Lien entre le pib et l'énergie, par Gaël Giraud ads - 2014.03.06

How Dependent isOutput Growthfrom PrimaryEnergy ?

Gael GiraudCNRS, PSE,

University Paris Iand

Z. Kahraman ,TSP

V. Acurio, F.McIsaac, N. Pham,

CES, Paris I

I. Why is thisrelationshipimportant ?I.1. Kaya’sequation

I. Why is thisrelationshipimportant ?I.2. Why is thisrelationshipignored ?

II. The empiricalestimationII.1. A PMGapproach

II. The empiricalestimation

III. The Bayesianestimation of aDSGE modelHouseholdThe stochasticdiscount factorFirmsThe final goodfirmIntermediategood firmsFlexible pricesPrices à la CalvoGovernmentEquilibrium

How Dependent is Output Growthfrom Primary Energy ?

Gael GiraudCNRS, PSE, University Paris I

andZ. Kahraman , TSP

V. Acurio, F. McIsaac, N. Pham, CES, Paris I

March 6, 2014




Z. Kahraman ,TSP


CES, Paris I






I. Why is this relationship important ?I.1. Kaya’s equation

◦

Source : BP statistical review, 2012, Shilling et al. 1977, EIA, 2012,et Banque Mondiale (PIB), 2012.




Z. Kahraman ,TSP


CES, Paris I






◦

Source : OECD.




Z. Kahraman ,TSP


CES, Paris I






◦

Source : OECD.




Z. Kahraman ,TSP


CES, Paris I






◦∆

YPop

= ∆( EPop

× YE

).

∆ YPop := growth of GDP per capita.

∆ EPop := growth of energy consumption per capita.

∆YE := growth of energy efficiency.

◦ Taking the log...

∆ lnYPop

= ∆ lnEPop

+ ∆ lnYE.




Z. Kahraman ,TSP


CES, Paris I






◦∆

YPop

= ∆( EPop

× YE

).

∆ YPop := growth of GDP per capita.

∆ EPop := growth of energy consumption per capita.

∆YE := growth of energy efficiency.

◦ Taking the log...

∆ lnYPop

= ∆ lnEPop

+ ∆ lnYE.




Z. Kahraman ,TSP


CES, Paris I






◦ The relationship in terms of per capita quantities :

Source : BP statistical review, 2012, Shilling et al. 1977, EIA, 2012,et Banque Mondiale (PIB), 2012.




Z. Kahraman ,TSP


CES, Paris I






◦ A break in the consumption of primary energy per capita

Source : Jancovici, BP statistical review, 2012, Shilling et al. 1977,EIA, 2012, et Banque Mondiale (PIB), 2012.




Z. Kahraman ,TSP


CES, Paris I






◦ 1965-1981 : world average3.5% = 2.5% + 1%

◦ 1981-2013 : world average1.5% = 0.5% + 1%

◦ Japan : 2000-2013 :0% = 0% + 0%...




Z. Kahraman ,TSP


CES, Paris I






◦◦ 1965-1981 : world average3.5% = 2.5% + 1%

◦ 1981-2013 : world average1.5% = 0.5% + 1%

◦ Japan : 2000-2013 :0% = 0% + 0%...




Z. Kahraman ,TSP


CES, Paris I






◦◦ 1965-1981 : world average3.5% = 2.5% + 1%

◦ 1981-2013 : world average1.5% = 0.5% + 1%

◦ Japan : 2000-2013 :0% = 0% + 0%...




Z. Kahraman ,TSP


CES, Paris I






◦◦ 1965-1981 : world average3.5% = 2.5% + 1%

◦ 1981-2013 : world average1.5% = 0.5% + 1%

◦ Japan : 2000-2013 :0% = 0% + 0%...




Z. Kahraman ,TSP


CES, Paris I






◦◦




Z. Kahraman ,TSP


CES, Paris I






◦




Z. Kahraman ,TSP


CES, Paris I






◦




Z. Kahraman ,TSP


CES, Paris I






◦




Z. Kahraman ,TSP


CES, Paris I






◦




Z. Kahraman ,TSP


CES, Paris I






I. Why is this relationship important ?I.2. Why is this relationship ignored ?

◦ No such obvious relation in terms of energy prices.




