GTAP Models: Sets and Variables
Sets | |
---|---|
NSAV_COMM | Non-Savings Commodities (NS) |
TRAD_COMM | Traded Commodities (TC) |
DEMD_COMM | Demanded Commodities (DC) |
PROD_COMM | Produced Commodities (PC) |
ENDW_COMM | Endowment Commodities (EC) |
ENDWS_COMM | Sluggish Endowment Commodities (ECS) |
ENDWM_COMM | Mobile Endowment Commodities (ECM) |
CGDS_COMM | Capital Goods Commodities ("cgds") |
ENDWC_COMM | Capital Endowment Commodity ("capital") |
Subsets | |
---|---|
PROD_COMM | in NSAV_COMM |
DEMD_COMM | in NSAV_COMM |
CGDS_COMM | in NSAV_COMM |
ENDW_COMM | in DEMD_COMM |
TRAD_COMM | in DEMD_COMM |
TRAD_COMM | in PROD_COMM |
CGDS_COMM | in PROD_COMM |
ENDWS_COMM | in ENDW_COMM |
ENDWM_COMM | in ENDW_COMM |
ENDWC_COMM | in NSAV_COMM |
ENDWC_COMM | in ENDW_COMM |
Example: The 3x3 (3 regions x 3 sectors) economy | |
---|---|
REG | = {usa, eu, row} |
NSAV_COMM | = {land, labor, capital, food, manufacturing, services, capital goods} |
TRAD_COMM | = {food, manufacturing, services} |
DEMD_COMM | = {land, labor, capital, food, manufacturing, services} |
PROD_COMM | = {food, manufacturing, services, capital goods} |
ENDW_COMM | = {land, labor, capital} |
ENDWS_COMM | = {land, capital} |
ENDWM_COMM | = {labor} |
CGDS_COMM | = {capital goods} |
ENDWC_COMM | = {capital} |
Value flows evaluated at agents' prices |
---|
EVOA_{ir} value of endowment commodity i output or supplied, in region r, evaluated at agent's prices
EVOA_{i,r} = PS_{i,r} * QO_{i,r} with i = ENDW_COMM and r = REG EVFA_{ijr} value of purchases of demanded commodity i by firms in sector j, in region r, evaluated at agent's prices EVFA_{ijr} = PFE_{ijr} * QFE_{ijr} i = TRAD_COMM; j = ENDW_COMM; r = REG VDFA_{ijr }value of purchases of domestic tradeable commodity i by firms in sector j of region r evaluated at agents' prices VDFA_{ijr} = PFD_{ijr} * QFD_{ijr} i = TRAD_COMM; j = ENDW_COMM; r = REG VIFA_{ijr }value of purchases of imported tradeable commodity i by firms in sector j of region r evaluated at agents' prices VIFA_{ijr} = PFM_{ijr} * QFM_{ijr} i = TRAD_COMM; j = ENDW_COMM; r = REG VDPA_{ir} value of expenditure on domestic tradable commodity i, by private household in region r evaluated at agent's prices VDPA_{ir} = PPD_{ir} * QPD_{ir} i = TRAD_COMM; r = REG VIPA_{ir }value of expenditure on imported tradeable commodity i by firms in sector j of region r evaluated at agents' prices VIPA_{ir} = PPM_{ir} * QPM_{ir} i = TRAD_COMM; r = REG VDGA_{i} value of government's expenditure on domestic tradable commodity i, in region r, evaluated at agent's prices VDGA_{ir} = PGD_{ir} * QGD_{ir} i = TRAD_COMM; r = REG VIGA_{i} value of government's expenditure on imported tradable commodity i, in region r, evaluated at agent's prices VIGA_{ir} = PGM_{ir} * QGM_{ir} i = TRAD_COMM; r = REG SAVE_{r} value of (net) savings in region r SAVE_{r} = PSAVE_{r} * QSAVE_{r} r = REG VKB_{r} value of beginning-of-period capital stock in region r VKB_{r} = PCGDS_{r} * KB_{r} r = REG VDEP_{r} value of capital depreciation expenditure in region r VDEP_{r} = PCGDS_{r} * KB_{r} r = REG |
Value flows evaluated at market prices |
---|
VFM_{ijr} value of purchases of endowment commodity i by firms in sector j in region r, evaluated at market prices
VFM_{ijr} = PM_{ir} * QFE_{ijr} i = ENDWM_COMM; j = PROD_COMM; r = REG VDFM_{ijr} value of purchases of domestic tradable commodity i by firms in sector j in region r, evaluated at market prices VDFM_{ijr} = PM_{ir} * QFD_{ijr} i = TRAD_COMM; j = PROD_COMM VIFM_{ijr} value of purchases of imported tradable commodity i by firms in sector j in region r, evaluated at market prices VIFM_{ijr} = PIM_{ir} * QFM_{ijr} i = TRAD_COMM; j = PROD_COMM; r = REG VDPM_{ir} value of private household's purchases of domestic tradable commodity i in region r, evaluated at market prices VDPM_{ir} = PM_{ir} * QPD_{ir} i = TRAD_COMM; r = REG VIPM_{ir} value of private household's purchases of imported tradable commodity i in region r, evaluated at market prices VIPM_{ir} = PIM_{ir} * QPM_{ir} i = TRAD_COMM; r = REG VDGM_{ir} value of government's expenditure on domestic tradable commodity i, in region r, evaluated at market prices VDGM_{ir} = PM_{ir} * QGD_{ir} i = TRAD_COMM; r = REG VIGM_{ir} value of government's expenditure on imported tradable commodity i, in region r, evaluated at market prices VIGM_{ir} = PIM_{ir} * QGM_{ir} i = TRAD_COMM; r = REG VXMD_{irs} value of exports of tradable commodity i from source r to destination s, evaluated at (exporter's) market prices VXMD_{irs} = PM_{ir} * QXS_{irs} i = TRAD_COMM; r = REG; s= REG VIMS_{irs} value of imports of tradable commodity i from source r to destination s, evaluated at (importer's) market prices VIMS_{irs} = PMS_{ir} * QXS_{irs} i = TRAD_COMM; r = REG; s = REG VST_{ir} value of sales of tradable commodity i to the international transport sector in region r, evaluated at market prices VST_{ir} = PM_{ir} * QST_{ir} i = MARG_COMM; r = REG |
