Stock-flow consistent models and Climate-Economy Modelling
Stock-flow consistent models andClimate-Economy Modelling
M. R. Grasselli
Mathematics and Statistics - McMaster University
Joint work with Emma Holmes, Daniel Presta and Ben Bolker (McMaster)Gael Giraud, Etienne Espagne, Devrim Yilmaz, Antoine Godin (AFD)
Jose M. Pedraza-Ramırez, Vegan Pather, Nomvelo Sibisi, Kilian Wohlleben(FMTC)
OECD-NAEC MasterclassesParis, March 06 2020
Stock-flow consistent models and Climate-Economy Modelling
Introduction
Climate Risk
I Physical impact: losses from extreme events were $ 320 billionin 2017 and are estimated by Allianz (2018) to reach annualaverage of $1 trillion within 10 years.
I Stranded assets: assets of fossil fuel companies and othercompanies whose future revenues depend on a carbon bubbleestimated to be $4 trillion (Mercure et al, Nature ClimateChange (2018).
I Transition to low-carbon economy: risk associated withdivesting trillions of dollars from carbon intensive industriesinto low-carbon.
Stock-flow consistent models and Climate-Economy Modelling
Introduction
Portfolio Decarbonization
Stock-flow consistent models and Climate-Economy Modelling
Introduction
Investment needs and opportunities
I Required low-carbon infrastructure investment ranges from5% to 15% of global infrastructure investment, estimated tobe around $6 trillion per year.
I Cost of adaptation is estimated to range from $150 to $300billion per year by 2030.
I This $450 to $1,200 billion range should be compared withthe current annual financial flow of $400 billion directedtowards green investment.
I Current flows need to be tripled in order to cover the fundinggap for the low-carbon transition.
Stock-flow consistent models and Climate-Economy Modelling
Introduction
Green Finance - Climate Policy Initiatives Organization2018 Finance Update
Actors 2015 2016
Private 267 230Commercial FI 54 42Corporates 46 28Households 39 44Institutional Investors 3 2Private Equity 2 1Project Developers 124 113Public 205 224Governments and their agencies 17 19Climate Funds 2 3Public FI (Bilateral) 17 14Public FI (Multilateral) 44 48Public FI (National) 124 140Total 472 455
Stock-flow consistent models and Climate-Economy Modelling
Introduction
Green bonds
Stock-flow consistent models and Climate-Economy Modelling
SFC Climate Models
A SFC Climate Model
Stock-flow consistent models and Climate-Economy Modelling
SFC Climate Models
The Economic Module
Basic Definitions
Y 0 =K
ν= aL, Y = (1 −DY )(1 − A)Y 0
Π = pY − wL− rD − TC − pδK
ω =wL
pY, d =
D
pY, π =
Π
pY
I = κ(π)Y , K = I − δDK
D = pI + Πd − Π − pδDK
Πd = ∆(π)pY
i =p
p= ηp(mc − 1)
Stock-flow consistent models and Climate-Economy Modelling
SFC Climate Models
The Economic Module
Differential Equations
ω = ω(φ(λ) − i − α)
λ = λ(g − α− β)
d = −d(i + g) + κ(π) + ∆(π) − π − νδD1 −DY
N = qN
(1 − N
PN
)with
π = 1 − ω − rd − pcσ + δDY
1 −DY
g =κ(π)(1 −DY )
ν− δD
Stock-flow consistent models and Climate-Economy Modelling
SFC Climate Models
The Economic Module
Special case - the Keen model
If we decouple this model from the climate, it reduces to
ω = ω [Φ(λ) − α]
λ = λ
[κ(1 − ω − rd)
ν− α− β − δ
](1)
d = d
[r − κ(1 − ω − rd)
ν+ δ
]+ κ(1 − ω − rd) − (1 − ω)
Stock-flow consistent models and Climate-Economy Modelling
SFC Climate Models
The Economic Module
Example: convergence to the good equilibrium in a Keenmodel
0.7
0.75
0.8
0.85
0.9
0.95
1
λ
ωλYd
0
1
2
3
4
5
6
7
8x 10
7
Y
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
d
0 50 100 150 200 250 300
0.7
0.8
0.9
1
1.1
1.2
1.3
time
ωω
0 = 0.75, λ
0 = 0.75, d
0 = 0.1, Y
0 = 100
d
λ
ω
Y
Figure: Grasselli and Costa Lima (2012)
Stock-flow consistent models and Climate-Economy Modelling
SFC Climate Models
The Economic Module
Example: explosive debt in a Keen model
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
λ
0
1000
2000
3000
4000
5000
6000
Y
0
0.5
1
1.5
2
2.5x 10
6
d
0 50 100 150 200 250 3000
5
10
15
20
25
30
35
time
ωω
0 = 0.75, λ
0 = 0.7, d
0 = 0.1, Y
0 = 100
ωλYd
λ
Y d
ω
Figure: Grasselli and Costa Lima (2012)
Stock-flow consistent models and Climate-Economy Modelling
SFC Climate Models
The Economic Module
Example: explosive debt in a Keen model
0
1
2
3
4
5
6
7
8
9
10
d
−7
−6
−5
−4
−3
−2
−1
0
1
dd/d
t
0 10 20 30 40 50 60 70 80 90
0.4
0.5
0.6
0.7
0.8
0.9
1
time
λω
0 = 0.75, λ
0 = 0.7, d
0 = 0.1
Stock-flow consistent models and Climate-Economy Modelling
SFC Climate Models
The Economic Module
Corporate Debt share in the US 1950-2014
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1950 1960 1970 1980 1990 2000 2010
ShadedareasindicateUSrecessions-2014research.stlouisfed.org
NonfinancialBusiness;CreditMarketInstruments;Liability,Level/GrossDomesticProduct
(Bil.of$/Bil.of$)
Stock-flow consistent models and Climate-Economy Modelling
SFC Climate Models
The Economic Module
Alternative insight 3: private debt matters
Figure: Change in debt and unemployment.
