Description
This general equilibrium model has been used to study the adjustment policies of the Indian government in response to internal and external shocks. The original version, (GANGES,SEQ=97), was formulated as an optimization model. However, the model consist of a set of nonlinear equations and it has only one solution. This version is formulated directly as a system of nonlinear equations using the CNS = Constrained Nonlinear System model type.
Large Model of Type : CNS
Category : GAMS Model library
Main file : gancns.gms
$title Macro-Economic Framework for India (GANCNS,SEQ=210)
$onText
This general equilibrium model has been used to study the
adjustment policies of the Indian government in response to
internal and external shocks.
The original version, (GANGES,SEQ=97), was formulated as an
optimization model. However, the model consist of a set of
nonlinear equations and it has only one solution. This version
is formulated directly as a system of nonlinear equations using
the CNS = Constrained Nonlinear System model type.
Mitra, P, and Tendulkar, S, Coping with Internal and External
Exogenous Socks: India. Tech. rep., The World Bank, 1986.
Keywords: constrained nonlinear systems, general equilibrium model, macro economics
$offText
$sTitle Set Definitions
Set
i '6 sectors of the economy' / agricult 'agriculture sector'
cons-good 'consumer goods sector'
cap-good 'capital goods sector'
int-good 'intermediate goods sector'
pub-infr 'public infrastructure sector'
service 'services sector' /
sa(i) 'agriculture sector' / agricult /
sc(i) 'capital goods sector' / cap-good /
si(i) 'public infrastructure sector' / pub-infr /
ss(i) 'services sector' / service /
im(i) 'importing sectors'
ie(i) 'exporting sectors'
manufact(i) 'manufacturing sectors' / cons-good, cap-good, int-good /
ty 'income categories'
/ yself 'self-employment income'
ywage 'wage income'
ycap 'land or capital income'
yinfr 'income from government subsidies via infrastructure'
ynonp 'non-production income' /
li(ty) 'production income categories';
li(ty) = yes;
li("ynonp") = no;
Set
r 'regions'
/ urban 'urban regions'
rural 'rural regions' /
ri(r,i) 'mapping between regions and sectors'
/ rural.agricult
urban.(cons-good,cap-good,int-good,pub-infr,service) /
datvar 'input variables'
/ return-cap 'income from capital investments'
return-inf 'income from infrastructure'
self-empl 'income from self employment'
wage-labor 'income from wage and labor'
dom-inter 'domestically produced intermediate goods'
imp-inter 'imported intermediate goods'
pub-cons 'public consumption (domestic and imported)'
fix-inv 'fixed capital investments (domestic and imported)'
change-sto 'change in stock'
cons-imp 'household consumption - imported'
xvoli 'constant term used in calculating export volume' /
taxvar 'tax variables'
/ dom-inter 'indirect taxes on domestic intermediate inputs'
imp-inter 'indirect taxes on imported intermediate inputs'
dom-cons 'total taxes on final domestic consumption'
imp-cons 'total taxes on final imported consumption'
profits 'total taxes on profits'
self-emp 'total taxes on self-employment income'
tax-wage 'total taxes on wage income' /
stockvar 'stock variables'
/ capital 'total capital stock (millions of rupees)'
infrast 'total infrastructure stock (millions of rupees)'
wage-labor 'total labor force (millions of persons)'
self-empl 'total self-employment (millions of persons)' /
sigma 'elasticity of substitution parameters'
/ sigmax 'between final demands for domestic and imported capital goods'
sigmaz 'between value added and intermediate inputs'
sigman 'between domestic and imported intermediate inputs'
sigmav 'between capital. self-employment and wage labor'
sigmas 'between land and agriculture labor'
eta 'export elasticity' /;
Alias (i,j), (ty,tz), (manufact,manuf);
Set
acv 'gdp expenditure categories'
/ ndp 'net domestic product'
gdp 'gross domestic product'
privc 'private consumption'
gdpmp 'gdp at market prices'
govc 'government consumption'
gfi 'gross fixed investment'
chan-sto 'change in stock'
invest 'total of gfi and change in stock'
exports 'exports'
imports 'imports' /
indicat 'target indicators at constant prices'
/ gdpmp 'gdp at market prices'
privc 'private consumption'
gfi 'fixed investment'
invest 'investment and change in stock'
exports 'total exports'
imports 'total imports'
gdpgrt 'growth rate of gdp at market prices'
cnsgrt 'growth rate of private consumption'
gfigrt 'growth rate of fixed investment'
invgrt 'growth rate of total investment'
expgrt 'growth rate of exports'
impgrt 'growth rate of imports'
cnsshr 'consumption to gdp at market prices ratio'
gfishr 'gfi to gdpmp ratio'
expshr 'exports to gdpmp ratio'
impshr 'imports to gdpmp ratio' /
years 'time horizon for tracking'
/ 7374 '1973-74 -- base year'
7475 '1974-75'
7576 '1975-76'
7677 '1976-77'
7778 '1977-78'
7879 '1978-79'
7980 '1979-80'
8081 '1980-81'
8182 '1981-82'
8283 '1982-83'
8384 '1983-84 -- last year of tracking' /
t(years) 'current year';
t(years) = no;
t("7374") = yes;
$sTitle Input Data Tables
Table dat(datvar,i) 'factor remuneration (current millions of rupees)'
agricult cons-good cap-good int-good pub-infr service
return-cap 64493.3 6406.5 5434.4 8567.9 4401.9 27677.2
self-empl 148431.0 4937.3 13714.3 6488.8 38411.1
wage-labor 48364.6 12560.5 16267.7 17072.2 9941.2 73786.0
dom-inter 77681.1 68904.0 54658.1 47254.0 6872.7 48988.9
imp-inter 2356.0 3201.3 2307.3 9801.7 1.3 572.0
pub-cons 816.9 544.0 4730.1 4423.9 2986.2 36832.5
fix-inv 623.9 139.5 76198.8 2970.4 252.1 5076.3
change-sto 7092.5 5944.2 1756.4 6073.7 272.2
cons-imp 3159.9 504.3 5235.6 4170.9
xvoli 2977.8 10046.2 990.9 5984.0 ;
im(i) = yes$dat("cons-imp",i);
ie(i) = yes$dat("xvoli",i);
Table rate(*,i) 'various tax and margin rates (unitless)'
