Climateeconomy model scenario runs and sensitivity analysis using DICE2016
Data files
Oct 04, 2023 version files 473.23 KB

DICE_BASELINE_high_time_pref.xlsx

DICE_BASELINE_low_time_pref.xlsx

DICE_BASELINE_run.xlsx

DICE_OPTIMAL_high_damage.xlsx

DICE_OPTIMAL_high_time_pref.xlsx

DICE_OPTIMAL_low_time_pref.xlsx

DICE_OPTIMAL_run.xlsx

README.md
Abstract
This paper assesses the prospects for climate stabilization from both positive and normative economic perspectives, and with an eye to the conditions necessary for collective action across the three domains: domestic, international, and intergenerational. While it is wellestablished that international freeriding and transaction costs pose major impediments to successful environmental agreements, this analysis identifies the intergenerational domain as the source of intractability due to long delays between enduring mitigation costs and enjoying their eventual climate benefits. This lag causes the net benefits for medianaged voters’ to be negative over their expected remaining lifespans. Drawing on estimates from several Integrated Assessment Models of the benefits and costs of climate stabilization actions, the analysis concludes that a program of domestic and international climate actions will be hopelessly stymied by the failure of the actions to pass individual and collective rationality tests. However, the dire implications of this conclusion leaves the door open to the possibility that some change in circumstances could undercut this conclusion. The assignment of rights, in particular, has that potential. Indeed, these circumstances echo the canonical insights from Ron Coase’s observation in The Problem of Social Cost (1960) that the arrangement of rights can have large effects on welfare when transaction costs for an externality are high. Current climate rights amount to a de facto open access right to pollute the atmosphere. Were a right to a stable climate for both for current and future generations recognized, added weight or leverage would apply in support of climate stabilization policies and international agreements. These legal changes could represent a counterweight to offset the inadequacy of support from the current selfinterested generation. Indeed, some recent climate litigation argues that many nations’ constitutions already encompass an affirmative right to a stable climate, a proposition that could represent an inimitable means to break the climate impasse.
README: Climateeconomy model scenario runs and sensitivity analysis using DICE2016
The dataset files included here include the model runs of the DICE climateeconomy models developed by William Nordhaus and used in this paper
to simulate various trajectories of climate change and economic outcomes. The tables represent summaries of the outputs for the specific model run.
Included are the following model runs: i)baseline scenario with no climate policy intervention; ii) an optimal climate policy scenario; iii) and
sensitivity analyses for a highdamage scenario; and iv) two version of the model with a lower time preference and a higher time preference.
The identificaion of these scenarios is indicated in the file name.
Description of the Data and file structure
The outputs from these models were combined with demographic data to evaluate the incidence of net benefits for current medianaged voters
in different countries, longterm net benefits, and net benefits to subsequent generations.
Below each set of yeartoyear output values is a summary of the model results and comparison of welfare measures for the baseline run or
in comparison to the baseline run.
Cells containing "n/a" occur in columns with no corresponding annual values (e.g., variable for which only a summation total is
displayed in the first numerical column).
Additional documentation of these models can be found at https://williamnordhaus.com/dicericemodels.
The variables included are for DICEModel parameters as documented by Nordhaus for the GAMS version as follows:
