Presentation by Frederick van der Ploeg, "Policy issues in combating climate change"

1. Policy issues in combating climate change
How to determine optimal trade-off between growth and combating global warming?
What is the first-best optimal global climate policy?
Time paths for carbon tax and renewable subsidy?
Allow for green Ramsey growth IAM with exhaustible fossil fuel and directed technical change (learning by doing in renewable use): “Third Way” for climate policy.
When to abandon fossil fuel and to phase in renewable energy?
How much fossil fuel to leave in the crust of the earth (‘stranded assets’)?
How much better than business as usual?
How well do second-best climate policies fare which rely on renewable subsidy only. Green Paradox?

2. Distinguishing features
Fossil fuel extraction cost increase as less reserves are left, which gives rise to untapped fossil fuel.
Price of fossil fuel consists of this cost, the scarcity rent and the carbon tax (set to the social cost of carbon).
Renewable energy becomes cheaper as more is used (learning by doing – directed technical change). This gives rise to an intermediate phase where renewable and fossil fuel energy are used alongside each other.
Social price of renewable energy corresponds to this cost minus a learning-by-doing subsidy.
Temporary population boom & ongoing technical progress.

3. Messages
Need aggressive renewable subsidy to bring renewable energy quickly into use and a gradually rising carbon tax to price and phase out fossil fuel energy.
Optimal carbon tax is a fixed proportion of world GDP with log utility, Cobb-Douglas production, 100% depreciation, zero fossil fuel extraction costs, and exponential damages (Golosov et al., 2014) .
But relationship between the optimal carbon tax and GDP is hump-shaped with CES production, EIS = 0.5, less than 100% depreciation and more realistic global warming damages.
The simple formula for the optimal carbon tax performs badly if it has to address multiple market failures.

4. Carbon cycle
20% of carbon emissions stays up forever in the atmosphere and the remaining part has a mean lifetime of 300 years.
About half carbon impulse is removed after thirty years.
The equilibrium climate sensitivity  is set to 3 in line with IPCC (2007), so doubling of carbon stock leads to 3 additional degrees Celsius. Has been revised downwards.
Ignores time lag of about 70 years between peak temperature and emissions (Gerlagh and Liski, 2013).
Ignores positive feedback: e.g., release of carbon from the ocean floors at higher temperatures

5. What’s left of GDP after damages from warming?
Our IAM supposes damages rise quite rapidly!
0.7
0.75
0.8
0.85
0.9
0.95
1
380
580
780
980
Net output after damages
Atmospheric stock of carbon (ppm by vol. CO2)
Nordhaus
Nordhaus-Weitzman
Golosov et al.

6. A Green Ramsey IAM
Social planner maximizes utilitarian welfare with rate of impatience  and intergenerational inequality aversion IIA = 1/E.I.S. = 1/ subject to:
capital accumulation driven by what is left of output net of climate damages after depreciation, energy costs and consumption of final goods,
accumulation of the permanent and the transient components of the carbon stock,
depletion of fossil fuel reserves, and
accumulation of stock of cumulative knowledge in using renewable energy.

7. Efficiency conditions
Keynes-Ramsey rule: the interest rate is the rate of impatience plus the wealth effect – higher growth and more inequality aversion imply a higher discount rate and thus a lower social cost of carbon and less stranded assets.
Hotelling rule: capital gains on extra barrel in ground must equal return from taking out an extra barrel (interest minus marginal increase in extraction cost). Hence, scarcity rent of depleting an extra barrel of oil is the present value of all future marginal increases in extraction costs resulting from this.

8. Social benefit of using renewable energy and social cost of carbon
The social cost of carbon (SCC) is the present value of all future marginal climate damages resulting from burning an additional ton of carbon. The carbon tax should equal to internalize global warming externalities.
The SCC increases if time impatience is less, climate damages impact production more, decay of atmospheric carbon is less and the climate sensitivity is bigger.
Social benefit of using an extra unit of renewable energy is the present value of all future reductions in marginal cost of renewable energy. A renewable subsidy ensures this social benefit of learning-by-doing externalities is internalized.

9. Phases, timing & how much reserves to abandon
Initial fossil fuel only phase.
Intermediate phase – joint use of fossil fuel and renewable.
Final carbon-free phase: only use renewable energy.
Energy price cannot jump at phase switches  switch time.
Zero scarcity rent and condition that social cost of fossil fuel and energy are same  fossil fuel left untapped.
Stranded assets thus increase with SCC and decrease with cost of renewable energy and renewable subsidy at that time.