agricult cons-good cap-good int-good pub-infr service
dep-prof 0.0729 0.2369 0.4319 0.1921 0.7191 0.3166
dep-lab 0.0106 0.0832 0.0094 0.0958 0.0761
taxrat-dom 0.0212 0.0865 0.0972 0.1212 0.1268 0.1056
taxrat-imp 0.3134 0.1629 0.4247 0.2790 0.8461 0.6715
taxrfd-dom - 0.0013 0.32 0.40 0.40
taxrfd-imp 0.0731 0.6728 0.3781 0.7236
tradm-fd 0.14480 0.01368 0.03103
tradm-exp 0.16257 0.50 0.33460 0.13017
tradm-imp 0.50 0.07130 ;
Table tax(taxvar,i) 'tax data (current millions of rupees)'
agricult cons-good cap-good int-good pub-infr service
dom-inter 1649.8 5964.3 5314.1 5727.0 871.5 5171.3
imp-inter 738.5 521.6 989.2 2734.6 1.1 384.1
dom-cons -5570.9 16739.9 2303.2 4032.0 47.1 318.8
imp-cons 231.0 339.7 1979.6 1079.0
profits 704.7 597.8 942.5 484.2 3044.5
self-emp 222.2 617.1 292.0 1728.5
tax-wage 565.2 732.0 768.2 447.4 3320.4;
Table stock(stockvar,i) 'stock data (current millions of rupees)'
agricult cons-good cap-good int-good pub-infr service
capital 515946.4 29570.0 43475.2 68543.2 168695.0 417500.0
infrast 1881.2 1403.9 2145.8 9995.2 4621.0 2694.2
wage-labor 43.325 1.697 2.198 2.307 1.343 9.971
self-empl 132.735 3.545 9.847 4.659 27.578;
Table elast(sigma,i) 'elasticity parameters (unitless)'
agricult cons-good cap-good int-good pub-infr service
sigmax 0.5 0.5 0.5 0.5 0.5 0.5
sigmaz 0.9 1.1 1.1 1.1 1.1 1.1
sigman 1.5 1.5 1.5 1.5 1.5 1.5
sigmav 0.9 0.7 0.7 0.7 0.7 0.7
sigmas 0.5 0.7 0.7 0.7 0.7 0.7
eta 1.5 1.5 1.0 1.5 1.0;
Table a(i,j) 'domestic input output coefficients matrix (unitless)'
agricult cons-good cap-good int-good pub-infr service
agricult 0.760190 0.549245 0.129944 0.112517 0.000146 0.206418
cons-good 0.075543 0.196520 0.005262 0.036037 0.010709 0.026161
cap-good 0.029948 0.012795 0.117179 0.039635 0.555240 0.112295
int-good 0.062838 0.086158 0.522219 0.524852 0.100921 0.305633
service 0.071481 0.155282 0.225396 0.286959 0.332984 0.349493;
Table am(i,j) 'imports input output coefficients matrix (unitless)'
agricult cons-good cap-good int-good pub-infr service
agricult 0.0011 0.843906 0.027276
cons-good 0.002833 0.127355 0.000087 0.045681
cap-good 0.000387 0.081846 0.006631 0.048316 0.00056
int-good 0.996067 0.028352 0.918067 0.920412 0.951684 0.99944;
Table ayi(i,r) 'shares for allocation of sectoral income to regions (unitless)'
rural
agricult 1.0
cons-good .4635
service .4635;
ayi(i,"urban") = 1 - ayi(i,"rural");
Parameter ayt(r) 'shares for allocation of transfers to regions (unitless)' / rural .8 /;
ayt("urban") = 1 - ayt("rural");
Table ac(i,r) 'expenditure shares (unitless)'
urban rural
agricult 0.32629 0.482105
cons-good 0.257648 0.26756
cap-good 0.028424 0.02644
int-good 0.039263 0.015185
pub-infr 0.011206 0.00897
service 0.337169 0.19974 ;
Table gamma(i,r) 'per capita committed consumption (units)'
urban rural
agricult 2.228551 2.037878
cons-good 0.300443 0.332562
cap-good -.02261 0.002407
int-good 0.096637 0.128932
pub-infr 0.07928 0.092737
service -.59266 0.064369;
Table conpar(*,r) 'various consumer parameters'
urban rural
alpha 0.376842 0.309118
beta 0.76777 0.77814
pop 122. 458. ;
Table baseprice(i,*) 'base year prices'
pv00 v00 pk00 pg00 pc00 pq00
agricult 1.0050 2616.0656 0.1258 1.0076 1.1483 1.0042
cons-good 1.0155 249.8925 0.2320 1.1071 1.3423 1.0064
cap-good 0.9617 303.6711 0.1001 0.7277 1.3668 0.9763
int-good 0.9820 310.7917 0.1180 0.9207 1.3761 0.9829
pub-infr 1.0500 157.2187 0.0306 1.2566 1.0977 1.0647
service 1.0045 1443.4865 0.0691 1.0624 1.0023 1.0023;
Scalar
nct 'net current transfer' / 19.20 /
nfi 'net factor income' / -32.50 /
gtra 'interest on national debt' / 46.7 /
gtrb 'domestic current transfers' / 90.9 /;
$sTitle Time Series of exogenous Data
Table series(*,years) 'exogenous data series'
7374 7475 7576 7677 7778 7879 7980 8081 8182 8283 8384
cg 503.336 511.10 645.46 697.87 702.24 750.71 754.74 809.06 856.64 971.38 1008.49
xsa 1.000 .9366 1.1158 .9504 1.1097 1.0306 .8981 1.1041 1.0356 0.9796 1.1364
er 7.791 7.796 8.653 8.939 8.563 8.206 8.076 7.893 8.929 9.628 10.312
usdefl 1.0000 1.0878 1.1862 1.2539 1.3274 1.4259 1.5469 1.6845 1.8422 1.9595 2.0354
indefl 1.0000 1.1665 1.1181 1.1948 1.2395 1.2648 1.4572 1.6157 1.7789 1.9119 2.1381
savf 47.9 96.1 57.9 -103.1 -90.3 -57.5 -29.9 199.6 241.2 237.0 265.0
gtra 47.70 34.00 49.10 60.10 69.70 93.40 100.80 149.00 184.20 270.40 270.40
gtrb 90.90 115.00 135.00 154.70 176.20 200.50 239.20 283.50 331.10 400.50 400.50
nfi -32.50 -29.10 -25.50 -23.30 -23.30 -15.60 15.30 29.80 -.70 -68.10 -68.10
nct 19.20 27.40 52.80 73.90 102.20 104.20 162.40 225.70 222.10 252.70 252.70
dmsa 31.60 40.69 59.36 39.79 5.68 3.76 3.74 3.90 15.51 13.69 21.66
dmco 5.04 1.76 2.28 5.68 21.95 13.64 8.62 20.23 16.48 11.93 16.31
dmsi 41.71 42.14 40.96 42.23 43.62 44.06 48.47 48.85 46.00 40.42 29.07
idshr 0.7954 0.7604 0.8201 0.8746 0.9281 0.8280 0.8111 0.8253 0.8346 0.8575 0.8583
const 133.125 134.88 136.67 138.47 140.31 142.17 144.05 145.96 147.91 149.885 152.64
totlab 65.09 67.88 70.75 73.75 76.84 80.06 83.39 86.84 90.43 95.14 97.10
pkvsa 0.1807 0.1537 0.1511 0.2071 0.2071 0.2080 0.1845 0.1861 0.1696 0.1585 0.1605
pkvni 0.2909 0.3703 0.2967 0.2322 0.2752 0.2912 0.3356 0.2924 0.3038 0.2777 0.2725
pkvsi 0.1167 0.1350 0.1827 0.1761 0.1830 0.1504 0.1770 0.1825 0.1952 0.2549 0.2457
pkvss 0.4117 0.3411 0.3695 0.3846 0.3346 0.3505 0.3029 0.3390 0.3314 0.3092 0.3213
pim1 1.0000 1.2582 1.5165 1.4615 1.4451 1.5495 1.8956 1.7261 1.5030 1.3932 1.3841
pim2 1.0000 1.9203 1.5072 1.6667 1.4783 1.4710 1.8261 1.1915 1.3386 1.1637 1.2940
pim3 1.0000 1.3826 1.8261 2.0174 1.7913 2.2957 2.7826 1.9146 1.6529 1.6123 1.5498
pim4 1.0000 1.6423 1.9238 1.6655 1.6548 1.6830 1.9890 1.9275 2.0165 2.0239 2.0025
pim5 1.0000 2.2036 2.4820 2.7695 2.8593 2.8533 4.5350 6.8905 8.1604 7.7164 6.9373
pim6 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000
