Acemoglu Presentation WCERE

8/8/2019 Acemoglu Presentation WCERE

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The Environment and Directed Technical Change

Daron Acemoglu (MIT)

With Philippe Aghion, Leonardo Burstzyn and David HemousJune 29, 2010.

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The environment and directed technical change Introduction

Introduction

Growing concern that economic growth is not sustainable becauseof

Negative impact on the environment (pollution, global warming)Depletion of natural resources (in particular, oil).

Discussion among climate scientists focusing on eects ofenvironmental change on health, conict,... and on eect ofenvironmental regulation.

Economic analyses using computable general equilibrium models withexogenous technology (and climatological constraints; e.g., Nordhaus,

1994, 2002).

Key issues for economic analyses: (1) economic costs and benets ofenvironmental policy; (2) costs of delaying intervention (3) role ofdiscounting and risk aversion

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Context

Most of previous literature (with exogenous technological change)involves three dierent type of answers:

1 Nordhaus approach: intervention should be limited and gradual;small long-run growth costs.

2 Stern/Al Gore approach: intervention needs to be large, immediateand maintained permanently; large long-run growth costs.

3 Greenpeace approach: only way to avoid disaster is zero growth.

Our paper: yet another approach.

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Importance of Technology

All these approaches essentially ignore the essence of technologicalresponses.

Evidence that technological change and technology adoption respondto prot incentives

Newell, Jae and Stavins (1999): energy prices on direction oftechnological change in air conditioningPopp (2002): relates energy prices and energy saving innovation

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Th i d di d h i l h I d i


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This paper

Once directed technical change is factored in, a very dierent answer.

1 Immediate and decisive intervention is necessary (in contrast to

Nordhaus)2 Temporary intervention may be sucient (in contrast to Stern/Al Gore)3 Long-run growth costs very limited or zero (in contrast to all of them).4 Two instrumentsnot onenecessary for optimal environmental

regulation.

Therefore, more optimistic than all, and as proactive as any.

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Th i t d di t d t h i l h I t d ti


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Why?

Two sector model with clean and dirty inputs with two key

externalitiesEnvironmental externality: production of dirty inputs createsenvironmental degradation.

Researchers work to improve the technology depending on expected

prots and build on the shoulders of giants in their sector.! Knowledge externality: advances in dirty (clean) inputs make their

future use more protable.

Policy interventions can redirect technical change towards cleantechnologies.

New important parameter: elasticity of substitution between cleanand dirty inputs! e.g., whether clean energy replaces fossil fuel (high elasticity) orwhether producing components for clean cars entails CO2 emissions

(low elasticity)6



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Why? (Continued)

1 Immediate and decisive intervention is necessary (in contrast to

Nordhaus)! without intervention, innovation is directed towards dirty sectors; thus

gap between clean and dirty technology widens; thus cost ofintervention (reduced growth when clean technologies catch up withdirty ones) increases

2 Temporary intervention may be sucient (in contrast to Stern/AlGore), long-run growth costs limited (in contrast to all of them)

! once government intervention has induced a technological lead in cleantechnologies, rms will spontaneously innovate in clean technologies (ifclean and dirty inputs are suciently substitutes).

3 Two instruments, not one:

! optimal policy involves both a carbon tax and a subsidy to cleanresearch to redirect innovation to green technologies

! too costly in terms of foregone short-run consumption to use carbon

tax alone7



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Factoring in Exhaustible Resource

Baseline model without exhaustible resources.

Oil will likely become more expensive over the next 20 years.

Directed technical change implies that this will also redirectinnovations towards clean technologies.

Environmental disaster may be avoided without governmentintervention

The market may reallocate research away from dirty technologies byitself

... but it need not be the case

Interestingly, structure of optimal environmental regulation fairlysimilar with exhaustible resources.

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Roadmap

1 The basic model

2 Environmental disaster and prevention

3 Optimal policy4 Simple calibration

5 Exhaustible resource in the production of the dirty input

6 Global interactions

7 Conclusion

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The environment and directed technical change Basic model


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Model (1): production

Innite horizon in discrete time (suppress time dependence for now)

Final good Y produced competitively with a clean intermediary inputYc, and a dirty input Yd

Y = Y1

c + Y

1

d

1

Most of the analysis: > 1, the two inputs are substitute.

For j2 fc, dg, input Yj produced with labor Lj and a continuum ofmachines xji:

Yj = L1

j

Z10

A1ji x

jidi

Machines produced monopolistically using the nal good

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g

Model (2): consumption

Constant mass 1 of innitely lived representative consumers withintertemporal utility:

t=0

1

(1 + )tu(Ct, St)

where u increasing and concave, with

limS!0 u(C, S) = ;u

S(C, S) = 0

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g

Model (3): environment

Production of dirty input depletes environmental stock S:

St+1 = Ydt + (1 + ) St if S2 (0, S) . (1)

Reecting at the upper bound S (< ): baseline (unpolluted) level

of environmental quality.

