Natural Resources in a Monetary Macro-dynamics - Work in ... Resources in a Monetary Macro-dynamics Work in progress Ga el Giraud AFD, CNRS, Chair Energy and Prosperity ... Ga el Giraud

Natural Resources in a Monetary Macro-dynamicsWork in progress

Gael Giraud

AFD, CNRS, Chair Energy and ProsperityOlivier Vidal, Cyril Francois (ISTerre)

Sandra Bouneau, Xavier Doligez (Inst. Nucl. Phys.)Matheus Grasselli (Fields), Adrien Nguyen-Huu (CERMICS), Antonin Pottier (CERNA)

Daniel Cordobas, Florent McIsaac, Fatma Rostom, Ekaterina Zatsepina, AntoineMonserand (E & P), Emmanuel Bovari (AFD)

ENS Ulm, X, ENSAE.

Les Houches, Feb. 2016

Gael Giraud (AFD) Natural Resources in a Monetary Macro-dynamicsLes Houches, Feb. 2016 1 / 88

1 Intro

2 The Goodwin-Keen dynamicsBackground materialEstimation of Goodwin’s Model

3 The multisectoral case


Intro

Plan

1 Intro




Intro

Intro: Changing our models

Grasselli’s (2014, INET) slide.


Intro


Intro


Intro

◦ Need for new macro-economic models to assess:

◦ the role of energy in economics

◦ the impact of climate change.

◦ the feasibility of energy shift scenarios.


Intro






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Intro

The cost share theorem (I).

Figure : The cost share of (primary) energy in the US (1970-2010).


Intro

◦ The cost share theorem (II).

maxx

Y (x)− p · x , (1)

◦εi :=

xiY (x)

× ∂Y

∂x ji(x) =

pixip · x

, (2)


Intro


maxx

Y (x)− p · x , (1)

◦εi :=

xiY (x)

× ∂Y

∂x ji(x) =

pixip · x

, (2)


Intro


maxx

Y (x)− p · x , (3)

s.t.f (x) = 0

◦ Shadow prices.

εi =xi(pi − λ∂f (x)

∂xi

)p · x − λxi ∂f (x)

∂xi

. (4)

Ayres & Kummel (2010).


Intro


maxx

Y (x)− p · x , (3)

s.t.f (x) = 0

◦ Shadow prices.

εi =xi(pi − λ∂f (x)

∂xi

)p · x − λxi ∂f (x)

∂xi

. (4)

Ayres & Kummel (2010).


Intro

Giraud & Kahraman (2014).

Figure : An estimation of the energy dependency ratio around 0.6.

Confirmation by DSGE-Bayesian estimation techniques (Giraud et al.(2015)).


Intro

Bouleau & Chorro (2015).

Figure : Financialized prices doe not necessarily reflect real scarcity


Intro

◦ Most neo-classical models have no energy in the production function.

◦ No matter either.

◦ No money... (Or only neutral and exogenous.)

◦ No global out-of-equilibrium dynamics. (Even the stock/flow distinctionis hard in GET)

◦ No emergence phenomena (Sonnenschein-Mantel-Debreu (1975)).

◦ No non-linearity/non-gaussianity in the presumed dynamics (Cf. DSGE)

◦ No private debt. (Exception: Krugman & Eggertson (2012) but nomoney...)

◦ No banking sector (only financial intermediaries).

◦ No underemployment (at least when the labor market is perfectlyflexible).

◦ No bad surprise (or only “black swans”) courtesy of “rationalexpectations”.


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Intro

Purpose of present research programme

◦ Offer a truly dynamic, stock-flow consistent, multisectoral monetarymacro-economic model.

◦ Which can be empirically estimated and simulated.

◦ Where money is non-neutraland endogenous money creation (by banking sector) is possible.

◦ Mass unemployment can occur.

◦ Financial crashes can be the source of real shocks.

◦ The “new stylized facts” (Stiglitz) can be observed.

◦ Private debts matter.In particular, debt-deflation can occur.


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Intro

Purpose of present research programme (cont’d)

◦ Various sectors, including energy and other natural resources, can bedisaggregated.Input-ouput analysis.

◦ Dynamics of EROI can be taken into account.

◦ Climate back-loops can be analyzed.

◦ New stylized facts about inequality (Stiglitz (2015)):Growing inequality between capital incomes and wages.

◦ Average wages have stagnated (even though productivity increased).The share of capital increased.

◦ Increases in wealth/output ratio (Piketty (2014))

◦ The return to capital has not declined.