Value flows evaluated at world prices |
---|
VXWD_{irs} value of exports of tradable commodity i from source r to destination s, evaluated at world (fob) prices
VXWD_{irs} = PFOB_{irs} * QXS_{irs} i = TRAD_COMM; r = REG; s = REG VIWS_{irs} value of imports of tradable commodity i from source r to destination s, evaluated at world (cif) prices VIWS_{irs} = PCIF_{irs} * QXS_{irs} i = TRAD_COMM; r = REG; s = REG |
Technology Parameters |
---|
ESUBVA_{j} with j = PROD_COMM
substitution parameter between primary factors in the CES value-added nest of the nested CES production function of sector j of all regions (i.e. elasticity of substitution between primary production factors; for example, in a situation where land doesn't play a role in production, hence labor and capital are the only primary factors, this parameter indicates how sensitive is the K/L ratio to a 1 percent change in the wage/rental ratio) ESUBD_{i} with i = TRAD_COMM substitution parameter between domestic and composite imported commodities in the Armington utility/production structure of agent/sector i in all regions ESUBM_{i} with i = TRAD_COMM substitution parameter among imported commodities from different sources in the Armington utility/production structure of agent/sector i in all regions. |
CDE Preference Parameters and Associated Elasticities |
---|
SUBPAR_{ir} with i = TRAD_COMM; r = REG
substitution parameter for tradable commodity i in the CDE minimum expenditure function of region r INCPAR_{ir} with i = TRAD_COMM; r = REG expansion parameter for tradable commodity i in the CDE minimum expenditure function of region r. ALPHA_{ir} 1 - sub. parameter in the CDE minimum expenditure function ALPHA_{ir} = 1 - SUBPAR_{ir} i = TRAD_COMM; r = REG APE_{ikr} Allen partial elst.of sub between composite i and k in r APE_{ikr} = ALPHA_{ir} + ALPHA_{kr}- S_{n}CONSHR_{nr}*ALPHA_{nr} i = k= n = TRAD_COMM; r = REG EY_{ir} income elasticity of private household demand for i in r EY_{ir} = (1/S_{n} CONSHR_{nr}*INCPAR_{nr}) * (INCPAR_{ir} * (1.0 - ALPHA_{ir}) + S_{n}CONSHR_{nr}*INCPAR_{nr}*ALPHA_{nr}) + (ALPHA_{ir} - S_{n}CONSHR_{nr}*ALPHA_{nr}) EP_{ikr} uncompensated cross-price elasticity private household demand for i wrt k in r EP_{ikr} = (APE_{ikr} - EY_{ir})*CONSHR_{kr} i = k = TRAD_COMM; r = REG |
Mobility Parameter |
---|
ETRAE_{i} with i = ENDW_COMM
transformation parameter between uses for a sluggish primary factor i in the one level CET production function (i.e. this parameter indicates how easy/difficult it is to transfer a sluggish factor (say, capital) from one sector to another; the closer is ETRAE to zero, the more immobile is the factor between alternative uses) RORFLEX_{r} with r = REG flexibility of expected net rate of return on capital stock in region r with respect to investment (if a region's capital stock increases by 1%, then it is expected that the net rate of return on capital will decline by RORFLEX%) RORDELTA binary coefficient that determines the mechanism of allocating investment across regions (when RORDELTA=1, investment is allocated across regions to equate the change in the expected rates of return, rore(r), when RORDELTA=0, investment is allocated across regions to maintain the existing composition of capital stocks). |
Value Flows |
---|
VOA_{ir} value of non-saving commodity i output or supplied in region r evaluated at agents' prices
VOA_{ir} = EVOA_{ir} i = ENDW_COMM; r = REG VFA_{ijr} value of purchases of demanded commodity i by firms in sector j of regin r evaluated at agents' prices VFA_{ijr} = EVFA_{ijr} i = ENDW_COMM; j = PROD_COMM; r = REG VOM_{ir} value of non-saving commodity i output or supplied in region r evaluated at market prices VOM_{ir} = S_{j}VFM_{ijr} i = ENDW_COMM;j = PROD_COMM; r = REG VDM_{ir} value of domestic sales of tradable commodity i in region r evaluated at market prices VDM_{ir} = VDPM_{ir} + VDGM_{ir} + S_{j}VDFM_{ijr} i = TRAD_COMM; j = PROD_COMM; r = REG VIM_{ir} value of aggregate imports of tradable commodity i in region r evaluated at market prices VIM_{ir} = VIPM_{ir} + VIGM_{ir} + S_{j}VIFM_{ijr} i = TRAD_COMM; j = PROD_COMM; r = REG VPA_{ir} value of private household expenditure on tradable commodity i in region r evaluated at agents' prices VPA_{ir} = VDPA_{ir} + VIPA_{ir} i = TRAD_COMM; r = REG PRIVEXP_{r} total consumption expenditure by private household in regin r PRIVEXP_{r} = S_{i}VPA_{ir} i = TRAD_COMM VGA_{ir} value of government expenditure on tradable commodity i in region r evaluated at agents' prices VGA_{ir} = VDGA_{ir} + VIGA_{ir} i = TRAD_COMM; r = REG GOVEXP_{r} total consumption expenditure by government in region r GOVEXP_{r} = S_{i}VGA_{ir} i = TRAD_COMM; r = REG INCOME_{r} total expenditure equals net income in region r INCOME_{r} = PRIVEXP_{r} + GOVEXP_{r} + SAVE_{r} r = REG REGINV_{r} gross investment in region r that equals value of output of "capital goods" sector REGINV_{r} = S_{k}VOA_{kr} k = CGDS_COMM