Stock-flow consistent models and Climate …...Stock-ow consistent models and Climate-Economy Modelling Conclusions Conclusions I Climate change is the most formidable challenge faced

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


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.


Introduction

Portfolio Decarbonization


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.


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


Introduction

Green bonds


SFC Climate Models

A SFC Climate Model


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)


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


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)


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)


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



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


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$/Bil.of$)


SFC Climate Models

The Economic Module

Alternative insight 3: private debt matters

Figure: Change in debt and unemployment.


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



SFC Climate Models

The Climate Module

Global Emissions


SFC Climate Models

The Climate Module

Emissions per country


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)


SFC Climate Models

The Climate Module

Carbon intensity


SFC Climate Models

The Climate Module

Carbon price

2020 2040 2060 2080 2100

050

100

150

200

250

300

year

p c


SFC Climate Models

The Climate Module

Carbon price gap


SFC Climate Models

The Climate Module

Backstop technology


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


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.


SFC Climate Models

The Climate Module

Exogenous radiative forcing


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


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)


SFC Climate Models

The Climate Module

Damage functions


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


AFD paper

Example 1: No feedback - Bovari et al (2018a)


AFD paper

Example 2: Effect of temperature on equilibrium values


AFD paper

Example 3: Dynamic effects


AFD paper

Example 4: Sensitivity analysis - Bovari et al (2018b)


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


McMaster paper

Two-regions dynamics


McMaster paper

Policy scenarios


FMTC paper

Benchmark scenario


FMTC paper

No policy scenario


FMTC paper

Sensitivity with respect to abatement costs


FMTC paper

Sensitivity with respect to backstop technology


FMTC paper

Sensitivity with respect to green bond premium


FMTC paper

Tax and subsidy scenarios


FMTC paper

Cap and trade (1)


FMTC paper

Cap and trade (2)


FMTC paper

Carbon price comparison


FMTC paper

Temperature comparison


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.


FMTC paper

Stochastic orbits of a Goodwin model with productivityshocks

Figure: Figure 3 in Nguyen Huu and Costa Lima (2014)


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).


FMTC paper

Parameter sweep


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


Conclusions

Merci

Documents

Stock-flow consistent models and Climate …...Stock-ow consistent models and Climate-Economy Modelling Conclusions Conclusions I Climate change is the most formidable challenge faced