Organizing Committee:Glenn Rudebusch (Federal Reserve Bank of San Francisco)Michael Bauer (University of Hamburg)Stephie Fried (Arizona State University)Òscar Jordà (Federal Reserve Bank of San Francisco)Toan Phan (Federal Reserve Bank of Richmond)

Suboptimal Climate Policy

Per Krusell(based on work w John Hassler, Conny Olovsson, and Michael Reiter)

IIES(IIES, Sveriges Riksbank, IHS/NYU-Abu Dhabi)

San Francisco Fed: Virtual Seminar on Climate Economics,October 2020

What to do about climate change?

A scientific consensus:

I that humans cause warming

I that warming can be substantial.

Less agreement (or at least uncertainty) on

I how much warming

I how warming affects human welfare.

Thus, the “optimal” path emissions sits in wide range.

However: consensus that we should limit emissions substantially.

The question is HOW?

How, in principle

The problem of climate change is trivial!

I Humans cause warming as a byproduct of economic activity.

I This is a classic case of a pure externality.

I 100 years ago an economist figured out what to do in suchcases (Pigou, 1920): apply a tax equal to the total marginal“externality damage” the polluter is otherwise not paying for.I.e., markets need some help in correcting the pricing.

I No research since has quibbled with this basic insight.

I Carbon spreads super-quickly in atmosphere: damage identicalregardless of where it is emitted ⇒ global tax!

I Thousands of (famous) economists have signed a petitionurging the adoption of a carbon tax.

Given this, is there nothing interesting left to work on for us?

A resounding NO

Important things to do for many parts of economics.

Here my focus: macro. Message: develop and USE integratedassessment models (IAMs, a la Nordhaus):

I Policymakers seem reluctant to just go for a carbon tax. Solet’s consider policies that are closer toimplementation—compare them and inform.

I This task is what economists know how to do: we are expertson understanding how markets operate and how differentregulations/taxes act.

Note: the idea is to analyze suboptimal policy

I to be distinguished from “second-best” policy;

I we are pushing for quantitative analysis, for examplecomputing how much more certain policy packages hurt ourwelfare (than, say, a global carbon tax) if the goal is to limitwarming by x degrees by 2200.

Contribution here, in concrete terms, I

Methodological: we offer a framework—an IAM—for quantitativeanalysis of policy, designed so that it can be built upon further.Key features:

I it is decentralized;

I it is rich enough to be taken seriously: it can be used addressimportant questions;

I it allows significant heterogeneity; and

I it builds entirely on “modern macro”.

We use the framework to ask three quantitative questions.

Contribution here, in concrete terms, II

The three questions:

1. What if the right kind of policy is used but at the wrong level?I Highly relevant question as there is much uncertainty both

about the climate conditional on emissions and about damages.I We compare a global carbon tax that turns out to be (much)

too high ex post to one that is (much) too low ex post.I Insight: the former error is not very costly but the latter is.

2. What if we use a particular form of bad policy design:different carbon tax rates around the world?I Can be super-costly (we look at different concrete cases).

3. What if we can promote green energy instead of taxingcarbon?I Very likely very bad idea.

People, preferences, technology, nature

I discrete, infinite time, one final goodI r regions

I r − 1 regions consume but do not produce oilI 1 region produces but does not consume oil

I within each region, representative agentI output in each region

I C-D in capital, labor, energy compositeI energy composite nested CES in oil(s), other fossil, greenI TFP incorporates damages from changed climate

I capital accumulation neoclassical

I fuels produced with constant marginal costs in terms ofoutput (oil at zero), vary across fuels and regions

I exogenous technical change (in various parts)

I climate/carbon cycle modules: (roughly) as in Nordhaus

Markets, policies

I perfect competition everywhere (implies only oil gives “rents”)

I restrictions: the only between-country trade involves oil (ruleout intertemporal trade)

I governments’ actionsI local, i.e., no interregional transfersI run balanced budgetsI tax fossil energy sectorI rebate in proportion to incomes

Comments

Some potentially important things abstracted from in this model:

I intertemporal trade between countries (competitiveeverywhere, implies only oil gives “rents”)

I endogenous technology (e.g., R&D into green)

I uncertainty

I nonlinearities (e.g., tipping points in damages ornatural-science part)

These can be useful additions but much can be said without them.