Intro










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The Goodwin-Keen dynamics

Plan

1 Intro




The Goodwin-Keen dynamics Background material

The Goodwin-Keen dynamicsBackground material

◦ Goodwin’s (1967) adaptation of Lotka-Volterra dynamics:

qt = min{atLt ;

ktν

}(5)

◦(Weak) efficiency : aLt =

ktν

= qt . (6)

◦

Demography and labor productivity :Nt

Nt=: η and

atat

=: α (7)





qt = min{atLt ;

ktν

}(5)


ktν

= qt . (6)

◦


Nt=: η and

atat

=: α (7)





qt = min{atLt ;

ktν

}(5)


ktν

= qt . (6)

◦


Nt=: η and

atat

=: α (7)





qt = min{atLt ;

ktν

}(5)


ktν

= qt . (6)

◦


Nt=: η and

atat

=: α (7)



◦ Linear short-term Phillips curve: wages versus employment. (Mankiw(2010)).

λt :=LtNt.

wt

wt= ρλt − γ, (8)

◦Wage share : ωt := wtLt/qt =

wt

at, (9)

Profit share : πt := (1− ωt)qt , (10)

◦Investment: It := πt = (1− ωt)qt . (11)




λt :=LtNt.

wt

wt= ρλt − γ, (8)


wt

at, (9)






λt :=LtNt.

wt

wt= ρλt − γ, (8)


wt

at, (9)





◦ I = S

◦ Say’s law (to be relaxed)

◦Capital accumulation:

ktkt

= (1− ωt)qtkt− δ. (12)



◦ I = S



ktkt

= (1− ωt)qtkt− δ. (12)



◦ I = S



ktkt

= (1− ωt)qtkt− δ. (12)



◦ Goodwin’s 2-dim dynamics

λtλt

=(1− ωt)

ν− (δ + α + η) (13)

ωt

ωt= ρλt − γ − α. (14)

◦ Conservative dynamical system.



◦ Goodwin’s 2-dim dynamics

λtλt

=(1− ωt)

ν− (δ + α + η) (13)

ωt

ωt= ρλt − γ − α. (14)

◦ Conservative dynamical system.



◦



◦



◦ Grasselli and Costa-Lima (2012) version:

λtλt

=(1− ωt)

ν− (δ + α + η) (15)

ωt

ωt=

φ1

(1− λt)2− φ0 − α (16)



◦



◦



◦ Which Investment function should we adopt?

◦ Let the data speak!Phenomenological approach at the aggregate level.GAMLSS : (multivariable) polynomial approximation with non-Gaussianresidual. (Vodouris et al. (2014))Monte-Carlo.



◦ Which Investment function should we adopt?

◦ Let the data speak!Phenomenological approach at the aggregate level.GAMLSS : (multivariable) polynomial approximation with non-Gaussianresidual. (Vodouris et al. (2014))Monte-Carlo.



◦ Extension to a monetary economy (Grasselli-Nguyen-Huu (2014)):Nominal short-term Phillips Curve:

w

w= Φ(λ) + γi(ω)

γ ∈ [0, 1]: measure of money illusion.

◦ Relaxation dynamics for prices:

i(ω) =p

p= ηp

(µwL

pY− 1) = ηp

(µw

pa− 1)

= ηp(µω − 1).

Unit cost: wLpY = long-run prices (Ricardo).

µ > 1 = mark-up (imperfect competition). ηp ' Calvo parameter(DSGE).Endogenous money creation (Giraud & Grasselli (2016)).



◦ Extension to a monetary economy (Grasselli-Nguyen-Huu (2014)):Nominal short-term Phillips Curve:

w

w= Φ(λ) + γi(ω)

γ ∈ [0, 1]: measure of money illusion.

◦ Relaxation dynamics for prices:

i(ω) =p

p= ηp

(µwL

pY− 1) = ηp

(µw

pa− 1)

= ηp(µω − 1).

Unit cost: wLpY = long-run prices (Ricardo).

µ > 1 = mark-up (imperfect competition). ηp ' Calvo parameter(DSGE).Endogenous money creation (Giraud & Grasselli (2016)).



◦ Leontief : no substitution can ever take place.Replace the Leontief function by a CES production function.

Y = τ[πK−η + (1− π)(aL)−η

]− 1η ,

the Goodwin-Keen model exhibits a unique (globally stable) equilibrium(Ploeg (1985)).

◦ The dynamical system becomes structurally stable (S. Smale).