Absorbing at the lower bound S = 0.

> 0: rate of environmental regeneration (measures amount ofpollution that can be absorbed without extreme adverse

consequences)S is general quality of environment, inversely related to CO2concentration (what we do below for calibration).

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Model (4): innovation

At the beginning of every period scientists (of mass s = 1) workeither to innovate in the clean or the dirty sector.

Given sector choice, each randomly allocated to one machine in theirtarget sector.

Every scientist has a probability j of success (without congestion).

if successful, proportional improvement in quality by > 0 and thescientist gets monopoly rights for one period, thus

Ajit = (1 + ) Ajit1;

if not successful, no improvement and monopoly rights in that machinerandomly allocated to an entrepreneur who uses technology

Ajit = Ajit1.

simplifying assumption, mimicking structure in continuous time models.

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Model (5): innovation (continued)

Therefore, law of motion of quality of input in sector j2 fc, dg is:

Ajt =

1 + jsjt

Ajt1

Note: knowledge externality; building on the shoulders of giants,

but importantly giants in the same sectorIntuition: Fuel technology improvements do not directly facilitatediscovery of alternative energy sources

Assumption

Ad0 suciently higher than Ac0.

Capturing the fact that currently fossil-fuel technologies are moreadvanced than alternative energy/clean technologies.

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The environment and directed technical change Laissez-faire equilibrium


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Laissez-faire equilibrium: direction of innovation

Scientists choose the sector with higher expected prots jt:

ct

dt=

c

d

pctpdt

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| { z } price eect

LctLdt|{z}

market size eect

Act1Adt1| {z }

direct productivity eect

The direct productivity eect pushes towards innovation in the moreadvanced sector

The price eect towards the less advanced, price eect stronger when smallerThe market size eect towards the more advanced when > 1

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Laissez-faire equilibrium (continued)

Use equilibrium machine demands and prices in terms of technologylevels (state variables) and let (1 ) (1 ) (< 0 if > 1):

ct

dt=

cd

1 + csct1 + dsdt

1 Act1Adt1

.

Implications: innovation in relatively advanced sector if > 1

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Laissez-faire equilibrium production levels

Equilibrium input production levels

Yd =1

Ac + A

d

+

A+c Ad;

Y = AcAdAc + A

d

1

Recall that (1 ) (1 ).

In particular, given the assumption that Ad0 suciently higher thanAc0, Yd will always grow without bound under laissez-faire

If > 1, then all scientists directed at dirty technologies, thusgYd ! d

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The environment and directed technical change Environmental disaster


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Roadmap

1 The basic model


3

Optimal policy4 Simple calibration



7 Conclusion

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Sketch of proof

Look at eect of a temporary clean research subsidy

Key role: redirecting technical change; innovation can be redirected

towards clean technologyIf > 1, then subsequent to an extended period of taxation,innovation will remain in clean technology

Is this sucient to prevent an environmental disaster?

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Sketch of proof (continued)

Even with innovation only in the clean sector, production of dirty

inputs may increaseon the one hand: innovation in clean technology reduces laborallocated to dirty input ) Yd #on the other hand: innovation in clean technology makes nal goodcheaper an input to production of dirty input ) Yd "

which of these two eects dominates, will depend upon .With clean research subsidy (because > 1 and thus < 0):

Yd =1

Ac + A

d

+

A+c Ad ! A

+c

If + > 0 or < 1/(1 ), then second eect dominates, andlong run growth rate of dirty input is positive equal to(1 + c)

+ 1If + < 0 or > 1/(1 ), then rst eect dominates, so that Yd

decreases over time.21



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Cost of intervention and delay

Concentrate on strong substitutability case ( > 1/ (1 ))

While Act catches up with Adt, growth is reduced.

T: number of periods necessary for the economy under the policyintervention to reach the same level of output as it would have donewithin one period without intervention

If intervention delayed, not only the environment gets furtherdegraded, but also technology gap Adt1/Act1 increases, growth is

reduced for a longer period.

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Complementary case

Suppose instead that clean and dirty inputs are complements, i.e.,

< 1.

Innovation is directed towards the more backward sector

price eect dominates the direct productivity eect and market sizeeect now favors innovation in the more backward sector

typically innovation rst occurs in clean, then in both, asymptoticallybalanced between the two sectors.

Asymptotic growth rate of dirty input:gYd ! cd/ (c + d) < d (growth rate in substitute case):disaster occurs sooner than in the substitute case.

... but it is unavoidable using only a temporary clean research subsidy.

