# Variables in v11

Extracted from https://www.gtap.agecon.purdue.edu/models/setsVariables.asp

## Sets

Variable Label | Variable Name |
---|---|

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

Variable Label | Variable Name |
---|---|

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

Variable Label | Variable Name |
---|---|

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

EVOAir value of endowment commodity i output or supplied, in region r, evaluated at agent’s prices

- EVOAi,r = PSi,r * QOi,r with i = ENDW_COMM and r

EVFAijr value of purchases of demanded commodity i by firms in sector j, in region r, evaluated at agent’s prices

- EVFAijr = PFEijr * QFEijr i = TRAD_COMM; j = ENDW_COMM; r = REG

VDFAijr value of purchases of domestic tradeable commodity i by firms in sector j of region r evaluated at agents’ prices

- VDFAijr = PFDijr * QFDijr i = TRAD_COMM; j = ENDW_COMM; r = REG

VIFAijr value of purchases of imported tradeable commodity i by firms in sector j of region r evaluated at agents’ prices

- VIFAijr = PFMijr * QFMijr i = TRAD_COMM; j = ENDW_COMM; r = REG

VDPAir value of expenditure on domestic tradable commodity i, by private household in region r evaluated at agent’s prices

- VDPAir = PPDir * QPDir i = TRAD_COMM; r = REG

VIPAir value of expenditure on imported tradeable commodity i by firms in sector j of region r evaluated at agents’ prices

- VIPAir = PPMir * QPMir i = TRAD_COMM; r = REG

VDGAi value of government’s expenditure on domestic tradable commodity i, in region r, evaluated at agent’s prices

- VDGAir = PGDir * QGDir i = TRAD_COMM; r = REG

VIGAi value of government’s expenditure on imported tradable commodity i, in region r, evaluated at agent’s prices

- VIGAir = PGMir * QGMir i = TRAD_COMM; r = REG

SAVEr value of (net) savings in region r

- SAVEr = PSAVEr * QSAVEr r = REG

VKBr value of beginning-of-period capital stock in region r

- VKBr = PCGDSr * KBr r = REG

VDEPr value of capital depreciation expenditure in region r

- VDEPr = PCGDSr * KBr r = REG

## Value flows evaluated at market prices

VFMijr value of purchases of endowment commodity i by firms in sector j in region r, evaluated at market prices

VFMijr = PMir * QFEijr i = ENDWM_COMM; j = PROD_COMM; r = REG

VFMijr = PMESijr * QFEijr i = ENDWS_COMM; j = PROD_COMM; r = REG

VDFMijr value of purchases of domestic tradable commodity i by firms in sector j in region r, evaluated at market prices

- VDFMijr = PMir * QFDijr i = TRAD_COMM; j = PROD_COMM

VIFMijr value of purchases of imported tradable commodity i by firms in sector j in region r, evaluated at market prices

- VIFMijr = PIMir * QFMijr i = TRAD_COMM; j = PROD_COMM; r = REG

VDPMir value of private household’s purchases of domestic tradable commodity i in region r, evaluated at market prices

- VDPMir = PMir * QPDir i = TRAD_COMM; r = REG

VIPMir value of private household’s purchases of imported tradable commodity i in region r, evaluated at market prices

- VIPMir = PIMir * QPMir i = TRAD_COMM; r = REG

VDGMir value of government’s expenditure on domestic tradable commodity i, in region r, evaluated at market prices

- VDGMir = PMir * QGDir i = TRAD_COMM; r = REG

VIGMir value of government’s expenditure on imported tradable commodity i, in region r, evaluated at market prices

- VIGMir = PIMir * QGMir i = TRAD_COMM; r = REG

VXMDirs value of exports of tradable commodity i from source r to destination s, evaluated at (exporter’s) market prices

- VXMDirs = PMir * QXSirs i = TRAD_COMM; r = REG; s= REG

VIMSirs value of imports of tradable commodity i from source r to destination s, evaluated at (importer’s) market prices

- VIMSirs = PMSir * QXSirs i = TRAD_COMM; r = REG; s = REG

VSTir value of sales of tradable commodity i to the international transport sector in region r, evaluated at market prices