◦ It better fits the data (more on this infra).




Y = τ[πK−η + (1− π)(aL)−η

]− 1η ,







Y = τ[πK−η + (1− π)(aL)−η

]− 1η ,






Some remarks (III)

◦ The capital-output ratio, ν, is no more constant.

νt =

(1− ωt

π

)−1/η 1

τ

◦ Time

nu

1950 1970 1990 2010

1.67

51.

695

Figure : US: 1945-2013



Some remarks (III)

◦ The capital-output ratio, ν, is no more constant.

νt =

(1− ωt

π

)−1/η 1

τ

◦ Time

nu

1950 1970 1990 2010

1.67

51.

695

Figure : US: 1945-2013


The Goodwin-Keen dynamics Estimation of Goodwin’s Model



◦ Empirical validation of Solow’s workhorse model?An accounting tautology:Fisher (1971), Shaikh (1974), and McCombie (2001).

◦ Constant growth rate of 3.5% fits historical US GDP with an accuracyof R2 = 0.98 (1929-2011, data from the BEA).

◦ Solow (1990): US post-war data in the (ω, λ) plot.Harvie (2000) Data from OECD confirm unsatisfactory quantitativeestimations.

◦ Grasselli (2015) correcting Harvie (2000).

◦ McIsaac (2016).







◦ McIsaac (2016).







◦ McIsaac (2016).







◦ McIsaac (2016).







◦ McIsaac (2016).



Estimation strategy

◦ Infer the aggregate behavioral functions using GAMLSS (Vodouris et al.(2014))+ Estimate the non-linear (reduced) dynamical system using MaxLikelihood techniques.

◦ One drawback with quarterly data: there are not enough data to infercontinuous processes (macro data 6= financial data!)

◦ One way to overcome this problem is to use intensive numericaltechniques (borrowed from finance)

◦ Simulate the transition probability using the Brownian bridge andMonte-Carlo techniques.

◦ We extend Gunham et al. (2002) to a multidimensional setting.



Estimation strategy








Estimation strategy








Estimation strategy








Estimation strategy










Prvision (2)



The Methodology

Step 1 : We estimate the model from 1948:Q1 to 2001:Q1

Step 2 : We simulate 500 paths of the model under consideration andtake the median scenario.

Step 3 : We compare the values we forecast to the true value.

Step 4 : We add one quarter and we redo everything from step 1 untilthe end of the sample, 2014:Q4.



The Period per Period Forecasting Error

Forecast Error for lambda, h = 4

Time

Err

or F

orec

ast

2002 2004 2006 2008 2010 2012

0e+

004e

−04

8e−

04

Figure : Red : Squared VAR error forecast. Black : Squared Goodwin CES errorforecast



◦ Nguyen-Huu and Costa-Lima (2014) :A Brownian perturbation of the Goodwin-Lotka-Volterra dynamics.

ωt

ωt= φ(λt)− α + ν2(λt)dt + ν(λt)dWt

λtλt

= κ(ωt)− η + ν2(λt)dt + ν(λt)dWt

atat

= αdt + ν(λt)dWt .

◦ Study of the stochastic orbits of the system around an equilibrium.



◦ Nguyen-Huu and Costa-Lima (2014) :A Brownian perturbation of the Goodwin-Lotka-Volterra dynamics.

ωt

ωt= φ(λt)− α + ν2(λt)dt + ν(λt)dWt

λtλt

= κ(ωt)− η + ν2(λt)dt + ν(λt)dWt

atat

= αdt + ν(λt)dWt .

◦ Study of the stochastic orbits of the system around an equilibrium.



Goodwin (1967) and Keen (1995)



◦ Keen’s (1998) augmentation with private debt.

I (πt) := κ(πt)qt :=(eD+Eπt + G

)qt , (17)

◦Dt = It(πt)− Πt . (18)

◦ dt := Dtqt

.Πt := qt − wtLt − rDt= Net profit.πt := 1− ωt − rdt = Net profit share





)qt , (17)

◦Dt = It(πt)− Πt . (18)

◦ dt := Dtqt






)qt , (17)

◦Dt = It(πt)− Πt . (18)

◦ dt := Dtqt




◦

ω

ω:= Φ(λ)− α

d = d[r − κ(π)

ν− δ]− (α + β + δ)

λ

λ=

κ(π)

ν− (δ + α + η).

◦ Non-conservative system (a fraction of wealth, rD, is pumped out bythe banking system).