pie1 1.0000 1.3202 1.3051 1.3065 1.9159 1.3546 0.8066 1.3053 1.5555 1.2789 1.2691
pie2 1.0000 1.2412 1.3048 1.5450 1.8197 1.8975 1.9845 2.0995 2.2128 2.1709 2.0801
pie3 1.0000 0.8929 1.2857 1.2929 1.3857 1.3286 1.5500 1.3552 1.6076 1.5771 1.5111
pie4 1.0000 1.3776 1.4375 1.4746 1.4763 1.4986 1.6509 1.7620 2.0759 2.0366 1.9914
totpu 122.00 124.89 129.90 134.85 140.05 145.70 151.39 157.26 163.23 169.38 175.89
totpr 458.00 468.11 477.10 485.15 493.95 503.30 512.61 521.74 530.77 539.62 549.11
gdpmp 5944.2 8611.2 9261.9
privc 4340.3 4157.8 4311.7 4206.7 4847.8 4981.0 4479.0 4961.4 5280.9 5460.3 5940.0
gfi 902.9 917.9 1182.3 1314.2 1394.7 1481.2 1456.4 1610.0 1715.0 1785.1 1895.1
invest 1135.2 1207.2 1441.6 1502.6 1502.8 1788.9 1795.5 1950.9 2054.8 2081.8 2207.9
exports 283.0 306.0 356.6 426.8 410.5 444.0 518.5 517.0 516.2 532.9 559.1
imports 317.6 275.9 279.2 278.7 363.1 394.1 377.9 554.4 598.6 599.9 624.6
cns-curr 4340.3
gfi-curr 902.9 1093.0 1324.8 1526.7 1714.6 1882.5 2090.2 2521.7 2971.6 2971.6 2971.6
inv-curr 1135.2 1450.9 1641.8 1766.9 1854.8 2293.3 2622.8 3144.3 3668.0 3668.0 3668.0
gdpmp-curr 5944.2 6968.1 7202.3 7586.7 8716.1 9610.3 10120.4 11989.6 14161.5 14161.5 14161.5
exp-curr 283.0 383.5 481.2 613.9 663.6 711.5 838.1 902.9 1025.3 1025.3 1025.3
imp-curr 317.6 477.9 566.4 561.4 652.2 742.6 985.9 1357.9 1487.9 1487.9 1487.9
cns-defl 1.0000 1.2019 1.1389 1.1759 1.2342 1.2820 1.4608 1.6117 1.7851 1.7851 1.7851
gdpc 5377.2 5423.5 5936.0 5981.1 6508.0 6882.3 6518.0 7030.2 7406.3 7534.4 7958.1
ax1 1 .9677 1.0504 .9931 1.0141 1.0149 .9884 1.0823 1.0238 .9726 1.0623
ax2 1 1.2461 1.2442 1.2179 1.3060 1.5719 1.7899 1.7452 1.6679 1.8441 1.8293
ax3 1 1.1884 1.3716 1.6430 1.6913 1.6744 1.9078 1.4786 1.5309 2.0376 1.8724
ax4 1 .7520 .5640 .7232 .8045 .8531 .6947 .5982 .6997 .7295 .7110
ax5 1 .7509 .5631 .6157 .6351 .5144 .3781 .4568 .5778 .5619 .7504
ax6 1 .9837 .7377 .8285 .9107 .8105 .7230 .7224 .7740 .7775 .7132
exscale 1 .9000 1.0890 1.1165 1.0487 1.0540 1.0337 .8801 1.1469 1.2994 1.2439
betar 1 1 1.0372 1.0554 1.1103 1.0940 .9958 .9817 .9359 .9576 1.0020
betau 1 1 .9000 .8100 .8930 .8930 .8037 .8941 1.1175 1.1052 1.1100
thetai .12098 .53921 .16502 .14852 .16845 .19778 .16345 .12949 .17234 .18768;
series("cns-curr",years) = series("privc",years)*series("cns-defl",years);
series("pim1",years) = series("pim1",years)/series("usdefl",years);
series("pim2",years) = series("pim2",years)/series("usdefl",years);
series("pim3",years) = series("pim3",years)/series("usdefl",years);
series("pim4",years) = series("pim4",years)/series("usdefl",years);
series("pim5",years) = series("pim5",years)/series("usdefl",years);
series("pim6",years) = series("pim6",years)/series("usdefl",years);
series("pie1",years) = series("pie1",years)/series("usdefl",years);
series("pie2",years) = series("pie2",years)/series("usdefl",years);
series("pie3",years) = series("pie3",years)/series("usdefl",years);
series("pie4",years) = series("pie4",years)/series("usdefl",years);
$sTitle Parameter Declarations
Parameter
pie(i) 'international prices (rp per unit)'
pim(i) 'import prices by commodity (rp per unit)'
dw(r) 'initial wage rates (rp per unit)'
dcpi(r) 'initial cpi (rp per unit)'
k(i) 'capital and land (units)'
dg(i) 'initial infrastructure input by sector (units)'
totlab 'total employment in urban sectors (units)'
dsa(i) 'stock available from last year (units)'
aq(sc) 'scaling for q-production function (unitless)'
az(i) 'scaling for z-production function (unitless)'
an(i) 'scaling for n-production function (unitless)'
as(i) 'scaling for s-production function (unitless)'
av(i) 'scaling for v-production function (unitless)'
aex(i) 'scale of export demands (units)'
depp(i) 'depreciation rate for land or capital income (unitless)'
depl(i) 'depreciation rate for self-employment income (unitless)'
trmd(i) 'trade margin rate on domestic demand (unitless)'
trmx(i) 'trade margin rate on exports (unitless)'
trmm(i) 'trade margin rate on imports (unitless)'
thetak(i) 'enterprise savings rates (unitless)'
ratinf 'share of infrastructure in output of pub-infr (unitless)'
idshr 'share of gross fixed investment in total investment (unitless)'
dstshr 'share of change in stock in total investment (unitless)'
aid(i) 'sector i share of gross fixed investment (unitless)'
adst(i) 'sector i share of change in stocks (unitless)'
cg(i) 'government demand (units)'
deltaq(sc) 'share parameter for q (unitless)'
deltax(i) 'share parameter for x (unitless)'
deltaz(i) 'share parameter for z (unitless)'
deltan(i) 'share parameter for n (unitless)'
deltas(i) 'share parameter for s (unitless)'
deltav(i) 'share parameter for v (unitless)'
sigmaq(sc) 'elasticity of substitution between x and m (unitless)'
sigmax(i) 'elasticity of substitution between z and g (unitless)'
sigmaz(i) 'elasticity of substitution between v and n (unitless)'
sigman(i) 'elasticity of substitution between nd and nm (unitless)'
sigmav(i) 'elasticity of substitution between s and lw (unitless)'
sigmas(i) 'elasticity of substitution between h and ls (unitless)'
rhoq(sc) 'ces function exponent for q (unitless)'
rhox(i) 'ces function exponent for x (unitless)'
rhoz(i) 'ces function exponent for z (unitless)'
rhon(i) 'ces function exponent for n (unitless)'
rhov(i) 'ces function exponent for v (unitless)'
rhos(i) 'ces function exponent for s (unitless)'
alpha(r) 'intercept of housejold expenditure function (unitless)'
pop(r) 'population by region (units)'
eta(i) 'export elasticity (unitless)'
mu 'social weight on equity (unitless)'
psi 'weight for private utility in obj (unitless)'
ksi 'weight for investment in obj (unitless)'
er 'exchange rate (rp per $)'
usdefl 'gdp deflator for us dollar (unitless)'
indefl 'gdp deflator for indian rupee (unitless)';
Parameter
rcons(*,acv) 'gdp expenditure by sector (constant prices)'