- VSTir = PMir * QSTir i = MARG_COMM; r = REG

## Value flows evaluated at world prices

VXWDirs value of exports of tradable commodity i from source r to destination s, evaluated at world (fob) prices

- VXWDirs = PFOBirs * QXSirs i = TRAD_COMM; r = REG; s = REG

VIWSirs value of imports of tradable commodity i from source r to destination s, evaluated at world (cif) prices

- VIWSirs = PCIFirs * QXSirs i = TRAD_COMM; r = REG; s = REG

## Technology Parameters

ESUBVAj 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)

ESUBDi 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

ESUBMi 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

SUBPARir with i = TRAD_COMM; r = REG substitution parameter for tradable commodity i in the CDE minimum expenditure function of region r

INCPARir with i = TRAD_COMM; r = REG expansion parameter for tradable commodity i in the CDE minimum expenditure function of region r.

ALPHAir 1 - sub. parameter in the CDE minimum expenditure function

- ALPHAir = 1 - SUBPARir i = TRAD_COMM; r = REG

APEikr Allen partial elst.of sub between composite i and k in r

- APEikr = ALPHAir + ALPHAkr- SnCONSHRnr*ALPHAnr i = k= n = TRAD_COMM; r = REG

APEiir = 2.0*ALPHAir - SnCONSHRnr*ALPHAnr - ALPHAir / CONSHRir

EYir income elasticity of private household demand for i in r

- EYir = (1/Sn CONSHRnr*INCPARnr) * (INCPARir * (1.0 - ALPHAir) + SnCONSHRnr*INCPARnr*ALPHAnr) + (ALPHAir - SnCONSHRnr*ALPHAnr) i = n = TRAD_COMM; r = REG

EPikr uncompensated cross-price elasticity private household demand for i wrt k in r

- EPikr = (APEikr - EYir)*CONSHRkr i = k = TRAD_COMM; r = REG

## Mobility Parameter

ETRAEi 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)

RORFLEXr 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

VOAir value of non-saving commodity i output or supplied in region r evaluated at agents’ prices

VOAir = EVOAir i = ENDW_COMM; r = REG

VOAir = SjVFAjir i = PROD_COMM; j = DEMD_COMM; r = REG

VFAijr value of purchases of demanded commodity i by firms in sector j of regin r evaluated at agents’ prices

VFAijr = EVFAijr i = ENDW_COMM; j = PROD_COMM; r = REG

VFAijr = VDFAijr + VIFAijr i =TRAD_COMM; j = PROD_COMM; r = REG

VOMir value of non-saving commodity i output or supplied in region r evaluated at market prices

VOMir = SjVFMijr i = ENDW_COMM;j = PROD_COMM; r = REG

VOMir = VDMir + VSTir + SsVXMDirs i = MARG_COMM; r = REG; s = REG

VOMir = VDMir + SsVXMDirs i = NMRG_COMM; r = REG; s = REG

VOMir = VOAir i = CGDS_COMM; r = REG

VDMir value of domestic sales of tradable commodity i in region r evaluated at market prices

- VDMir = VDPMir + VDGMir + SjVDFMijr i = TRAD_COMM; j = PROD_COMM; r = REG

VIMir value of aggregate imports of tradable commodity i in region r evaluated at market prices

- VIMir = VIPMir + VIGMir + SjVIFMijr i = TRAD_COMM; j = PROD_COMM; r = REG

VPAir value of private household expenditure on tradable commodity i in region r evaluated at agents’ prices

- VPAir = VDPAir + VIPAir i = TRAD_COMM; r = REG

PRIVEXPr total consumption expenditure by private household in regin r

- PRIVEXPr = SiVPAir i = TRAD_COMM

VGAir value of government expenditure on tradable commodity i in region r evaluated at agents’ prices

- VGAir = VDGAir + VIGAir i = TRAD_COMM; r = REG

GOVEXPr total consumption expenditure by government in region r

- GOVEXPr = SiVGAir i = TRAD_COMM; r = REG

INCOMEr total expenditure equals net income in region r

- INCOMEr = PRIVEXPr + GOVEXPr + SAVEr r = REG

REGINVr gross investment in region r that equals value of output of “capital goods” sector

