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How Dependent is
Output Growth
from Primary
Energy ?
Gael Giraud
CNRS, PSE,
University Paris I
and
Z. Kahraman ,
TSP
V. Acurio, F.
McIsaac, N. Pham,
CES, Paris I
I. Why is this
relationship
important ?
I.1. Kaya’s
equation
I. Why is this
relationship
important ?
I.2. Why is this
relationship
ignored ?
II. The empirical
estimation
II.1. A PMG
approach
II. The empirical
estimation
III. The Bayesian
estimation of a
DSGE model
Household
The stochastic
discount factor
Firms
How Dependent is Output Growth
from Primary Energy ?
Gael Giraud
CNRS, PSE, University Paris I
and
Z. Kahraman , TSP
V. Acurio, F. McIsaac, N. Pham, CES, Paris I
March 6, 2014
How Dependent is
Output Growth
from Primary
Energy ?
Gael Giraud
CNRS, PSE,
University Paris I
and
Z. Kahraman ,
TSP
V. Acurio, F.
McIsaac, N. Pham,
CES, Paris I
I. Why is this
relationship
important ?
I.1. Kaya’s
equation
I. Why is this
relationship
important ?
I.2. Why is this
relationship
ignored ?
II. The empirical
estimation
II.1. A PMG
approach
II. The empirical
estimation
III. The Bayesian
estimation of a
DSGE model
Household
The stochastic
discount factor
Firms
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 is
Output Growth
from Primary
Energy ?
Gael Giraud
CNRS, PSE,
University Paris I
and
Z. Kahraman ,
TSP
V. Acurio, F.
McIsaac, N. Pham,
CES, Paris I
I. Why is this
relationship
important ?
I.1. Kaya’s
equation
I. Why is this
relationship
important ?
I.2. Why is this
relationship
ignored ?
II. The empirical
estimation
II.1. A PMG
approach
II. The empirical
estimation
III. The Bayesian
estimation of a
DSGE model
Household
The stochastic
discount factor
Firms
◦
Source : OECD.
How Dependent is
Output Growth
from Primary
Energy ?
Gael Giraud
CNRS, PSE,
University Paris I
and
Z. Kahraman ,
TSP
V. Acurio, F.
McIsaac, N. Pham,
CES, Paris I
I. Why is this
relationship
important ?
I.1. Kaya’s
equation
I. Why is this
relationship
important ?
I.2. Why is this
relationship
ignored ?
II. The empirical
estimation
II.1. A PMG
approach
II. The empirical
estimation
III. The Bayesian
estimation of a
DSGE model
Household
The stochastic
discount factor
Firms
◦
Source : OECD.
How Dependent is
Output Growth
from Primary
Energy ?
Gael Giraud
CNRS, PSE,
University Paris I
and
Z. Kahraman ,
TSP
V. Acurio, F.
McIsaac, N. Pham,
CES, Paris I
I. Why is this
relationship
important ?
I.1. Kaya’s
equation
I. Why is this
relationship
important ?
I.2. Why is this
relationship
ignored ?
II. The empirical
estimation
II.1. A PMG
approach
II. The empirical
estimation
III. The Bayesian
estimation of a
DSGE model
Household
The stochastic
discount factor
Firms
◦
∆
Y
Pop
= ∆
E
Pop
×
Y
E
.
∆ Y
Pop := growth of GDP per capita.
∆ E
Pop := growth of energy consumption per capita.
∆Y
E := growth of energy efficiency.
How Dependent is
Output Growth
from Primary
Energy ?
Gael Giraud
CNRS, PSE,
University Paris I
and
Z. Kahraman ,
TSP
V. Acurio, F.
McIsaac, N. Pham,
CES, Paris I
I. Why is this
relationship
important ?
I.1. Kaya’s
equation
I. Why is this
relationship
important ?
I.2. Why is this
relationship
ignored ?
II. The empirical
estimation
II.1. A PMG
approach
II. The empirical
estimation
III. The Bayesian
estimation of a
DSGE model
Household
The stochastic
discount factor
Firms
◦
∆
Y
Pop
= ∆
E
Pop
×
Y
E
.