NETINV_{r} net investment in region r NETINV_{r} = S_{k}VOA_{kr} - VDEP_{r} k = CGDS_COMM GLOBINV global net investment GLOBINV = S_{r}NETINV = S_{r}SAVE_{r} r = REG INVKERATIO_{r} ratio of gross investment to end-of-period capital stock in region r INVKERATIO_{r} = REGINV_{r} / (VKB_{r} + NETINV_{r}) r = REG GRNETRATIO_{r} ratio of gross to net rate of return on capital in regin r (VOA_{capital,r} is gross return to capital) GRNETRATIO_{r} = S_{k}VOA_{kr} / (S_{k}VOA_{kr} - VDEP_{r}) with k = ENDWC_COMM; r = REG GDP_{r} gross domestic product in region r (trade is valued at worl prices) GDP_{r} = S_{i}VPA_{ir} + S_{i}VGA_{ir} + S_{k}VOA_{kr} + S_{i}S_{s}VXWD_{irs}+ S_{m}VST_{ms} - S_{i}S_{s}VIWS_{irs} i = TRAD_COMM; k = CGDS_COMM; r = REG; s = REG VT international margin suply VT = S_{i}S_{r}VST_{ir} i = TRAD_COMM; r = REG VXW_{ir} value of exports of tradable commodity i from source r evaluated at world (fob) prices VXW_{ir} = S_{s}VXWD_{irs}+VST_{ir} i = MARG_COMM; r = REG VXWREGION_{r} value of exports from source r evaluated at world (fob) prices VXWREGION_{r} = S_{i}VXW_{ir} i = TRAD_COMM; r = REG VXWCOMMOD_{i} value of exports of tradable commodity i evaluated at world (fob) prices VXWCOMMOD_{i}= S_{r}VXW_{ir} i = TRAD_COMM; r = REG VIW_{ir} value of imports of tradable commodity i into region r evaluated at world (cif) prices VIW_{ir}= S_{s}VIWS_{isr} i = TRAD_COMM; r = REG; s = REG VIWREGION_{r} value of imports into region r evaluated at world (cif) prices VIWREGION_{r} = S_{i}VIW_{ir} i = TRAD_COMM; r = REG VIWCOMMOD_{i} value of imports of tradable commodity i evaluated at world (cif) prices VIWCOMMOD_{i}= S_{r}VIW_{ir} i = TRAD_COMM; r = REG VXWLD value of worldwide commodity exports evaluated at world (fob) prices VXWLD= S_{r}VXWREGION_{r} r = REG PW_PM_{ir} ratio of world (fob) to domestic market prices for tradable commodity i in region PW_PM_{ir} = S_{s}VXWD_{irs} / S_{s}VXMD_{irs} i = TRAD_COMM; r = REG; s = REG VOW_{ir} value of output of tradable commodity i in region r, evaluated at world (fob) prices VOW_{ir} = VDM_{ir} * PW_PM_{ir} + S_{s}VXWD_{irs} + VST_{ir} i = MARG_COMM; r = REG; s = REG VWOW_{i} value of world supply of tradable commodity i evaluated at world (fob) prices VWOW_{i} = S_{r}VOW_{ir}i = TRAD_COMM; r = REG VTMFSD_{mirs} int'l margin usage, by margin, freight, source, and destination m = MARG_COMM;i = TRAD_COMM; r = REG; s = REG VTFSD_{irs} aggregate value of svces in the shipment of i from r to s VTFSD_{irs} = S_{m}VTMFSD_{mirs} In a balanced data base VIWS_{irs} = VXWD_{irs} + VTFSD_{irs} i = TRAD_COMM; m = MARG_COMM; r = REG; s = REG VTMPROV_{m} international margin services provision VTMPROV_{m} = S_{r}VST_{mr} m = MARG_COMM; r = REG VTRPROV_{r} international margin supply, by region VTRPROV_{r} = S_{m}VST_{mr} m = MARG_COMM; r = REG VTMUSE_{m} international margin services usage, by type VTMUSE_{m} = S_{i}S_{r}S_{s}VTMFSD_{mirs} m = MARG_COMM; i = TRAD_COMM; r = s = REG VTMUSESHR_{mirs} share of i,r,s usage in global demand for m VTMUSESHR_{mirs} = VTFSD_{irs} / VT m = MARG_COMM; i = TRAD_COMM; r = s = REG VTSUPPSHR_{mr} share of region r in global supply of margin m VTSUPPSHR_{mr} = VTRPROV_{r} / VT if VTMPROV_{m} <> 0.0 then VTSUPPSHR_{mr} = VST_{mr} / VTMPROV_{m} m = MARG_COMM; r = REG VTUSE international margin services usage; VTUSE=S_{m}S_{i}S_{r}S_{s}VTMFSD_{mirs} m = MARG_COMM; i = TRAD_COMM; r = s = REG VWOU_{i} value of world output of i at user prices VWOU_{i} = S_{s}[(VPA_{is} + VGA_{is}) + S_{j}VFA_{ijs}] s = REG; j = PROD_COMM VENDWREG_{r} value of primary factors, at mkt prices, by region VENDWREG_{r} = S_{i} VOM_{ir} i = ENDOW_COMM; r = REG VENDWWLD value of primary factors, at mkt prices, worldwide VENDWWLD = S_{r} VENDWREG_{r} r = REG VPAEV_{ir} private household expend. on i in r valued at agent's prices, for EV calculation VPAEV_{ir} = qpev_{ir} i = TRAD_COMM, r = REG VPAREGEV_{r} private consumption expenditure in region r, for EV calculation VPAREGEV_{r} = S_{i}VPAEV_{ir } i = TRAD_COMM, r = REG YG_{r} regional government consumption expenditure, in region r r = REG |
Shares |
---|
SHRDFM_{ijr} share of domestic sales of tradable commodity i used by firms in sector j of regin r evaluated at market prices