◦

ω

ω:= Φ(λ)− α

d = d[r − κ(π)

ν− δ]− (α + β + δ)

λ

λ=

κ(π)

ν− (δ + α + η).

◦ Non-conservative system (a fraction of wealth, rD, is pumped out bythe banking system).



◦



◦



◦



◦ A crash scenario



◦



◦



◦ Grasselli and Costa-Lima (2012)The Goodwin-Kenn dynamics admits 3 equilibria.

◦ 1 equilibrium with crash and finite debt: non-stable.1 equilibrium without crash (“good equilibrium”): locally stable.1 equilibrium with crash and infinite debt: locally stable. (“badequilibrium”).



◦ Grasselli and Costa-Lima (2012)The Goodwin-Kenn dynamics admits 3 equilibria.

◦ 1 equilibrium with crash and finite debt: non-stable.1 equilibrium without crash (“good equilibrium”): locally stable.1 equilibrium with crash and infinite debt: locally stable. (“badequilibrium”).



Turbulences (Pomeau-Manneville (1992))



Adding government (Keen (1998) and Grasselli et al.(2013)







◦ Adding government. (Keen (1998) and Grasselli et al. (2013)

Gt = g(λt)qt . (19)

gt := Gtqt.

◦Tt = τt(πt)qt . (20)

tt := Ttqt.

◦Dgt = rDg

t + Gt − Tt . (21)

◦πt := 1− ωt − tt + gt − rdt , (22)




Gt = g(λt)qt . (19)

gt := Gtqt.

◦Tt = τt(πt)qt . (20)

tt := Ttqt.

◦Dgt = rDg

t + Gt − Tt . (21)

◦πt := 1− ωt − tt + gt − rdt , (22)




Gt = g(λt)qt . (19)

gt := Gtqt.

◦Tt = τt(πt)qt . (20)

tt := Ttqt.

◦Dgt = rDg

t + Gt − Tt . (21)

◦πt := 1− ωt − tt + gt − rdt , (22)




Gt = g(λt)qt . (19)

gt := Gtqt.

◦Tt = τt(πt)qt . (20)

tt := Ttqt.

◦Dgt = rDg

t + Gt − Tt . (21)

◦πt := 1− ωt − tt + gt − rdt , (22)



◦ When the State succeeds in stabilizing the unstable dynamics of“capitalism”



◦



◦ KAM theory? Mather-Aubry?



◦



◦



◦



◦ When the State fails



◦



◦



◦



◦ Of course the Ricardian equivalence “theorem” fails. (Cf. Keen (2014)).

◦ Public policy should be analyzed using:optimal control theory.What do we want to minimize? Inflation, underemployment, carbonfootprint, pollution...

◦ Viability theory (JP Aubin).

◦ ... with public investment (for the energy shift!).





















◦ If investment is defined as:

I = κ(d)Y

where κ′(d) < 0 + other regularity conditions.

◦ Then, the “good” equilibrium becomes unstable and the unique stableequilibrium (McIsaac - Rostom (2015)):

(ωd , λd , dd) = (0, 0,+∞)

◦ Should investment depend upon π or d? Or both?Let the data speak!




I = κ(d)Y



(ωd , λd , dd) = (0, 0,+∞)





I = κ(d)Y



(ωd , λd , dd) = (0, 0,+∞)




◦ Some extensions:- Adding a banking system: Giraud & Kockerols (2015).European Parliament Report.

◦ Phillips curve with delay → Chaotic system with fractal attractor.

◦ Dropping Say’s law: dynamics of Inventories + endogenous utilizationrate of capital (Grasselli & Nguyen-Huu (2014)).

◦ Heterogenous households: inequality in income and wealth.Giraud & Grasselli (2016) : r > g + i (Piketty notwithstanding).Default and collateral.Debt, capital and wealth.Price bubbles.





















◦ What still needs to be done:Capital vintage (Putty-Clay technology).

◦ Endogenous labor productivity (Verdoorn’s law).

◦ Uncertainty (entropy) versus investment.

◦ Stochastic financial markets.

◦ Endogenous velocity of money.

◦ Sensitivity analysis (error calculus, N. Bouleau).