Addition of these elements “straightforward” (especially for doingpositive analysis); basic model super-easy to solve.

(If time: comment on the merits of “really complicated models”.)

Some key equations, economics

∞∑t=0

βt log(Ci ,t)

Ei ,t =

λ1Oρ

i ,t +n∑

j=2

λjeρj ,i ,t

1ρ

; Oi ,t ≡ l

λoil1 eρh1,i ,t +l∑

j=1

λoilj+1eρhn+j ,i ,t

1ρh

Ci ,t + Ki ,t+1 = Ai ,tL1−α−νi ,t Kα

i ,tEνi ,t − p1,te1,i ,t −

n+l∑j=2

pj ,i ,tej ,i ,t

Rt+1 = Rt −r∑

i=2

e1,i ,t , s.t. Rt ≥ 0

Some key equations, natural sciences

Ai ,t = exp (zi ,t − γi ,tSt−1)

St =∞∑s=0

(1− ds)r∑

i=2

Mi ,t−s with Mi ,t =n+l∑j=1

gjej ,i ,t

Tt = Tt−1 + σ1

(η

ln 2ln

(St−1S0

)− κTt−1 − σ2

(Tt−1 − T L

t−1

))

T Lt = T L

t−1 + σ3

(Tt−1 − T L

t−1

)

Theoretical characterization

Rt+1 = βRt Ki ,t+1 =αβ

1− ν(1 + Γi ,t) Yi ,t

Yi ,t = (1− ν)Ai ,tL1−α−νi ,t Kα

i ,tEνi ,t

Ei ,t =

ν e(zi,t−γi,tSt−1)L1−α−νi ,t Kαi ,t

Pt,i

11−ν

Pi ,t =

λ 11−ρ1

(POi ,t

) ρρ−1

+n∑

j=2

λ1

1−ρj p

ρρ−1

j ,i ,t

ρ−1ρ

Theoretical characterization, cont’d

POi ,t = l−1

(λoil1

) 11−ρh p

ρhρh−1

1,i ,t +l∑

j=1

(λoilj+1

) 11−ρh p

ρhρh−1

n+j ,i ,t

ρh−1

ρh

Oi ,t =

(λ1

Pi ,t

POi ,t

) 11−ρ

Ei ,t

ej ,i ,t =Oi ,t

l

(lλoilj

POi ,t

pj ,i ,t

) 11−ρh

, j ∈ {1, n + 1, . . . n + l}

ej ,i ,t =

(λj

Pt,i

pj ,i ,t

) 11−ρ

Ei ,t , j ∈ {2, ..., n}

Numerical solution

I Find path for oil prices such that

r∑i=2

e1,i ,t = (1− β)Rt

at all points in time. Each period is solved in isolation.

I In experiments where we target a temperature at a certaindate, iterations on paths.

Calibration

Everything calibrated to data (except some features that areassumed common across regions).

I 8 oil-consuming regions: Europe, the U.S., China, SouthAmerica, India, Africa, “Oceania”; oil-producing regioncomprises OPEC and Russia

I energy:I oil (incl. natural gas), fracking; coal and greenI fracking only in U.S.I energy elasticities calibrated to values from meta study (Stern,

2012): 0.95 except between oil and fracking output (10)I relative prices of fuels same across regions, match data

I TFPs in rich world grow at common rate, fast-growing andsome convergence in rest

I initial capital stocks calibrated so that MPKi s equal at time 0

I initial stock of oil and energy production parameters set tomatch uses and emissions

Outputs and emissions

Share of CO2 emissions, Data11%

16%

35%

3%

9%

3%

10%

13%Share of CO2 emissions, Model

11%

14%

35%5%

8%

5%

11%

13%

EUUSChinaAfricaIndia, Pakistan, BangladeshSouth AmericaOceaniaOil Countries

Share of GDP, Data

19%

18%

21%4%

8%

6%

13%

12%Share of GDP, Model

18%

18%

18% 6%

9%

6%

13%

12%

Shows our calibrated matches the key regional features.

