Description
A general equilibrium model is used to study the impact of changes in oil prices and evaluate policies dealing with external shocks.
Large Model of Type : NLP
Category : GAMS Model library
Main file : gangesx.gms
$title Macro-Economic Framework for India (GANGESX,SEQ=107)
$onText
A general equilibrium model is used to study the impact of changes
in oil prices and evaluate policies dealing with external shocks.
Mitra, P, Adjustments in Oil Importing Developing Countries: A
Comparative Economic Analysis. Cambridge University Press, New York,
NY, 1993.
Keywords: nonlinear programming, general equilibrium model, macro economics,
Indian economy, economic policy, price policy, petroleum products
OUTLINE:
1. Set definitions
1.a Sectors
1.b Income types
1.c Sets for controlling input data
2. Base year data
3. Historical time series
4. Parameter declarations
4.a For core model formulation
4.b For reports and tracking
5. Variable declarations
5.a For core model formulation
5.b For the tracking model
6. Parameter calibration
7. Setting parameters for tracking versions
8. Equation declarations
9. Core model equations
9.a Production technology
9.b Income generation
9.c Expenditure system
9.d Investment and stock changes
9.e Domestic budget constraints
9.f Other final demands and market clearing requirements.
9.g The savings-investment balance equation
9.h The static model utility function
9.i Equations determining tracking indicators
10. Variable initialization
11. Core model versions
12. Core model closure
13. Tracking model version
1. Set definitions
1.a Sectors
In this section, the sets of the model are declared. The model contains 6
sectors, each of which also belongs to either the rural or urban area. Some
sectors are singled out as subsets because they are treated in a special manner
in various parts of the model. Note that the importing and exporting sectors
are not specified here. They are later determined from the data tables.
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$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 /
r 'regions' / urban 'urban region'
rural 'rural region' /
ri(r,i) 'mapping between regions and sectors'
/ rural. agricult
urban.(cons-good,cap-good,int-good,pub-infr,service) /;
Alias (i,j), (manufact,manuf);
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1.b Income types
In addition to the sectoral description, we will need an income classification
scheme. ty covers the types of income considered.
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Set
ty 'income categories' / yself 'self-employment income'
ywage 'wage income'
ycap 'land and capital income'
yinfr 'income from government subsidies via infrastructure'
ynonp 'non-production income' /
li(ty) 'production income categories';
* li contains all types except non-production income
li(ty) = yes;
li("ynonp") = no;
Alias (ty,tz);
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1.c Sets for controlling input data
It is convenient to define sets for controlling data types. The ones used in
this model are shown below.
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Set
datvar 'input variables'
/ return-cap 'income from capital investments (mm rupees)'
return-inf 'income from infrastructure (mm rupees)'
self-empl 'income from self-employment (mm rupees)'
wage-labor 'income from wage labor (mm rupees)'
dom-inter 'domestically produced intermediate goods value (mm rupees)'
imp-inter 'imported intermediate goods value (mm rupees)'
pub-cons 'public consumption (domestic and imported) (mm rupees)'
fix-inv 'fixed capital investment (domestic and imported) (mm rupees)'
change-sto 'change in stocks (mm rupees)'
cons-imp 'household consumption - imported (mm rupees)'
xvoli 'constant term used in calculating export volume (mm rupees)' /
taxvar 'tax variables'
/ dom-inter 'indirect taxes on domestic intermediate inputs (mm rupees)'
imp-inter 'indirect taxes on imported intermediate inputs (mm rupees)'
dom-cons 'total taxes on final domestic consumption (mm rupees)'
imp-cons 'total taxes on final imported consumption (mm rupees)'
profits 'total taxes on profits (mm rupees)'
self-emp 'total taxes on self-employment income (mm rupees)'
tax-wage 'total taxes on wage income (mm rupees)' /
stockvar 'stock variables'
/ capital 'total capital stock (mm rupees)'
infrast 'total infrastructure stock (mm rupees)'
wage-labor 'total labor force (mm persons)'
self-empl 'total self-employment (mm persons)' /
sigma 'elasticity of substitution parameters'
/ sigmax 'between final demands for domestic and imported cap goods'
sigmaz 'between value added and intermediate inputs'
sigman 'between domestic and imported intermediate inputs'
sigmav 'between capital and self-employment and wage labor'
sigmas 'between land and agriculture labor'
eta 'export elasticity' /
acv 'gdp expenditure categories'
/ ndp 'net domestic product (mm rupees)'
gdp 'gross domestic product (mm rupees)'
privc 'private consumption (mm rupees)'
gdpmp 'gdp at market prices (mm rupees)'
govc 'government consumption (mm rupees)'
gfi 'gross fixed investment (mm rupees)'
chan-sto 'change in stocks (mm rupees)'
invest 'total of gfi and change in stocks (mm rupees)'
exports 'exports (mm rupees)'
imports 'imports (mm rupees)' /
indicat 'target indicators at constant prices'
/ gdpmp 'gdp at market prices (mm rupees)'
privc 'private consumption (mm rupees)'
gfi 'fixed investment (mm rupees)'
invest 'investment and change in stocks (mm rupees)'
exports 'total exports (mm rupees)'