Z. Kahraman ,TSP


CES, Paris I






◦




Z. Kahraman ,TSP


CES, Paris I






◦ The cost-share theorem

maxx

Y (x)− p · x (1)

◦εi :=

xi

Y (x)× ∂Y∂xi

(x) =pixi

p · x(2)




Z. Kahraman ,TSP


CES, Paris I






◦ The cost-share theorem

maxx

Y (x)− p · x (1)

◦εi :=

xi

Y (x)× ∂Y∂xi

(x) =pixi

p · x(2)




Z. Kahraman ,TSP


CES, Paris I






◦max

xY (x)− p · x s.t. f (x) = 0 (3)

f (·) : geological, technical, political... constraints.

◦

εi =xi(pi − λ∂f (x)

∂xi

)p · x − λxi

∂f (x)∂xi

. (4)

λ = Lagrange multiplier.

◦ Decoupling between output elasticity and cost share.




Z. Kahraman ,TSP


CES, Paris I






◦max

xY (x)− p · x s.t. f (x) = 0 (3)

f (·) : geological, technical, political... constraints.◦


∂xi

)p · x − λxi

∂f (x)∂xi

. (4)






Z. Kahraman ,TSP


CES, Paris I






◦max

xY (x)− p · x s.t. f (x) = 0 (3)

f (·) : geological, technical, political... constraints.◦


∂xi

)p · x − λxi

∂f (x)∂xi

. (4)






Z. Kahraman ,TSP


CES, Paris I






II. The empirical estimationII.1. A PMG approach

◦ Cointegration 6= Correlation.




Z. Kahraman ,TSP


CES, Paris I






◦




Z. Kahraman ,TSP


CES, Paris I






II. The empirical estimationII.1. A PMG approach

From 1970 to 2011.




Z. Kahraman ,TSP


CES, Paris I






◦ Variables under scrutiny:Logarithm of:

-Primary energy consumption (million tons of oil equivalents) -BP Statistical Review of World Energy 2012.

- GDP (in 2000 U.S $) World Bank, World DevelopmentIndicators.

- Gross Fixed Capital Formation (in 2000 U.S $) World Bank,World Development Indicators.

- Population data - World Bank, World Development Indicators.




Z. Kahraman ,TSP


CES, Paris I






◦ The main equation:

lnGDPi,t = βi,0+βi,1 lnNRJi,t+βi,2 lnEFFi,t−1+βi,3 lnKi,t+εi,t .

All the variables are per capita.

◦ Energy efficiency is lagged in order to avoid tautologicalover-identification.




Z. Kahraman ,TSP


CES, Paris I






◦ The main equation:

lnGDPi,t = βi,0+βi,1 lnNRJi,t+βi,2 lnEFFi,t−1+βi,3 lnKi,t+εi,t .

All the variables are per capita.◦ Energy efficiency is lagged in order to avoid tautological

over-identification.




Z. Kahraman ,TSP


CES, Paris I






Is there a (hidden) long-run relationship ?

◦

◦ Westerlund panel cointegration test also strongly reject the(no-cointegration) null hypothesis.




Z. Kahraman ,TSP


CES, Paris I






Is there a (hidden) long-run relationship ?

◦

◦ Westerlund panel cointegration test also strongly reject the(no-cointegration) null hypothesis.




Z. Kahraman ,TSP


CES, Paris I






Can we quantify this long-run relationship ?An ECM approach:

◦




Z. Kahraman ,TSP


CES, Paris I






Is there a causality link ?

◦ Kraft & Kraft (1978), D. Stern (1993), Ozturk (2010), D. Stern(2011)Non-conclusive causal relationship between quantitiesExcept for Sweden over 1 century (Stern (2011)).Strong relationship in terms of prices. (Cf. Hamilton...)

◦ Granger panel tests (valid since cointegration):




Z. Kahraman ,TSP


CES, Paris I






Is there a causality link ?

◦ Kraft & Kraft (1978), D. Stern (1993), Ozturk (2010), D. Stern(2011)Non-conclusive causal relationship between quantitiesExcept for Sweden over 1 century (Stern (2011)).Strong relationship in terms of prices. (Cf. Hamilton...)

◦ Granger panel tests (valid since cointegration):




Z. Kahraman ,TSP


CES, Paris I






III. The Bayesian estimation of a DSGE model

I We construct a New-Keynesian model with capital and oil inthe production function and consumption.

I We observe impact of shocks in the economy, for instance,shock in energy price, capital price shock or governmentexpenditure shock.




Z. Kahraman ,TSP


CES, Paris I






III. The Bayesian estimation of a DSGE modelModel

An open small economyI A representative agent invests, works and consumes - Final

consumption good and energy -I A continuum of competitive final good producersI Continuum of imperfectly competitive intermediate good

producersI Government rules fiscal policy and monetary policyI Energy is imported, i.e. no energy produced within the

country, with an exogenous price.I Exogenous process for the price of capital.