◦ Medium and Long-term back-testing.
























































The multisectoral case

Plan

1 Intro





A modular approach

Goodwin



A modular approach

Goodwin Goodwin-Keen



A modular approach

Goodwin Goodwin-Keen Prices



A modular approach


Banks



A modular approach


Banks

Inventories



A modular approach


Banks

Inventories

Government



A modular approach


Banks

Inventories

Government

Finance



A modular approach


Banks

Inventories

Government

FinanceInequality



A modular approach


Banks

Inventories

Government

FinanceInequality

Multisectoral extension



A modular approach


Banks

Inventories

Government

FinanceInequality


Climate back-loops



A modular approach


Banks

Inventories

Government

FinanceInequality


Climate back-loops

Open economy



Bardi/Bihouix’s vicious circle



◦ Sectors i = 1, ..., n. Throughput:

Qi =Ki

νi, (23)

◦ Leontief:

Qi = minj=1,...,n

{Ki

νi,Liaì,Qij

aji

}, (24)

aji = quantity of j needed to produce 1 unit of i .

◦ Example: 1= capital, 2= consumption.

Q1 = Q11 + Q21 + C1 + I

Q2 = Q12 + Q22 + C2.

C1= consumption of durable goods.




Qi =Ki

νi, (23)

◦ Leontief:

Qi = minj=1,...,n

{Ki

νi,Liaì,Qij

aji

}, (24)



Q1 = Q11 + Q21 + C1 + I

Q2 = Q12 + Q22 + C2.





Qi =Ki

νi, (23)

◦ Leontief:

Qi = minj=1,...,n

{Ki

νi,Liaì,Qij

aji

}, (24)



Q1 = Q11 + Q21 + C1 + I

Q2 = Q12 + Q22 + C2.




◦ I-O matrix

A :=

[a11 a12

a21 a22

],−→Q :=

[Q1

Q2

],−→C :=

[C1

C2

],−→I :=

[I0

]. (25)

ajj= 1/jROI.

◦ More generally: sector 1= Grundkapitalk = I − δk : monetary accounting equation.

◦ Supply = Demand

−→Q = A

−→Q +

−→C +

−→I . (26)

◦ Output:

−→Y :=

−→Q − A

−→Q = [In − A]

−→Q , (27)

−→Y =

−→C +

−→I . (28)



◦ I-O matrix

A :=

[a11 a12

a21 a22

],−→Q :=

[Q1

Q2

],−→C :=

[C1

C2

],−→I :=

[I0

]. (25)

ajj= 1/jROI.


◦ Supply = Demand

−→Q = A

−→Q +

−→C +

−→I . (26)

◦ Output:

−→Y :=

−→Q − A

−→Q = [In − A]

−→Q , (27)

−→Y =

−→C +

−→I . (28)



◦ I-O matrix

A :=

[a11 a12

a21 a22

],−→Q :=

[Q1

Q2

],−→C :=

[C1

C2

],−→I :=

[I0

]. (25)

ajj= 1/jROI.


◦ Supply = Demand

−→Q = A

−→Q +

−→C +

−→I . (26)

◦ Output:

−→Y :=

−→Q − A

−→Q = [In − A]

−→Q , (27)

−→Y =

−→C +

−→I . (28)



◦ I-O matrix

A :=

[a11 a12

a21 a22

],−→Q :=

[Q1

Q2

],−→C :=

[C1

C2

],−→I :=

[I0

]. (25)

ajj= 1/jROI.


◦ Supply = Demand

−→Q = A

−→Q +

−→C +

−→I . (26)

◦ Output:

−→Y :=

−→Q − A

−→Q = [In − A]

−→Q , (27)

−→Y =

−→C +

−→I . (28)



◦GDP := −→p ·

−→Y . (29)

◦ ri return of sector i :

ri :=pi −

∑j pj .aji − .a`p1.νi

, i = 1, 2. (30)

◦ θi ∈ [0, 1] = fraction of investment devoted to sector i .∑

i θi = 1.Investment obeys a simple arbitrage rule (though with viscosity):

θ1 = σ.θ1.θ2.(r1 − r2), θ2 = σ.θ1.θ2.(r2 − r1). (31)



◦GDP := −→p ·

−→Y . (29)


ri :=pi −


, i = 1, 2. (30)



θ1 = σ.θ1.θ2.(r1 − r2), θ2 = σ.θ1.θ2.(r2 − r1). (31)



◦GDP := −→p ·

−→Y . (29)


ri :=pi −


, i = 1, 2. (30)



θ1 = σ.θ1.θ2.(r1 − r2), θ2 = σ.θ1.θ2.(r2 − r1). (31)



◦pi = ηi .

(Pi − pi

), i = 1, 2, (32)

◦

Pi =n∑

j=1

pj .aji + wa` + r .p1.νi , (33)

where r := 1/n∑

i ri average return.Resilience at the steady state: capital must be constantly renewed (6=Sraffa).