DICE MODEL 2016 CODE  GAMS
$ontext
This is the beta version of DICE2016R. The major changes are outlined in Nordhaus,
"Revisiting the social cost of carbon: Estimates from the DICE2016R model,"
September 30, 2016," available from the author.
Version is DICE2016R091916ap.gms
$offtext
$title DICE2016R September 2016 (DICE2016R091216a.gms)
set t Time periods (5 years per period) /1*100/
PARAMETERS
** Availability of fossil fuels
fosslim Maximum cumulative extraction fossil fuels (GtC) /6000/
**Time Step
tstep Years per Period /5/
** If optimal control
ifopt Indicator where optimized is 1 and base is 0 /1/
** Preferences
elasmu Elasticity of marginal utility of consumption /1.45 /
prstp Initial rate of social time preference per year /.015 /
** Population and technology
gama Capital elasticity in production function /.300 /
pop0 Initial world population 2015 (millions) /7403 /
popadj Growth rate to calibrate to 2050 pop projection /0.134 /
popasym Asymptotic population (millions) /11500 /
dk Depreciation rate on capital (per year) /.100 /
q0 Initial world gross output 2015 (trill 2010 USD) /105.5 /
k0 Initial capital value 2015 (trill 2010 USD) /223 /
a0 Initial level of total factor productivity /5.115 /
ga0 Initial growth rate for TFP per 5 years /0.076 /
dela Decline rate of TFP per 5 years /0.005 /
** Emissions parameters
gsigma1 Initial growth of sigma (per year) /0.0152 /
dsig Decline rate of decarbonization (per period) /0.001 /
eland0 Carbon emissions from land 2015 (GtCO2 per year) / 2.6 /
deland Decline rate of land emissions (per period) / .115 /
e0 Industrial emissions 2015 (GtCO2 per year) /35.85 /
miu0 Initial emissions control rate for base case 2015 /.03 /
** Carbon cycle
* Initial Conditions
mat0 Initial Concentration in atmosphere 2015 (GtC) /851 /
mu0 Initial Concentration in upper strata 2015 (GtC) /460 /
ml0 Initial Concentration in lower strata 2015 (GtC) /1740 /
mateq Equilibrium concentration atmosphere (GtC) /588 /
mueq Equilibrium concentration in upper strata (GtC) /360 /
mleq Equilibrium concentration in lower strata (GtC) /1720 /
* Flow paramaters
b12 Carbon cycle transition matrix /.12 /
b23 Carbon cycle transition matrix /0.007 /
* These are for declaration and are defined later
b11 Carbon cycle transition matrix
b21 Carbon cycle transition matrix
b22 Carbon cycle transition matrix
b32 Carbon cycle transition matrix
b33 Carbon cycle transition matrix
sig0 Carbon intensity 2010 (kgCO2 per output 2005 USD 2010)
** Climate model parameters
t2xco2 Equilibrium temp impact(oC per doubling CO2) / 3.1 /
fex0 2015 forcings of nonCO2 GHG (Wm2) / 0.5 /
fex1 2100 forcings of nonCO2 GHG (Wm2) / 1.0 /
tocean0 Initial lower stratum temp change (C from 1900) /.0068 /
tatm0 Initial atmospheric temp change (C from 1900) /0.85 /
c1 Climate equation coefficient for upper level /0.1005 /
c3 Transfer coefficient upper to lower stratum /0.088 /
c4 Transfer coefficient for lower level /0.025 /
fco22x Forcings of equilibrium CO2 doubling (Wm2) /3.6813 /
** Climate damage parameters
a10 Initial damage intercept /0 /
a20 Initial damage quadratic term
a1 Damage intercept /0 /
a2 Damage quadratic term /0.00236 /
a3 Damage exponent <> /4.00 /
** Abatement cost
expcost2 Exponent of control cost function / 2.6 /
pback Cost of backstop 2010$ per tCO2 2015 / 550 /
gback Initial cost decline backstop cost per period / .025 /
limmiu Upper limit on control rate after 2150 / 1.2 /
tnopol Period before which no emissions controls base / 45 /
cprice0 Initial base carbon price (2010$ per tCO2) / 2 /
gcprice Growth rate of base carbon price per year /.02 /
** Scaling and inessential parameters
* Note that these are unnecessary for the calculations
* They ensure that MU of first period's consumption =1 and PV cons = PV utilty
scale1 Multiplicative scaling coefficient /0.0302455265681763 /
scale2 Additive scaling coefficient /10993.704/ ;
* Program control variables
sets tfirst(t), tlast(t), tearly(t), tlate(t);
PARAMETERS
l(t) Level of population and labor