Z. Kahraman ,TSP


CES, Paris I






The Bayesian estimation of a DSGE modelHouseholdThe problem of the representative household is

max E0

∞∑t=0

βt[u(Ct , Lt)], 0 < β < 1,

subject to : Pe,tCe,t +

∫ 1

0Pq,t(i)Cq,t(i)di + Pi,t It + Bt + Tt

≤ (1 + it−1)Bt−1 + WtLt + Dt + rkt Pk,tKt ,

whereI the consumption flow of household is defined as:

Ct := ΘxC xe,tC

1−xq,t ,

I Ce,t = h’s consumption of energy,

I Cq,t :=(∫ 1

0 Cq,t(i)1− 1ε di) εε−1 is a CES index of domestic

goods (or Dixit-Stiglitz agregator),I x ∈ (0, 1) is the share of oil in consumption,

Θx := x−x(1− x)−(1−x).




Z. Kahraman ,TSP


CES, Paris I






The Bayesian estimation of a DSGE modelNo Ponzi scheme

Transversality condition (no Ponzi scheme)

limk→∞

Et

Bt+kt+k−1∏

s=0(1 + is−1)

≥ 0, ∀t.




Z. Kahraman ,TSP


CES, Paris I






The Bayesian estimation of a DSGE modelHousehold’s optimal expenditure allocation

Household maximizes her consumption Ct under the budgetconstraint : Pc,tCt = Pq,tCq,t + Pe,tCe,t , this yield to this optimalallocation of expenditures:

Pq,tCq,t = (1− x)Pc,tCt

Pe,tCe,t = xPc,tCt

Where : Pc,t = Pxe,tP

(1−x)q,t is the CPI index.




Z. Kahraman ,TSP


CES, Paris I






The Bayesian estimation of a DSGE modelFOC of Household

Using the Lagrangian associated with the maximization problem ofthe household one has the following conditions:

Marg. util. of cons. :

Ct : λt =1

CtPc,t

The Labor supply :

Lt : λt =LφtWt

The Euler equation :

Bt : λt = βEt

((1 + it)λt+1

)The Fisher equation :

Kt+1 : λtPi,t = βEtλt+1(rkt+1 + 1− δ

)Pk,t+1.




Z. Kahraman ,TSP


CES, Paris I






The Bayesian estimation of a DSGE modelStochastic discount factor

We define the stochastic discount factors as follow:1)the stochastic discount factor from date t to date t + 1

dt,t+1 :=βuC (Ct+1, Lt+1)

uC (Ct , Lt)

Pc,t

Pc,t+1, i .e,

11 + it

= Et(dt,t+1).

2)the stochastic discount factor from date t to date t + k

dt,t+k :=t+k−1∏

s=t

∆s+1s , then, dt,t+k :=

βkuC (Ct+k , Lt+k)

uC (Ct , Lt)

Pc,t

Pc,t+k.




Z. Kahraman ,TSP


CES, Paris I






The Bayesian estimation of a DSGE modelFinal good producersWe assume that there is a continuum of final good producers,perfectly competitive (no market power) and maximize profits.The production function of final good firm h is given by

Qht =

( ∫[0,1]

Qht (i)

ε−1ε di

) εε−1

ε denotes the elasticity of substitution across intermediate goods.The higher ε, the smaller is the market power of eachintermediate-good producer.Given all intermediate goods prices and the final good price, theproblem of final good firm is that

maxYt(·)

Pq,tYt −∫

[0,1]

Pq,t(i)Yt(i)di

subject to : Yt =( ∫[0,1]

Yt(i)ε−1ε di

) εε−1




Z. Kahraman ,TSP


CES, Paris I






The Bayesian estimation of a DSGE modelFinal good producers (2)

The input demand functions associated with the problem are

Yt(i) =

(Pq,t(i)Pq,t

)−εYt

Note that the final good producer is in a perfect competitiondrives the firm’s profits to 0 i.e.

Pq,tYt −∫[0;1]

Pq,t(i)Yt(i)di = 0

Consequently, we have the aggregate level of price:

Pq,t =

(∫[0;1]

Pq,t(i)1−ε

) 11−ε




Z. Kahraman ,TSP


CES, Paris I






The Bayesian estimation of a DSGE modelIntermediate good firms

By contrast with final-good producing firm, the intermediate-goodproducing ones live in a imperfectly competitive environment.We consider the following production functionCobb-Douglas:

Qt(i) = AtEt(i)αmLt(i)αnKt(i)αk

αm, αl , αk ≥ 0, αm + αl + αk ≤ 1




Z. Kahraman ,TSP


CES, Paris I






The Bayesian estimation of a DSGE modelThe strategy of firm i

The strategy of firm i :I Given prices Pe,t and Wt , and demand Qt(i), firm i chooses

quantities Et(i) and Lt(i) in order to minimize cost.I Choose price Pq,t(i) to maximize her utility. We are going to

consider two cases: flexible price and Calvo price setting.