SHRFM_{ijr} = VDFM_{ijr} / VDM_{ir} i = TRAD_COMM; j = PROD_COMM; r = REG SHRDPM_{i} share of domestic sales of commodity i used by private household in region r evaluated at market prices SHRDPM_{ir} = VDPM_{ir} / VDM_{ir} i = TRAD_COMM; r = REG SHRDGM_{i} share of domestic sales of commodity i used by the government in region r evaluated at market prices SHRDGM_{ir} = VDGM_{ir} / VDM_{ir} i = TRAD_COMM; r = REG SHRIFM_{ijr} share of aggregate imports of tradable commodity i used by firms in sector j of regin r evaluated at market prices SHRIFM_{ijr} = VIFM_{ijr} / VIM_{ir} i = TRAD_COMM; j = PROD_COMM; r = REG SHRIPM_{ir} share of aggregate imports of commodity i used by private household in region r evaluated at market prices SHRIPM_{ir} = VIPM_{ir} / VIM_{ir} i = TRAD_COMM; r = REG SHRIGM_{ir} share of aggregate imports of commodity i used by the government in region r evaluated at market prices SHRIGM_{ir} = VIGM_{ir} / VIM_{ir} i = TRAD_COMM; r = REG FMSHR_{ijr} share of imports in the composite for tradable commodity i used by firms in sector j of region r evaluated at agents' prices FMSHR_{ijr} = VIFA_{ijr} / VFA_{ijr} i = TRAD_COMM; j = PROD_COMM; r = REG PMSHR_{ir} share of imports in the composite for tradable commodity i used by private household in region r evaluated at agents' prices PMSHR_{ir} = VIPA_{ir} / VPA_{ir} i = TRAD_COMM; r = REG GMSHR_{ir} share of impotrs in the composite for tradable commodity i used by the government in region r evaluated at agents' prices GMSHR_{ir} = VIGA_{ir} / VGA_{ir} i = TRAD_COMM; r = REG CONSHR_{ir} budget share of the composite for tradable i in total private household expenditure in regin r evaluated at agents' prices CONSHR_{ir} = VPA_{ir} / PRIVEXP_{r} i = TRAD_COMM; r = REG MSHRS_{irs} market share of source r in the aggregate imports of tradable commodity i in region s evaluated at market prices MSHRS_{irs} = VIMS_{irs} / S_{r}VIMS_{irs} i = TRAD_COMM; r = s = REG SVA_{ijr} share of endowment commodity i in value-added of sector j of region r evaluated at agents' prices SVA_{ijr}= VFA_{ijr} / S_{k}VFA_{kjr} i = ENDW_COMM; j = PROD_COMM; k = ENDW_COMM; r = REG REVSHR_{ijr} share of endowment commodity i used by fiorms in sector j of regin r evaluated at market prices REVSHR_{ijr}= VFM_{ijr} / S_{k}VFM_{kjr} i = ENDW_COMM; j = PROD_COMM; k = PROD_COMM; r = REG FOBSHR_{irs} share of fob price in the cif price for tradable commodity i exported from source r to destination s FOBSHR_{irs}= VXWD_{irs} / VIWSCOST_{irs} i = TRAD_COMM; r = s = REG XSHRPRIV_{r} private expenditure share in regional income XSHRPRIV_{r} = PRIVEXP_{r}/INCOME_{r} r = REG XSHRGOV_{r} government expenditure share in regional income XSHRGOV_{r} = GOVEXP_{r}/INCOME_{r} r = REG XSHRSAVE_{r} saving share in regional income XSHRSAVE_{r} = SAVE_{r}/INCOME_{r} r = REG SHRDM_{ir} share of domestic sales of i in r i = TRAD_COMM; r = REG SHRDM_{ir} = VDM_{ir} / VOM_{ir} SHRST_{mr} share of sales of m to global transport services in r m = MARG_COMM; r = REG SHRST_{mr} = VST_{mr} / VOM_{mr} SHRXMD_{irs} share of export sales of i to s in r i = TRAD_COMM; r = s = REG SHRXMD_{irs} = VXMD_{irs} / VOM_{ir} i = TRAD_COMM; r = s = REG SHREM_{ijr} share of mobile endowments i used by sector j at mkt prices SHREM_{ijr} = VFM_{ijr} / VOM_{ir} i = ENDWM_COMM; j = PROD_COMM; r = REG TRNSHR_{irs} share of transport price in the cif price for tradable commodity i exported from source r to destination s TRSHR_{irs}= VTFSD_{irs} / VIWSCOST_{irs} XWCONSHR_{ir} expansion-parameter-weighted consumption share XWCONSHR_{ir} = CONSHR_{ir}*INCPAR_{ir}/UELASPRIV_{r} i = TRAD_COMM; r = REG XSHRPRIVEV_{r} private expenditure share in regional income, for EV calculation r = REG XSHRPRIVEV_{r} = PRIVEXPEV_{r}/INCOMEEV_{r} r = REG XSHRGOVEV_{r} government expenditure share in regional income, for EV calculation r = REG XSHRGOVEV_{r} = GOVEXPEV_{r}/INCOMEEV_{r} r = REG XSHRSAVEEV_{r} saving share in regional income, for EV calculation r = REG XSHRSAVEEV_{r} = SAVEEV_{r}/INCOMEEV_{r} r = REG XWCONSHREV_{ir} expansion-parameter-weighted consumption share, for EV calculation XWCONSHREV_{ir} = CONSHREV_{ir}*INCPAR_{ir}/UELASPRIVEV_{r} i = TRAD_COMM, r = REG CONSHREV_{ir} share of private household consn devoted to good i in r, for EV calculation CONSHREV_{ir} = VPAEV_{ir}/VPAREGEV_{r} STC_{ijr} share of i in total costs of j in r STC_{ijr} = VFA_{ijr} / S_{k} VFA_{kjr} i = k = DEMD_COMM; j = PROD_COMM; r = REG |
Quantity Variables |
---|
QO_{ir} quantity of non-saving commodity i output or supplied in region r
i = NSAV_COMM r = REG QOES_{ijr} quantity of sluggish endowment i supplied to sector j firm of region r i = ENDWS_COMM; j = PROD_COMM; r = REG QDS_{ir} quantity of domestic sales of tradable commodity i in region r i = TRAD_COMM; r = REG QXS_{irs} quantity of exports of tradable commodity i from source r to destination s i = TRAD_COMM; r = s = REG QST_{ir} quantity of sales of marginal commodity i to the international transport sector in region r i = MARG_COMM; r = REG QFE_{ijr} quantity of endowment i demanded by sector j firm in region r i = ENDW_COMM; j = PROD_COMM; r = REG QVA_{jr} quantity index of land-labor-capital composite (value-added) in sector j firm in region r j = PROD_COMM; r = REG QF_{ijr} quantity of composite tradable commodity i demanded by sector j firm in region r i = TRAD_COMM; j = PROD_COMM; r = REG QFD_{ijr} quantity of domestic tradable i demanded by sector j firm in region r i = TRAD_COMM; j = PROD_COMM; r = REG QFM_{ijr} quantity of imported tradable i demanded by sector j firm in region r i = TRAD_COMM; j = PROD_COMM; r = REG QP_{ir} quantity of composite