Presentation given during the OECD Expert workshop on Economic Modelling of Climate and Related Tipping Points by Yonyang Cai, The Ohio State University

1. Economic Implications of Multiple Interacting
Tipping Points
Yongyang Cai
The Ohio State University
October 18, 2021

2. Climate Change Policy Analysis
Question: What can and should be the policy response to rising carbon
concentration in the face of uncertainty?
Create a Framework: Dynamic Stochastic Integration of Climate and
Economy (DSICE)
I climate risk: stochastic climate tipping process
I uncertain tipping time
I multiple interacting tipping points
I multiple tipping points with domino effect
I uncertain damage level
I uncertain duration of tipping process which unfolds damage
gradually (e.g., sea level rise)
I economic risk: stochastic growth with calibration from empirical
consumption data
I parameter uncertainty

3. Papers
I Lontzek, Cai, Judd, and Lenton (2015). Stochastic integrated
assessment of climate tipping points indicates the need for strict
climate policy. Nature Climate Change, 5, 441–444.
I Cai, Judd, Lenton, Lontzek, and Narita (2015). Environmental
tipping points significantly affect the cost-benefit assessment of
climate policies. Proceedings of the National Academy of Sciences,
112(15), 4606–4611.
I Cai, Lenton, and Lontzek (2016). Risk of multiple interacting
tipping points should encourage rapid CO2 emission reduction.
Nature Climate Change, 6, 520–525.
I Cai and Lontzek (2019). The social cost of carbon with economic
and climate risks. Journal of Political Economy, 127(6), 2684–2734.1
1An earlier working paper version is Cai, Judd, and Lontzek (2017).

4. Schematic of DSICE
Based on Professor William Nordhaus’s DICE model

5. DICE vs DSICE
I DICE: a deterministic dynamic optimization model
I More carbon emissions from economic activities —> higher
atmospheric carbon concentration —> higher atmospheric
temperature —> higher damage to the economy
I A social planner chooses optimal consumption and mitigation to
maximize the social welfare
I DSICE: a stochastic extension of DICE
I incorporating a climate tipping module (and economic risk)
I a social planner maximizes the expected social welfare

6. Climate Tipping Module
I Climate tipping process is modelled as a Markov chain with the
probability transition matrix
1 − pt pt
0 1
,
where pt is the tipping probability at time t
I Tipping probability depends on the contemporaneous atmospheric
temperature
pt = 1 − exp −b1 max 0, TAT
t − 1
,
where b1 is the hazard rate, TAT
t,1 is atmospheric temperature
I Damage factor (damage is assumed to be proportional to output):
Ωt =
1 − Jt
1 + π1TAT
t + π2(TAT
t )2
I Jt is damage level from climate tipping process (0 before a tipping
event occurs; gradually increases to its upper bound in many years)
I π1, π2: parameters in the quadratic damage function of DICE
I It cannot be captured by changing the shape (e.g., increasing the
exponents) of the damage function of global warming.

7. Carbon tax (Lontzek et al., NCC 2015)
Left: optimal carbon tax (10,000 simulation paths); Right: Cumulative
probabilities of tipping (average of 10,000 simulation paths)
I Default parameter case: duration - 50 years; final damage level -
10%; hazard rate b1 = 0.0025

8. Carbon tax (continued)
I In comparison with DICE, the tipping risk causes an immediate 50%
increase of carbon tax in the initial year
I The threat of the tipping risk creates an incentive to reduce the
tipping probability and to delay or cancel the potential tipping event.
I Higher carbon taxes — more mitigation — lower atmospheric
carbon concentration — lower atmospheric temperature — lower
tipping probability.
I If the tipping event occurs, this incentive disappears and the carbon
tax will drop down immediately, although the damage from the
tipping process just starts to unfold from zero and will take 50 years
to fully unfold.

9. Growth rates of carbon tax (Lontzek et al., NCC 2015)
Black line: growth rates of DICE carbon tax; Blue line: growth rates of
the expected additional carbon tax when including a tipping point; Red
lines: growth rates of the additional carbon tax when the exponent of the
damage function in DICE is increased to fourth (solid line) and sixth
(dashed line) order.