imports 'total imports (mm rupees)'
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 gdpmp'
expshr 'ratio of exports to gdpmp'
impshr 'ratio of imports to gdpmp' /
years 'time horizons for tracking history'
/ 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 is used to control tracking. we set it first to 73-74
t(years) = no;
t("7374") = yes;
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2. Base year data
In this section follows data for the base year, used to calibrate the
coefficients of the model
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$sTitle Input Data Tables
Table dat(datvar,i) 'factor remunerations (current mm rupees)'
agricult cons-good cap-good int-good pub-infr service
return-cap 64493.3 6406.5 5434.4 8567.9 4401.9 27677.2
self-empl 148431.0 4937.3 13714.3 6488.8 38411.1
wage-labor 48364.6 12560.5 16267.7 17072.2 9941.2 73786.0
dom-inter 77681.1 68904.0 54658.1 47254.0 6872.7 48988.9
imp-inter 2356.0 3201.3 2307.3 9801.7 1.3 572.0
pub-cons 816.9 544.0 4730.1 4423.9 2986.2 36832.5
fix-inv 623.9 139.5 76198.8 2970.4 252.1 5076.3
change-sto 7092.5 5944.2 1756.4 6073.7 272.2
cons-imp 3159.9 504.3 5235.6 4170.9
xvoli 2977.8 10046.2 990.9 5984.0 ;
* here we select the exporting and importing sectors
im(i) = yes$dat("cons-imp",i);
ie(i) = yes$dat("xvoli",i);
Table rate(*,i) 'various depreciation and 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 revenue data (current mm 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 mm 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;
* we generate urban shares as the residual
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'
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;
* conpar gives parameters needed for the expenditure system
Table conpar(*,r) 'various consumer parameters'
urban rural
alpha 0.376842 0.309118
beta 0.76777 0.77814
pop 122. 458. ;
* in baseprice, pv00 is value added price, v00 is value added,
* pk00 is returns to capital, pg00 infrastructure prices, pc00 consumer
* prices, and pq00 composite output prices.
Table baseprice(i,*) 'base year prices and values'
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 transfers (mm rupees)' / 19.20 /
nfi 'net factor income (mm rupees)' / -32.50 /
gtra 'interest on national debt (mm rupees)' / 46.7 /
gtrb 'domestic current transfers (mm rupees)' / 90.9 /;
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3. Historical time series
In this next section, the time series of various exogenous data are given.
These are used for historical and tracking runs.
A brief explanation is
cg government consumption
xsa agricultural total factor productivity
er exchange rate to usd
usdefl us gdp deflator
indefl indian gdp deflator
savf foreign savings
gtra interest on national debt
gtrb domestic current transfers
nfi net factor income
nct net current transfers
idshr share of gross fixed investment in total investment
totlab total labor in urban sectors
pkv.. b-matrix coefficients
pim. international import prices
pie. international export prices
totpu total urban population
totpr total rural population
gdpmp gdp at market prices
privc private consumption
gfi gross fixed investment
invest total investment
exports export volume
imports import volume
cns-curr consumption at current market prices
gfi-curr gross fixed investment at current market prices
inv-curr total investment at current market prices
gdpmp-curr gdp at current market prices
exp-curr exports at current market prices
imp-curr imports at current market prices
cns-defl consumption deflator
ax. total factor productivity by sector
exscale export volume scale factor
beta. expenditure parameter by area
thetai infrastructural savings rate
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$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
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;
* here, these series are recalculated to yield other useful quantities
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);
$onText
4. Parameter declarations
4.a For core model formulation
We now declare those parameters that are actually used in the model formulation
the cryptic references to x, q, etc. are to variables defined later
$offText
$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 stock (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 household 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 objective function (unitless)'
ksi 'weight for investment in objective function (unitless)'
er 'exchange rate (rp per $)'
usdefl 'gdp deflator for usd (unitless)'
indefl 'gdp deflator for indian rupee (unitless)';
$onText
4.b For reports and tracking
The next parameters are primarily used for reporting, for tracking
exercises and for historical runs
$offText
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';
$onText
5. Variable declarations
5.a For core model formulation
We now define the variables that are used in the static (single period) model
laid out below. To understand the relationships among x, g, q, etc., remember
the nested ces tree production structure:
q composite output
/ \
x m domestic production and final imports
/ \
z g gross domestic prod. and infrastructure
/ \
/ \
v n value added and intermediates
/ \ / \
s lw nd nm value added aggregate/wage labor and
/ \ domestic/imported intermediates
k ls capital and self-employed labor
$offText
$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;
$onText
5.b For the tracking model
The next variables are used for tracking exercises.