∆ Y
Pop := growth of GDP per capita.
∆ E
Pop := growth of energy consumption per capita.
∆Y
E := growth of energy efficiency.
◦ Taking the log...
∆ ln
Y
Pop
= ∆ ln
E
Pop
+ ∆ ln
Y
E
.
How Dependent is
Output Growth
from Primary
Energy ?
Gael Giraud
CNRS, PSE,
University Paris I
and
Z. Kahraman ,
TSP
V. Acurio, F.
McIsaac, N. Pham,
CES, Paris I
I. Why is this
relationship
important ?
I.1. Kaya’s
equation
I. Why is this
relationship
important ?
I.2. Why is this
relationship
ignored ?
II. The empirical
estimation
II.1. A PMG
approach
II. The empirical
estimation
III. The Bayesian
estimation of a
DSGE model
Household
The stochastic
discount factor
Firms
◦ 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 is
Output Growth
from Primary
Energy ?
Gael Giraud
CNRS, PSE,
University Paris I
and
Z. Kahraman ,
TSP
V. Acurio, F.
McIsaac, N. Pham,
CES, Paris I
I. Why is this
relationship
important ?
I.1. Kaya’s
equation
I. Why is this
relationship
important ?
I.2. Why is this
relationship
ignored ?
II. The empirical
estimation
II.1. A PMG
approach
II. The empirical
estimation
III. The Bayesian
estimation of a
DSGE model
Household
The stochastic
discount factor
Firms
◦ 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 is
Output Growth
from Primary
Energy ?
Gael Giraud
CNRS, PSE,
University Paris I
and
Z. Kahraman ,
TSP
V. Acurio, F.
McIsaac, N. Pham,
CES, Paris I
I. Why is this
relationship
important ?
I.1. Kaya’s
equation
I. Why is this
relationship
important ?
I.2. Why is this
relationship
ignored ?
II. The empirical
estimation
II.1. A PMG
approach
II. The empirical
estimation
III. The Bayesian
estimation of a
DSGE model
Household
The stochastic
discount factor
Firms
◦ 1965-1981 : world average
3.5% = 2.5% + 1%
How Dependent is
Output Growth
from Primary
Energy ?
Gael Giraud
CNRS, PSE,
University Paris I
and
Z. Kahraman ,
TSP
V. Acurio, F.
McIsaac, N. Pham,
CES, Paris I
I. Why is this
relationship
important ?
I.1. Kaya’s
equation
I. Why is this
relationship
important ?
I.2. Why is this
relationship
ignored ?
II. The empirical
estimation
II.1. A PMG
approach
II. The empirical
estimation
III. The Bayesian
estimation of a
DSGE model
Household
The stochastic
discount factor
Firms
◦◦ 1965-1981 : world average
3.5% = 2.5% + 1%
◦ 1981-2013 : world average
1.5% = 0.5% + 1%
How Dependent is
Output Growth
from Primary
Energy ?
Gael Giraud
CNRS, PSE,
University Paris I
and
Z. Kahraman ,
TSP
V. Acurio, F.
McIsaac, N. Pham,
CES, Paris I
I. Why is this
relationship
important ?
I.1. Kaya’s
equation
I. Why is this
relationship
important ?
I.2. Why is this
relationship
ignored ?
II. The empirical
estimation
II.1. A PMG
approach
II. The empirical
estimation
III. The Bayesian
estimation of a
DSGE model
Household
The stochastic
discount factor
Firms
◦◦ 1965-1981 : world average
3.5% = 2.5% + 1%
◦ 1981-2013 : world average
1.5% = 0.5% + 1%
◦ Japan : 2000-2013 :
0% = 0% + 0%...
How Dependent is
Output Growth
from Primary
Energy ?
Gael Giraud
CNRS, PSE,
University Paris I
and
Z. Kahraman ,
TSP
V. Acurio, F.
McIsaac, N. Pham,
CES, Paris I
I. Why is this
relationship
important ?
I.1. Kaya’s
equation
I. Why is this
relationship
important ?
I.2. Why is this
relationship
ignored ?