rcurr(*,acv) 'gdp expenditure by sector (current prices)'
er0 'foreign exchange rate in previous period (rp per $)'
pim0(i) 'import prices in previous period (rp per unit)'
pnm0(i) 'price of intermediate imports in previous period (rp per unit)'
pc0(i) 'consumer prices in previous period (rp per unit)'
v0(i) 'value added in previous period (units)'
pv0(i) 'prices of value added in previous period (rp per unit)'
pls0(r) 'wage of self-employment in previous period (rp per unit)'
pk0 (i) 'return on land or capital in previous period (rp per unit)'
pq0 (i) 'price of output in previous year (rp per unit)'
ax0(i) 'previous period ax (unitless)'
beta0(r) 'previous period beta (unitless)'
exscale0 'previous period exscale (unitless)'
gdptg 'gdpmp - target'
cnstg 'private consumption - target'
gfitg 'fixed investments - target'
invtg 'total investments - target'
exptg 'exports - target'
imptg 'imports - target'
gdppr 'gdp at market prices in previous period'
cnspr 'private consumption in previous period'
gfipr 'fixed investments in previous period'
invpr 'total investments in previous period'
exppr 'exports in previous period'
imppr 'imports in previous period'
pim00(i) 'import prices - base year (rp per unit)'
pnm00(i) 'price of intermediate imports in base period (rp per unit)'
k00(i) 'land and capital in base period (units)'
er00 'exchange rate in base period (1973-74) (rp per $)'
mc00(r) 'mean per capita consumption in base period (current)'
v00(i) 'value added in base period (units)'
pv00(i) 'price of v in base period (rp per unit)'
pc00(i) 'consumer prices in base period (rp per unit)'
pg00(i) 'price of infrastructure in base period (rp per unit)'
pls00(r) 'wage of self-employment in base period (rp per unit)'
w00(r) 'wage rates of organized labor in base period (rp per unit)'
pk00(i) 'return to land or capital in base period (rp per unit)'
pq00(i) 'output prices in base period (rp per unit)'
gdp00 'gdpmp in base period'
cns00 'private consumption in base period'
gfi00 'fixed investments in base period'
inv00 'investments in base period'
exp00 'exports in base period'
imp00 'imports in base period'
c00(r) 'base year consumption by region'
cg0(i) 'base year public consumption'
ytotal(*,*,*) 'income totals for urban-rural-total'
conex(*,r) 'per capita consumption'
pcinc(*,r) 'per capita income'
savrat(*,r) 'savings ratio'
totco(*,*) 'total consumption by sector (quantity and value at constant prices)'
shrco(i,r) 'shares of consumption by sector and class (constant prices)'
elsup(*) 'elasticities of supply'
elcon(*,*,*) 'elasticities of consumption'
ut1(r) 'utility at current period'
ut0(r) 'utility at base period'
cli(*) 'cost of living index (with respect to base period)'
taxdir 'tax revenue -- direct'
taxind 'tax revenue -- indirect'
taximp 'tax revenue -- net import duty'
infras 'income from infrastructure'
govr 'net tax revenue + infrastructure income'
govsav 'government savings'
tgovr 'savg + infrastructure income'
govtrn 'government transfer'
govcon 'government consumption'
govex 'government expenditure'
gap 'defined as (govr - govex - tgovr)'
dsapq(*) 'dsa*pq'
totdepr 'total depreciation (capital and self-employment income)'
deprec0(i) 'depreciation evaluated at previous years prices'
gva(*) 'gross value added'
gdp(*) 'gross domestic product'
grthr(acv) 'growth ratios of constant price components of gdp'
deflnac 'deflators comparable to nac deflators (based on previous year)'
dflnacb(i) 'price deflators relative to base period'
relnacb0(i) 'relative price deflators in base period'
relnacb(i) 'relative price deflators in current period'
chgnacb(i) 'change in relative price deflators'
exppi 'export price index'
imppi 'import price index'
tradeterm 'terms of trade'
xparm(*,*) 'parameters for static experiments'
match(*,*) 'actual and target values'
parm(*,*) 'current values of parameters'
pkv(i) 'b matrix coefficients'
chgv(i) 'change in v';
$sTitle Variable Declarations
Variable
x(i) 'gross output (units)'
g(i) 'flow of infrastructure (units)'
q(i) 'aggregate supply (units)'
pq(i) 'price of final output (rp per unit)'
m(i) 'final import demands (units)'
pm(i) 'post-tax and trade margin import prices (rp per unit)'
z(i) 'z output (units)'
v(i) 'value added (units)'
n(i) 'intermediate net of infrastructure (units)'
px(i) 'price of output (rp per unit)'
pz(i) 'price of z (rp per unit)'
s(i) 'value added subaggregate (units)'
lw(i) 'employment of wage labor (units)'
pv(i) 'price of value added (rp per unit)'
ls(i) 'self employment labor (units)'
ps(i) 'price of s output (rp per unit)'
pnd(i) 'price of domestic intermediate (rp per unit)'
w(r) 'wage rates of organized labor (rp per unit)'
cpi(r) 'consumer price index (rp per unit)'
pls(r) 'wage rate of self employment labor (rp per unit)'
pnm(i) 'price of intermediate imports (rp per unit)'
pn(i) 'price of intermediate goods (rp per unit)'
pk(i) 'return to capital (rp per unit)'
pc(i) 'price of consumer goods (rp per unit)'
fd(i) 'domestic final demand (units)'
nd(i) 'domestic intermediate goods (units)'
nm(i) 'import intermediate goods (units)'
marg 'trade margin service demand (units)'
pg(i) 'rent for infrastructure (rp per unit)'
y(ty,i) 'factor income for sectors of economy (current)'
fy(ty,i) 'fixed price factor income (base year rp)'
wtr(ty) 'world transfers (current)'
gtr(ty) 'government transfers (current)'
fwtr(ty) 'fixed price world transfers (base year rp)'
fgtr(ty) 'fixed price government transfers (base year rp)'
yh(ty,r) 'income by region and income type (current)'
fyh(ty,r) 'fixed price income by region and income type (base year rp)'
ym(r) 'mean per capita real income by region (units)'
mc(r) 'mean per capita real consumption (units)'
ch(i,r) 'private consumption (units)'
savh(r) 'household savings (current)'