tradable i demanded by private household in region r i = TRAD_COMM; r = REG QPD_{ir} quantity of domestic tradable i demanded by private household in region r i = TRAD_COMM; r = REG QPM_{ir} quantity of imported tradable i demanded by private household in region r i = TRAD_COMM; r = REG QG_{ir} quantity of composite tradable commodity i demanded by government household in region r i = TRAD_COMM; r = REG QGD_{ir} quantity of domestic tradable commodity i demanded by government household in region r i = TRAD_COMM; r = REG QGM_{ir} quantity of imported tradable commodity i demanded by government household in region r i = TRAD_COMM; r = REG QIM_{ir} quantity of aggregate imports of tradable commodity i demanded by region r using market prices as weights i = TRAD_COMM; r = REG QIW_{ir} quantity of aggregate imports of tradable commodity i demanded by region r using cif prices as weights i = TRAD_COMM; r = REG QXW_{ir} quantity of aggregate exports of tradable commodity i supplied from region r using fob prices as weights i = TRAD_COMM; r = REG QIWREG_{r }volume of merchandise imports demanded by region r r = REG QXWREG_{r }volume of merchandise exports supplied by region r r = REG QIWCOM_{i }volume of global merchandise imports of tradable commodity i i = TRAD_COMM; r = REG QXWCOM_{i }volume of global merchandise exports of tradable commodity i i = TRAD_COMM; r = REG QXWWLD_{ }volume of world trade QOW_{i }quantity index for world supply of tradable commodity i i = TRAD_COMM EXPAND_{ir} Change in investment levels relative to endowment stock i = ENDWC_COMM; r = REG QOWU_{ir}quantity index for world supply of good i at user prices i = TRAD_COMM; r = REG QTMFSD_{mirs} international usage margin m on i from r to s m = MARG_COMM; i = TRAD_COMM; r = s = REG QTM_{m} global margin usage m = MARG_COMM QCGDS_{r} quantity of capital goods sector supplied in region r r = REG QSAVE_{r} quantity of savings demanded in region r r = REG GLOBALCGDS quantity of global supply of capital for net investment KSVCES_{r} quantity of capital services in region r r = REG KB_{r} quantity of beginning-of-period capital stock in region r r = REG KE_{r} quantity of end-of-period capital stock in region r r = REG QGDP_{r} quantity index for GDP in region r r = REG WALRAS_DEM quantity demanded in the omitted market - equals global demand for savings WALRAS_SUP quantity supplied in the omitted market - equals global supply of new capital goods composite POP_{r} population in region r r = REG COMPVALAD_{ir} composition of value added for good i and region r i = TRAD_COMM; r = REG |
Price Variables |
---|
PM_{ir} market price of non-saving commodity i in region r
i = NSAV_COMM; r = REG PMES_{ijr} market price for sluggish endowment i supplied to firm j in region r i = ENDWS_COMM; j = PROD_COMM; r = REG PS_{ir} supply price of non-saving commodity i in region r i = NSAV_COMM; r = REG PFE_{ijr} demand price for endowment i by firms in sector j of region r i = ENDW_COMM; j = PROD_COMM; r = REG PVA_{jr} price of value-added in sector j j = PROD_COMM; r = REG PF_{ijr} demand price for composite tradable i by firms in sector j of region r i = TRAD_COMM; j = PROD_COMM; r = REG PFD_{ijr} demand price for domestic tradable i by firms in sector j of region r i = TRAD_COMM; j = PROD_COMM; r = REG PFM_{ijr} demand price for imported tradable i by firms in sector j of region r i = TRAD_COMM; j = PROD_COMM; r = REG PP_{ir} private household's demand price for composite tradable i in region r i = TRAD_COMM; r = REG PPD_{ir} private household's demand price for domestic tradable i in region r i = TRAD_COMM; r = REG PPM_{ir} private household's demand price for imported tradable i in region r i = TRAD_COMM; r = REG PG_{ir} government household's demand price for composite tradable i in region r i = TRAD_COMM; r = REG PGD_{ir} government household's demand price for domestic tradable i in region r i = TRAD_COMM; r = REG PGM_{ir} government household's demand price for imported tradable i in region r i = TRAD_COMM; r = REG PSAVE_{r} price of savings in region r r = REG PCGDS_{r} price of investment good in region r - equals PS(cgds,r) r = REG PGDP_{r} price index for GDP in region r r = REG PPRIV_{r} price index for private household expenditure in region r r = REG PGOV_{r} price index for government household expenditure in region r r = REG PFOB_{irs} world fob price of tradable commodity i exported from source r to destination s (prior to including transport margins) i = TRAD_COMM; r = s = REG PCIF_{irs} world cif price of tradable commodity i imported from source r to destination s ) after including transport margins) i = TRAD_COMM; r = s = REG PMS_{irs} market price by source of tradable commodity i imported from source r to destination s i = TRAD_COMM; r = s = REG PIM_{ir} market price of aggregate imports of tradable commodity i in region r i = TRAD_COMM; r = REG PIW_{ir} world price of aggregate imports of