$offText
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)';
$onText
6. Parameter calibration
This section states various calibration and initialization maneuvres. They
basically amount to turning the model below on its head and determine
coefficients using required endogenous values. Crucial in this respect is the
selection of various prices and coefficients which when kept fixed make the
model triangular. These assumptions are stated first. In particular, we choose
as many prices as possible to be set to 1 for convenience.
Although the calibration looks messy, it is really quite straightforward
we switch to a notation where variables are capitalized and parameters are
lower case.
$offText
$sTitle Compute Parameters and Coefficients
mu = 1;
psi = 1;
ksi = 7;
pie(i) = 1;
pim(i) = 1;
pim00(i) = pim(i);
pg.l(i) = 1;
pg00(i) = baseprice(i,"pg00");
px.l(i) = 1;
ps.l(i) = 1;
pv.l(i) = 1;
pn.l(i) = 1;
pz.l(i) = 1;
pq.l(i) = 1;
* scaling
dat(datvar,i) = dat(datvar,i)/100;
tax(taxvar,i) = tax(taxvar,i)/100;
stock(stockvar,i) = stock(stockvar,i)/100;
* these statements massage historical data
sigmax(i) = elast("sigmax",i)*1.20;
sigmaq(sc) = 0.90;
sigmaz(i) = elast("sigmaz",i)*1.20;
sigman(i) = elast("sigman",i)*1.20;
sigmav(i) = elast("sigmav",i)*1.20;
sigmas(i) = elast("sigmas",i)*1.20;
eta(i) = elast("eta",i) * 1.20;
* calculate rho from sigma using definition
rhox(i) = 1/sigmax(i) - 1;
rhoq(sc) = 1/sigmaq(sc) - 1;
rhoz(i) = 1/sigmaz(i) - 1;
rhon(i) = 1/sigman(i) - 1;
rhov(i) = 1/sigmav(i) - 1;
rhos(i) = 1/sigmas(i) - 1;
* copy from data base
k(i) = stock("capital",i);
pk.l(i) = dat("return-cap",i)/k(i);
pk00(i) = baseprice(i,"pk00");
pls.l("rural") = 11.182506;
pls.l("urban") = 13.928;
pls00("rural") = 11.2507;
pls00("urban") = 13.7343;
ls.l(i) = stock("self-empl",i)*100;
* display k,pk.l,pls.l,ls.l;
* calibrate deltas using equation firsts, s using equation values,
* and as using equation prods
deltas(i)$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;
* more data points
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 equation firstv, v using equation valuev,
* and av using equation 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 equation 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 equation 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 equation firstn, n using equation valuen,
* and an using equation 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 equation firstz, z using equation valuez,
* and az using equation 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 equation firstx, x using equation valuex,
* and ax using equation 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 equation 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 equation valueq, deltaq using equation 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;
* stock changes available and total labor
dsa(i) = 0;
totlab = sum(i$(not sa(i)), ls.l(i) + lw.l(i));
* calibrate pc using equation pcdet
trmd(i) = rate("tradm-fd",i);
tfd.l(i) = rate("taxrfd-dom",i);
pc.l(i) = pq.l(i)*(1 + tfd.l(i) + trmd(i) );
pc00(i) = baseprice(i,"pc00");
* parameters for linear expenditure share estimation
alpha(r) = conpar("alpha",r);
beta.l(r) = conpar("beta",r);
pop(r) = conpar("pop",r);
* other parameters
tw.l(sa) = 0;
tw.l(i)$(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$ri(r,i), w.l(r))*lw.l(i)*(1 - tw.l(i));
y.l("ycap",i) = pk.l(i)*k(i)*(1 - thetak(i))*(1 - tk.l(i));
y.l("yinfr",i) = pg.l(i)*g.l(i)*(1 - thetai.l);
gtr.l("ynonp") = (gtra + gtrb)/indefl;
wtr.l("ynonp") = (nct + nfi)*(er00/er)/usdefl;
* calibrate private consumption using equations yhdef, mean, meanc, and les
yh.l(ty,r) = sum(i, ayi(i,r)*y.l(ty,i)) + ayt(r)*(gtr.l(ty) + wtr.l(ty));