10. Growth rates of carbon tax (continued)
I The expected additional carbon tax to address the tipping point
threat grows at roughly half the average rate of the DICE carbon
tax. Such a flat carbon tax path is also obtained when the discount
rate is prescribed to be lower.
I Tipping points add a source of risk to the economic system, which
increases the variance of future output.
I Increasing the capital stock in DICE will increase future expected
output, and the marginal benefit from investment today is
discounted at the market interest rate.
I Increasing mitigation expenditures will increase future expected
output (again discounted at the market interest rate) by reducing
expected damages, but will also reduce the variance of future output
under tipping risks (further increasing social welfare).This implies a
discount rate that is less than the interest rate.
I Using a larger exponent of the damage function (e.g., degree 4 or 6)
enhances the growth rate of the carbon price (implying a higher
discount rate). Hence, adjusting the shape of a deterministic
damage function qualitatively fail to capture the implications of
stochastic tipping points.

11. Carbon tax with environmental tipping points (Cai et al.,
PNAS 2015)
I Substitutability between nonmarket and market goods is limited.
When environmental goods and services become scarcer, their
relative price increases

12. Carbon tax with environmental tipping points (continued)
I An environmental tipping point, even if it only has nonmarket
impacts, could substantially increase the present optimal carbon tax
I an immediate two-thirds increase in optimal carbon tax under the
default case (5% loss in nonmarket goods; 5% annual probability at
4 °C increase)
I If the tipping point has a 5% damage on both market and nonmarket
goods, the optimal carbon tax increases by more than a factor of 3.

13. Multiple Interacting Tipping Points (Cai et al., NCC 2016)
Five tipping elements: GIS (Greenland Ice Sheet), AMOC (Atlantic
thermohaline circulation), AMAZ (Amazon rainforest), ENSO (El
Nino-Southern Oscillation), WAIS (West Antarctic Ice Sheet)

14. Sample Paths (Cai et al., NCC 2016)
Sample paths of the social cost of carbon (SCC) in US dollars per ton of
CO2 with multiple tipping points interacting and not interacting.

15. Sample Paths (continued)
I The no-interactions sample path shows that passing a tipping point
reduces the incentive to mitigate and therefore lowers the SCC.
I However, with interactions,
I tipping of the GIS significantly increases the likelihood of AMOC
tipping (which is assumed to be the most damaging event);
I hence, this causes a large increase in the SCC to try to avoid AMOC
tipping.
I Subsequent tipping of AMOC greatly reduces the SCC, as the
incentive to avoid AMOC tipping disappears.
I Tipping of ENSO increases the SCC because it significantly increases
the likelihood of tipping the Amazon.
I Subsequent tipping of the Amazon halves the SCC because only
WAIS left to tip and AMAZ tipping does not change the likelihood
of WAIS tipping.

16. Multi-Stage Tipping Process with Domino Effect
I Multi-stage climate tipping process with domino effect
I pre-tipping stage
I (four) intermediate stages (irreversible damage)
I final absorbing stage (irreversible damage)
I once the first tipping event occurs, the other four tipping events will
occur afterwards
I Uncertain tipping times
I Uncertain damage level
I Uncertain duration of the intermediate stages (using exponential
distribution of state transition time)

17. Sample Paths for DSICE with Only Tipping (Cai and
Lontzek, JPE 2019)
Two sample paths of damage and SCC: A different simulation path has
different tipping times, different damage levels, and different durations.

18. Sample Paths for DSICE with Only Tipping (continued)
I The first tipping event’s probability depends on the
contemporaneous atmospheric temperature; the other tipping events
have a constant tipping probability
I Before the first tipping event, since its tipping probability depends
on the contemporaneous atmospheric temperature, there is an
incentive to reduce the tipping probability
I When the first tipping event occurs, the damage jumps up
immediately, since the other tipping events’ probabilities are
constant, the incentive disappears, then the SCC drops down
immediately; when the other tipping events occur, the damage also
jumps up immediately, but their tipping probability cannot be
reduced, so the SCC has no big drops.

19. Summary
I The discount rate for potential future damage from tipping events is
lower than market interest rate
I A climate tipping point significantly increases the SCC or carbon tax
if the tipping probability depends on temperature, even with
conservative assumptions about tipping damage level, duration and
hazard rate.
I If an environmental tipping risk has loss in nonmarket goods, it
could increase the SCC significantly
I If a tipping event occurs and there are no more other tipping events,
the SCC drops down immediately
I If there are multiple tipping events, after one tipping event occurs, if
it increases the likelihood of other tipping events significantly and
their tipping probabilities depend on temperature, then the SCC
jumps up; otherwise the SCC jumps down.
I For an extended discussion about parameter uncertainty, economic
climate risk, model/scenario uncertainty, ambiguity, policy
uncertainty in climate change economics and how to deal with them:
I Cai, Y (2021). The role of uncertainty in controlling climate change.
Oxford Research Encyclopedia of Economics and Finance. Oxford
University Press.