Coping with the Collapse: A Stock-Flow Consistent

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Coping with the Collapse: A Stock-Flow Consistent, MonetaryMacro-dynamics of Global Warming

June 23, 2016

Gaël Giraud Florent Mc Isaac Emmanuel Bovari Ekaterina ZatsepinaAFD - Agence Française de Développement; Chair Energy and Prosperity; CES - Centre d’Economie de la

Sorbonne

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� Outlines

1 Introduction

2 The Keen (1995) Model

3 Macroeconomic model for climate change

4 Climate Module

5 Public Policy Module

6 Numerical Simulations

7 Further Work

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� Introduction

� The Limits to Growth was published (Meadows et al., 1972 andMeadows et al., 1974).

� Turner (2008, 2012, 2014) and Hall and Day (2009) tend toconfirm the LtG standard run scenarios.

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� IntroductionSustainable path or collapse?

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� Introduction

� Consistent with increasing capital costs and net energy (thedecline of energy returned on energy invested, EROI).

� Growing scarcity of natural resources (energy, minerals, water...),while climate change plays little role, if any. (Caveat: Pollution).

� The question of whether global warming might per se induce asimilar breakdown of the world economy (cf. COP 21).

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� IntroductionPaper’s framework

� We explicitly model the financial side of the world economy inorder to assess the possible negative feedback of debt on theability of the world economy to cope with the collapse.

� Pivotal role of private debt.� Losses due to environmental damages force the global

productive sector to invest a growing part of its wealth inrestoring and maintaining capital.

� The persistent level of debt may endanger the world economicengine itself as it is based on the promise of future wealthcreation.

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� Depending upon the speed at which labor productivity increasescompared to the severity of global warming, the shrink ofinvestment induced by the burden of private debt may preventthe world economy from further adapting to the climate turmoil,leading ultimately to a collapse around the end of the twenty-firstcentury.

� The global collapse captured in this paper can be interpreted asthe result of a debt-deflation depression in the sense given to thisconcept by Irving Fisher (1933).

� That part of the world economy might be on the verge of fallinginto a liquidity trap is illustrated, today, by the two “lost decades”of Japan, of course, but also the recessionary state of theSouthern part of the Eurozone, obstinately negative long-terminterest rates on international financial markets and, last but notleast, the brutal contraction of the world nominal GDP in 2015(-6%, IMF (2016)).

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� These paradoxes may be viewed as signals of the translation ofa secular decline induced by biophysical constraints into thefinancial sphere.

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� GEMMES

GEMMESGEneral Monetary Multisectoral Macrodynamics for the Ecological

Shifts

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� GEMMES

Goodwin Goodwin-Keen Prices

Banks

Inventories

Government

SpeculationInequalities

Multisectoral

Climate backloop

Open economy

Resources

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� Outlines

1 Introduction



4 Climate Module



7 Further Work

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� The Keen (1995) ModelOverview

1. Since the financial crisis of 2007-2009, the ideas of HymanMinsky around the intrinsic instability of a monetary marketeconomy have experienced a significant revival.

2. Goodwin (1967): Lotka-Volterra logic of the wage share and theemployment rate.

3. Keen (1995): ’Black Swan’ event, or a Minsky moment can occur.4. Investment financed by endogenous money creation.

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� The Keen (1995) ModelPrivate debt matters

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� The Keen (1995) ModelStock and Flow consistent model

Balance Sheet Households Firms Banks Government SumCapital stock K KLoan −D DSum (net worth) X f X b XTransactions current capitalConsumption −C CInvestment I −IGovernment spend. G −GMemo [GDP] [GDP]Wages W −WInterests on debt −rD rDFirms’ net profit −Π Π

Financial Balances −D Πb

Flow of fundsInvestment I IChange in Loans −D DColumn sum Π D IChange in Net worth X f = Π + (p − δp)K X b = Πb X

Table: Stock-Flow Table

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� The Keen (1995) ModelThe model

λ: the employment rate.