tradable commodity i in region r i = TRAD_COMM; r = REG PXW_{ir} price index for aggregate exports of tradable commodity i from region r i = TRAD_COMM; r = REG PIWREG_{r} price index of merchandise imports in region r r = REG PXWREG_{r} price index of merchandise exports from region r r = REG PIWCOM_{i} price index of global merchandise imports of tradable commodity i i = TRAD_COMM PXWCOM_{i} price index of global merchandise exports of tradable commodity i i = TRAD_COMM PXWWLD price index of world trade PR_{ir} ratio of domestic market price to market price of imports for tradable commodity i in region r i = TRAD_COMM; r = REG PW_{i} world price index for total supply of tradable commodity i in region r i = TRAD_COMM PSW_{r} price index received for tradable commodities produced in region r including sales of net investment to the global bank r = REG PDW_{r} price index paid for tradable commodities used in region r including purchases of savings from the global bank r = REG TOT_{r} terms of trade for region r r = REG PT_{m} price of margin services supplied m = MARG_COMM PCGDSWLD world average price of capital goods (net investment weights) PWU_{i} world price index for total good i supplies at user prices i = TRAD_COMM PTRANS_{irs} cost index for international transport of i from r to s i = TRAD_COMM; r = s = REG RENTAL_{r} rental rate on capital stock in regin r - equals PS(CGDS,r) r = REG RORC_{r} current net rate of return on capital stock in region r r = REG RORE_{r} expected net rate of return on capital stock in region r r = REG RORG global net rate of return on capital stock P_{r} price index for disposition of income by regional household PFACTREAL_{ir} ratio of return to primary factor i to cpi in r i = ENDOW_COMM; r = REG PFACTOR_{r} market price index of primary factors, by region PFACTWLDworld price index of primary factors |
Technical Change Variables |
---|
AO_{ir} output augmenting technical change in sector j of region r
j = PROD_COMM; r = REG AFE_{ijr} primary factor i augmenting technical change in sector j of region r i = ENDW_COMM; j = PROD_COMM; r = REG AF_{ijr} intermediate input i augmenting technical change in sector j of region r i = TRAD_COMM; j = PROD_COMM; r = REG AVA_{jr} value-added augmenting technical change in sector j of region r j = PROD_COMM; r = REG AMS_{irs} import i from region r augmenting tech change in region s i = TRAD_COMM, r = s = REG AOSEC_{j} output tech change of sector j, worldwide j = PROD_COMM AOREG_{r} output tech change in region r r = REG AOALL_{jr} output augmenting technical change in sector j of r j = PROD_COMM; r = REG ESUBT_{j} elasticity of substitution among composite intermediate inputs in production j = PROD_COMM AFCOM_{i} intermediate tech change of input i, worldwide i = TRAD_COMM AFSEC_{j} intermediate tech change of sector j, worldwide j = PROD_COMM AFREG_{r} intermediate tech change in region r r = REG AFALL_{ijr} intermediate input i augmenting tech change by j in r i = TRAD_COMM,j = PROD_COMM; r = REG AFECOM_{i} factor input tech change of input i, worldwide i = ENDW_COMM AFESEC_{j} factor input tech change of sector j, worldwide j = PROD_COMM AFEREG_{r} factor input tech change in region r r = REG AFEALL_{ijr} primary factor i augmenting tech change sector j in r i = ENDW_COMM; j = PROD_COMM; r = REG AMS_{irs} reduction in effective price associated with delivery of i from r to s i = TRAD_COMM; r = REG; s = REG ATMFSD_{mirs} tech change in m's shipping of i from region r to s m = MARG_COMM; i = TRAD_COMM; r = s = REG ATM_{m} tech change in mode m, worldwide; m = TRAD_COMM ATF_{i} tech change shipping of i, worldwide i = TRAD_COMM ATS_{r} tech change shipping from region r r = REG ATD_{s} tech change shipping to s s = REG ATALL_{mirs} tech change in m's shipping of i from region r to s m = MARG_COMM; i = TRAD_COMM; r = REG; s = REG AU_{r} input-neutral shift in utility function r = REG |
Policy Variables |
---|
TO_{ir} power of the tax on output (or income) of non-savings commodity i in region r
i = NSAV_COMM; r = REG TF_{ijr} power of the tax on endowment commodity i demanded by sector j of regin r i = ENDW_COMM; j = PROD_COMM; r = REG TFD_{ijr} power of the tax on domestic tradable commodity i demanded by sector j of region r i = TRAD_COMM; j = PROD_COMM; r = REG TFM_{ijr} power of the tax on imported tradable commodity i demanded by sector j of region r i = TRAD_COMM; j = PROD_COMM; r = REG TPD_{ir} power of the tax on domestic tradable commodity i purchased by private household in region r i = TRAD_COMM; r = REG TPM_{ir} power of the tax on imported tradable commodity i purchased by private household in region r i = TRAD_COMM; r = REG TGD_{ir} power of the tax on domestic tradable commodity i purchased by government household in region r i = TRAD_COMM; r = REG TGM_{ir} power of the tax on imported tradable commodity i purchased by government household in region r i = TRAD_COMM; r = REG