If the clean sector is the more advanced, innovation will take place indirty once the subsidy is removed, and long-run growth rate of dirtyinput remains the same.

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Undirected technical change

Compare with a model where scientists randomly allocated acrosssectors so as to ensure equal growth in the qualities of clean and dirtymachines, thus gYd ! cd/ (c + d) < d

Proposition

The role of directed technical change.When > 1/ (1 ):

1 An environmental disaster under laissez-faire arises earlier withdirected technical change than in the equivalent economy with

undirected technical change.2 However, a temporary clean research subsidy can prevent an

environmental disaster with directed technical change, but not in theequivalent economy with undirected technical change.

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The environment and directed technical change Optimal environmental regulation


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Roadmap

1 The basic model


3




7 Conclusion

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Optimal environmental regulation

Proposition

Optimal environmental regulation.The social planner can implement the social optimum through a "carbontax" on the use of the dirty input, a clean research subsidy and a subsidyfor the use of all machines (all taxes/subsidies are nanced lump sum).

1 If > 1 and the discount rate is suciently small, then in nitetime innovation ends up occurring only in the clean sector, theeconomy grows at ratec and the optimal subsidy on prots in theclean sector, qt, is temporary.

2 The optimal carbon tax, t, is temporary if > 1/ (1 ) but not if1 < < 1/ (1 ).

Parts 1 and 2 Us vs. Stern/Al Gore.

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Carbon tax

Optimal carbon tax schedule is given by

t =t+1

tpdt,

t

is the marginal utility of a unit of consumption at time tt+1 is the shadow value of one unit of environmental quality at timet+ 1, equal to the discounted marginal utility of environmental qualityas of period t+ 1

If > 1/ (1 ), dirty input production tends towards 0 and

environmental quality St reaches S in nite time, carbon tax becomesnull in nite time.

If gap between the two technologies is high, relying on carbon tax toredirect technical change would reduce too much consumption.

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The environment and directed technical change Simple Calibration


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Roadmap

1 The basic model


3




7 Conclusion

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C f


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Calibration: preferences and technology

1 period = 5 years

= 1/3 : share of capital

c = d = 0.1, = 1: long-run growth 2% per year

Ac1, Ad1 to match Yc1, Yd1 with 2002 - 2006 production ofnon fossil fuel, fossil fuel energy

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C lib i ili


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Calibration: utility

Choose

u(Ct, St) =( (St) Ct)1

1 .

With = 2. Same as previous literature.

(S) = (disaster (S))

1

disaster (disaster (S))(1 )disaster

,

where is strictly increasing and concave in S.

This denes a exible family of continuous functions parameterized by

, such that (0) = 0Compute to match with the mapping between temperature andnal output in Nordhaus DICE 2007 model over the range oftemperature increases up to 3C.

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C lib ti 2 i t t t


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Calibration: 2 important parameters

Choose the elasticity of substitution between clean and dirty input as = 3 or 10 (low or high).

Choose , time discount rate (/year here) as = 0.001 (Stern;discount factor' 0.999) and = 0.015 (Nordhaus; discountfactor' 0.985).

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Si l ti ti l li hi h l ti it f b tit ti


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Simulation: optimal policy, high elasticity of substitution

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Si latio o ti al olic lo elasticit of s bstit tio


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Simulation: optimal policy, low elasticity of substitution

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Simulation: cost of delaying optimal policy implementation


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Simulation: cost of delaying optimal policy implementation

Welfare costs of delayed intervention as functions of and (Percentage reductions in consumption relative to immediate optimal

policy)

Elasticity of substitution 10 3

Discount rate 0.001 0.015 0.001 0.015

delay = 10 years 8.75 1.87 2.71 0.05

delay = 20 years 14.02 1.92 4.79 0.12

delay = 30 years 17.65 1.99 6.88 0.23

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Simulation: cost of using only carbon tax


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Simulation: cost of using only carbon tax

Welfare costs of relying solely on the carbon tax as functions of and

(Percentage reductions in consumption relative to optimal policy)

Elasticity of substitution 10 3

Discount rate 0.001 0.015 0.001 0.015

Welfare cost 0.95 1.58 1.74 2.70

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The environment and directed technical change Exhaustible resources

Roadmap


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Roadmap

1 The basic model


3 Optimal policy

4 Simple calibration



7

Conclusion

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Exhaustible resources


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Exhaustible resources

Polluting activities (CO2 emissions) often use an exhaustible resource(most importantly, oil).

Implications for evolution of production and direction of research.Questions:

Does this make environmental disaster less likely? Yes.Does it change the structure of optimal environmental regulation? No.