- REGINVr = SkVOAkr k = CGDS_COMM

NETINVr net investment in region r

- NETINVr = SkVOAkr - VDEPr k = CGDS_COMM

GLOBINV global net investment

- GLOBINV = SrNETINV = SrSAVEr r = REG

INVKERATIOr ratio of gross investment to end-of-period capital stock in region r

- INVKERATIOr = REGINVr / (VKBr + NETINVr) r = REG

GRNETRATIOr ratio of gross to net rate of return on capital in regin r (VOAcapital,r is gross return to capital)

- GRNETRATIOr = SkVOAkr / (SkVOAkr - VDEPr) with k = ENDWC_COMM; r = REG

GDPr gross domestic product in region r (trade is valued at worl prices)

- GDPr = SiVPAir + SiVGAir + SkVOAkr + SiSsVXWDirs+ SmVSTms - SiSsVIWSirs i = TRAD_COMM; k = CGDS_COMM; r = REG; s = REG

VT international margin suply

- VT = SiSrVSTir i = TRAD_COMM; r = REG

VXWir value of exports of tradable commodity i from source r evaluated at world (fob) prices

VXWir = SsVXWDirs+VSTir i = MARG_COMM; r = REG

VXWir = SsVXWDirs i = NMRG_COMM; r = REG

VXWREGIONr value of exports from source r evaluated at world (fob) prices

- VXWREGIONr = SiVXWir i = TRAD_COMM; r = REG

VXWCOMMODi value of exports of tradable commodity i evaluated at world (fob) prices

- VXWCOMMODi= SrVXWir i = TRAD_COMM; r = REG

VIWir value of imports of tradable commodity i into region r evaluated at world (cif) prices

VIWir= SsVIWSisr i = TRAD_COMM; r = REG; s = REG

VIWREGIONr value of imports into region r evaluated at world (cif) prices

VIWREGIONr = SiVIWir i = TRAD_COMM; r = REG

VIWCOMMODi value of imports of tradable commodity i evaluated at world (cif) prices

VIWCOMMODi= SrVIWir i = TRAD_COMM; r = REG

VXWLD value of worldwide commodity exports evaluated at world (fob) prices

VXWLD= SrVXWREGIONr r = REG

PW_PMir ratio of world (fob) to domestic market prices for tradable commodity i in region

PW_PMir = SsVXWDirs / SsVXMDirs i = TRAD_COMM; r = REG; s = REG

VOWir value of output of tradable commodity i in region r, evaluated at world (fob) prices

VOWir = VDMir * PW_PMir + SsVXWDirs + VSTir i = MARG_COMM; r = REG; s = REG

VOWir = VDMir * PW_PMir + SsVXWDirs i = NMRG_COMM; r = REG; s = REG

VWOWi value of world supply of tradable commodity i evaluated at world (fob) prices

VWOWi = SrVOWiri = TRAD_COMM; r = REG

VTMFSDmirs int’l margin usage, by margin, freight, source, and destination m = MARG_COMM;i = TRAD_COMM; r = REG; s = REG

VTFSDirs aggregate value of svces in the shipment of i from r to s

VTFSDirs = SmVTMFSDmirs In a balanced data base VIWSirs = VXWDirs + VTFSDirs i = TRAD_COMM; m = MARG_COMM; r = REG; s = REG

VTMPROVm international margin services provision

VTMPROVm = SrVSTmr m = MARG_COMM; r = REG

VTRPROVr international margin supply, by region

VTRPROVr = SmVSTmr m = MARG_COMM; r = REG

VTMUSEm international margin services usage, by type

VTMUSEm = SiSrSsVTMFSDmirs m = MARG_COMM; i = TRAD_COMM; r = s = REG In a balanced data base, VTMPROV = VTMUSE