Z. Kahraman ,TSP


CES, Paris I






The Bayesian estimation of a DSGE modelFirms minimize cost function

the problem of firm i is

minimize cost: Pe,tEt(i) + WtLt(i) + rkt Pi,tKt(i)

subject to Et(i), Lt(i),Kt(i) ≥ 0,F (Et(i), Lt(i),Kt(i)) ≥ Qt(i)




Z. Kahraman ,TSP


CES, Paris I






The Bayesian estimation of a DSGE modelExample with Coob Douglas function

Cobb-Douglas:


αm, αn, αk ≥ 0, αm + αn + αk ≤ 1

Then the first-order conditions:

Et(i) : Pe,t = λt(i)αeAtEαe−1t Lt(i)αlKt(i)αk

Lt(i) : Wt = λt(i)αlAtEt(i)αeLt(i)αl−1Kt(i)αk

Kt(i) : rkt Pq,t = λt(i)αkAtEt(i)αeLt(i)αlKt(i)αk−1.

By rewriting the system:

λt(i)Qt(i) =WtLt(i)αn

=rkt Kt(i)Pq,t

αk=

Et(i)Pe,t

αe.




Z. Kahraman ,TSP


CES, Paris I






The Bayesian estimation of a DSGE modelCobb-Douglas production function

Cobb-Douglas:


αm, αn, αk ≥ 0, αm + αn + αk ≤ 1

Denote Ft :=( Atα

αee ααn

n ααkk

Pαee,tW

αnt (rk

t Pi,t)αk

) −1αe+αn+αk , then

cost function: cost(Qt(i)) = (αe + αn + αk)FtQt(i)1

αe+αn+αk ,

marginal cost: mct(i) := λt(i) = FtQt(i)1

αe+αn+αk−1

Now, firm i chooses price Pq,t(i) to maximize her utility. We aregoing to consider two cases: flexible price and Calvo price setting.




Z. Kahraman ,TSP


CES, Paris I






The Bayesian estimation of a DSGE modelCobb-Douglas production function

Cobb-Douglas:


αm, αn, αk ≥ 0, αm + αn + αk ≤ 1

Denote Ft :=( Atα

αee ααn

n ααkk

Pαee,tW

αnt (rk

t Pi,t)αk

) −1αe+αn+αk , then

cost function: cost(Qt(i)) = (αe + αn + αk)FtQt(i)1

αe+αn+αk ,

marginal cost: mct(i) := λt(i) = FtQt(i)1

αe+αn+αk−1

Now, firm i chooses price Pq,t(i) to maximize her utility. We aregoing to consider two cases: flexible price and Calvo price setting.




Z. Kahraman ,TSP


CES, Paris I






The Bayesian estimation of a DSGE modelFlexible prices (1)

At each date t, firm i’s problem is

maxPq,t(i)

Pq,t(i)Qt(i)− cost(Qt(i))

subject to Qt(i) =(Pq,t(i)

Pq,t

)−εQt .

Note that this problem does not depend on i , consequently itssolution Pq,t(i) does not depend on i , i.e., Pq,t(i) = P∗q,t for every

i . Combining with the fact that Pq,t :=( ∫[0,1]

Pq,t(i)1−εdi) 11−ε , we

have Pq,t(i) = Pq,t for every i .




Z. Kahraman ,TSP


CES, Paris I






The Bayesian estimation of a DSGE modelFlexible prices (2)

FOC of P∗q,t gives

P∗q,t =ε

ε− 1mc∗t ,

where

I mc∗t := FtQ1

αe+αn+αk−1

t ,

I Ft :=( Atα

αee ααn

n ααkk

Pαee,tW

αnt (rk

t Pi,t)αk

) −1αe+αn+αk .

I εε−1 is the price markup, greater than 1 similar as a tax, notethan when ε→ +∞ this markup is 1.




Z. Kahraman ,TSP


CES, Paris I






The Bayesian estimation of a DSGE modelCalvo setting (1)

AssumptionCalvo price settingA fraction, θ, of intermediate good firms cannot change price:

Pq,t(i) = Pq,t−1(i).