TXS_{irs} power of the tax on exports of tradable commodity i from source r to destination r (levied in region r) i = TRAD_COMM; r = s = REG TMS_{irs} power of the tax on imports of tradable commodity i from source r to destination s (levied in region s) i = TRAD_COMM; r = s = REG TX_{ir} power of the variable export tax on exports of tradable commodity from region r - destination generic i = TRAD_COMM; r = REG TM_{ir} power of the variable import tax (levy) on imports of tradable commodity i in region s - source generic i = TRAD_COMM; r = REG TP_{r} region-wide shock to tax on purchases by private household in region r r = REG ATPM_{ir} actual tax on imported traded commodity i purchased by private households in region r i = TRAD_COMM; r = REG ATPD_{ir} actual tax on domestic traded commodity i purchased by private households in region r i = TRAD_COMM; r = REG DGTAX_{ir} tax on government consumption of domestic good i in region r r = REG IGTAX_{ir} tax on government consumption of imported good i in region r r = REG TGC_{r} government consumption tax payments in r TGC_{r} = S_{i}DGTAX_{ir} + IGTAX_{ir} i = TRAD_COMM; r = REG DPTAX_{ir} tax on private consumption of domestic good i in region r DPTAX_{ir} = VDPA_{ir} - VDPM_{ir} i = TRAD_COMM; r = REG IPTAX_{ir} tax on private consumption of imported good i in region r IPTAX_{ir} = VIPA_{ir} - VIPM_{ir} i = TRAD_COMM; r = REG TPCr private consumption tax payments in r TPC_{r} = S_{i}DPTAX_{ir} + IPTAX_{ir} i = TRAD_COMM; r = REG DFTAX_{ijr} tax on use of domestic intermediate good i by j in r DFTAX_{ijr} = VDFA_{ijr} - VDFM_{ijr} i = TRAD_COMM; j = PROD_COMM; r = REG IFTAX_{ijr }tax on use of imported intermediate good i by j in r IFTAX_{ijr} = VIFA_{ijr} - VIFM_{ijr} i = TRAD_COMM; j = PROD_COMM; r = REG TIU_{r} firms' tax payments on intermediate goods usage in r TIU_{r} = S_{j}S_{i}(DFTAX_{ijr} + IFTAX_{ijr}) i = TRAD_COMM; j = PROD_COMM; r = REG ETAX_{ijr} tax on use of endowment good i by industry j in region r ETAX_{ijr} = VFA_{ijr} - VFM_{ijr} i = ENDW_COMM; j = PROD_COMM; r = REG TFU_{r} firms' tax payments on primary factor usage in r TFU_{r} = S_{i}S_{j}ETAX_{ijr} i = ENDW_COMM; j = PROD_COMM; r = REG PTAX_{ir} output tax on good i in region r PTAX_{ir} = VOM_{ir} - VOA_{ir} i = NSAV_COMM; r = REG TOUT_{r} production tax payments in r TOUT_{r} = S_{i}PTAX_{ir} i = PROD_COMM; r = REG XTAXD_{irs }tax on exports of good i from source r to destination s XTAXD_{irs} = VXWD_{irs} - VXMD_{irs} i = TRAD_COMM; r = s = REG TEX_{r} export tax payments in r TEXr = S_{i}S_{s}XTAXD_{irs} i = TRAD_COMM; r = s = REG MTAX_{irs} tax on imports of good i from source r in destination s MTAX_{irs} = VIMS_{irs} - VIWS_{irs} i = TRAD_COMM; r = s = REG TIM_{r} import tax payments in r TIM_{r} = S_{i}S_{s}MTAX_{isr} i = TRAD_COMM; r = s = REG TOTTAX_{r} Total tax receipts in r TOTTAX_{r} = TPC_{r} + TGC_{r} + TIU_{r} + TFU_{r} + TOUT_{r} + TEX_{r} + TIM_{r} + TINC_{r} r = REG TGCR_{r} change in ratio of government consumption tax to INCOME in region r r = REG TPCR_{r} change in ratio of private consumption tax to INCOME in region r r = REG TIUR_{r} change in ratio of tax on intermediate usage to INCOME in region r r = REG TFUR_{r} change in ratio of tax on primary factor usage to INCOME in region r r = REG TOUTR_{r} change in ratio of output tax to INCOME in region r nbsp; r = REG TEXPR_{r} change in ratio of export tax to INCOME in region r r = REG TIMPR_{r} change in ratio of import tax to INCOME in region r r = REG TINC_{r} income tax payments in r TINC_{r} = S_{i}PTAX_{ir} i = ENDOW_COMM; r = REG TINCR_{r} change in ratio of income tax to INCOME in region r r = REG DTAXR_{r} change in ratio of taxes to INCOME in r r = REG |
Regional Household Preference Parameters and Shifters |
---|
DPARPRIV_{r} private consumption distribution parameter
DPARPRIV_{r} = UELASPRIV_{r}*XSHRPRIV_{r}/UTILELAS_{r} r = REG DPARGOV_{r} government consumption distribution parameter DPARGOV_{r} = XSHRGOV_{r}/UTILELAS_{r} r = REG DPARSAVE_{r} saving distribution parameter DPARSAVE_{r} = XSHRSAVE_{r}/UTILELAS_{r} r = REG DPARSUM_{r} sum of distribution parameters r = REG dpav_{r} change in average distribution parameter r = REG dpsum_{r} change in sum of the distribution parameters r = REG dppriv_{r} change in private consumption distribution parameter r = REG dpgov_{r} change in government consumption distribution parameter r = REG dpsave_{r} change in saving distribution parameter r = REG |
Slack Variables |
---|
profitslack_{jc} slack variable in the ZEROPROFITS equation (this is exogenous as long as output level, QO(j), is determined endogenously)
