$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. $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 / 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); $onText 1.b Income types In addition to the sectoral description, we will need an income classification scheme. ty covers the types of income considered. $offText 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); $onText 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. $offText 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; $onText 2. Base year data In this section follows data for the base year, used to calibrate the coefficients of the model $offText $sTitle Input Data Tables Table dat(datvar,i) 'factor remunerations (current mm rupees)' agricult cons-good cap-good int-good pub-infr service return-cap 64493.3 6406.5 5434.4 8567.9 4401.9 27677.2 self-empl 148431.0 4937.3 13714.3 6488.8 38411.1 wage-labor 48364.6 12560.5 16267.7 17072.2 9941.2 73786.0 dom-inter 77681.1 68904.0 54658.1 47254.0 6872.7 48988.9 imp-inter 2356.0 3201.3 2307.3 9801.7 1.3 572.0 pub-cons 816.9 544.0 4730.1 4423.9 2986.2 36832.5 fix-inv 623.9 139.5 76198.8 2970.4 252.1 5076.3 change-sto 7092.5 5944.2 1756.4 6073.7 272.2 cons-imp 3159.9 504.3 5235.6 4170.9 xvoli 2977.8 10046.2 990.9 5984.0 ; * here we select the exporting and importing sectors im(i) = yes$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 /; $onText 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 $offText $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)'; $onText 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. $offText $sTitle Equations of the Model valueq(i).. q(i)*pq(i) =e= x(i)*px(i) + (m(i)*pm(i))$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)); $onText 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. $offText yself(i).. y("yself",i) =e= sum(r$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)); $onText 9.c Expenditure system These equations state the expenditure system. They represent behavioral assumptions. $offText 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))); $onText 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. $offText iddet(i).. id(i) =e= aid(i)*idshr*invtot; dstdet(i).. dst(i) =e= adst(i)*dstshr*invtot; $onText 9.e Domestic budget constraints Domestic budget constraints, representing accounting identities, with proper accounting for taxes and transfers. $offText hbudget(r).. savh(r) + sum(i, pc(i)*ch(i,r)) =e= sum(ty, yh(ty,r)); gbudget.. sum(i, pq(i)*cg(i)) + sum(ty, gtr(ty)) + savg =e= sum(i, sum(j, am(j,i)*tnm(j)*pim(j))*nm(i) + sum(j, a(j,i)*pq(j)*tnd(j))*nd(i) + ((tfm(i)+taum(i))*pim(i)*m(i))$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)); $onText 9.f Other final demands and market clearing requirements. Other final demands and market clearing requirements. Export demands are downward sloping. $offText fddef(i).. fd(i) =e= sum(r, ch(i,r)) + id(i) + cg(i); export(ie).. ex(ie) =e= exscale*aex(ie)*(er00*pie(ie)/(pq(ie)*(1 + trmx(ie))))**eta(ie); margdet.. marg*sum(ss, pq(ss)) =e= sum(i, trmd(i)*pq(i)*fd(i)) + sum(ie, trmx(ie)*pq(ie)*ex(ie)) + sum(i, (pim(i)*trmm(i)*m(i))$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)); $onText 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; $onText 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. $offText $sTitle Variable Initialization y.fx("ynonp",i) = 0; wtr.fx(li) = 0; gtr.fx(li) = 0; fy.fx("ynonp",i) = 0; fwtr.fx(li) = 0; fgtr.fx(li) = 0; thetai.fx = thetai.l; ls.lo(i) = .001; ls.fx(i)$(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); $onText 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. $offText 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 /;