savf 'foreign savings (current $)'
savg 'government savings (current)'
ex(i) 'total exports (units)'
invtot 'total gross investments (units)'
id(i) 'investment demand by sector (units)'
dst(i) 'changes in stock by sector (units)'
ax(i) 'efficiency variable (unitless)'
exscale 'scaling of export demand (unitless)'
tnd(i) 'tax rate on domestic intermediate (unitless)'
tnm(i) 'tax rate on imported intermediate (unitless)'
tfd(i) 'tax rate on final demand (unitless)'
tfm(i) 'import tax rate (unitless)'
tk(i) 'tax rate on capital (profits) (unitless)'
tw(i) 'tax rate on wages (income tax) (unitless)'
thetai 'infrastructural savings rate (unitless)'
taum(i) 'implicit tax on imports due to price differences (unitless)'
lambda(r) 'rate of wage adjustment parameter (unitless)'
beta(r) 'slope of household expenditure function (unitless)'
util(r) 'regional per capita utility (utils)'
utility 'objective value (utils)';
Positive Variable pk;
Variable
dumtg 'sum of square deviations (absolute)'
dumgrt 'sum of square deviations in tracking'
dumshr 'sum of square deviations (on shares)'
ogdpmp 'model generated gdp at market prices'
ogdp 'model generated gdp at factor prices'
ocns 'model generated private consumption'
ogfi 'model generated gross fixed investment'
ochs 'model generated stock changes'
oinv 'model generated total investment'
oexp 'model generated exports'
oimp 'model generated imports'
deprec00(i) 'depreciation evaluated at base prices (base year rp)'
deprec(i) 'depreciation evaluated at current prices (current)';
$sTitle Compute Parameters and Coefficients
mu = 1;
psi = 1;
ksi = 7;
pie(i) = 1;
pim(i) = 1;
pim00(i) = pim(i);
pg.l(i) = 1;
pg00(i) = baseprice(i,"pg00");
px.l(i) = 1;
ps.l(i) = 1;
pv.l(i) = 1;
pn.l(i) = 1;
pz.l(i) = 1;
pq.l(i) = 1;
dat(datvar,i) = dat(datvar,i)/100;
tax(taxvar,i) = tax(taxvar,i)/100;
stock(stockvar,i) = stock(stockvar,i)/100;
sigmax(i) = elast("sigmax",i)*1.20;
sigmaq(sc) = 0.90;
sigmaz(i) = elast("sigmaz",i)*1.20;
sigman(i) = elast("sigman",i)*1.20;
sigmav(i) = elast("sigmav",i)*1.20;
sigmas(i) = elast("sigmas",i)*1.20;
* calculate rho from sigma using definition
rhox(i) = 1/sigmax(i) - 1;
rhoq(sc) = 1/sigmaq(sc) - 1;
rhoz(i) = 1/sigmaz(i) - 1;
rhon(i) = 1/sigman(i) - 1;
rhov(i) = 1/sigmav(i) - 1;
rhos(i) = 1/sigmas(i) - 1;
eta(i) = elast("eta",i)*1.20;
k(i) = stock("capital",i);
pk.l(i) = dat("return-cap",i)/k(i);
pk00(i) = baseprice(i,"pk00");
pls.l("rural") = 11.182506;
pls.l("urban") = 13.928;
pls00("rural") = 11.2507;
pls00("urban") = 13.7343;
ls.l(i) = stock("self-empl",i)*100;
display k, pk.l, pls.l, ls.l;
* calibrate deltas using firsts, s using values, and as using prods
deltas(i)$ls.l(i) = (k(i)/ls.l(i))**(1/sigmas(i))*pk.l(i)/sum(r$ri(r,i), pls.l(r));
deltas(i)$ls.l(i) = deltas(i)/(1 + deltas(i));
deltas(i)$(not ls.l(i)) = 1;
s.l(i) = dat("return-cap",i) + dat("self-empl",i);
as(i) = s.l(i)*(deltas(i)*k(i)**(-rhos(i)) + ((1 - deltas(i))*ls.l(i)**(-rhos(i)))$(not si(i)))**(1/rhos(i));
display deltas, s.l, ps.l, as;
dw("rural") = 11.163208;
dw("urban") = 74.00;
w.l(r) = dw(r);
w00(r) = dw(r);
lw.l(i) = stock("wage-labor",i)*100;
display w.l, lw.l;
* calibrate deltav using firstv, v using valuev, and av using prodv
deltav(i) = (s.l(i)/lw.l(i))**(1/sigmav(i))*ps.l(i)/sum(r$ri(r,i), w.l(r));
deltav(i) = deltav(i)/(1 + deltav(i));
v.l(i) = s.l(i) + dat("wage-labor",i);
av(i) = v.l(i)*(deltav(i)*s.l(i)**(-rhov(i)) + (1 - deltav(i))*lw.l(i)**(-rhov(i)))**(1/rhov(i));
v00(i) = baseprice(i,"v00");
pv00(i) = baseprice(i,"pv00");
display deltav, v.l, pv.l, av;
* calibrate pnm using pnmdet
trmm(i) = rate("tradm-imp",i);
tnm.l(i) = rate("taxrat-imp",i);
pnm.l(i) = sum(j, am(j,i)*pim(j)*(1 + trmm(j) + tnm.l(j)));
pnm0(i) = pnm.l(i);
pnm00(i) = pnm.l(i);
nm.l(i) = (dat("imp-inter",i)*(1 + trmm(i)) + tax("imp-inter",i))/pnm.l(i);
display trmm, tnm.l, pnm.l, nm.l;
* calibrate pnd using pnddet
tnd.l(i) = rate("taxrat-dom",i);
pnd.l(i) = sum(j, a(j,i)*pq.l(j)*(1 + tnd.l(j)));
nd.l(i) = (dat("dom-inter",i) + tax("dom-inter",i))/pnd.l(i);
display tnd.l, pnd.l, nd.l;
* calibrate deltan using firstn, n using valuen, and an using prodn
deltan(i) = (nd.l(i)/nm.l(i))**(1/sigman(i))*pnd.l(i)/pnm.l(i);
deltan(i) = deltan(i)/(1 + deltan(i));
n.l(i) = nd.l(i)*pnd.l(i) + nm.l(i)*pnm.l(i);
an(i) = n.l(i)*(deltan(i)*nd.l(i)**(-rhon(i)) + (1 - deltan(i))*nm.l(i)**(-rhon(i)))**(1/rhon(i));
display deltan, n.l, pn.l, an;
* calibrate deltaz using firstz, z using valuez, and az using prodz
deltaz(i) = (v.l(i)/n.l(i))**(1/sigmaz(i))*pv.l(i)/pn.l(i);
deltaz(i) = deltaz(i)/(1 + deltaz(i));
z.l(i) = n.l(i) + v.l(i);
az(i) = z.l(i)*(deltaz(i)*v.l(i)**(-rhoz(i)) + (1 - deltaz(i))*n.l(i)**(-rhoz(i)))**(1/rhoz(i));
display deltaz, z.l, pz.l, az;
* calibrate deltax using firstx, x using valuex, and ax using prodx
g.l(i) = stock("infrast",i);
dg(i) = g.l(i);
deltax(i) = (z.l(i)/g.l(i))**(1/sigmax(i))*pz.l(i)/pg.l(i);
deltax(i) = deltax(i)/(1 + deltax(i));
x.l(i) = z.l(i) + g.l(i);
ax.l(i) = x.l(i)*(deltax(i)*z.l(i)**(-rhox(i)) +(1 - deltax(i))*g.l(i)**(-rhox(i)))**(1/rhox(i));
display g.l, deltax, x.l, ax.l;
* calibrate taum using pmdef and taumdet
pm.l(im) = px.l(im);
tfm.l(i) = rate("taxrfd-imp",i);
taum.l(im) = px.l(im)/pim(im) - (1 + trmm(im) + tfm.l(im));
taum.l(i)$(not im(i)) = 0;
taum.l(sc) = 0;
pm.l(im) = pim(im)*(1 + trmm(im) + tfm.l(im) + taum.l(im));
m.l(im) = dat("cons-imp",im);
display pm.l, taum.l, m.l;
* calibrate q using valueq, deltaq using firstq, and aq using prodq
q.l(i) = x.l(i) + m.l(i);
q.l(sc) = x.l(sc) + (1 + trmm(sc) + tfm.l(sc))*m.l(sc);
deltaq(sc) = (x.l(sc)/m.l(sc))**(1/sigmaq(sc))*px.l(sc)/pm.l(sc);
deltaq(sc) = deltaq(sc)/(1 + deltaq(sc));
aq(sc) = q.l(sc)*(deltaq(sc)*x.l(sc)**(-rhoq(sc)) + (1 - deltaq(sc))*m.l(sc)**(-rhoq(sc)))**(1/rhoq(sc));
pq0(i) = pq.l(i);