λ :=LN.

L: the labor force, and N: the total population.

NN

= β.

a: the labor productivity.aa

= α.

w : the wage per worker, W = wL: the total wage, ω: the wage sharead Y : the production.

ω =WY

=wLaL

=wa

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K : the stock of capital.K = I − δK .

The Leontief production function

Y = min(

Kν,aL)

=Kν

= aL.

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D: the aggregate debt.D = I − Π.

withΠ := Y − W − rD: the real profit of the firm, and r : the interestrate.π: the profit-to-production ratio.

π =Π

Y.

d : the debt-production ratio.

d =DY.

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� The Keen (1995) ModelAggregate behaviours

� The Short-term Phillips Curve (Mankiw, 2010).

ww

= φ(λ).

� The Investment Function : it evolves positively with the profitshare.

IY

= κ (π) .

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� The Keen (1995) ModelThe three-dimensional system

One can retrieve the following set of equations:

ω = ω [φ(λ) − α]

λ = λ

[κ(π)

ν− δ − α− β

]d = d

[r − κ(π)

ν+ δ

]+ κ(π) − (1 − ω)

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� The Keen (1995) ModelAggregate behaviours

� Phenomenological approach: φ(.) and κ(.) are empiricallyestimated.

� Sonnenschein-Mantel-Debreu (1975): anything can happen.� Agent-based model.

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� The Keen (1995) ModelEquilibria analysis

Three long run equilibria exist:� An unstable equilibrium at (0,0,d0)

� A good equilibrium locally stable� A bad equilibrium locally stable

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� Simulations - good equilibrium with finite debt

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� Simulations - bad equilibrium with infinite debt

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� Basin of Attraction

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� The Keen (1995) ModelPossible outcome induced by climate change

� Depending upon the basin of attraction where the state of theeconomy is driven by climate damages, the ultimate breakdownmay occur as the inescapable consequence of the business asusual trajectory.

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� Outlines

1 Introduction



4 Climate Module



7 Further Work

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� Macroeconomic model for climate change

� Modelling:� The macroeconomics is borrowed from Keen (1995).

� Stock-Flow consistent.� Phenomenological functions.

� The climate feed-back loop is in line with Nordhaus’ DICE model(2013).

� Estimation� Calibration of the climate and public policy modules in line with

Norhdaus’ DICE model (2013).� Macroeconomic module estimation in progress: panel analysis to

benefit wider volatility.

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� Macroeconomic model for climate changeProduction, capital and debt accumulation

The real output

Y = (1 − D)Kν.

The investment function with abatement cost

I = (κ(π) − µG)Y .

Population grows according to a UN scenario,

NN

= q(1 − N

M).

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� Macroeconomic model for climate changeMonetary economy

The wage dynamic evolves according to a short-term Phillips curve

ww

= Φ(λ) + γi .

The price dynamics,

i =pp,

= ηp(mω − 1) + iLT .

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� Macroeconomic model for climate changeImpact of climate change

As an example, for deterministic exponential scenario, climatechange positively impact the share of wages

ω

ω=

ww

− aa

+D

1 − D− i

= φ(λ) − α +D

1 − D− (1 − γ)i .

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� Macroeconomic model for climate change

Households Firms Banks SumBalance SheetCapital stock +pt Kt +pt KtLoan −Dt +Dt

Sum (net worth) X ft X b

t Xt

Transactions current capitalConsumption −pt Ct +pt CtInvestment +pt It −pt ItAccounting memo [GDP] [pt Yt (1 − Dt )]Wages +Wt −WtInterests on debt −rDt +rDtFirms’ net profit −Πt +ΠtDividends +Dit −DitFinancial Balances −Dt +Πb

t

Flow of fundsGFCF +pt It +pt ItChange in Loans −Dt +Dt

Column sum Πt − Dit Dt pt ItChange in Net worth X f

t = Πt − Dit + (pt − δpt )Kt X bt = Πb

t Xt

Table: Balance sheet, transactions, and flow of funds for a three-sectoreconomy.