10. A simple formula for the social cost of carbon
With IIA = 1, Cobb-Douglas production, 100% depreciation each decade and no capital needed to extract fossil fuel, the SCC is proportional to world GDP (Golosov et al., 2014):
A lower discount rate  pushes up the SCC.
The optimal ratio of the carbon tax to GDP is independent of technology and the depreciation rate.
Does not take account of other market distortions.
5112.379100.20.80.393.tGDP      

11. Calibration
Intergenerational inequality aversion is 2 > 1.
Time impatience is 10%/decade or 0.96%/year.
Depreciation of capital is 0.5 per decade or 6.7%/year.
Factor substitution elasticity 0.5, capital share 0.35 and energy share 0.06.
World population is 6.5 billion in 2010, grows initially at 1% per year and flattens off to a plateau of 8.6 billion.
Total factor productivity growth starts at 2% per year and flattens off at 3 times initial level.
Fossil fuel extraction costs quadruple if another 2000 GtC is extracted (0.35 divided by fraction of initial reserves that are left so ).

12. Calibration continued
Use initial world GDP (63 $T) to back out initial TFP.
Use Nordhaus’ cost of decarbonising economy (5.6% of GDP) and cost of producing conventional energy (6.4%), through learning by doing this cost can be reduced by 60% to a lower limit of 5% of GDP, and cost of energy drops by 20% in a decade if all energy is renewable.
This gives production cost per unit of renewable energy as b(B t) = 0.8 + 1.2 exp(0.008 Bt).

13. Policy simulations
Calibration in line with standard parameters but on upper end of renewable estimates (more available).
Solution decade by decade from 2010 to 2600.
4 policy scenarios: ‘laissez-faire’, ‘only tax’, ‘only subsidy’, and ‘optimal’ (solid lines).
Colour coding:

14. 0
100
200
300
400
500
600
700
2010
2060
2110
2160
2210
2260
2310
$trillions (2010)
Capital Stock, Kt
0
1
2
3
4
5
6
2010
2060
2110
2160
2210
2260
2310
°C (above pre-industrial)
Mean Global Temperature, Tt
0
5
10
15
20
25
2010
2060
2110
2160
2210
GtC / yr
Fossil Fuel Use, Ft
0
5
10
15
20
25
30
35
40
2010
2060
2110
2160
2210
GtC / yr
Renewable Energy Use, Rt

15. 0
100
200
300
400
500
600
700
800
2010
2060
2110
2160
2210
2260
2310
$ / tC
Social Cost of Carbon, τt
0
100
200
300
400
500
2010
2060
2110
2160
2210
2260
2310
$ / tC
Subsidy for Renewable Energy, νt
0
500
1000
1500
2000
2500
3000
2010
2060
2110
2160
2210
GtC
Cumulative Emissions
0
50
100
150
200
250
300
350
2010
2060
2110
2160
2210
2260
2310
$ / tC
Hotelling Rent, ϴst

16. 1000
2000
3000
4000
2010
2060
2110
2160
GtC
Fossil Reserves, St
300
500
700
900
1100
2010
2060
2110
2160
$ / tC
Production cost of renewables b(Bt)

17. Global warming, the great transition and stranded assets
The optimal policy mix combines a carbon tax from 100$/tC in 2010 to 275$/tC in 2050 with a renewable subsidy starting with 160$/tCe, rising rapidly to 380$/tCe in 2030 and then tapering off to zero quickly
So quickly make renewable energy competitive and have a gradually rising carbon tax to price fossil fuel out of the market. This policy limits warming to 2.3°C.
Under “laissez faire” temperature rises to 5.3°C. Missing markets lead to a transitory capital over-accumulation, inducing severe climate damage and a fall in capital stock. Rising extraction costs drive transition.
The optimal transition uses 400 GtC in total, but under “laissez faire” uses more than 2,500 GtC.
No policy  welfare loss is 73% of today’s global GDP.

18. National second best outcome
30 years of climate negotiations have utterly failed. How about national renewable subsidies?
Level and duration of subsidy increases compared with first best to compensate for lack of carbon tax.
Temperature is limited to 3.70 C and the welfare loss is only 10% of GDP compared to first best.
If only a carbon tax is in place, the welfare loss is only 3% of GDP compared to first best.
Important to prioritize the carbon tax, but renewable subsidy is not such a bad second-best instrument to avert the worst of global warming.