ym.l("urban") = 14.52382;
ym.l("rural") = 7.36096;
mc.l(r) = exp(alpha(r) + beta.l(r)*log(ym.l(r)));
ch.l(i,r) = (pop(r)*(pc.l(i)*gamma(i,r) + ac(i,r)*(mc.l(r) - sum(j, pc.l(j)*gamma(j,r)))))/pc.l(i);
ch.lo(i,r) = pop(r)*gamma(i,r) + 0.1;
cpi.l(r) = (sum(i, pc.l(i)*ch.l(i,r)))/sum(i, ch.l(i,r));
dcpi(r) = cpi.l(r);
* calibrate investment using equations iddet and dstdet
id.l(i) = dat("fix-inv",i);
id.l(ss) = 0;
dst.l(i) = dat("change-sto",i)/pq.l(i);
invtot.l = sum(i, id.l(i) + dst.l(i));
idshr = sum(i, id.l(i))/invtot.l;
dstshr = sum(i, dst.l(i))/invtot.l;
aid(i) = id.l(i)/sum(j, id.l(j));
adst(i) = dst.l(i)/sum(j, dst.l(j));
* calibrate export demand using equation export
trmx(i) = rate("tradm-exp",i);
ex.l(i) = dat("xvoli",i)/pq.l(i);
aex(i) = ex.l(i)/(er00*pie(i)/(pq.l(i)*(1 + trmx(i))))**eta(i);
* public consumption in real terms
cg(i) = dat("pub-cons",i)/pc.l(i);
* calibrate fd using equation fddef, marg using margdet
fd.l(i) = sum(r, ch.l(i,r)) + id.l(i) + cg(i);
marg.l = (sum(i, trmd(i)*pq.l(i)*fd.l(i) + trmx(i)*pq.l(i)*ex.l(i)
+ (pim(i)*trmm(i)*m.l(i))$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);
$onText
7. Setting parameters for tracking versions
These parameters are used for tracking exercises.
$offText
$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;
$onText
8. Equation declarations
Here, we declare the model equations. they are subsequently defined.
$offText
$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)';
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9. Core model equations
9.a Production technology
Here comes the production technology description. for explanation, see the
above nested ces tree. The equations generally fall in groups of three in this
section:
valuex states the material balance in current prices for the output
of x (product exhaustion - which is consistent with the assumption of
constant returns to scale)
prodx states the ces production function for x
firstx states the first order condition for profit maximization of cost
minimization under this technology.
In addition to such equations, we also have a number of price equations, which
should be straight forward (margings and taxes are all accounted for).
Since the production equations also implicitly account for the factor markets,
we also include the labor market clearing equation here.
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$sTitle Equations of the Model
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$(not sa(i)), lw(i) + ls(i));
pcdet(i).. pc(i) =e= pq(i)*(1 + tfd(i) + trmd(i));
cpidet(r).. cpi(r)*sum(i, ch(i,r)) =e= sum(i, pc(i)*ch(i,r));
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9.b Income generation
Income generation is defined next. we both state income at current and at
base year prices. These equations are just definitions, accounting for taxes
and transfers. In some cases, since parameters may be fixed in the current year
prices, they are first deflated and next reinflated using the relevant model
generated price index. This ensures that we do not have an implicit numeraire
problem.
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yself(i).. y("yself",i) =e= sum(r$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$ri(r,i), w00(r))*lw(i)*(1 - tw(i));
fycap(i).. fy("ycap",i) =e= pk00(i)*k(i)*(1 - thetak(i))*(1 - tk(i));
fyinfr(i).. fy("yinfr",i) =e= pg00(i)*g(i)*(1 - thetai);
yhdef(ty,r).. yh(ty,r) =e= sum(i, ayi(i,r)*y(ty,i)) + ayt(r)*(gtr(ty) + wtr(ty));
fyhdef(ty,r).. fyh(ty,r) =e= sum(i, ayi(i,r)*fy(ty,i)) + ayt(r)*(fgtr(ty) + fwtr(ty));
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9.c Expenditure system
These equations state the expenditure system. They represent behavioral assumptions.