pq00(i) = baseprice(i,"pq00");
display q.l, deltaq, pq.l;
dsa(i) = 0 ;
totlab = sum(i$(not sa(i)), ls.l(i) + lw.l(i));
* calibrate pc using pcdet
trmd(i) = rate("tradm-fd",i);
tfd.l(i) = rate("taxrfd-dom",i);
pc.l(i) = pq.l(i)*(1 + tfd.l(i) + trmd(i));
pc00(i) = baseprice(i,"pc00");
* parameters for linear expenditure share estimation
alpha(r) = conpar("alpha",r);
beta.l(r) = conpar("beta",r);
pop(r) = conpar("pop",r);
* other parameters
tw.l(sa) = 0;
tw.l(i)$(not sa(i)) = 0.045;
tk.l(sa) = 0;
tk.l(i)$(not sa(i)) = 0.11;
thetak(si) = 1.0;
thetai.l = 0;
usdefl = 1.0;
indefl = 1.0;
er00 = sum(t, series("er",t));
er = er00;
* calibrate y, gtr and wtr using income determination equations
y.l("yself",i) = sum(r$ri(r,i), pls.l(r) )*ls.l(i)*(1 - tw.l(i));
y.l("ywage",i) = sum(r$ri(r,i), w.l(r))*lw.l(i)*(1 - tw.l(i));
y.l("ycap",i) = pk.l(i)*k(i)*(1 - thetak(i))*(1 - tk.l(i));
y.l("yinfr",i) = pg.l(i)*g.l(i)*(1 - thetai.l);
gtr.l("ynonp") = (gtra + gtrb)/indefl;
wtr.l("ynonp") = (nct + nfi)*(er00/er)/usdefl;
* calibrate private consumption using yhdef, mean, meanc, and les
yh.l(ty,r) = sum(i, ayi(i,r)*y.l(ty,i)) + ayt(r)*(gtr.l(ty) + wtr.l(ty));
ym.l("urban") = 14.52382;
ym.l("rural") = 7.36096;
mc.l(r) = exp(alpha(r) + beta.l(r)*log(ym.l(r)));
ch.l(i,r) = (pop(r)*(pc.l(i)*gamma(i,r) + ac(i,r)*(mc.l(r) - sum(j, pc.l(j)*gamma(j,r)))))/pc.l(i);
ch.lo(i,r) = pop(r)*gamma(i,r) + 0.1;
cpi.l(r) = (sum(i, pc.l(i)*ch.l(i,r)))/sum(i, ch.l(i,r));
dcpi(r) = cpi.l(r);
* calibrate investment using iddet and dstdet
id.l(i) = dat("fix-inv",i);
id.l(ss) = 0;
dst.l(i) = dat("change-sto",i)/pq.l(i);
invtot.l = sum(i, id.l(i) + dst.l(i));
idshr = sum(i, id.l(i))/invtot.l;
dstshr = sum(i, dst.l(i))/invtot.l;
aid(i) = id.l(i)/sum(j, id.l(j));
adst(i) = dst.l(i)/sum(j, dst.l(j));
* calibrate export demand using export
trmx(i) = rate("tradm-exp",i);
ex.l(i) = dat("xvoli",i)/pq.l(i);
aex(i) = ex.l(i)/(er00*pie(i)/(pq.l(i)*(1 + trmx(i))))**eta(i);
cg(i) = dat("pub-cons",i)/pc.l(i);
* calibrate fd using fddef, marg using margdet
fd.l(i) = sum(r, ch.l(i,r)) + id.l(i) + cg(i);
marg.l = (sum(i, trmd(i)*pq.l(i)*fd.l(i) + trmx(i)*pq.l(i)*ex.l(i)
+ (pim(i)*trmm(i)*m.l(i))$im(i)
+ sum(j, am(j,i)*pim(j)*trmm(j))*nm.l(i)))/sum(ss, pq.l(ss));
* calibrate savings using budget constraints
savh.l(r) = sum(ty, yh.l(ty,r)) - sum(i, pc.l(i)*ch.l(i,r));
savg.l = sum(i, sum(j, am(j,i)*tnm.l(j)*pim(j))*nm.l(i)
+ sum(j, a(j,i)*pq.l(j)*tnd.l(j))
+((tfm.l(i) + taum.l(i))*pim(i)*m.l(i))$im(i)
+ tw.l(i)*sum(r$ri(r,i), w.l(r))*lw.l(i)
+ sum(r$ri(r,i), pls.l(r))*ls.l(i)*tw.l(i)
+ tk.l(i)*pk.l(i)*k(i)*(1 - thetak(i))
+ tfd.l(i)*pq.l(i)*sum(r, ch.l(i,r)))
- sum(i, pq.l(i)*cg(i)) - sum(ty, gtr.l(ty));
lambda.l(r) = 1.0;
ratinf = 0.758039594;
depp(i) = rate("dep-prof",i);
depl(i) = rate("dep-lab",i);
$sTitle Parameters for Objective Function
Parameter
wtot 'weights sum'
wgdp 'weight for gdp tracking'
wcns 'weight for private consumption tracking'
winv 'weight for investment tracking'
wexp 'weight fot export tracking'
wimp 'weight for import tracking'
gdpgrt 'growth rate of gdp at market prices'
cnsgrt 'growth rate of private consumption'
gfigrt 'growth rate of fixed investment'
invgrt 'growth rate of total investment'
expgrt 'growth rate of exports'
impgrt 'growth rate of imports'
cnsshr 'ratio of consumption to gdp at market prices'
gfishr 'ratio of gfi to gdp at market prices'
expshr 'ratio of exports to gdp at market prices'
impshr 'ratio of imports to gdp at market prices';
gdptg = sum(t, series("gdpmp",t));
cnstg = sum(t, series("privc",t));
gfitg = sum(t, series("gfi",t));
invtg = sum(t, series("invest",t));
exptg = sum(t, series("exports",t));
imptg = sum(t, series("imports",t));
gdpgrt = sum(t, series("gdpc",t)/series("gdpc",t));
cnsgrt = sum(t, series("privc",t)/series("privc",t));
gfigrt = sum(t, series("gfi",t)/series("gfi",t));
invgrt = sum(t, series("invest",t)/series("invest",t));
expgrt = sum(t, series("exports",t)/series("exports",t));
impgrt = sum(t, series("imports",t)/series("imports",t));
cnsshr = sum(t, series("privc",t))/gdptg;
gfishr = sum(t, series("gfi",t))/gdptg;
expshr = sum(t, series("exports",t))/gdptg;
impshr = sum(t, series("imports",t))/gdptg;
wgdp = 1.0;
wcns = 1.0;
winv = 1.0;
wexp = 1.0;
wimp = 1.0;
wtot = wgdp + wcns + winv + wexp + wimp;
wgdp = wgdp/wtot;
wcns = wcns/wtot;
winv = winv/wtot;
wexp = wexp/wtot;
wimp = wimp/wtot;
gdp00 = gdptg;
cns00 = cnstg;
gfi00 = gfitg;
inv00 = invtg;
exp00 = exptg;
imp00 = imptg;
gdppr = gdptg;
cnspr = cnstg;
gfipr = invtg;
invpr = invtg;
exppr = exptg;
imppr = imptg;
$sTitle Equation Declarations
Equation
obj 'objective function (utils)'
objgrt 'objective function for growth rate tracking'
qgdpmp 'determination of gdp at market prices'
qgdp 'determination of gdp at factor prices'
qcns 'determination of private consumption'
qgfi 'determination of gross fixed investment'
qchs 'determination of stock changes'
qinv 'determination of total investment'
qexp 'determination of exports'
qimp 'determination of imports'
qdep00(i) 'determination of depreciation at base year prices'
qdep(i) 'determination of depreciation'
valueq(i) 'value of final output of capital goods (current)'
prodq(sc) 'ces production function for final output of capital goods (units)'
firstq(sc) 'first order condition for cost min of q (units)'
pmdef(i) 'definition of post-tax import prices (rp per unit)'
supply(i) 'total non-capital goods supply (units)'
taumdet(i) 'determination of taum (rp per unit)'
infalloc(i) 'allocation of infrastructure (units)'
valuex(i) 'value of gross output (current)'
prodx(i) 'ces production function for gross output (units)'
firstx(i) 'first order condition for profit max of gross output (units)'
valuez(i) 'value of ces z subaggregate (current)'
prodz(i) 'ces production function for ces z subaggregate (units)'