19. Market price of fossil fuel and renewable ($/tC)
200
400
600
800
1000
1200
2010
2060
2110
2160
2210
2260
2310
$ / tC

20. Scarcity rents and Green Paradox
Optimal carbon policies and renewable subsidies lower market prices of fossil fuel but increase social prices of fossil fuel, so it becomes less attractive to use them for business. Hotelling rents fall.
Under laissez faire the Hotelling rent is very large.
With only renewable subsidy, the renewable subsidy depresses fossil fuel use and the Hotelling rent. Without a carbon tax, the market price of fossil energy falls below laissez faire so more fossil fuel is used than under laissez faire (blue line lower than brown line - Green Paradox effect).

21. 1
2
3
4
2010
2060
2110
2160
2210
2260
2310
1 / $
Social Cost of Carbon / Output
SCC/GDP is not flat, but hump shaped
Golosov et al (2014)
The carbon tax has to work
much harder if there is no
renewable subsidy in place
(red versus green).
The simple formula for
the carbon of Golosov et
al (2014) under-estimates
optimal carbon tax.

22. Robustness
5 different carbon cycles used by climate scientists and by FUND, PAGE and DICE: SCC not very robust but renewable subsidies are fairly robust.
SCC is higher and climate policy more aggressive with more fossil fuel left unburned if climate sensitivity is higher, impatience is less, technical progress and population growth are more rapid, and factor substitution is easier.
But climate policy less aggressive if there is lag between warming up and higher carbon concentration and if climate damages are additive instead of multiplicative.
 SCC and carbon tax more upfront if there is less inequality aversion.

23. Remarks
Endogenous total factor and energy productivities allows for further substitution possibilities between energy and the (K,L)-aggregate in the longer run (see estimates of Hassler et al. (2011)). This justifies a more ambitious climate policy.
US Interagency Working Group (2010) recommends SCC of 80$/tC rising to 165$/tC in 2050 based on discount rate of 3% per year. A discount rate of 2.5% would give 129 and 238$/tC in line with our estimates.
Acemoglu et al. (2012) and Mattauch et al. (2013) argue for an aggressive subsidy to kick-start green innovation; Nordhaus and Stern Review argue for a rising carbon tax. We argue for a combination of these policies.

24. DEALING WITH CLIMATE CATASTROPHES
Real possibility that a discontinuous change in damages or in carbon cycle will take place. This change can be abrupt as with shifts in monsoonal systems, but loss of ice sheets have slow onsets and can take thousands of years to have its full effect (Greenland 7m and Western Antarctica 3m, say) and may already be occurring.
Shifts can be regional with local forcing agents like aerosols as with monsoons or more global with global forcing agent CO2 or CH4.
9 big catastrophes are waiting to happen, not all at same time.
Collapse of the Atlantic thermohaline circulation is fairly imminent and might occur at relatively low levels of global warming. This affects regions differently, but might capture this with negative TFP shock.

25. Possible Tipping Points
Duration before effect is fully realized (in years)
Additional Warming by 2100
0.5-1.5 C
1.5- 3.0C
3-5 C
Reorganization of Atlantic Meridional Overturning Circulation
about 100
0-18%
6-39%
18- 67%
Greenland Ice Sheet collapse
at least 300
8-39%
33- 73%
67- 96%
West Antarctic Ice Sheet collapse
at least 300
5-41%
10- 63%
33- 88%
Dieback of Amazon rainforest
about 50
2-46%
14- 84%
41- 94%
Strengthening of El Niño-Southern Oscillation
about 100
1-13%
6-32%
19- 49%
Dieback of boreal forests
about 50
13-43%
20- 81%
34- 91%
Shift in Indian Summer Monsoon
about 1
Not formally assessed
Release of methane from melting permafrost
Less than 100
Not formally assessed.
Probabilities of Various Tipping Points from Expert Elicitation

26. Non-marginal climate policies
Estimated SCC is quite low with normal discount rate. But catastrophe induces higher SCC as hazard of catastrophe rises with temperature.
Curb risk of catastrophe  SCC and carbon taxes.
Be better prepared  social benefit of capital (SBC) and thus rationale for precautionary capital accumulation.
Convexity of hazard function matters for SCC.
Opposing effects of more intergenerational inequality aversion and thus more risk aversion on SCC and SBC: i.e., on carbon taxes and capital subsidy.