al(t) Level of total factor productivity
sigma(t) CO2equivalentemissions output ratio
rr(t) Average utility social discount rate
ga(t) Growth rate of productivity from
forcoth(t) Exogenous forcing for other greenhouse gases
gl(t) Growth rate of labor
gcost1 Growth of cost factor
gsig(t) Change in sigma (cumulative improvement of energy efficiency)
etree(t) Emissions from deforestation
cumetree(t) Cumulative from land
cost1(t) Adjusted cost for backstop
lam Climate model parameter
gfacpop(t) Growth factor population
pbacktime(t) Backstop price
optlrsav Optimal longrun savings rate used for transversality
scc(t) Social cost of carbon
cpricebase(t) Carbon price in base case
photel(t) Carbon Price under no damages (Hotelling rent condition)
ppm(t) Atmospheric concentrations parts per million
atfrac(t) Atmospheric share since 1850
atfrac2010(t) Atmospheric share since 2010 ;
* Program control definitions
tfirst(t) = yes$(t.val eq 1);
tlast(t) = yes$(t.val eq card(t));
* Parameters for longrun consistency of carbon cycle
b11 = 1  b12;
b21 = b12*MATEQ/MUEQ;
b22 = 1  b21  b23;
b32 = b23*mueq/mleq;
b33 = 1  b32 ;
* Further definitions of parameters
a20 = a2;
sig0 = e0/(q0*(1miu0));
lam = fco22x/ t2xco2;
l("1") = pop0;
loop(t, l(t+1)=l(t););
loop(t, l(t+1)=l(t)*(popasym/L(t))**popadj ;);
ga(t)=ga0*exp(dela*5*((t.val1)));
al("1") = a0; loop(t, al(t+1)=al(t)/((1ga(t))););
gsig("1")=gsigma1; loop(t,gsig(t+1)=gsig(t)*((1+dsig)**tstep) ;);
sigma("1")=sig0; loop(t,sigma(t+1)=(sigma(t)*exp(gsig(t)*tstep)););
pbacktime(t)=pback*(1gback)**(t.val1);
cost1(t) = pbacktime(t)*sigma(t)/expcost2/1000;
etree(t) = eland0*(1deland)**(t.val1);
cumetree("1")= 100; loop(t,cumetree(t+1)=cumetree(t)+etree(t)*(5/3.666););
rr(t) = 1/((1+prstp)**(tstep*(t.val1)));
forcoth(t) = fex0+ (1/17)*(fex1fex0)*(t.val1)$(t.val lt 18)+ (fex1fex0)$(t.val ge 18);
optlrsav = (dk + .004)/(dk + .004*elasmu + prstp)*gama;
*Base Case Carbon Price
cpricebase(t)= cprice0*(1+gcprice)**(5*(t.val1));
VARIABLES
MIU(t) Emission control rate GHGs
FORC(t) Increase in radiative forcing (watts per m2 from 1900)
TATM(t) Increase temperature of atmosphere (degrees C from 1900)
TOCEAN(t) Increase temperatureof lower oceans (degrees C from 1900)
MAT(t) Carbon concentration increase in atmosphere (GtC from 1750)
MU(t) Carbon concentration increase in shallow oceans (GtC from 1750)
ML(t) Carbon concentration increase in lower oceans (GtC from 1750)
E(t) Total CO2 emissions (GtCO2 per year)
EIND(t) Industrial emissions (GtCO2 per year)
C(t) Consumption (trillions 2005 US dollars per year)
K(t) Capital stock (trillions 2005 US dollars)
CPC(t) Per capita consumption (thousands 2005 USD per year)
I(t) Investment (trillions 2005 USD per year)
S(t) Gross savings rate as fraction of gross world product
RI(t) Real interest rate (per annum)
Y(t) Gross world product net of abatement and damages (trillions 2005 USD per year)
YGROSS(t) Gross world product GROSS of abatement and damages (trillions 2005 USD per year)
YNET(t) Output net of damages equation (trillions 2005 USD per year)
DAMAGES(t) Damages (trillions 2005 USD per year)
DAMFRAC(t) Damages as fraction of gross output
ABATECOST(t) Cost of emissions reductions (trillions 2005 USD per year)
MCABATE(t) Marginal cost of abatement (2005$ per ton CO2)
CCA(t) Cumulative industrial carbon emissions (GTC)
CCATOT(t) Total carbon emissions (GtC)
PERIODU(t) One period utility function
CPRICE(t) Carbon price (2005$ per ton of CO2)
CEMUTOTPER(t) Period utility
UTILITY Welfare function;
NONNEGATIVE VARIABLES MIU, TATM, MAT, MU, ML, Y, YGROSS, C, K, I;
EQUATIONS
*Emissions and Damages
EEQ(t) Emissions equation
EINDEQ(t) Industrial emissions
CCACCA(t) Cumulative industrial carbon emissions
CCATOTEQ(t) Cumulative total carbon emissions
FORCE(t) Radiative forcing equation
DAMFRACEQ(t) Equation for damage fraction
DAMEQ(t) Damage equation
ABATEEQ(t) Cost of emissions reductions equation
MCABATEEQ(t) Equation for MC abatement
CARBPRICEEQ(t) Carbon price equation from abatement
