Will the Paris Accord Accelerate Climate...

Will the Paris Accord Accelerate Climate Change?

Laurence Kotlikoff, Andrey Polbin, and Andrey Zubarev

RANEPA

The 22th of June, 2017

Motivation

Since 2010, global oil production has risen by 10 per cent, globalcoal production by 9 per cent, and global natural gas productionby 11 per cent.The 2015 Paris Accord is an agreement amongst many countries toimpose tax on CO2 emissions after 2020. It is meant to control ourplanet’s rising temperature. But it may be doing the opposite ingradually, rather than immediately reducing CO2 emissions.The Accord effectively tells dirty-energy producers to "use it orlose it". This may be accelerating their extraction and burning offossil fuels and, thereby, be permanently raising temperatures.The same is true of policies that accelerate technical improvementin clean energy. Telling dirty energy producers that they will facemuch stiffer competition from clean energy sources in the relativelynear term sends the same "use it or lose it"message and also leadto a faster burn.

Andrey Zubarev Paris Accord 27.05.2017 2 / 22

Empirics, IPCC


The model

We use a simple OLG model to illustrate this long-noted GreenParadox. It is mostly inspired by the recent papers Cai et al.(2013), and Golosov et al. (2014), studying optimal carbontaxation policy.In our model, delaying abatement can lead to larger changes inclimate than doing nothing, reducing welfare for all generations. Incontrast, immediate policy action can raise welfare for allgenerations.We treat climate damage as a negative externality imposed bytoday’s generations on tomorrow’s. It is, in part, irreversible andcan tip the climate to permanently higher temperatures.


Model description: production sector

Final goods’ production sector:

Yt = AtKαy,tL

βy,tE

1−α−βt

Clean energy production:

St = BtKθs,tL

ϕs,tH

1−θ−ϕt

Oil Ot and clean energy St are perfect substitutes:

Et = St +Ot

The value of land Ht is

Qt =

∞∑s=0

nt+sHt+s

(s∏i=0

1

1 + rt+i

)


Model description: oil extraction

The value of oil extracting firm:

Vt =

∞∑s=0

(pt+s − τt+s)Ot+s

(s∏i=0

1

1 + rt+i

)

where τt is an absolute tax.Dynamics of oil reserves:

Rt = Rt−1 −Ot, Rt ≥ 0

Hotelling rule for the period T of total extraction:

pt − τt =pt+1 − τt+1

1 + rt+1, t ≤ T − 1

pT − τT ≥ pT+1 − τT+1

1 + rT+1


Model description: households

Households’ utility function:

U = (1 −m) log cyt +m log cot+1

Budget constraint:

cyt +cot+1

1 + rt+1= wtLt +

τt+1Ot+1

1 + rt+1


Model description: carbon cycle

CO2 components:Jt = J1,t + J2,t.

The permanent component:

J1,t = J1,t−1 + dLOt

The temporary concentration component:

J2,t = (1 − d)J2,t−1 + d0(1 − dL)Ot

where dL is a share of emissions absorbed by the oceans and othercarbon sinks, and d0 is the extent to which non-absorbed carbonreaches the atmosphere.


Model description: damages and growth rates

We modified the Golosov et al. (2014) formulation by makingclimate damage the sum of two components. The first one is afunction of the maximum past CO2 concentration level. Thesecond captures tipping point damage, which is triggered if CO2

concentration exceeds a critical threshold. The explicit formulalooks like

Dt = 1 − exp(−γmaxs≤t

([Js − J̄ ])) + gG

where g = 0 for Js < J∗ and g = 1 for Js ≥ J∗.Damages and productivity:

At = (1 −Dt)Zt

Exogenous growth rates:

Zt = Z0exp(gZt)

Bt = B0exp(gBt)


Balanced growth path

Growth rate for output, capital, investment, consumption, rentalprice of land, value of land and wage:

gY =gZ + (1 − α− β)gB

1 − α− θ(1 − α− β)

Growth rate for clean energy production:

gS = gB + θgZ + (1 − α− β)gB

1 − α− θ(1 − α− β)

Price of energy growth rate:

gP =gZ(1 − θ) − gBβ

1 − α− θ(1 − α− β)


Calibration

Parameters of production function are α = 0.3, β = 0.65, and(1− α− β) = 0.05, saving rate is m = 0.5, depreciation rate δ = 1.

The climate change parameters, γ, dL, d0, and d, are set to .009,.2, 1, and .2 correspondingly.

If the climate isn’t tipped, the long-run damage to outputproductivity, absent policy, is 30 per cent. We set G such thatsteady-state damages, if the tipping point is triggered, equal 50 percent of output productivity.


Calibration

The capital, labour, and land shares in the production function forclean energy (the coefficients θ, φ, and (1 − θ − φ) ) are set to .2,.2, and .6, respectively. The long-run growth rate of output is 1 percent, the long-run growth rate of clean energy is also 1 per cent,and the long-run growth rate of the price of energy is zero.

Labour and land endowment, oil reserves, and productivityparameters were calibrated to produce actual consumption of cleanenergy of 5% and oil depletion in 90-120 years.