27. Final remarks
Usual estimates of the SCC are low unless a very low time impatience, say 0.1%, is used as in the Stern Review.
Taking account of small risks of climate disasters leads to bigger SCC even with usual discount rates.
Need more research on both estimates of current risks of catastrophe and how these risks increase with temperature.
Catastrophic changes in system dynamics unleashing positive feedback are much more dangerous than total factor productivity or capital stock calamities .
Catastrophe provides a much better policy narrative.

28. THANK YOU

29. JOINT OECD/NBER CONFERENCE
PARIS, 25-26/9/2014
RICK VAN DER PLOEG
UNIVERSITY OF OXFORD
BASED ON “ABANDONING FOSSIL FUEL: HOW MUCH AND HOW FAST?” WITH ARMON REZAI
AND “CLIMATE TIPPING AND ECONOMIC GROWTH: PRECAUTIONARY SAVING AND THE SOCIAL COST OF CARBON” WITH AART DE ZEEUW
The Future of Productivity: Sustainability Issues

30. Global warming damages: what is left?
 Nordhaus’ RICE (2007):
 Golosov et al. (2013):
 Ackerman & Stanton (2012):
 We take the last one, since it captures relatively high
damages at high temperatures and is more realistic.
2 2
1 1
( ) .
1 0.00284 1 ( /18.8)
Z T
T T
 
 
5 ( ) exp 2.379 Z Et   10 (2.13Et 581).
2 6.76
1
( ) .
1 ( / 20.2) ( / 6.08)
Z T
T T

 

31. Carbon stocks
No modelling of carbon in lower and upper part of oceans here.
No sudden release of methane from the permafrost or other climatic catastrophes here.
Initial stock of carbon in atmosphere is 802 GtC or 377 ppmv CO2.
It has recently gone over 400 ppmv CO2.
Initial stock of 4000 GtC of fossil fuel reserves. The challenge is to lock a large part up in the crust of the earth.
Initial stock of physical capital is 200 trillion $

32. Transition times and carbon budget
Only fossil fuel
Simultaneous use
Renewable Only
Carbon used
Social optimum
2010-2020
2030-2040
2050 –
400 GtC
Carbon tax only
2010-2050
N.A.
2060 –
730 GtC
Renewable subsidy only
2010-2050
2060-2080
2090 –
1250 GtC
No policy
2010-2110
N.A.
2120 –
2510 GtC

33. BACKGROUND SLIDES
Robustness to different carbon cycles
Sensitivity runs
Climate policies in face of catastrophe

34. Robustness: 5 Climate Cycles
There exists large difference between estimates of the social cost of carbon.
Many models… even more modelers.
Systematic comparison of prominent climate cycles necessary to understand importance of economics and science for policy prescriptions
Comparison of:
Oxford cycle (Allen et al., 2013)
FUND (Anthoff and Tol, 2009)
DICE (Nordhaus, 2014)
GL (Gerlagh and Liski, 2014)
GHKT ( Golosov et al., 2014)

35. Robustness – Temperature
0.5
1
1.5
2
2.5
2010
2060
2110
2160
2210
2260
2310
2360
2410
°C above pre-industrial
GHKT
GL
Oxford
DICE
FUND

36. Interpretation
Oxford model closest to geo-sciences. Best approximation of diffusive and advective forces governing carbon and temperature cycles between atmospheric and oceanic layers.
Lowest Transient Climate Response (TCR), upward and downward.
The climate cycle of FUND and GL exhibits higher TCR but also faster recovery.
DICE appears very sensitive (highest TCR) and slow recovery.
GHKT lacks temperature lag and recovers extremely fast.
These temperature responses mirror the carbon tax (SCC)…

37. Little Robustness – Social Cost of Carbon
0
50
100
150
200
250
300
2010
2030
2050
2070
2090
2110
2130
2150
2170
2190
$ / tC
GHKT
GL
Oxford
DICE
FUND

38. Large Robustness – Renewable Subsidy
0
200
400
600
800
1000
1200
2010
2030
2050
2070
2090
2110
2130
2150
2170
2190
$ / tC
GHKT
GL
Oxford
DICE
FUND