A fraction, 1− θ, set price optimally:

Pq,t(i) = Poq,t(i).

We have "Aggregate Price Relationship"

Pq,t =( ∫[0,1]

Pq,t(i)1−εdi) 1

1−ε

=(θP1−ε

q,t−1 + (1− θ)(Poq,t)1−ε

) 11−ε

.




Z. Kahraman ,TSP


CES, Paris I







At date t, denote Qt,t+k(i) be the output at date t + k for firm ithat last reset its price in period t. Firm i’s problem is

maxPq,t(i)

Et

[ ∞∑k=0

θkdt,t+k[Pq,t(i)Qt,t+k(i)− cost(Qt,t+k(i))

]]s.t Qt,t+k(i) =

(Pq,t(i)Pq,t+k

)−εQt+k , ∀k ≥ 0.

Note that this problem does not depend on i , hence its solutionPq,t(i) also, we write

Pq,t(i) = Poq,t




Z. Kahraman ,TSP


CES, Paris I







FOC for Poq,t ,

Et

∞∑k=0

θkdt,t+kQot,t+k

[Po

q,t −Mpmcot,t+k

]= 0,

where mcot,t+k := Ft+k(Qo

t,t+k)1

αe+αl +αk−1, and

Qot,t+k =

( Poq,t

Pq,t+k

)−εQt+k for every k ≥ 0.




Z. Kahraman ,TSP


CES, Paris I






Denote

Aot := Et

∞∑k=0

θkdt,t+kQot,t+k ,

Bot := Et

∞∑k=0

θkdt,t+kQot,t+kmco

t,t+k .

We have

Poq,tA

ot = MpBo

t ,

Aot := Qo

t,t + θEtdt,t+1Aot+1,

Bot := Qo

t,tmcot,t + θEtdt,t+1Bo

t+1.




Z. Kahraman ,TSP


CES, Paris I






The Bayesian estimation of a DSGE modelMonetary policy

Denote Πq,t :=Pq,t

Pq,t−1.

The Central Bank sets the nominal short-term interest rate

it + 1 =1β×(

Πq,t

)φπ×(Py ,tYt

PyY

)φy

Where Y denotes the steady state value of nominal GDP impliedby the model and Py is the steady state of the GDP deflator.




Z. Kahraman ,TSP


CES, Paris I






The Bayesian estimation of a DSGE modelGovernment budget constraint :

Government budget constraint

(1 + it−1)Bt−1 + Gt = Bt + Tt ,

where Gt is the nominal government spending which is exogenous

log(Gt) = (1− ρg ) log(ωQ) + ρg log(Gt−1) + εgt ,

Where ωQ denotes the steady state share of government spendingin output.




Z. Kahraman ,TSP


CES, Paris I






The Bayesian estimation of a DSGE modelDefinition of equilibrium

(i) Household, firms maximize their utility.(ii) Markets clearing

Capital: Kt =

∫[0,1]

Kt(i)di ,

Labor: Lt =

∫[0,1]

Lt(i)di ,

Energy: Et =

∫[0,1]

Et(i)di ,

The good market equilibriumPc,tCt + Pi,t It + Gt = Pq,tQt − Pe,tEt .

(iii) Government budget constraint

(1 + it−1)Bt−1 + Gt = Bt + Tt ,




Z. Kahraman ,TSP


CES, Paris I






The Bayesian estimation of a DSGE modelEquilibrium (2)

(iv) The production function( ∫[0,1]

(Pq,t(i)Pq,t

) −εαe+αl +αk di

)αe+αl+αkQt = AtEαe

t Lαlt Kαk

t .

In Calvo setting :

Define vt :=∫[0,1]

(Pq,t(i)Pq,t

) −εαe+αl +αk di . Then we have

vt = θΠεq,tvt−1 + (1− θ)(Po

q,t

Pq,t

)−ε(iv) The marginal cost of firms.




Z. Kahraman ,TSP


CES, Paris I






The Bayesian estimation of a DSGE modelShocks

Define

St :=Pe,t

Pq,t

Sk,t :=Pk,t

Pq,t

We do simulation with

log(St) = ρs log(St−1) + εt

log(Sk,t) = ρk,s log(Sk,t−1) + νt




Z. Kahraman ,TSP


CES, Paris I






III. The Bayesian estimation approachIII. Estimating the parameters

◦ Estimating the parameters of a New-Keynesian DSGE modelUS: 1984 Q1 - 2007Q1. αe= Oil input elasticity.

Economy & Finance

Lien entre le pib et l'énergie, par Gaël Giraud ads - 2014.03.06