lien entre le pib et l'énergie, par gaël giraud ads - 2014.03.06
DESCRIPTION
Slides de présentation de Gaël Giraud, utilisés lors des Ateliers du Shift du 06 mars 2014 pour présenter les liens entre le PIB et l'énergie.TRANSCRIPT
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
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
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.
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
◦
Source : OECD.
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
◦
Source : OECD.
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
◦∆
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.
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
◦∆
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.
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
◦ The relationship in terms of per capita quantities :
Source : BP statistical review, 2012, Shilling et al. 1977, EIA, 2012,et Banque Mondiale (PIB), 2012.
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
◦ 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.
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
◦ 1965-1981 : world average3.5% = 2.5% + 1%
◦ 1981-2013 : world average1.5% = 0.5% + 1%
◦ Japan : 2000-2013 :0% = 0% + 0%...
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
◦◦ 1965-1981 : world average3.5% = 2.5% + 1%
◦ 1981-2013 : world average1.5% = 0.5% + 1%
◦ Japan : 2000-2013 :0% = 0% + 0%...
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
◦◦ 1965-1981 : world average3.5% = 2.5% + 1%
◦ 1981-2013 : world average1.5% = 0.5% + 1%
◦ Japan : 2000-2013 :0% = 0% + 0%...
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
◦◦ 1965-1981 : world average3.5% = 2.5% + 1%
◦ 1981-2013 : world average1.5% = 0.5% + 1%
◦ Japan : 2000-2013 :0% = 0% + 0%...
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 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 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 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 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 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
I. Why is this relationship important ?I.2. Why is this relationship ignored ?
◦ No such obvious relation in terms of energy prices.
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 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
◦ The cost-share theorem
maxx
Y (x)− p · x (1)
◦εi :=
xi
Y (x)× ∂Y∂xi
(x) =pixi
p · x(2)
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
◦ The cost-share theorem
maxx
Y (x)− p · x (1)
◦εi :=
xi
Y (x)× ∂Y∂xi
(x) =pixi
p · x(2)
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
◦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.
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
◦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.
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
◦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.
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
II. The empirical estimationII.1. A PMG approach
◦ Cointegration 6= Correlation.
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 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
II. The empirical estimationII.1. A PMG approach
From 1970 to 2011.
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
◦ 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.
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
◦ 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.
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
◦ 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.
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
Is there a (hidden) long-run relationship ?
◦
◦ Westerlund panel cointegration test also strongly reject the(no-cointegration) null hypothesis.
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
Is there a (hidden) long-run relationship ?
◦
◦ Westerlund panel cointegration test also strongly reject the(no-cointegration) null hypothesis.
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
Can we quantify this long-run relationship ?An ECM approach:
◦
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
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):
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
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):
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
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.
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
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.
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
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).
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
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.
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
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.
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
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.
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
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.
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
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
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
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
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
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
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
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.
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
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)
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
The Bayesian estimation of a DSGE modelExample with Coob Douglas function
Cobb-Douglas:
Qt(i) = AtEt(i)αmLt(i)αnKt(i)αk
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.
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
The Bayesian estimation of a DSGE modelCobb-Douglas production function
Cobb-Douglas:
Qt(i) = AtEt(i)αmLt(i)αnKt(i)αk
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.
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
The Bayesian estimation of a DSGE modelCobb-Douglas production function
Cobb-Douglas:
Qt(i) = AtEt(i)αmLt(i)αnKt(i)αk
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.
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
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 .
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
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.
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
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
.
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
The Bayesian estimation of a DSGE modelCalvo setting (2)
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
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
The Bayesian estimation of a DSGE modelCalvo setting (3)
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.
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
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.
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
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.
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
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.
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
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 ,
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
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.
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
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
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
III. The Bayesian estimation approachIII. Estimating the parameters
◦ Estimating the parameters of a New-Keynesian DSGE modelUS: 1984 Q1 - 2007Q1. αe= Oil input elasticity.