39. Social Cost of Carbon - Sensitivity
0
400
800
1200
1600
2010
2060
2110
2160
2210
2260
2310
$ / t C
Baseline
IES = ∞
K(0) = 100
ρ = 0
ω = 6
ξ = 0
A(∞) = 5
CES = 0.5
Lag Temp.
L(∞) = 10.6

40. Interpretation
SCC is higher and climate policy is more aggressive requiring a higher carbon tax and renewable subsidy, leaving more fossil fuel unburned and thus using less fossil fuel if:
the equilibrium climate sensitivity  is higher (6 not 3),
the discount rate  is lower (0 not 0.96%/year),
technological progress is more rapid (A( ) = 5 not 3),
elasticity of factor substitution  is higher (o.5 not 0),
population explosion is more substantial (L() = 10.6 not 8.6 billion).
But climate policy less aggressive if:
there is a lag between warming up and higher carbon concentration,
intergenerational inequality aversion is weaker,
global warming damages are additive ( = 0), not multiplicative ( = 1).
SCC and carbon tax more upfront if EIS =  and IIA = 0.
Climate policy not much affected if:
the initial capital stock K0 is half the size (100 not 200 trillion $).

41. Climate catastrophe and Mr Bean
In ‘doomsday’ scenario with complete disaster, the discount rate is increased so frantic consumption and less investment. Mr Bean!
With no ‘doomsday’ the world goes on after disaster hits. Then precaution is needed. Since consumption will fall after disaster, SBC > 0 and if this is not internalized a capital subsidy is required. Hence, now the discount rate is reduced.
The SBC is bigger if the hazard and size of the disaster are bigger.
And if CRIIA bigger.
1/ ()10. BACHEC     

42. SBC and SCC
 Social benefit of capital or SBC:
 Social cost of carbon or SCC (using utility discount
rate or market interest rate:
1/
'( )
( ) 1 ( ) 1 0.
'( )
A B
B A
U C C
H E H P
U C C


    
         
      
 
   
 
      
              
( ), ( ) ( ),
' ( ) ( ') ( '), ( ') ( ') '
' ( )
( ') '
( ) exp
' ( ) ( ), ( ) ( ), exp / ' ( ) .
B A
s
B t
s
t
t
B A B
t
V K s E s V K s
H E s r s K s E s H E s ds
U C s
H E s ds
t ds
H P s V K s E s V K s ds U C t
 
 




 
    
  

      





43. Calibration of linear and quartic hazard functions
H(P) = 2.926 x 10-5 x P & H(P) = 2.33 x 10-15 x P4
 Expected time for hit at initial P is 42 years for linear and 1000 years for quartic hazard function
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
820
1020
1220
1420
1620
1820
2020
2220
Calibrated hazard rate
Atmospheric carbon stock (GtC)
H(2324 GtC=6 degrees Celsius) =0.068
linear h
Exog h (linear)
quartic h
Exog h (quartic)

44. No shock
After calamity
Before calamity
Exogenous h = 2.4%
Linear H(P)
Quartic H(P)
Capital stock, K (T US $)
356
202
486
535
346
Fossil fuel use (GtC)
10.1
5.7
11.1
8.9
5.5
Renewable use (TBTU)
11.3
6.4
12.5
12.7
10.8
World GDP (T US $)
75.9
43.1
83.9
85.1
72.3
Net output, Y (T US $)
52.8
30.0
53.8
52.4
49.9
Consumption, C (T US $)
52.8
30.0
53.8
53.6
52.0
Carbon stock, E (GtC)
1,679
954
1,857
1,482
911
Temperature, Temp
4.6
2.1
5.0
4.1
1.9
Precautionary return (%)
0.0
0.0
1.2
1.6
0.1
Carbon tax (US $/tC)
0.0
0.0
0.0
136
381

45. 38
48
58
68
78
88
0
10
20
30
40
50
60
Global GDP (trillion 2010 US $)
h=0.024
linear h
naive
quartic h
no calamity

46. Gradual damages A(Temp) and the SCC
Before-disaster SCC has in general 3 components:
      ((') conventional Pigouvian social cost of carbon((') 'raising t()'()(),(),()'() '() ()(),,() '() ststHEsdstHEsdsAPttAEsFKsFssUCsedsUCtHEsVKsEsedsUCt                  he stakes' effect((') 'risk averting' effect(),()(),,(),0.'() '() stBAHEsdstVKsEsVKsEstTHPsedsUCt  