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Direction of innovation


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Direction of innovation

Ratio of expected prots from innovation in clean versus dirty ismodied to:

ct

dt = constant

c

c(Qt)2 (1)

d

(1 + c

sct)1

(1 + dsdt)11

Act1

A1dt1

,

where 1 (1 1) (1 )

Provided that > 1, increasing cost of extraction helps switching

towards clean innovation (again price eect vs market size eect).

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Environmental disaster in the laissez-faire equilibrium


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Environmental disaster in the laissez faire equilibrium

Proposition

When the two inputs are substitutes ( > 1), innovation in the long-runwill be directed towards the clean sector only and the economy will growat a ratec. Provided that S is suciently high, an environmentaldisaster is avoided under laissez-faire.

Either the increase in the cost of dirty input production due todepletion of exhaustible resources or the full depletion of the resourcecreate enough incentives for research to switch to clean technologies.

This prevents an environmental disaster provided that initial

environmental stock is large enough.

(In complement case ( < 1), dirty input and so the resource areessential. Resource stock is depleted in nite time and economicgrowth is not sustainable).

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How does optimal environmental regulation look like with exhaustibleresources?

Answer: generally similar to that without exhaustible resources, butalso a resource tax so that the exhaustible resource does not getdepleted completely.

Proposition

The social planner can implement the social optimum through a tax onthe use of the dirty input, a subsidy on clean research, a subsidy on the

use of all machines and a resource tax (all taxes/subsidies are imposed asa lump sum way to the corresponding agents). The resource tax must bemaintained forever.

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The Hotelling case (1)


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Firms in perfect competition own innitesimal amount of the

resource. Cost of extraction constant c(Qt) = c; Pt price of theresource determined by the Hotelling rule:

Pt+1 c

Pt c= 1 + rt = (1 + )

u/C(Ct, St)

u/C(Ct+1, St+1)

net price raises at a rate equal to the interest rate of the economy.Case where utility is both separable in consumption and environmentquality and CRRA with respect to consumption with a constantcoecient of relative risk aversion . Price of resource asymptoticallygrows at rate

r = + gwhere g is the asymptotic growth rate of the economy.Importantly price of the resource is higher (there are rents) butresource is never exhausted (marginal product of the resource isunbounded).

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g ( )

Proposition

A disaster is more easily avoided than without the resource, but notnecessarily avoided.

1 If the discount rate and the elasticity of substitution are bothsuciently high ( > [(1 1) /2]max (d, c) and

> (2 1 )1) then innovation switches to the clean sector only

and a disaster is avoided under laissez-faire provided that the initialenvironmental quality (S) is suciently high.

2 If the discount rate and the elasticity of substitution are sucientlylow (1 (1 ) > 2 (/ (c) + )) a disaster cannot beavoided under laissez-faire.

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g ( )

Intuition:

If price of the resource increases more slowly than the dirty productivityAdt, innovation keeps occurring in the dirty sector forever and theeconomy runs into disaster.If price increases suciently fast, innovation shifts to clean sectors. Forhigh elasticity of substitution production of dirty input decreases.

High pushes towards higher prices.As before temporary subsidy to clean research can implement theswitch.

Threshold on from which a disaster can be avoided is lower and

decreasing in the share 2 of the resource in the production of dirtyinput (producing dirty involves incurring a resource price that grows atrate + c).

Optimal policy remains identical but the resource tax now becomesuseless

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Global interactions

Roadmap


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p

1 The basic model


3 Optimal policy

4 Simple calibration



7

Conclusion

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Global interactions

Two-country case


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y

Two countries: North (N), identical to the economy studied so far,and that the South (S) imitating Northern technologies.

Thus there are two externalities:

1 environmental externality: dirty input productions by both contributeto global environmental degradation

St+1 =

YNdt + YS

dt

+ (1 + ) St for S2 (0, S).

2 knowledge externality: South imitates North technologies=) ratio of expected prots from imitation in the two sectors in the

SouthSct

Sdt

=c(pSct)

11 LSctA

Nct

d(pSdt)

11 LSdtA

Ndt

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Global interactions

Global Interactions


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Do we need global coordination to avoid disasters?

In autarky, the answer is no again because advances in the North willinduce the South to also switch to clean technologies.But free trade may undermine this result by creating pollution havens.

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Global interactions Conclusion

Summary: preventing an environmental disaster


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Starting with more advanced dirty technology, the laissez-faireeconomy typically ends up in an environmental disaster.

Temporary policy intervention can redirect technical change andprevents a disaster (for high elasticity of substitution)

Exhaustible resources sometimes make it possible for the laissez-faireeconomy to avoid an environmental disaster.

Optimal policy involves:

the use of two instruments, carbon tax (for environmental externality)

and clean research subsidy (for knowledge externality)acting now, even with Nordhaus discount rate for reasonable degree ofsubstitutability between clean and dirty inputs

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