VTMUSESHRmirs share of i,r,s usage in global demand for m

VTMUSESHRmirs = VTFSDirs / VT m = MARG_COMM; i = TRAD_COMM; r = s = REG if VTMUSEm <> 0.0 then VTMUSESHRmirs = VTMFSDmirs / VTMUSEm

VTSUPPSHRmr share of region r in global supply of margin m

VTSUPPSHRmr = VTRPROVr / VT if VTMPROVm <> 0.0 then VTSUPPSHRmr = VSTmr / VTMPROVm m = MARG_COMM; r = REG

VTUSE international margin services usage;

VTUSE=SmSiSrSsVTMFSDmirs m = MARG_COMM; i = TRAD_COMM; r = s = REG

VWOUi value of world output of i at user prices

VWOUi = Ss[(VPAis + VGAis) + SjVFAijs] s = REG; j = PROD_COMM

VENDWREGr value of primary factors, at mkt prices, by region

VENDWREGr = Si VOMir i = ENDOW_COMM; r = REG

VENDWWLD value of primary factors, at mkt prices, worldwide

VENDWWLD = Sr VENDWREGr r = REG

VPAEVir private household expend. on i in r valued at agent’s prices, for EV calculation

VPAEVir = qpevir i = TRAD_COMM, r = REG

VPAREGEVr private consumption expenditure in region r, for EV calculation

VPAREGEVr = SiVPAEVir i = TRAD_COMM, r = REG YGr regional government consumption expenditure, in region r r = REG

## Quantity Variables

QOir quantity of non-saving commodity i output or supplied in region r | i = NSAV_COMM r = REG

QOESijr quantity of sluggish endowment i supplied to sector j firm of region r | i = ENDWS_COMM; j = PROD_COMM; r = REG

QDSir quantity of domestic sales of tradable commodity i in region r | i = TRAD_COMM; r = REG

QXSirs quantity of exports of tradable commodity i from source r to destination s | i = TRAD_COMM; r = s = REG

QSTir quantity of sales of marginal commodity i to the international transport sector in region r | i = MARG_COMM; r = REG

QFEijr quantity of endowment i demanded by sector j firm in region r | i = ENDW_COMM; j = PROD_COMM; r = REG

QVAjr quantity index of land-labor-capital composite (value-added) in sector j firm in region r | j = PROD_COMM; r = REG

QFijr quantity of composite tradable commodity i demanded by sector j firm in region r | i = TRAD_COMM; j = PROD_COMM; r = REG

QFDijr quantity of domestic tradable i demanded by sector j firm in region r | i = TRAD_COMM; j = PROD_COMM; r = REG

QFMijr quantity of imported tradable i demanded by sector j firm in region r | i = TRAD_COMM; j = PROD_COMM; r = REG

QPir quantity of composite tradable i demanded by private household in region r | i = TRAD_COMM; r = REG

QPDir quantity of domestic tradable i demanded by private household in region r | i = TRAD_COMM; r = REG

QPMir quantity of imported tradable i demanded by private household in region r | i = TRAD_COMM; r = REG

QGir quantity of composite tradable commodity i demanded by government household in region r | i = TRAD_COMM; r = REG

QGDir quantity of domestic tradable commodity i demanded by government household in region r | i = TRAD_COMM; r = REG

QGMir quantity of imported tradable commodity i demanded by government household in region r | i = TRAD_COMM; r = REG

QIMir quantity of aggregate imports of tradable commodity i demanded by region r using market prices as weights | i = TRAD_COMM; r = REG

QIWir quantity of aggregate imports of tradable commodity i demanded by region r using cif prices as weights | i = TRAD_COMM; r = REG

QXWir quantity of aggregate exports of tradable commodity i supplied from region r using fob prices as weights | i = TRAD_COMM; r = REG

QIWREGr volume of merchandise imports demanded by region r | r = REG

QXWREGr volume of merchandise exports supplied by region r | r = REG

QIWCOMi volume of global merchandise imports of tradable commodity i | i = TRAD_COMM; r = REG

QXWCOMi volume of global merchandise exports of tradable commodity i | i = TRAD_COMM; r = REG