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� Macroeconomic model for climate changeProductivity

� The Business as usual Scenario

aa

= α

� The Burke et al.(2015) Scenario

aa

= α1Tα + α2T 2α

� The Kaldor-Verdoorn (2002) Scenario

aa

= α + ηg

� The Gordon (2014) Scenario - productivity growth is 1,3%

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� Outlines

1 Introduction



4 Climate Module



7 Further Work

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� Climate ModuleCO2 Emissions

Global emissions are the sum of industrial and land-use emissions

E := Eind + Eland ,

where industrial emissions depend on output,

Eind := Yσ(1 − n),

with,

σ

σ= −gσ

gσgσ

= δgσwith δgsigma < 0

and the land-use emissions,

Eland

Eland= δE with δE < 0

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� Climate ModuleCO2 Accumulation

The CO2 evolves according to a three-layer model, the atmosphere(AT), the upper ocean (UP) and the lower ocean (LO),

˙CO2AT

˙CO2UP

˙CO2LO

=

E00

+

−φ12 φ12

CATeqCUPeq

0

φ12 −φ12CATeqCUPeq

− φ23 φ23CUPeqCLOeq

0 φ23 −φ23CUPeqCLOeq

COAT

2COUP

2COLO

2

.

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� Climate ModuleRadiative Forcing

Radiative forcing is the sum of the radiative forcing due to CO2 andother gases,

F := Find + Fexo,

with,

Find (t) =F2×CO2

log(2)log

(CCO2(t)

CCO2(t0)

),

Fexo = δFexo Fexo

(1 − Fexo

F maxexo

).

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� Climate ModuleTemperature Increase

The temperature dynamics is a two-layer model, with T being themean atmospheric temperature deviation with respect to its value in1900 and T0 represents the deep-ocean temperature deviation.

CT = F − (RF )T − γ∗(T − T0)

C0T0 = γ∗(T − T0)

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� Climate ModuleDamage Function (1/2)

� The Nordhaus’s Damage function (2013),

D = 1 − 11 + π1T + π2T 2

� The Weitzman’s (2010) and Dietz-Stern’s (2015) Damagefunctions,

D = 1 − 11 + π1T + π2T 2 + π3T 6.754

� In Weitzman (2010), π3 is calibrated so that D = 50% wheneverT = 6.

� In Dietz-Stern (2015), π3 is calibrated so that D = 50% wheneverT = 4.

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� Climate ModuleDamage Function (2/2)

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1,0

0 1 2 3 4 5 6

Da

ma

ge

s (

fra

ctio

n o

f o

utp

ut)

Temperature increase (°C)

Nordhaus Weitzman Dietz and Stern

Figure: Comparison of the proposed Damage functions as percentage ofoutput.

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� Outlines

1 Introduction



4 Climate Module



7 Further Work

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� Public Policy ModuleAbatement Costs

The abatement costG := θ1nθ2

with θ1 and θ2 borrowed from Nordhaus (2013). n, the reduction rateof emissions implied by the abatement cost evolves according to,

n = min

{(pc

pBS

) 1θ2−1

; 1

}.

Prices are exogenously given so that,

˙pBS

pBS= δpBS , with δpBS < 0

pC

pC= δpC , with δpC > 0

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� Outlines

1 Introduction



4 Climate Module



7 Further Work

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� Numerical SimulationsScenarios - Baseline Calibration

Parameter ValueYinit 64.4565Ninit 4.5510ωinit 0.5849λinit 0.6910dinit 1.4393pinit 1ηp 0.0819

markup 1.610Monetary illusion -

δ 0.0625ν 2.8956r 0.0303

dfi 0.1672α 0.0226

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� Numerical SimulationsThe BAU Scenario

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Employment Rate Inflation Rate (right axis)0,0

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Real Ouput Growth

Labor Productivity Growth

Population Growth

Debt to Nominal GDP Ratio (right axis)

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Real Output in $ 2010

Emissions per Capita in tCO2 (right axis)

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Atmospheric Temperature Change in °CDamage to Real Output Ratio (right axis)

Figure: Trajectories of the main simulation outputs in the BAU case.