Stock-flow consistent models and Climate-Economy Modelling
SFC Climate Models
The Economic Module
Basin of convergence for Keen model
0.5
1
1.5
0.40.5
0.60.7
0.80.9
11.1
0
2
4
6
8
10
ωλ
d
Figure: Grasselli and Costa Lima (2012)
Stock-flow consistent models and Climate-Economy Modelling
SFC Climate Models
The Climate Module
Global Emissions
Stock-flow consistent models and Climate-Economy Modelling
SFC Climate Models
The Climate Module
Emissions per country
Stock-flow consistent models and Climate-Economy Modelling
SFC Climate Models
The Climate Module
Emissions
E = Eind + Eland , Eind = σ(1 − n)Y 0, Eland = δElandEland
σ = gσσ, gσ < 0 (carbon intensity)
gσ = δgσgσ, δgσ < 0
n = min
{(pCpBS
) 1θ−1
, 1
}, θ > 1 (emission rate)
˙pBSpBS
= δBS ≤ 0 (backstop technology)
pCpC
= δC (·) ≥ 0 (carbon)
A =σpBSn
θ
θ(abatement cost)
TC = pCEind (carbon tax)
Stock-flow consistent models and Climate-Economy Modelling
SFC Climate Models
The Climate Module
Carbon intensity
Stock-flow consistent models and Climate-Economy Modelling
SFC Climate Models
The Climate Module
Carbon price
2020 2040 2060 2080 2100
050
100
150
200
250
300
year
p c
Stock-flow consistent models and Climate-Economy Modelling
SFC Climate Models
The Climate Module
Carbon price gap
Stock-flow consistent models and Climate-Economy Modelling
SFC Climate Models
The Climate Module
Backstop technology
Stock-flow consistent models and Climate-Economy Modelling
SFC Climate Models
The Climate Module
Carbon cycle
˙CO2AT
˙CO2UP
˙CO2LO
=
E00
+ Φ
COAT2
COUP2
COLO2
where
Φ =
−φ12 φ12CATUP 0
φ12 −φ12CATUP − φ23 φ23C
UPLO
0 φ23 −φ23CUPLO
Stock-flow consistent models and Climate-Economy Modelling
SFC Climate Models
The Climate Module
Radiative Forcing
The accumulation of CO2 increases radiative forcing
F := Find + Fexo
as follows
Find :=Fdbl
log(2)log
(COAT
2
COAT2preind
)where Fdbl is an exogenous parameter that represents the effect onforcing of a doubling of pre-industrial CO2 levels and Fexo increasesexogenously over time.