*Climate and carbon cycle
MMAT(t) Atmospheric concentration equation
MMU(t) Shallow ocean concentration
MML(t) Lower ocean concentration
TATMEQ(t) Temperatureclimate equation for atmosphere
TOCEANEQ(t) Temperatureclimate equation for lower oceans
*Economic variables
YGROSSEQ(t) Output gross equation
YNETEQ(t) Output net of damages equation
YY(t) Output net equation
CC(t) Consumption equation
CPCE(t) Per capita consumption definition
SEQ(t) Savings rate equation
KK(t) Capital balance equation
RIEQ(t) Interest rate equation
* Utility
CEMUTOTPEREQ(t) Period utility
PERIODUEQ(t) Instantaneous utility function equation
UTIL Objective function ;
** Equations of the model
*Emissions and Damages
eeq(t).. E(t) =E= EIND(t) + etree(t);
eindeq(t).. EIND(t) =E= sigma(t) * YGROSS(t) * (1(MIU(t)));
ccacca(t+1).. CCA(t+1) =E= CCA(t)+ EIND(t)*5/3.666;
ccatoteq(t).. CCATOT(t) =E= CCA(t)+cumetree(t);
force(t).. FORC(t) =E= fco22x * ((log((MAT(t)/588.000))/log(2))) + forcoth(t);
damfraceq(t) .. DAMFRAC(t) =E= (a1*TATM(t))+(a2*TATM(t)**a3) ;
dameq(t).. DAMAGES(t) =E= YGROSS(t) * DAMFRAC(t);
abateeq(t).. ABATECOST(t) =E= YGROSS(t) * cost1(t) * (MIU(t)**expcost2);
mcabateeq(t).. MCABATE(t) =E= pbacktime(t) * MIU(t)**(expcost21);
carbpriceeq(t).. CPRICE(t) =E= pbacktime(t) * (MIU(t))**(expcost21);
*Climate and carbon cycle
mmat(t+1).. MAT(t+1) =E= MAT(t)*b11 + MU(t)*b21 + (E(t)*(5/3.666));
mml(t+1).. ML(t+1) =E= ML(t)*b33 + MU(t)*b23;
mmu(t+1).. MU(t+1) =E= MAT(t)*b12 + MU(t)*b22 + ML(t)*b32;
tatmeq(t+1).. TATM(t+1) =E= TATM(t) + c1 * ((FORC(t+1)(fco22x/t2xco2)*TATM(t))(c3*(TATM(t)TOCEAN(t))));
toceaneq(t+1).. TOCEAN(t+1) =E= TOCEAN(t) + c4*(TATM(t)TOCEAN(t));
*Economic variables
ygrosseq(t).. YGROSS(t) =E= (al(t)*(L(t)/1000)**(1GAMA))*(K(t)**GAMA);
yneteq(t).. YNET(t) =E= YGROSS(t)*(1damfrac(t));
yy(t).. Y(t) =E= YNET(t)  ABATECOST(t);
cc(t).. C(t) =E= Y(t)  I(t);
cpce(t).. CPC(t) =E= 1000 * C(t) / L(t);
seq(t).. I(t) =E= S(t) * Y(t);
kk(t+1).. K(t+1) =L= (1dk)**tstep * K(t) + tstep * I(t);
rieq(t+1).. RI(t) =E= (1+prstp) * (CPC(t+1)/CPC(t))**(elasmu/tstep)  1;
*Utility
cemutotpereq(t).. CEMUTOTPER(t) =E= PERIODU(t) * L(t) * rr(t);
periodueq(t).. PERIODU(t) =E= ((C(T)*1000/L(T))**(1elasmu)1)/(1elasmu)1;
util.. UTILITY =E= tstep * scale1 * sum(t, CEMUTOTPER(t)) + scale2 ;
*Resource limit
CCA.up(t) = fosslim;
* Control rate limits
MIU.up(t) = limmiu;
MIU.up(t)$(t.val<30) = 1;
** Upper and lower bounds for stability
K.LO(t) = 1;
MAT.LO(t) = 10;
MU.LO(t) = 100;
ML.LO(t) = 1000;
C.LO(t) = 2;
TOCEAN.UP(t) = 20;
TOCEAN.LO(t) = 1;
TATM.UP(t) = 20;
CPC.LO(t) = .01;
TATM.UP(t) = 12;
* Control variables
set lag10(t) ;
lag10(t) = yes$(t.val gt card(t)10);
S.FX(lag10(t)) = optlrsav;
* Initial conditions
CCA.FX(tfirst) = 400;
K.FX(tfirst) = k0;
MAT.FX(tfirst) = mat0;
MU.FX(tfirst) = mu0;
ML.FX(tfirst) = ml0;
TATM.FX(tfirst) = tatm0;
TOCEAN.FX(tfirst) = tocean0;
** Solution options
option iterlim = 99900;
option reslim = 99999;
option solprint = on;
option limrow = 0;
option limcol = 0;
model CO2 /all/;
* For base run, this subroutine calculates Hotelling rents
* Carbon price is maximum of Hotelling rent or baseline price
* The cprice equation is different from 2013R. Not sure what went wrong.
If (ifopt eq 0,
a2 = 0;
solve CO2 maximizing UTILITY using nlp;
photel(t)=cprice.l(t);
a2 = a20;
cprice.up(t)$(t.val
Methods
The quantitative analysis includes multiple components: 1) running integrated assessment models (RICE model, PACEICE, and DICE model) to evaluate the costs and benefits of climate policies, their distribution within countries, between countries, for medianage voters in different countries, and for future generations. The outputs from these models were combined with demographic data to evaluate the incidence of net benefits for current medianaged voters in different countries, longterm net benefits, and net benefits to subsequent generations.
Usage notes
IAM models are accessible in Excel spreadsheet formats; others are comprised of model outputs from publically accessible models.