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Em

plo

ym

ent

Rate

Wage Share


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Employment

Rate

Debt to

Nominal GDP

Ratio

Wage

Share

0,68

0,7

0,72

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0,57

0,6

0,63

1,26

1,35

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1,62


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� Numerical SimulationsThe BAU Scenario - Values

GDP Real Growth 2100 (wrt 2010) 1053%t CO2 per capita (2050) 7.72Temperature change in 2100 +3.94 ◦CCO2 concentration 2100 968.98 ppm

Table: Key values of the world economy by 2100 — the exogenous case.

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� Numerical SimulationsThe Kaldor-Verdoorn Scenario

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Figure: Trajectories of the main simulation outputs in the Kaldor-Verdoorncase.

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� Numerical SimulationsThe Kaldor-Verdoorn Scenario

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Em

plo

ym

ent

rate

Wage share

Figure: Trajectories of the main simulation outputs in the Kaldor-Verdoorncase.

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� Numerical SimulationsThe Kaldor-Verdoorn Scenario - Values


Table: Key values of the world economy by 2100 — the Kaldor-Verdoorncase.

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� Numerical SimulationsThe Burke et al. (2015) Scenario

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Figure: Trajectories of the main simulation outputs in the Burke et al. (2015)case.

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� Numerical SimulationsThe Burke et al. (2015) Scenario

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Em

plo

ym

ent

rate

Wage share

Figure: Trajectories of the main simulation outputs in the Burke et al. (2015)case.

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� Numerical SimulationsThe Burke et al. (2015) Scenario - Values


Table: Key values of the world economy by 2100 — The Burke et al. (2015)case.

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� Numerical SimulationsThe Weitzman Scenario

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Figure: Trajectories of the main simulation outputs in the Weitzman case.

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� Numerical SimulationsThe Weitzman Scenario

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plo

ym

ent

rate

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Figure: Trajectories of the main simulation outputs in the Weitzman case.

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� Numerical SimulationsThe Weitzman Scenario - Values


Table: Key values of the world economy by 2100 — the Weitzman case.

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� Numerical SimulationsThe Dietz-Stern Scenario

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Figure: Trajectories of the main simulation outputs in the Dietz-Stern case.

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� Numerical SimulationsThe Dietz-Stern Scenario

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plo

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Figure: Trajectories of the main simulation outputs in the Dietz-Stern case.

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� Numerical SimulationsThe Dietz-Stern Scenario - Values


Table: Key values of the world economy by 2100 — the Dietz-Stern case.

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� Numerical SimulationsThe Combined Burke et al. and Dietz-Stern Scenario

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Figure: Trajectories of the main simulation outputs in the Combined Burke etal. and Dietz-Stern case.

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� Numerical SimulationsThe Combined Burke et al. and Dietz-Stern Scenario

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plo

ym

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Figure: Phase portrait in the Combined Burke et al. and Dietz-Stern case

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� Numerical SimulationsThe Combined Burke et al. and Dietz-Stern - Values


Table: Key values of the world economy by 2100 — The Combined Burke etal. and Dietz-Stern case.

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� Numerical SimulationsThe Combined Burke et al. and Dietz-Stern - Demographic

4

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Bill

ion

of w

ork

ers

Calibrated speed of convergence Slower speed of convergence

Figure: Trajectories of the main simulation outputs in the Combined Burke etal. and Dietz-Stern - Demographic.

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� Numerical SimulationsThe Combined Burke-Dietz Scenario - Demographic

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Figure: Trajectories of the main simulation outputs in the Combined Burke etal. and Dietz-Stern - Demographic.

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� Numerical SimulationsThe Combined Burke et al. and Dietz-Stern - Demographic - Values


Table: Key values of the world economy by 2100 — the Combined Burke etal. and Dietz-Stern - Demographic.