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mean(r).. ym(r)*pop(r) =e= sum(ty, fyh(ty,r) );
meanc(r).. log(mc(r)) =e= alpha(r) + beta(r)*log(ym(r));
les(i,r).. pc(i)*ch(i,r) =e= pop(r)*(pc(i)*gamma(i,r)
+ ac(i,r)*(mc(r) - sum(j, pc00(j)*gamma(j,r)))
* prod(j, (pc(j)/pc00(j))**ac(j,r)));
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9.d Investment and stock changes
Investment and stock changes are proportional to total investment, which in
investment driven versions is exogenous, and in savings driven versions is endogenous.
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iddet(i).. id(i) =e= aid(i)*idshr*invtot;
dstdet(i).. dst(i) =e= adst(i)*dstshr*invtot;
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9.e Domestic budget constraints
Domestic budget constraints, representing accounting identities, with proper
accounting for taxes and transfers.
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hbudget(r).. savh(r) + sum(i, pc(i)*ch(i,r)) =e= sum(ty, yh(ty,r));
gbudget.. sum(i, pq(i)*cg(i)) + sum(ty, gtr(ty)) + savg
=e= sum(i, sum(j, am(j,i)*tnm(j)*pim(j))*nm(i)
+ sum(j, a(j,i)*pq(j)*tnd(j))*nd(i)
+ ((tfm(i)+taum(i))*pim(i)*m(i))$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));
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9.f Other final demands and market clearing requirements.
Other final demands and market clearing requirements.
Export demands are downward sloping.
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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));
$onText
9.g The savings-investment balance equation
The savings-investment balance equation - which is redundant by Walras' law.
$offText
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));
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9.h The static model utility function
The static model utility function - with a concern for inequality. This may be
used for two purposes: straight optimization runs, or simply for assigning
meaningful shadow prices to various policy instruments. Note the presence of
ksi*invtot - this is a proxy for intertemporal concerns about investment.
$offText
utildef(r).. util(r)*pop(r) =e= prod(i, (ch(i,r)-gamma(i,r)*pop(r))**ac(i,r));
obj.. utility =e= psi*((sum(r, pop(r)*util(r)))$(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;
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9.i Equations determining tracking indicators
This set of equations relate to the tracking models - they define
indicators used in the objective function of that model version. They are
really just a glue on if used in conjunction with the base model.
$offText
qdep00(i)..
deprec00(i) =e= pk00(i)*k(i)*depp(i) + sum(r$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;
$onText
10. Variable initialization
We need to bound certain variables to avoid numerical difficulties,
and to fix some. Also, some should be initialized to meaningful values.
That is the purpose of the next section.
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$sTitle Variable Initialization
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) = .100;
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;
$onText
11. Core model versions
We now state the two versions of the model: Ganges is the comparative static
version, and ganges0 is the base year version which includes tracking indicators.
$offText
$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;
$onText
12. Core model closure
This section determines model closure - in this case the model is closed to
be neoclassical or savings driven.
$offText
$sTitle Base Model Closure
g.fx(i) = g.l(i);
w.fx(r) = dw(r);
ls.fx(sa) = ls.l(sa);
savf.fx = 47.9;
ax.fx(i) = ax.l(i);
exscale.fx = 1;
tnd.fx(i) = tnd.l(i);
tnm.fx(i) = tnm.l(i);
tfd.fx(i) = tfd.l(i);
tfm.fx(i) = tfm.l(i);
tk.fx(i) = tk.l(i);
tw.fx(i) = tw.l(i);
taum.fx(sc) = 0;
taum.fx(i)$(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);
$onText
This statement solves the core model and also provides a report of tracking
indicators as generated from the model.
Although we have been careful in calibrating the model above, the base year
data are not 100 percent accurately balanced. Therefore you should not expect
all those prices that we assumed to be 1 in the calibration procedure to come
out as exactly 1 in the solution. Instead, for example px comes out as
---- var px price of output (rp per unit)
lower level upper marginal
agricult 0.001 1.004 +inf .
cons-good 0.001 1.006 +inf .
cap-good 0.001 0.974 +inf .
int-good 0.001 0.983 +inf .
pub-infr 0.001 1.065 +inf .
service 0.001 1.002 +inf .
these prices represent the general equilibrium solution to the model.
$offText
solve ganges0 using nlp maximizing utility;
* set a few parameters
ax0(i) = ax.l(i);
exscale0 = exscale.l;
beta0(r) = beta.l(r);
$onText
13. Tracking model version
Here are the additional equations required to make the base model into a
tracking model: an appropriate objective function (minimize ssq), a method
for allocating infrastructure, and a wage indexation scheme.
$offText
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);
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In the definition of the track model, note the presence of both objective
functions. You can either maximize utility or minimize dumgrt. If you do the
first, the model simply states the weighted tracking error. Otherwise, if you
minimize dumgrt, the model reports the associated utility level.
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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 /;