Before we start, a few basic points

2000 2020 2040 2060 2080 2100 2120 2140 2160 2180 2200

Time

0

1

2

3

4

5

6

7

8

9

10

Deg

rees

Cel

sius

Global mean temperature

No taxesCO2 taxes in EU onlyCoal Tax in EU onlyGlobal CO2 taxGlobal coal taxSwedish Tax

I It’s all about coal (taxing oil or not makes no difference).I A modest (EU-ETS level) tax helps a lot, if global.I No policy action (or only EU action or not taxing coal) leads

to huge warming.

Suboptimal policy I: right kind of tax, wrong level

HKRO (IIES, IIES, Riksbank and IHS) Integrated Assessment in a Multi-region World with Multiple Energy Sources and Endogenous Technical ChangeJune 2019 24 / 33

Black: global carbon tax based on most optimistic scenario forwarming and damages in range given by IPCC, but reality turnsout at other end of spectrum (very high warming and damages).Red: reverse.

Message: high tax excellent precautionary instrument.Logic: explain verbally.

Suboptimal policy II: non-uniform carbon tax

Target 2.6o heating by 2165, let Africa and India (1st graph) andChina partially (2nd) off the hook; losses relative to uniform tax.

EU US CH AF IND SA OC TOTAL-40

-20

0

20

Con

sum

ptio

n lo

ss (

in %

)re

lativ

e to

opt

imal

pol

icy

Welfare costs when China only imposes a low tax

EU US CH AF IND SA OC TOTAL-20

-15

-10

-5

0

5C

onsu

mpt

ion

loss

(in

%)

rela

tive

to o

ptim

al p

olic

y

Welfare costs when developing countries do not impose a tax

⇒ (i) non-uniform very bad idea; (ii) China crucial.

Suboptimal policy III: green energy push, no fossil taxThe Pigou tax implements the optimum ⇒ no green subsidyneeded. But suppose there is no Pigou tax.

Feed in higher exogenous green productivity growth (+ 2%/year).Fig. 1: baseline substitutability green-fossil, 0.95; fig. 2: higher, 2.

is less fast than for the economy as a whole.27

The benchmark results of the simulations are presented in the top graph in Figure 5.

They show, first, that the fact that the price of green energy falls over time by 2% has no

positive consequences for the climate. In fact, emissions are even larger in this scenario

than in the baseline case. The reason is that lower green-energy prices imply lower energy

prices in general, which increases the demand for all energy services, including for coal. The

figure also shows that the second scenario, where 2 increases and 3 falls, produces a

path of the global mean temperature that is virtually indistinguishable from that with global

Pigouvian taxes.

2020 2040 2060 2080 2100 2120 2140

Year

0

2

4

6

8Te

mp

era

ture

Climate change with different rates of technical change, = 0.95

Global coal tax, neutral techFast green, stagnant coalFast green, neutral coalNeutral green, stagnant coal

2020 2040 2060 2080 2100 2120 2140

Year

0

2

4

6

8

Tem

pe

ratu

re

Climate change with different rates of technical change, = 2

Figure 5: Top graph: global mean temperatures with different rates of technical change with

an elasticity of substitution between green and fossil energy sources set to 0.95. Bottom

graph: same as in the top graph but with the elasticity of substitution between green and

fossil energy sources set to 2.

The bottom graph shows that these results do not depend crucially on that the substitu-

27I.e., we do not assume technological regress: think of a case where the production of coal-based industry

does not improve whereas the final-goods sector sees TFP growth of 2 percent per year.

28

Doesn’t help the climate! Lower coal productivity growthhelps—like a tax. Green subsidy NOT good Pigou-tax substitute.

Summary remarks

There are productive ways for macroeconomics to be helpful in thearea of climate change.

In particular, a stripped-down IAM is used to obtain quantitativeanswers: a cost-benefit evaluation of bad, but realistic, policies.

Some of the answers were very surprising to us:

I best available estimates suggest the policy errors are highlyasymmetric, leading one to favor a high tax on carbon

I it’s very costly not to be able to use a global tax (orequivalent)—letting some off the hook is very expensive

I to push for green instead of taxing coal is very ineffective andhazardous for the climate.