Stock-flow consistent models and Climate-Economy Modelling
SFC Climate Models
The Climate Module
Exogenous radiative forcing
Stock-flow consistent models and Climate-Economy Modelling
SFC Climate Models
The Climate Module
Temperature and Damages
CT = F − FdblS
T − γ∗(T − TLO)
CLO˙TLO = γ∗(T − TLO)
D = 1 − 1
1 + ξ1T + ξ2T 2(Nordhaus)
DK = fkD
DY = (1 − fk)D
Stock-flow consistent models and Climate-Economy Modelling
SFC Climate Models
The Climate Module
Alternative Damage Functions
D = 1 − 1
1 + ξ1T + ξ2T 2 + ξ3T ζ(Dietz and Stern)
a
a= α1(Tpre + T ) + α2(Tpre + T )2 (Burke et al)
Stock-flow consistent models and Climate-Economy Modelling
SFC Climate Models
The Climate Module
Damage functions
Stock-flow consistent models and Climate-Economy Modelling
SFC Climate Models
The Climate Module
Model Schematic
Global
warming
CO2
accumulationDebt
Carbon
emission
Abatement
+Consumption
+Investment
DamageEconomic
production/
GDP
Energy Labour Capital
Reduces
Reduces
1
Stock-flow consistent models and Climate-Economy Modelling
AFD paper
Example 1: No feedback - Bovari et al (2018a)
Stock-flow consistent models and Climate-Economy Modelling
AFD paper
Example 2: Effect of temperature on equilibrium values
Stock-flow consistent models and Climate-Economy Modelling
AFD paper
Example 3: Dynamic effects
Stock-flow consistent models and Climate-Economy Modelling
AFD paper
Example 4: Sensitivity analysis - Bovari et al (2018b)
Stock-flow consistent models and Climate-Economy Modelling
McMaster paper
North-South Extension
I Different productivity, capital-to-output ratio, investment andconsumption functions
I Disaggregated damage functions
I Exchange rate mechanism
I Independent carbon pricing
I Subsidies and cooperation
I Migration
Stock-flow consistent models and Climate-Economy Modelling
McMaster paper
Two-regions dynamics
Stock-flow consistent models and Climate-Economy Modelling
McMaster paper
Policy scenarios
Stock-flow consistent models and Climate-Economy Modelling
FMTC paper
Benchmark scenario
Stock-flow consistent models and Climate-Economy Modelling
FMTC paper
No policy scenario
Stock-flow consistent models and Climate-Economy Modelling
FMTC paper
Sensitivity with respect to abatement costs
Stock-flow consistent models and Climate-Economy Modelling
FMTC paper
Sensitivity with respect to backstop technology
Stock-flow consistent models and Climate-Economy Modelling
FMTC paper
Sensitivity with respect to green bond premium
Stock-flow consistent models and Climate-Economy Modelling
FMTC paper
Tax and subsidy scenarios
Stock-flow consistent models and Climate-Economy Modelling
FMTC paper
Cap and trade (1)
Stock-flow consistent models and Climate-Economy Modelling
FMTC paper
Cap and trade (2)
Stock-flow consistent models and Climate-Economy Modelling
FMTC paper
Carbon price comparison
Stock-flow consistent models and Climate-Economy Modelling
FMTC paper
Temperature comparison
Stock-flow consistent models and Climate-Economy Modelling
FMTC paper
What about shocks?
I Nguyen Huu and Costa Lima (2014) introduce stochasticproductivity of the form
dat := atdαt = at(αdt − σ(λt)dt
leading to a modified model of the form
ω
ω= Φ(λ) − α + σ2(λt)dt + σ(λt)dWt
λ
λ=
1 − ω
ν− α− β − δ + σ2(λt)dt + σ(λt)dWt
I They then prove the existence of stochastic orbits generalizingthe original Goodwin cycles.
Stock-flow consistent models and Climate-Economy Modelling
FMTC paper
Stochastic orbits of a Goodwin model with productivityshocks
Figure: Figure 3 in Nguyen Huu and Costa Lima (2014)
Stock-flow consistent models and Climate-Economy Modelling
FMTC paper
Keen model with inflation
Consider a wage-price dynamics of the form
w
w= Φ(λ) + γi , (2)
i =p
p= −ηp
[1 − ξ
w
ap
]= ηp(ξω − 1) (3)
Denoting the firm sector net borrowing ratio by d = D/Y , themodel can now be described by the following system
ω = ω [Φ(λ) − α− (1 − γ)i(ω)]
λ = λ [g(π) − α− β]
d = κ(π) − π − d [i(ω) + g(π)]
(4)
where π = 1 − ω − rd and i(ω) = ηp(ξω − 1).
Stock-flow consistent models and Climate-Economy Modelling
FMTC paper
Parameter sweep
Stock-flow consistent models and Climate-Economy Modelling
Conclusions
Conclusions
I Climate change is the most formidable challenge faced by thehuman race
I Traditional macroeconomics is ill-equipped to contribute to it
I Integration of dynamic models with disequilibrium and slowlyadjusting variables is needed
I Finance is likely to play a fundamental role in the low-carbontransition
I Should try everything that is available: carbon tax, subsidies,green bonds, green securitization, green central banking, etc
I We need a Green Bubble
Stock-flow consistent models and Climate-Economy Modelling
Conclusions
Merci
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