BAU scenario

0 3 6 9

20

40

Ot

0 3 6 90

0.060.120.18

pt

0 3 6 90

1

2Vt

0 3 6 9

20

40

Jt

0 3 6 9

0.1

0.3

0.5Dt

0 3 6 90

0.060.120.18

τt

0 3 6 90

1

2logSt − gSt

0 3 6 9−4

−2

0lognt − gY t

0 3 6 9−0.6

−0.4

−0.2logQt − gY t

0 3 6 90

2

4logEt − gSt

0 3 6 90.5

1

1.5logKt − gY t

0 3 6 90

0.02

0.04Ks,t/Ky,t

0 3 6 91.5

2

2.5logwt − gY t

0 3 6 940

60

80rt

0 3 6 92

2.5

3logYt − gY t

0 3 6 91

1.5

2log cyt − gY t

0 3 6 91.5

2

2.5log cot − gY t


Delayed carbon tax

0 3 6 9

20

40

Ot

0 3 6 90

0.060.120.18

pt

0 3 6 90

1

2Vt

0 3 6 9

20

40

Jt

0 3 6 9

0.1

0.3

0.5Dt

0 3 6 90

0.060.120.18

τt

0 3 6 9−2

0

2logSt − gSt

0 3 6 9−10

−5

0lognt − gY t

0 3 6 9−1

−0.5

0logQt − gY t

0 3 6 90

2

4logEt − gSt

0 3 6 90

1

2logKt − gY t

0 3 6 90

0.02

0.04Ks,t/Ky,t

0 3 6 91

2

3logwt − gY t

0 3 6 90

50

100rt

0 3 6 91

2

3logYt − gY t

0 3 6 90

1

2log cyt − gY t

0 3 6 91

2

3log cot − gY t


Results

In the BAU scenario, an increase in damages and the induceddecline in capital as well as the long-run reduction in energyproduces a roughly one third decline in output compared to itslevel at time 0.Also, the damage inflicted on the economy lowers real wages, whichlimits the ability of young workers to save. Consequently, thecapital stock falls relative to its initial value. So too doesconsumption of the young and old. The relative scarcity of capitalleads to a higher real interest rate.With the delayed tax policy, dirty energy producers respond tothis "use it or lose it" policy by exhausting all oil reserves in theinitial period. Carbon concentration becomes sufficiently high totip the climate. Consequently, the delayed carbon tax policyproduces a Pareto loss: all generations suffer declines in remaininglifetime consumption of roughly 40 percent.


Immediate carbon tax

0 3 6 9

20

40

Ot

0 3 6 90

0.060.120.18

pt

0 3 6 90

1

2Vt

0 3 6 9

20

40

Jt

0 3 6 9

0.1

0.3

0.5Dt

0 3 6 90

0.060.120.18

τt

0 3 6 90

1

2logSt − gSt

0 3 6 9−4

−2

0lognt − gY t

0 3 6 9

−0.4

−0.2

0logQt − gY t

0 3 6 90

2

4logEt − gSt

0 3 6 90.5

1

1.5logKt − gY t

0 3 6 90

0.02

0.04Ks,t/Ky,t

0 3 6 91.5

2

2.5logwt − gY t

0 3 6 940

60

80rt

0 3 6 92

2.5

3logYt − gY t

0 3 6 91

1.5

2log cyt − gY t

0 3 6 91.5

2

2.5log cot − gY t


Anticipated jump of Bt in the next period

0 3 6 9

20

40

Ot

0 3 6 90

0.060.120.18

pt

0 3 6 90

1

2Vt

0 3 6 9

20

40

Jt

0 3 6 9

0.1

0.3

0.5Dt

0 3 6 90

0.060.120.18

τt

0 3 6 90

2

4logSt − gSt

0 3 6 9

−4

−2

0lognt − gY t

0 3 6 9−1

−0.5

0logQt − gY t

0 3 6 90

2

4logEt − gSt

0 3 6 90

1

2logKt − gY t

0 3 6 90

0.02

0.04Ks,t/Ky,t

0 3 6 91.5

2

2.5logwt − gY t

0 3 6 9−100

0

100rt

0 3 6 92

2.5

3logYt − gY t

0 3 6 90

1

2log cyt − gY t

0 3 6 91

1.5

2log cot − gY t

0 3 6 90

5

10logBt


Results

An immediate carbon tax policy gives dirty energy producers astrong incentive to delay production. This much slower fossil fuelburn reduces damages in both the short and long runs. It alsoproduces higher levels of consumption of all generations in allperiods of life alive at time 0 and thereafter. I.e., it produces aPareto gain.

If the market perceives that clean energy technology will improvesignificantly in the not-to-distant future, the price of energy willfall dramatically and most of the economy’s existing oil reserveswill be immediately extracted. Like delaying the imposition of asignificant carbon tax, this path of emissions tips the climate,dramatically and permanently exacerbating carbon damage. This,in turn, significantly reduces both output and capital formation,producing a substantial Pareto loss for all generations.


Conclusions

The world’s supply of dirty energy is, to a large extent, fixed. Thismeans that short of prohibiting its production and sale, most ofthe world’s dirty energy will be used. If it is used quickly, we’llhave a fast burn and the damage to the planet will, according tosome estimates, be massive and irreversible.

Delaying the implementation of carbon abatement policy givesdirty energy producers strong incentives to "use it or lose it." Thiscan significantly accelerate the production and sale of carbonleaving current and future generations worse off than in theabsence of any abatement policy.

In contrast, immediately implementing the same size carbon taxcan materially limit climate damage and raise welfare for allgenerations.


Thank you!

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