoe, N, Gasawa, K, and Hashimoto, H, Textbook of Computable General Equilibrium Modeling: Programming and Simulations, 2nd Edition. University of Tokyo Press, Tokyo, Japan, 2015.

Small Model of Type : NLP


Category : GAMS Model library


Main file : dyncge.gms

$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";