firstz(i) 'first order condition for cost min of ces subaggregate (units)'
valuen(i) 'value of intermediate production (current)'
prodn(i) 'ces production function for intermediates (units)'
firstn(i) 'first order condition for cost min of intermediates (units)'
pnddet(i) 'determination of domestic intermediates price (rp per unit)'
pnmdet(i) 'determination of imported intermediates price (rp per unit)'
values(i) 'value of value added subaggregate (current)'
prods(i) 'ces production function for value added subaggregate (units)'
firsts(i) 'first order condition for cost min of value added subagg (units)'
valuev(i) 'value added exemption (current)'
prodv(i) 'ces production function for value added (units)'
firstv(i) 'first order condition for value added maximization (units)'
wdet(r) 'determination of wage of organized labor (rp per unit)'
lmclear 'non-agricultural labor market clearing (units)'
pcdet(i) 'determination of consumer prices (rp per unit)'
cpidet(r) 'determination of cpi (rp per unit)'
yself(i) 'determination of self employed income (current)'
fyself(i) 'determination of self employed real income (base year rp)'
ywage(i) 'determination of labor income (current)'
fywage(i) 'determination of labor real income (base year rp)'
ycap(i) 'determination of capital and land income (current)'
fycap(i) 'determination of capital and land real income (base year rp)'
yinfr(i) 'determination of infrastructure income (current)'
fyinfr(i) 'determination of infrastructure real income (base year rp)'
wtrdet 'determination of transfers from abroad (current)'
gtrdet 'determination of government transfers (current)'
fwtrdet 'determination of real transfers from abroad (base year rp)'
fgtrdet 'determination of government real transfers (base year rp)'
yhdef(ty,r) 'definition of regional income (current)'
fyhdef(ty,r) 'definition of regional real income (base year rp)'
mean(r) 'mean per capita income determination (base year rp)'
meanc(r) 'determination of mean per capita consumption (base year rp)'
les(i,r) 'linear expenditure system (current)'
iddet(i) 'allocation of gross fixed investment (units)'
dstdet(i) 'allocation of stock changes (units)'
hbudget(r) 'household budget constraint (current)'
gbudget 'government budget constraint (current)'
fddef(i) 'definition of domestic final demands (units)'
export(i) 'downward sloping export demand curves (units)'
equil(i) 'market clearing conditions (units)'
margdet 'determination of total trade margins (current)'
fbudget 'rest of the world budget constraint (current)'
invsav 'investment savings equality (current)'
utildef(r) 'definition of regional utility (utils)';
$sTitle Equations of the Model
* objective function
qdep00(i).. deprec00(i) =e= pk00(i)*k(i)*depp(i) + sum(r$ri(r,i), pls00(r)*ls(i)*depl(i));
qdep(i).. deprec(i) =e= pk(i)*k(i)*depp(i) + sum(r$ri(r,i), pls(r)*ls(i)*depl(i));
qgdp.. ogdp =e= sum(i, pv00(i)*v(i)+deprec00(i));
qcns.. ocns =e= sum((i,r), pc00(i)*ch(i,r));
qgfi.. ogfi =e= sum(i, pc00(i)*id(i) + deprec(i)*idshr*sum(j, pc00(j)*aid(j))/sum(j, pc(j)*aid(j)));
qchs.. ochs =e= sum(i, pq00(i)*dst(i) + deprec(i)*dstshr*sum(j, pc00(j)*aid(j))/sum(j, pc(j)*aid(j)));
qinv.. oinv =e= ogfi + ochs;
qexp.. oexp =e= sum(ie, ex(ie)*pq00(ie)*(1 + trmx(ie)));
qimp.. oimp =e= sum(i, (m(i)*pim00(i)*(1 + trmm(i)))$im(i) + nm(i)*pnm00(i));
qgdpmp.. ogdpmp =e= ocns + sum(i, pc00(i)*cg(i)) + oinv + oexp - oimp;
* production equations
valueq(i).. q(i)*pq(i) =e= x(i)*px(i) + (m(i)*pm(i))$im(i);
prodq(sc).. q(sc) =e= aq(sc)*(deltaq(sc)*x(sc)**(-rhoq(sc)) + (1 - deltaq(sc))*m(sc)**(-rhoq(sc)))**(-1/rhoq(sc));
firstq(sc).. x(sc) =e= m(sc)*(pm(sc)*deltaq(sc)/(px(sc)*(1 - deltaq(sc))))**sigmaq(sc);
pmdef(im).. pm(im) =e= pim(im)*(1 + trmm(im) + tfm(im) + taum(im));
supply(i)$(not sc(i)).. q(i) =e= x(i) + m(i)$im(i);
taumdet(im)$(not sc(im)).. pm(im) =e= px(im);
valuex(i).. x(i)*px(i) =e= g(i)*pg(i) + z(i)*pz(i);
prodx(i).. x(i) =e= ax(i)*(deltax(i)*z(i)**(-rhox(i)) + (1 - deltax(i))*g(i)**(-rhox(i)))**(-1/rhox(i));
firstx(i).. z(i) =e= g(i)*(pg(i)*deltax(i)/(pz(i)*(1 - deltax(i))))**sigmax(i);
valuez(i).. z(i)*pz(i) =e= v(i)*pv(i) + n(i)*pn(i);
prodz(i).. z(i) =e= az(i)*(deltaz(i)*v(i)**(-rhoz(i)) + (1 - deltaz(i))*n(i)**(-rhoz(i)))**(-1/rhoz(i));
firstz(i).. v(i) =e= n(i)*(pn(i)*deltaz(i)/(pv(i)*(1-deltaz(i))))**sigmaz(i);
valuen(i).. n(i)*pn(i) =e= nd(i)*pnd(i) + nm(i)*pnm(i);
prodn(i).. n(i) =e= an(i)*(deltan(i)*nd(i)**(-rhon(i)) + (1 - deltan(i))*nm(i)**(-rhon(i)))**(-1/rhon(i));
firstn(i).. nd(i) =e= nm(i)*(deltan(i)*pnm(i)/((1 - deltan(i))*pnd(i)))**sigman(i);
pnddet(i).. pnd(i) =e= sum(j, a(j,i)*pq(j)*(1 + tnd(j)));
pnmdet(i).. pnm(i) =e= sum(j, am(j,i)*pim(j)*(1 + trmm(j) + tnm(j)));
values(i).. s(i)*ps(i) =e= k(i)*pk(i) + ls(i)*sum(r$ri(r,i), pls(r));
prods(i).. s(i) =e= as(i)*(deltas(i)*k(i)**(-rhos(i)) + ((1 - deltas(i))*ls(i)**(-rhos(i)))$(not si(i)))**(-1/rhos(i));
firsts(i)$(not si(i))..
k(i) =e= ls(i)*(sum(r$ri(r,i), pls(r))*deltas(i)/(pk(i)*(1 - deltas(i))))**sigmas(i);
valuev(i).. v(i)*pv(i) =e= lw(i)*sum(r$ri(r,i), w(r)) + ps(i)*s(i);
prodv(i).. v(i) =e= av(i)*(deltav(i)*s(i)**(-rhov(i)) + (1 - deltav(i))*lw(i)**(-rhov(i)))**(-1/rhov(i));
firstv(i).. s(i) =e= lw(i)*(sum(r$ri(r,i), w(r))*deltav(i)/(ps(i)*(1 - deltav(i))))**sigmav(i);
lmclear.. totlab =e= sum(i$(not sa(i)), lw(i) + ls(i));
pcdet(i).. pc(i) =e= pq(i)*(1 + tfd(i) + trmd(i));
cpidet(r).. cpi(r)*sum(i, ch(i,r)) =e= sum(i, pc(i)*ch(i,r));
* income generation
yself(i).. y("yself",i) =e= sum(r$ri(r,i), pls(r) )*ls(i)*(1 - tw(i));
ywage(i).. y("ywage",i) =e= sum(r$ri(r,i), w(r))*lw(i)*(1 - tw(i));
ycap(i).. y("ycap",i) =e= pk(i)*k(i)*(1 - thetak(i))*(1 - tk(i));
yinfr(i).. y("yinfr",i) =e= pg(i)*g(i)*(1 - thetai);