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� Numerical SimulationsPrice of Carbon

� we find the initial condition in 2010 that the growth rate thatmatch with the 2015 and 2055 values (2005 $US 12 and 29t/CO2 respectively)

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� Numerical SimulationsThe Combined Burke et al. and Dietz-Stern - Carbon Price

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Figure: Trajectories of the main simulation outputs in rhe Combined Burke etal. and Dietz-Stern - Carbon Price.

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� Numerical SimulationsThe Combined Burke et al. and Dietz-Stern - Carbon Price

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Em

plo

ym

ent

rate

Wage share

Figure: Trajectories of the main simulation outputs in the Combined Burke etal. and Dietz-Stern - Carbon Price.

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� Numerical SimulationsThe Combined Burke et al. and Dietz-Stern - Carbon Price- Values

GDP Real Growth 2100 (wrt 2010) 3.17%t CO2 per capita (2050) 5.54Temperature change in 2100 +3.22 ◦CCO2 concentration 2100 643.77 ppm

Table: Key values of the world economy by 2100 — the Combined Burke etal. and Dietz-Stern- Carbon Price.

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� Numerical SimulationsThe Combined Burke et al. and Dietz-Stern - Carbon Price - Sensitivity of

6

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0,8

1,0

0

1

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7

2000 2050 2100


Figure: Trajectories of the main simulation outputs in the CombinedBurke-Dietz Scenario - Carbon Price case.

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GDP Real Growth 2100 (wrt 2010) −9.1%t CO2 per capita (2050) 5.00Temperature change in 2100 +4.4552◦CCO2 concentration 2100 549.78 ppm

Table: Key values of the world economy by 2100 — the Combined Burke etal. and Dietz-Stern - Carbon Price.

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� Numerical SimulationsPrice of Carbon 2

� we find the initial condition in 2010 that the growth rate thatmatch with the 2015 and 2055 values (2005 $US 74 and 306t/CO2 respectively)

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� Numerical SimulationsThe Combined Burke et al. and Dietz-Stern - Carbon Price 2 - Sensitivity

of 6

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2000 2050 2100 2150 2200 2250 2300


-3

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Real Ouput Growth


Population Growth


0

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2000 2050 2100 2150 2200 2250 2300



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2000 2050 2100 2150 2200 2250 2300


Figure: Trajectories of the main simulation outputs in the Combined Burke etal. and Dietz-Stern - Carbon Price 2 - Sensitivity of 6 case.

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GDP Real Growth 2100 (wrt 2010) 272%t CO2 per capita (2050) 0.49Temperature change in 2100 +3.2293◦CCO2 concentration 2100 397.98 ppm

Table: Key values of the world economy by 2100 — the Combined Burke etal. and Dietz-Stern - Carbon Price.

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� Numerical SimulationsObjective 1.5

� According to the 2015 climate meeting, held in Paris, theuniversal agreement’s main goal is to stay, in this century, withinthe + 2 C of temperature anomaly and to drive efforts to limiteven further to + 1.5C above pre-industrial levels.

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� Numerical SimulationsObjective + 1.5◦ C

Sensitivity of 1.5 Sensitivity of 2.9Init price of 15 Init price of 80 Init price of 15 Init price of 80

Price in 2015 18.58 86.27 65.50 144.32Price in 2020 23.00 93.04 286.02 260.35Price in 2050 82.93 146.35 xxx xxx

Table: Price in order to prevent the temperature anomaly to reach the + 1.5◦

ceiling in 2100, prices are in 2005 US$/t CO2.

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� Outlines

1 Introduction



4 Climate Module



7 Further Work

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� Further WorkFurther work

� To model non-renewable energy, natural resource scarcity.� To introduce the public sector.� To refine the statistical framework.� To distinguish the agricultural from the industrial production.� To precise the determination of the damage functions.

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Thank you for your attention.

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