QXWWLD volume of world trade

QOWi quantity index for world supply of tradable commodity i | i = TRAD_COMM

EXPANDir Change in investment levels relative to endowment stock | i = ENDWC_COMM; r = REG

QOWUirquantity index for world supply of good i at user prices i = TRAD_COMM; r = REG

QTMFSDmirs international usage margin m on i from r to s m = MARG_COMM; i = TRAD_COMM; r = s = REG

QTMm global margin usage m = MARG_COMM

QCGDSr quantity of capital goods sector supplied in region r r = REG

QSAVEr quantity of savings demanded in region r r = REG

GLOBALCGDS quantity of global supply of capital for net investment

KSVCESr quantity of capital services in region r r = REG

KBr quantity of beginning-of-period capital stock in region r r = REG

KEr quantity of end-of-period capital stock in region r r = REG

QGDPr 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

POPr population in region r r = REG

COMPVALADir composition of value added for good i and region r i = TRAD_COMM; r = REG

## Price Variables

PMir market price of non-saving commodity i in region r i = NSAV_COMM; r = REG

PMESijr market price for sluggish endowment i supplied to firm j in region r i = ENDWS_COMM; j = PROD_COMM; r = REG

PSir supply price of non-saving commodity i in region r i = NSAV_COMM; r = REG

PFEijr demand price for endowment i by firms in sector j of region r i = ENDW_COMM; j = PROD_COMM; r = REG

PVAjr price of value-added in sector j j = PROD_COMM; r = REG

PFijr demand price for composite tradable i by firms in sector j of region r i = TRAD_COMM; j = PROD_COMM; r = REG

PFDijr demand price for domestic tradable i by firms in sector j of region r i = TRAD_COMM; j = PROD_COMM; r = REG

PFMijr demand price for imported tradable i by firms in sector j of region r i = TRAD_COMM; j = PROD_COMM; r = REG

PPir private household’s demand price for composite tradable i in region r i = TRAD_COMM; r = REG

PPDir private household’s demand price for domestic tradable i in region r i = TRAD_COMM; r = REG

PPMir private household’s demand price for imported tradable i in region r i = TRAD_COMM; r = REG

PGir government household’s demand price for composite tradable i in region r i = TRAD_COMM; r = REG

PGDir government household’s demand price for domestic tradable i in region r i = TRAD_COMM; r = REG

PGMir government household’s demand price for imported tradable i in region r i = TRAD_COMM; r = REG

PSAVEr price of savings in region r r = REG

PCGDSr price of investment good in region r - equals PS(cgds,r) r = REG

PGDPr price index for GDP in region r r = REG

PPRIVr price index for private household expenditure in region r r = REG

PGOVr price index for government household expenditure in region r r = REG

PFOBirs 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

PCIFirs world cif price of tradable commodity i imported from source r to destination s ) after including transport margins) i = TRAD_COMM; r = s = REG

PMSirs market price by source of tradable commodity i imported from source r to destination s i = TRAD_COMM; r = s = REG

PIMir market price of aggregate imports of tradable commodity i in region r i = TRAD_COMM; r = REG

PIWir world price of aggregate imports of tradable commodity i in region r i = TRAD_COMM; r = REG

PXWir price index for aggregate exports of tradable commodity i from region r i = TRAD_COMM; r = REG

PIWREGr price index of merchandise imports in region r r = REG

PXWREGr price index of merchandise exports from region r r = REG

PIWCOMi price index of global merchandise imports of tradable commodity i i = TRAD_COMM

PXWCOMi price index of global merchandise exports of tradable commodity i i = TRAD_COMM

PXWWLD price index of world trade

PRir ratio of domestic market price to market price of imports for tradable commodity i in region r i = TRAD_COMM; r = REG

PWi world price index for total supply of tradable commodity i in region r i = TRAD_COMM

PSWr price index received for tradable commodities produced in region r including sales of net investment to the global bank r = REG

PDWr price index paid for tradable commodities used in region r including purchases of savings from the global bank r = REG

TOTr terms of trade for region r r = REG

PTm price of margin services supplied m = MARG_COMM

PCGDSWLD world average price of capital goods (net investment weights)

