List of Parameters for GRAS
(GRAS version 1.1.3e, 2/27/2008)

※The column of GAMS is the name in Nordhaus's GAMS Program.
The column of GRAS shows the internal parameter names of GRAS.

GAMS
GRAS
Default
Comments
Model
T tt 60 Time periods
B_ELASMU alpha 2 Elasticity of marginal utility of consumption
B_PRSTP rho 0.015 Initial rate of social time preference per year
POP0 L0 6514 2005 world population millions
GPOP0 gL0 0.35 Growth rate of population per decade
POPASYM popasym 8600 Asymptotic population
A0 tfactor0 0.02722 Initial level of total factor productivity
GA0 gA0 0.092 Initial growth rate for technology per decade
DELA deltaA 0.001 Decline rate of technol change per decade
DK deltaK 0.1 Depreciation rate on capital per year
GAMA eta 0.3 Capital elasticity in production function
Q0  -- 61.1 2005 world gross output trill 2005 US dollars
K0 K0 137 2005 value capital trill 2005 US dollars
SIG0 sigma0 0.13418 CO2-equivalent emissions-GNP ratio 2005
GSIGMA gsigma0 -0.073 Initial growth of sigma per decade
DSIG dsig 0.003 Decline rate of decarbonization per decade
DSIG2 dsig2 0 Quadratic term in decarbonization
Carbon circulation/Global temperature
ELAND0 eland0 11 Carbon emissions from land 2005(GtC per decade)
MAT2000 mat2000 808.9 Concentration in atmosphere 2005 (GtC)
MU2000 mu2000 1255 Concentration in upper strata 2005 (GtC)
ML2000 ml2000 18365 Concentration in lower strata 2005 (GtC)
b11 b11   Carbon cycle transition matrix
Internally given except for b12,b23
b12 b12 0.189288
b21 b21  
b22 b22  
b23 b23 0.05
b32 b32  
b33 b33  
T2XCO2 t2xco2 3 Equilibrium temp impact of CO2 doubling oC
FEX0 fex0 -0.06 Estimate of 2000 forcings of non-CO2 GHG
FEX1 fex1 0.3 Estimate of 2100 forcings of non-CO2 GHG
TOCEAN0 TL0 0.0068 2000 lower strat. temp change (C) from 1900
TATM0 T0 0.7307 2000 atmospheric temp change (C)from 1900
C1 cr1 0.22 Climate-equation coefficient for upper level
C3 cr3 0.3 Transfer coeffic upper to lower stratum
C4 cr4 0.05 Transfer coeffic for lower level
FCO22X fco22x 3.8 Estimated forcings of equilibrium co2 doubling
A1 aa1 0 Damage intercept
A2 aa2 0.0028388 Damage quadratic term
A3 aa3 2 Damage exponent
EXPCOST2 expcost2 2.8 Exponent of control cost function
PBACK pback 1.17 Cost of backstop 2005 000$ per tC 2005
BACKRAT backrat 2 Ratio initial to final backstop cost
GBACK gback 0.05 Initial cost decline backstop pc per decade
LIMMIU UPMIU[T] 1 Upper limit on control rate
PARTFRACT1 partfract1 1 Fraction of emissions under control regime 2005
PARTFRACT2 partfract2 1 Fraction of emissions under control regime 2015
PARTFRACT21 partfract21 1 Fraction of emissions under control regime 2205
DPARTFRACT dpartfract 0 Decline rate of participation
FOSSLIM fosslim 6000 Maximum cumulative extraction fossil fuels
scale1 scale1 194 Scaling coefficient in the objective function
scale2 scale2 381800 Scaling coefficient in the objective function
GRAS original parameters
  modelname   model name
  LOINV 10 Lower limit of investment
  LOCONS 20 Lower limit of consumption
  LOEMIT 0 Lower limit of CO2 emission
  TRANSK 0.02 Transversality condition
  initmiu 0.05 Initial Value of CO2 reduction rate
  logutil 0 If this value is 1, utility function has logarthsmic form
  apco2lim 0 if this value is 1, CO2 limitation is applied.
  aptmplim 0 If this value is 1, temperature limitation is applied.
  fixmiu 1 Periods for fixing the reduction rate.
Time series parameters
  RMIU[T] 0.005 Initial values of reduction rate
  UPMIU[T} 1 Upper limit of reduction rate
  LOMIU[T] 0.01 Lower limit of reduction rate
  CO2LIM[T]
596.4X4.0
Upper limit of CO2emission
  TMPLIM[T] 20 Upper limit of temperature increase
Primary optimization parameters
  rmepsi 1.00E-04 Main loop convergence
  rmiter 5000 Main loop max iteration
  epsilon 1.00E-08 Quasi Newton loop convergence
  diffmethod 0 Method of Differentiation, 0 by Hand, 1 Numerical
  pdiff 1.00E-07 Width of partial differentiation
  maxiter 100000 Max iteration of quasi Newton loop
  gamma 100 Initial penalty value for constraint
Linear optimization parameters
  maxlsiter 1000 Max iteration of linear optimization
  penamul 10 Multiplier of the above penalty
  penabeta 0.25 Coefficient for penalty
  initmu 10 Initial values of lagrange multiplier
  lsmethod 0 1:Armijo method, 0:Wolfe method
  xi 0.3 Inclination judge in Armijo
  tau 0.5 Multiplier in Armijo
  armepsi 1.00E-08 Convergence in Armijo
  wlfinc 2 Multiplier in Wolfe
  wlfm1 0.3 Coefficient 1 in Wolfe
  wlfm2 0.9 Coefficient 2 in Wolfe
  lsepsi 1.00E-10 Distance limit in Wolfe
  wlftheta 0.5 New location coefficient in Wolfe