gtrdet.. gtr("ynonp") =e= (gtra + gtrb)/indefl*sum(i, pv(i)*v(i))/sum(i, pv00(i)*v00(i));
wtrdet.. wtr("ynonp") =e= (nct + nfi)*(er00/er)/usdefl*sum(i, pv(i)*v(i))/sum(i, pv00(i)*v00(i));
fgtrdet.. fgtr("ynonp") =e= (gtra + gtrb)/indefl;
fwtrdet.. fwtr("ynonp") =e= (nct + nfi)*(er00/er)/usdefl;
fyself(i).. fy("yself",i) =e= sum(r$ri(r,i), pls00(r) )*ls(i)*(1 - tw(i));
fywage(i).. fy("ywage",i) =e= sum(r$ri(r,i), w00(r))*lw(i)*(1 - tw(i));
fycap(i).. fy("ycap",i) =e= pk00(i)*k(i)*(1 - thetak(i))*(1 - tk(i));
fyinfr(i).. fy("yinfr",i) =e= pg00(i)*g(i)*(1 - thetai);
yhdef(ty,r).. yh(ty,r) =e= sum(i, ayi(i,r)*y(ty,i)) + ayt(r)*(gtr(ty) + wtr(ty));
fyhdef(ty,r).. fyh(ty,r) =e= sum(i, ayi(i,r)*fy(ty,i)) + ayt(r)*(fgtr(ty) + fwtr(ty));
mean(r).. ym(r)*pop(r) =e= sum(ty, fyh(ty,r));
meanc(r).. log(mc(r)) =e= alpha(r) + beta(r)*log(ym(r));
les(i,r).. pc(i)*ch(i,r) =e= pop(r)*(pc(i)*gamma(i,r)
+ ac(i,r)*(mc(r) - sum(j, pc00(j)*gamma(j,r)))
* prod(j, (pc(j)/pc00(j))**ac(j,r)));
iddet(i).. id(i) =e= aid(i)*idshr*invtot;
dstdet(i).. dst(i) =e= adst(i)*dstshr*invtot;
* domestic budget constraints
hbudget(r).. savh(r) + sum(i, pc(i)*ch(i,r)) =e= sum(ty, yh(ty,r));
gbudget.. sum(i, pq(i)*cg(i)) + sum(ty, gtr(ty)) + savg =e=
sum(i, sum(j, am(j,i)*tnm(j)*pim(j))*nm(i)
+ sum(j, a(j,i)*pq(j)*tnd(j))*nd(i)
+ ((tfm(i) + taum(i))*pim(i)*m(i))$im(i)
+ tw(i)*sum(r$ri(r,i), w(r))*lw(i)
+ sum(r$ri(r,i), pls(r))*ls(i)*tw(i)
+ tk(i)*pk(i)*k(i)*(1 - thetak(i))
+ tfd(i)*pq(i)*sum(r, ch(i,r))
+ tfd(i)*pq(i)*id(i));
* market clearing
fddef(i).. fd(i) =e= sum(r, ch(i,r)) + id(i) + cg(i);
export(ie).. ex(ie) =e= exscale*aex(ie)*(er00*pie(ie)/(pq(ie)*(1 + trmx(ie))))**eta(ie);
margdet.. marg*sum(ss, pq(ss)) =e= sum(i, trmd(i)*pq(i)*fd(i)) + sum(ie, trmx(ie)*pq(ie)*ex(ie))
+ sum(i, (pim(i)*trmm(i)*m(i))$im(i)
+ sum(j, am(j,i)*pim(j)*trmm(j))*nm(i));
equil(i).. q(i) + dsa(i) =e= fd(i) + sum(j, a(i,j)*nd(j)) + ex(i)$ie(i)
+ dst(i) + marg$ss(i) + sum(j, g(j))$si(i);
fbudget.. (savf/usdefl)*(er00/er)*sum(i, pc(i)*aid(i))/sum(i, pc00(i)*aid(i))
+ sum(ie, pq(ie)*(1 + trmx(ie))*ex(ie)) + sum(ty, wtr(ty))
=e= sum(im, pim(im)*m(im)) + sum(i, sum(j, am(j,i)*pim(j))*nm(i));
* savings and investments
invsav.. sum(r, savh(r)) + (savf/usdefl)*(er00/er)*sum(i, pc(i)*aid(i))/sum(i, pc00(i)*aid(i))
+ savg + thetai*sum(i, pg(i)*g(i)) + sum(i, thetak(i)*pk(i)*k(i))
=e= sum(i, dst(i)*pq(i) + id(i)*pc(i)) + sum(si, pq(si))*sum(i, g(i));
utildef(r).. util(r)*pop(r) =e= prod(i, (ch(i,r)-gamma(i,r)*pop(r))**ac(i,r));
obj.. utility =e= psi*((sum(r, pop(r)*util(r)))$(mu = 1)
+(1/mu*sum(r, pop(r)*util(r)**mu))$(mu <> 0 and mu <> 1)
+(sum(r, pop(r)*log(util(r))))$(not mu))
+ ksi*invtot;
$sTitle Variable Initialization
* bounds for variables
y.fx("ynonp",i) = 0;
wtr.fx(li) = 0;
gtr.fx(li) = 0;
fy.fx("ynonp",i) = 0;
fwtr.fx(li) = 0;
fgtr.fx(li) = 0;
thetai.fx = thetai.l;
ls.lo(i) = .001;
ls.fx(i)$(not ls.l(i)) = 0;
* initial values for variables
util.l(r) = 10;
utility.l = 10;
option decimals = 5;
display pc.l, pop, gamma, ac, mc.l;
x.lo(i) = .001;
g.lo(i) = .001;
z.lo(i) = .001;
v.lo(i) = .001;
n.lo(i) = .001;
fd.lo(i) = .001;
lw.lo(i) = .001;
nd.lo(i) = .001;
nm.lo(i) = .001;
m.lo(sc) = .001;
s.lo(i) = .001;
px.lo(i) = .001;
pg.lo(i) = .001;
pz.lo(i) = .001;
pv.lo(i) = .001;
pn.lo(i) = .001;
pc.lo(i) = .001;
pq.lo(i) = .001;
w.lo(r) = .001;
pnd.lo(i) = .001;
pnm.lo(i) = .001;
pm.lo(i) = .001;
ps.lo(i) = .001;
pk.lo(i) = .001;
pls.lo(r) = .001;
mc.lo(r) = .001;
ym.lo(r) = .001;
$sTitle Model Definitions
Model
ganges 'basic version of the India cge'
/ infalloc, wdet, valueq, prodq, firstq, supply, pmdef
taumdet, valuex, prodx, firstx, valuez, prodz, firstz
valuen, prodn, firstn, pnddet, pnmdet, values, prods
firsts, valuev, prodv, firstv, lmclear, pcdet, cpidet
yself, ywage, ycap, yinfr, gtrdet, wtrdet, fyself
fywage, fycap, fyinfr, fgtrdet, fwtrdet, yhdef, fyhdef
mean, meanc, les, iddet, dstdet, hbudget, fddef
export, equil, margdet, fbudget, invsav, utildef, obj /
ganges0 'base year version with tracking indicators'
/ utildef, obj, valueq, prodq, firstq, pmdef, supply, taumdet
valuex, prodx, firstx, valuez, prodz, firstz, valuen, prodn
firstn, pnddet, pnmdet, values, prods, firsts, valuev, prodv
firstv, lmclear, pcdet, cpidet, yself, ywage, ycap, yinfr
gtrdet, wtrdet, fyself, fywage, fycap, fyinfr, fgtrdet, fwtrdet
yhdef, fyhdef, mean, meanc, les, iddet, dstdet, hbudget
fddef, export, equil, margdet, fbudget, invsav, qdep00, qdep
qgdp, qcns, qgfi, qchs, qinv, qexp, qimp, qgdpmp /;
option limCol = 0;
$sTitle Base Model Closure
g.fx(i) = g.l(i);
w.fx(r) = dw(r);
ls.fx(sa) = ls.l(sa);
savf.fx = 47.9;
ax.fx(i) = ax.l(i);
exscale.fx = 1;
tnd.fx(i) = tnd.l(i);
tnm.fx(i) = tnm.l(i);
tfd.fx(i) = tfd.l(i);
tfm.fx(i) = tfm.l(i);
tk.fx(i) = tk.l(i);
tw.fx(i) = tw.l(i);
taum.fx(sc) = 0;
taum.fx(i)$(not im(i)) = 0;
beta.fx(r) = beta.l(r);
lambda.fx(r) = lambda.l(r);
m.fx(i)$(not sc(i)) = m.l(i);
solve ganges0 using cns;
ax0(i) = ax.l(i);
exscale0 = exscale.l;
beta0(r) = beta.l(r);
objgrt.. dumgrt =e= wgdp*sqr(ogdpmp/gdppr - gdpgrt)
+ wcns*sqr(ocns/cnspr - cnsgrt)
+ winv*sqr(oinv/invpr - invgrt)
+ wexp*sqr(oexp/exppr - expgrt)
+ wimp*sqr(oimp/imppr - impgrt);
infalloc(i).. g(i) =e= ratinf*dg(i)/sum(j, dg(j))*sum(si, x(si));
wdet(r).. w(r)*dcpi(r) =e= lambda(r)*cpi(r)*dw(r);
Model track 'ganges with tracking option'
/ infalloc, wdet, valueq, prodq, firstq, supply, pmdef, taumdet
valuex, prodx, firstx, valuez, prodz, firstz, valuen, prodn
firstn, pnddet, pnmdet, values, prods, firsts, valuev, prodv
firstv, lmclear, pcdet, cpidet, yself, ywage, ycap, yinfr
gtrdet, wtrdet, fyself, fywage, fycap, fyinfr, fgtrdet, fwtrdet
yhdef, fyhdef, mean, meanc, les, iddet, dstdet, hbudget
fddef, export, equil, margdet, fbudget, invsav, objgrt, qdep00
qdep, qgdp, qcns, qgfi, qchs, qinv, qexp, qimp
qgdpmp, utildef, obj /;