PWUi world price index for total good i supplies at user prices i = TRAD_COMM

PTRANSirs cost index for international transport of i from r to s i = TRAD_COMM; r = s = REG

RENTALr rental rate on capital stock in regin r - equals PS(CGDS,r) r = REG

RORCr current net rate of return on capital stock in region r r = REG

ROREr expected net rate of return on capital stock in region r r = REG

RORG global net rate of return on capital stock

Pr price index for disposition of income by regional household

PFACTREALir ratio of return to primary factor i to cpi in r i = ENDOW_COMM; r = REG

PFACTORr market price index of primary factors, by region

PFACTWLDworld price index of primary factors

## Technical Change Variables

AOir output augmenting technical change in sector j of region r | j = PROD_COMM; r = REG

AFEijr primary factor i augmenting technical change in sector j of region r | i = ENDW_COMM; j = PROD_COMM; r = REG

AFijr intermediate input i augmenting technical change in sector j of region r | i = TRAD_COMM; j = PROD_COMM; r = REG

AVAjr value-added augmenting technical change in sector j of region r | j = PROD_COMM; r = REG

AMSirs import i from region r augmenting tech change in region s | i = TRAD_COMM, r = s = REG

AOSECj output tech change of sector j, worldwide | j = PROD_COMM

AOREGr output tech change in region r | r = REG

AOALLjr output augmenting technical change in sector j of r | j = PROD_COMM; r = REG

ESUBTj elasticity of substitution among composite intermediate inputs in production | j = PROD_COMM

AFCOMi intermediate tech change of input i, worldwide | i = TRAD_COMM

AFSECj intermediate tech change of sector j, worldwide | j = PROD_COMM

AFREGr intermediate tech change in region r | r = REG

AFALLijr intermediate input i augmenting tech change by j in r | i = TRAD_COMM,j = PROD_COMM; r = REG

AFECOMi factor input tech change of input i, worldwide | i = ENDW_COMM

AFESECj factor input tech change of sector j, worldwide | j = PROD_COMM

AFEREGr factor input tech change in region r | r = REG

AFEALLijr primary factor i augmenting tech change sector j in r | i = ENDW_COMM; j = PROD_COMM; r = REG

AMSirs reduction in effective price associated with delivery of i from r to s | i = TRAD_COMM; r = REG; s = REG

ATMFSDmirs tech change in m’s shipping of i from region r to s | m = MARG_COMM; i = TRAD_COMM; r = s = REG

ATMm tech change in mode m, worldwide; | m = TRAD_COMM

ATFi tech change shipping of i, worldwide | i = TRAD_COMM

ATSr tech change shipping from region r | r = REG

ATDs tech change shipping to s | s = REG

ATALLmirs tech change in m’s shipping of i from region r to s | m = MARG_COMM; i = TRAD_COMM; r = REG; s = REG

AUr input-neutral shift in utility function | r = REG

## Policy Variables

TOir power of the tax on output (or income) of non-savings commodity i in region r | i = NSAV_COMM; r = REG

TFijr power of the tax on endowment commodity i demanded by sector j of regin r | i = ENDW_COMM; j = PROD_COMM; r = REG

TFDijr power of the tax on domestic tradable commodity i demanded by sector j of region r | i = TRAD_COMM; j = PROD_COMM; r = REG

TFMijr power of the tax on imported tradable commodity i demanded by sector j of region r | i = TRAD_COMM; j = PROD_COMM; r = REG

TPDir power of the tax on domestic tradable commodity i purchased by private household in region r | i = TRAD_COMM; r = REG

TPMir power of the tax on imported tradable commodity i purchased by private household in region r | i = TRAD_COMM; r = REG

TGDir power of the tax on domestic tradable commodity i purchased by government household in region r | i = TRAD_COMM; r = REG

TGMir power of the tax on imported tradable commodity i purchased by government household in region r | i = TRAD_COMM; r = REG

TXSirs 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

TMSirs 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

TXir power of the variable export tax on exports of tradable commodity from region r - destination generic | i = TRAD_COMM; r = REG