j = PROD_COMM; r = REG cgdslack_{r} slack variable in the CAPGOODS equation (this is exogenous as long as output level of new capital goods, QO("cgds"), is determined endogenously r = REG endwslack_{ir} slack variable in the MKTCLENDWM and ENDW_SUPPLY equations (this is exogenous as long as primary factor rental rates, PMi and PMESij are determined endogenously) i = ENDWS_COMM; r = REG tradslack_{ir} slack variable in the MKTCLTRD equation (this is exogenous as long as market price of tradable, PMi, is determined endogenously) i = TRAD_COMM; r = REG incomeslack_{r} slack variable in the INCOME equation (this is exogenous as long as income, Y, is determined endogenously) r = REG psaveslack_{r} slack variable in the SAVINGS equation (this is exogenous as long as level of savings, QSAVE, is determined endogenously) r = REG walraslack slack variable in the WALRAS equation (this is endogenous as long as price of savings, PSAVE, is determined exogenously which is the case in a standard GE closure. When any one of the GE links is broken, this is swapped with PSAVE, the numeraire price, thereby forcing global savings to equal global investment). incomeslack_{r} slack variable in the expression for regional income r = REG |
Value and Income Variables |
---|
vxwfob_{ir} percentage change in value of exports of tradable commodity i from source region r using fob weights (is identical to the linearized form of VXW_{ir})
i = TRAD_COMM; r = REG vxwreg_{r} percentage change in value of merchandise exports from region r using fob weights (is identical to the linearized form of VXWREGION_{r}) r = REG vxwcom_{i} percentage change in value of global merchandise exports of tradable commodity i using fob weights (is identical to the linearized form of VXWCOMMOD_{i}) i = TRAD_COMM viwcif_{ir} percentage change in value of imports of tradable commodity i into region r using fob weights (is identical to the linearized form of VIW_{ir}) i = TRAD_COMM; r = REG viwreg_{r} percentage change in value of merchandise imports into region r using cif weights (is identical to the linearized form of VIWREGION_{ir}) r = REG viwcom_{i} percentage change in value of global merchandise imports of tradable commodity i using fob weights (is identical to the linearized form of VIWCOMMOD_{i}) i = TRAD_COMM vxwwld percentage change in value of worlwide commodity exports using fob weights (is identical to the linearized form of VXWLD) valuew_{i} percentage change in value of global supply of tradable commodity i using fob weights (is identical to the linearized form of VWOW_{i}) i = TRAD_COMM valuewu_{i} value of world supply of good i at user prices i = TRAD_COMM vgdp_{r} percentage change in value of GDP in region r (is identical to the linearized form of GDP_{r}) r = REG y_{r} percentage change in regional household income (is identical to the linearized form of INCOME) r = REG yp_{r} percentage change in private household expenditure (is identical to the linearized form of PRIVEXP). r = REG FY_{r} primary factor income in r net of depreciation FY_{r} = S_{i}VOM_{ir} - VDEP_{r} i = ENDW_COMM; r = REG fincome_{r} pc change in factor income variable in r net of depreciation r = REG |
Utility Variables |
---|
U_{r} per capita utility from aggregate household expenditure in region r
r = REG
UP_{r} per capita utility from private household expenditure in region r r = REG UG_{r} aggregate utility from government household expenditure in region r r = REG UTILELAS_{r} elasticity of cost of utility wrt utility UTILELAS_{r} = (UELASPRIV_{r}*XSHRPRIV_{r} + XSHRGOV_{r} + XSHRSAVE_{r})/DPARSUM_{r} r = REG uelas_{r} pc change in elasticity of cost of utility wrt utility r = REG uepriv_{r} pc change in utility elasticity of private cons expenditure r = REG uelasev_{r} pc change in elasticity of cost of utility wrt utility, for EV calculation r = REG ueprivev_{r} pc change in utility elasticity of private cons expenditure, for EV calculation r = REG |
Welfare Variables |
---|
EV_{r} equivalent variation, in $ US million (positive figure indicates welfare improvement)
r = REG
WEV equivalent variation, in $ US million, for the world (positive figure indicates welfare improvement) ugev_{r} per capita utility from gov't expend., for EV calculation r = REG upev_{r} per capita utility from private expend., for EV calculation r = REG qsaveev_{r} total quantity of savings demanded, for EV calculation r = REG ypev_{r} private consumption expenditure, in region r, for EV calculation r = REG ygev_{r} government consumption expenditure, in region r, for EV calculation r = REG qpev_{ir} private household demand for commodity i in region r, for EV calculation i = TRAD_COMM, r = REG yev_{r} regional household income, in region r, for EV calculation ysaveev_{r} NET savings expenditure, for EV calculation dpavev_{r} average distribution parameter shift, for EV calculation r = REG |
Trade Balance Variables |
---|
DTBAL_{r} change in trade balance of region r , in US$ million (positive figure indicates increases in exports exceeds increases in imports)
r = REG DTBALi_{ir} change in trade balance for tradable commodity i in region r , in US$ million (positive figure indicates increases in exports exceeds increases in imports) i = TRAD_COMM; r = REG |