◦pi = ηi .

(Pi − pi

), i = 1, 2, (32)

◦

Pi =n∑

j=1

pj .aji + wa` + r .p1.νi , (33)

where r := 1/n∑

i ri average return.Resilience at the steady state: capital must be constantly renewed (6=Sraffa).



◦ Reduced form: 3n-dimensional dynamical system.

◦ Giraud,Nguyen-Huu, Pottier (2016) : whenever n = 2, there are twoconnected components of equilibria:

- the bad equilibrium;- a compact curve in R6, parameterized by θ1.Strong indeterminacy. Local stability requires tools from algebraictopology.

◦ At each (long-run) steady state, ri = rj ∀i , j .

◦ What if the matrix A varies slowly over time?
























◦ n = 3,

0 0 00.5 0.05 00 0 0



◦



◦



◦ n = 3, 0 0.5 0.10.3 0.2 0.10 0 0



◦



◦



◦ How to estimate/calibrate the matrix A? Its dynamics?

◦ Economist’s approach: the sectors are compatible with INAs.A depends upon prices.

◦ Application: Brazil, coming soon...

◦ Problem: How can we capture resource scarcity (not necessarily properlyreflected by prices)?





















◦ Physicist’s approach (I):Coupling of a Goodwin-Keen dim 1 with a physical matrix dim 4.Sector 1= matter (e.g., Copper in kg).Sector 2= energy (in j).Sector 3 = (Grund)Kapital for CopperSector 4 = (Grund)Kapital for Energy.

◦ A to be filled with EcoInvent (no price!).

A=

0 0 ? ?

50mj 1EROI ? ?

? 0 0 00 ? 0 0

◦ Bardi & Lavacchi (2009)

QCu = −RCu = k2KCuRCu

KCu = k1θCuI − k3KCu

Whenever θCuI = KCuRCu → Hubbert’s curve.Gael Giraud (AFD) Natural Resources in a Monetary Macro-dynamicsLes Houches, Feb. 2016 82 / 88




A=

0 0 ? ?

50mj 1EROI ? ?

? 0 0 00 ? 0 0








A=

0 0 ? ?

50mj 1EROI ? ?

? 0 0 00 ? 0 0






◦

Multiple?Hubbert curve fitted to historic oil production. Source: MaggioCacciola (2009).



◦ Link between physics and economics: YE ' constant at world level.



◦ Physicist’s approach (II):

◦ Coupling of a multisectoral Goodwin-Keen model with two physicalmatrices (dim 5)Assumption: The energy sector is independent from the rest of theeconomy.

◦ 4 sourcesNuclear energyFossil fuelRenewable for thermic purposes (biomass, solar, thermic...)Renewable for electricity (hydro, wind, PV, geo...)

◦






◦






◦






◦



◦ 4 final usages:Heat high temperature (Q-HT)Heat low temperature (Q-LT)FuelElectricity.

◦ The link usage/source reflects the energy mix:

kusage Vk =∑

jsource

ηjkEj .

In France:

Velec = 80%Enucl + 10%Efossil + 10%Erenew−E .

◦ bij ∈ [0, 1] : fraction of usage Vj (Q-HT, Q-LT, Fue, Elec) consumed forthe gross production of source i .

aij =∑

kusages

bjkηik .





kusage Vk =∑

jsource

ηjkEj .

In France:



aij =∑

kusages

bjkηik .





kusage Vk =∑

jsource

ηjkEj .

In France:



aij =∑

kusages

bjkηik .



◦ Fill the matrix A using EcoInvent...

◦ Analyze energy shift scenarios...Energiewende, Negatep, Ademe, Ancre, Negawatt...



◦ Fill the matrix A using EcoInvent...

◦ Analyze energy shift scenarios...Energiewende, Negatep, Ademe, Ancre, Negawatt...



◦ To go further...Combine both physicists’ approaches.

◦ Water cycle (vital, e.g., for Copper in Latin America).

◦ Labor productivity in the future? Gordon, Nature (temperatureimpact),...

◦ Recycling.

◦ Coupling the resource issue with climate back-loops.The perfect storm?






◦ Recycling.







◦ Recycling.







◦ Recycling.







◦ Recycling.



Documents

Natural Resources in a Monetary Macro-dynamics - Work in ... Resources in a Monetary Macro-dynamics Work in progress Ga el Giraud AFD, CNRS, Chair Energy and Prosperity ... Ga el Giraud