TMir power of the variable import tax (levy) on imports of tradable commodity i in region s - source generic | i = TRAD_COMM; r = REG

TPr region-wide shock to tax on purchases by private household in region r | r = REG

ATPMir actual tax on imported traded commodity i purchased by private households in region r | i = TRAD_COMM; r = REG

ATPDir actual tax on domestic traded commodity i purchased by private households in region r | i = TRAD_COMM; r = REG

DGTAXir tax on government consumption of domestic good i in region r | r = REG

IGTAXir tax on government consumption of imported good i in region r | r = REG

TGCr government consumption tax payments in r

TGCr = SiDGTAXir + IGTAXir i = TRAD_COMM; r = REG

DPTAXir tax on private consumption of domestic good i in region r

DPTAXir = VDPAir - VDPMir i = TRAD_COMM; r = REG

IPTAXir tax on private consumption of imported good i in region r

IPTAXir = VIPAir - VIPMir i = TRAD_COMM; r = REG

TPCr private consumption tax payments in r

TPCr = SiDPTAXir + IPTAXir i = TRAD_COMM; r = REG

DFTAXijr tax on use of domestic intermediate good i by j in r

DFTAXijr = VDFAijr - VDFMijr i = TRAD_COMM; j = PROD_COMM; r = REG

IFTAXijr tax on use of imported intermediate good i by j in r

IFTAXijr = VIFAijr - VIFMijr i = TRAD_COMM; j = PROD_COMM; r = REG

TIUr firms’ tax payments on intermediate goods usage in r

TIUr = SjSi(DFTAXijr + IFTAXijr) i = TRAD_COMM; j = PROD_COMM; r = REG

ETAXijr tax on use of endowment good i by industry j in region r

ETAXijr = VFAijr - VFMijr i = ENDW_COMM; j = PROD_COMM; r = REG

TFUr firms’ tax payments on primary factor usage in r

TFUr = SiSjETAXijr i = ENDW_COMM; j = PROD_COMM; r = REG

PTAXir output tax on good i in region r

PTAXir = VOMir - VOAir i = NSAV_COMM; r = REG

TOUTr production tax payments in r

TOUTr = SiPTAXir i = PROD_COMM; r = REG

XTAXDirs tax on exports of good i from source r to destination s

XTAXDirs = VXWDirs - VXMDirs i = TRAD_COMM; r = s = REG

TEXr export tax payments in r

TEXr = SiSsXTAXDirs i = TRAD_COMM; r = s = REG

MTAXirs tax on imports of good i from source r in destination s

MTAXirs = VIMSirs - VIWSirs i = TRAD_COMM; r = s = REG

TIMr import tax payments in r

TIMr = SiSsMTAXisr i = TRAD_COMM; r = s = REG

TOTTAXr Total tax receipts in r

TOTTAXr = TPCr + TGCr + TIUr + TFUr + TOUTr + TEXr + TIMr + TINCr r = REG

TGCRr change in ratio of government consumption tax to INCOME in region r r = REG

TPCRr change in ratio of private consumption tax to INCOME in region r r = REG

TIURr change in ratio of tax on intermediate usage to INCOME in region r r = REG

TFURr change in ratio of tax on primary factor usage to INCOME in region r r = REG

TOUTRr change in ratio of output tax to INCOME in region r nbsp; r = REG

TEXPRr change in ratio of export tax to INCOME in region r r = REG

TIMPRr change in ratio of import tax to INCOME in region r r = REG

TINCr income tax payments in r

TINCr = SiPTAXir i = ENDOW_COMM; r = REG

TINCRr change in ratio of income tax to INCOME in region r r = REG

DTAXRr change in ratio of taxes to INCOME in r r = REG

## Regional Household Preference Parameters and Shifters

DPARPRIVr private consumption distribution parameter

DPARPRIVr = UELASPRIVr*XSHRPRIVr/UTILELASr r = REG

DPARGOVr government consumption distribution parameter

DPARGOVr = XSHRGOVr/UTILELASr r = REG

DPARSAVEr saving distribution parameter

DPARSAVEr = XSHRSAVEr/UTILELASr r = REG

DPARSUMr sum of distribution parameters r = REG

dpavr change in average distribution parameter r = REG

dpsumr change in sum of the distribution parameters r = REG

dpprivr change in private consumption distribution parameter r = REG

dpgovr change in government consumption distribution parameter r = REG

dpsaver change in saving distribution parameter r = REG

## Slack Variables

profitslackjc slack variable in the ZEROPROFITS equation (this is exogenous as long as output level, QO(j), is determined endogenously) | j = PROD_COMM; r = REG

