DOI: 10.5061/dryad.18931zd21
title: Climate-economy model scenario runs and sensitivity analysis using DICE-2016

description: 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
 well-established 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 median-aged 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 self-interested 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.
description: The quantitative analysis includes multiple components: 1)
 running integrated assessment models (RICE model, PACE-ICE, and DICE
 model) to evaluate the costs and benefits of climate policies, their
 distribution within countries, between countries, for median-age 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 median-aged voters in different countries,
 long-term net benefits, and net benefits to subsequent
 generations.
description: IAM models are accessible in Excel spreadsheet formats; others
 are comprised of model outputs from publically accessible
 models.
description: # Climate-economy model scenario runs and sensitivity analysis using
 DICE-2016 *** The dataset files included here include the model runs of
 the DICE climate-economy 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 high-damage 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 median-aged voters in different countries,
 long-term net benefits, and net benefits to subsequent generations. Below
 each set of year-to-year 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/dicerice-models. The variables included are
 for DICE-Model parameters as documented by Nordhaus for the GAMS version
 as follows: DICE MODEL 2016 CODE - GAMS $ontext This is the beta version
 of DICE-2016R. The major changes are outlined in Nordhaus,
 "Revisiting the social cost of carbon: Estimates from the DICE-2016R
 model," September 30, 2016," available from the author. Version
 is DICE-2016R-091916ap.gms $offtext $title DICE-2016R September 2016
 (DICE-2016R-091216a.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
 non-CO2 GHG (Wm-2) / 0.5 / fex1 2100 forcings of non-CO2 GHG (Wm-2) / 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 (Wm-2) /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 &lt;&gt; /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)
 CO2-equivalent-emissions 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 long-run 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 long-run 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\*(1-miu0)); 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.val-1))); al("1") = a0; loop(t,
 al(t+1)=al(t)/((1-ga(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\*(1-gback)\*\*(t.val-1); cost1(t) =
 pbacktime(t)\*sigma(t)/expcost2/1000; etree(t) =
 eland0\*(1-deland)\*\*(t.val-1); cumetree("1")= 100;
 loop(t,cumetree(t+1)=cumetree(t)+etree(t)\*(5/3.666);); rr(t) =
 1/((1+prstp)\*\*(tstep\*(t.val-1))); forcoth(t) = fex0+
 (1/17)\*(fex1-fex0)\*(t.val-1)$(t.val lt 18)+ (fex1-fex0)$(t.val ge 18);
 optlrsav = (dk + .004)/(dk + .004\*elasmu + prstp)\*gama; \*Base Case
 Carbon Price cpricebase(t)= cprice0\*(1+gcprice)\*\*(5\*(t.val-1));
 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)
 Temperature-climate equation for atmosphere TOCEANEQ(t)
 Temperature-climate 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)\*\*(expcost2-1); carbpriceeq(t).. CPRICE(t) =E= pbacktime(t) \*
 (MIU(t))\*\*(expcost2-1); \*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)\*\*(1-GAMA))\*(K(t)\*\*GAMA); yneteq(t).. YNET(t) =E=
 YGROSS(t)\*(1-damfrac(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= (1-dk)\*\*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))\*\*(1-elasmu)-1)/(1-elasmu)-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)$(t.val&lt;30) = 1; \*\* Upper and lower bounds for stability
 K.LO(t) = 1; MAT.LO(t) = 10; MU.LO(t) = 100; ML.LO(t) = 1000; C.LO(t) = 2;
 TOCEAN.UP(t) = 20; TOCEAN.LO(t) = -1; TATM.UP(t) = 20; CPC.LO(t) = .01;
 TATM.UP(t) = 12; \* Control variables set lag10(t) ; lag10(t) = yes$(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