cgdslackr 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

endwslackir 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

tradslackir 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

incomeslackr slack variable in the INCOME equation (this is exogenous as long as income, Y, is determined endogenously) | r = REG

psaveslackr 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).

incomeslackr slack variable in the expression for regional income | r = REG

## Value and Income Variables

vxwfobir percentage change in value of exports of tradable commodity i from source region r using fob weights (is identical to the linearized form of VXWir) | i = TRAD_COMM; r = REG

vxwregr percentage change in value of merchandise exports from region r using fob weights (is identical to the linearized form of VXWREGIONr) | r = REG

vxwcomi percentage change in value of global merchandise exports of tradable commodity i using fob weights (is identical to the linearized form of VXWCOMMODi) | i = TRAD_COMM

viwcifir percentage change in value of imports of tradable commodity i into region r using fob weights (is identical to the linearized form of VIWir) | i = TRAD_COMM; r = REG

viwregr percentage change in value of merchandise imports into region r using cif weights (is identical to the linearized form of VIWREGIONir) | r = REG

viwcomi percentage change in value of global merchandise imports of tradable commodity i using fob weights (is identical to the linearized form of VIWCOMMODi) | i = TRAD_COMM

vxwwld percentage change in value of worlwide commodity exports using fob weights (is identical to the linearized form of VXWLD)

valuewi percentage change in value of global supply of tradable commodity i using fob weights (is identical to the linearized form of VWOWi) | i = TRAD_COMM

valuewui value of world supply of good i at user prices | i = TRAD_COMM

vgdpr percentage change in value of GDP in region r (is identical to the linearized form of GDPr) | r = REG

yr percentage change in regional household income (is identical to the linearized form of INCOME) | r = REG

ypr percentage change in private household expenditure (is identical to the linearized form of PRIVEXP). | r = REG

FYr primary factor income in r net of depreciation

FYr = SiVOMir - VDEPr | i = ENDW_COMM; r = REG

fincomer pc change in factor income variable in r net of depreciation r = REG

## Utility Variables

Ur per capita utility from aggregate household expenditure in region r r = REG

UPr per capita utility from private household expenditure in region r r = REG

UGr aggregate utility from government household expenditure in region r r = REG

UTILELASr elasticity of cost of utility wrt utility

UTILELASr = (UELASPRIVr*XSHRPRIVr + XSHRGOVr + XSHRSAVEr)/DPARSUMr r = REG

uelasr pc change in elasticity of cost of utility wrt utility r = REG

ueprivr pc change in utility elasticity of private cons expenditure r = REG

uelasevr pc change in elasticity of cost of utility wrt utility, for EV calculation r = REG

ueprivevr pc change in utility elasticity of private cons expenditure, for EV calculation r = REG

## Welfare Variables

EVr 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)

ugevr per capita utility from gov’t expend., for EV calculation r = REG

upevr per capita utility from private expend., for EV calculation r = REG

qsaveevr total quantity of savings demanded, for EV calculation r = REG

ypevr private consumption expenditure, in region r, for EV calculation r = REG

ygevr government consumption expenditure, in region r, for EV calculation r = REG

qpevir private household demand for commodity i in region r, for EV calculation i = TRAD_COMM, r = REG

yevr regional household income, in region r, for EV calculation

ysaveevr NET savings expenditure, for EV calculation

dpavevr average distribution parameter shift, for EV calculation r = REG

## Trade Balance Variables

DTBALr change in trade balance of region r , in US$ million (positive figure indicates increases in exports exceeds increases in imports) | r = REG

DTBALiir 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