II. The empirical
estimation
II.1. A PMG
approach
II. The empirical
estimation
III. The Bayesian
estimation of a
DSGE model
Household
The stochastic
discount factor
Firms
◦◦ 1965-1981 : world average
3.5% = 2.5% + 1%
◦ 1981-2013 : world average
1.5% = 0.5% + 1%
◦ Japan : 2000-2013 :
0% = 0% + 0%...
How Dependent is
Output Growth
from Primary
Energy ?
Gael Giraud
CNRS, PSE,
University Paris I
and
Z. Kahraman ,
TSP
V. Acurio, F.
McIsaac, N. Pham,
CES, Paris I
I. Why is this
relationship
important ?
I.1. Kaya’s
equation
I. Why is this
relationship
important ?
I.2. Why is this
relationship
ignored ?
II. The empirical
estimation
II.1. A PMG
approach
II. The empirical
estimation
III. The Bayesian
estimation of a
DSGE model
Household
The stochastic
discount factor
Firms
◦◦
How Dependent is
Output Growth
from Primary
Energy ?
Gael Giraud
CNRS, PSE,
University Paris I
and
Z. Kahraman ,
TSP
V. Acurio, F.
McIsaac, N. Pham,
CES, Paris I
I. Why is this
relationship
important ?
I.1. Kaya’s
equation
I. Why is this
relationship
important ?
I.2. Why is this
relationship
ignored ?
II. The empirical
estimation
II.1. A PMG
approach
II. The empirical
estimation
III. The Bayesian
estimation of a
DSGE model
Household
The stochastic
discount factor
Firms
◦
How Dependent is
Output Growth
from Primary
Energy ?
Gael Giraud
CNRS, PSE,
University Paris I
and
Z. Kahraman ,
TSP
V. Acurio, F.
McIsaac, N. Pham,
CES, Paris I
I. Why is this
relationship
important ?
I.1. Kaya’s
equation
I. Why is this
relationship
important ?
I.2. Why is this
relationship
ignored ?
II. The empirical
estimation
II.1. A PMG
approach
II. The empirical
estimation
III. The Bayesian
estimation of a
DSGE model
Household
The stochastic
discount factor
Firms
◦
How Dependent is
Output Growth
from Primary
Energy ?
Gael Giraud
CNRS, PSE,
University Paris I
and
Z. Kahraman ,
TSP
V. Acurio, F.
McIsaac, N. Pham,
CES, Paris I
I. Why is this
relationship
important ?
I.1. Kaya’s
equation
I. Why is this
relationship
important ?
I.2. Why is this
relationship
ignored ?
II. The empirical
estimation
II.1. A PMG
approach
II. The empirical
estimation
III. The Bayesian
estimation of a
DSGE model
Household
The stochastic
discount factor
Firms
◦
How Dependent is
Output Growth
from Primary
Energy ?
Gael Giraud
CNRS, PSE,
University Paris I
and
Z. Kahraman ,
TSP
V. Acurio, F.
McIsaac, N. Pham,
CES, Paris I
I. Why is this
relationship
important ?
I.1. Kaya’s
equation
I. Why is this
relationship
important ?
I.2. Why is this
relationship
ignored ?
II. The empirical
estimation
II.1. A PMG
approach
II. The empirical
estimation
III. The Bayesian
estimation of a
DSGE model
Household
The stochastic
discount factor
Firms
◦
How Dependent is
Output Growth
from Primary
Energy ?
Gael Giraud
CNRS, PSE,
University Paris I
and
Z. Kahraman ,
TSP
V. Acurio, F.
McIsaac, N. Pham,
CES, Paris I
I. Why is this
relationship
important ?
I.1. Kaya’s
equation
I. Why is this
relationship
important ?
I.2. Why is this
relationship
ignored ?
II. The empirical
estimation
II.1. A PMG
approach
II. The empirical
estimation
III. The Bayesian
estimation of a
DSGE model
Household
The stochastic
discount factor
Firms
I. Why is this relationship important ?
I.2. Why is this relationship ignored ?
◦ No such obvious relation in terms of energy prices.
How Dependent is
Output Growth
from Primary
Energy ?
Gael Giraud
CNRS, PSE,
University Paris I
and
Z. Kahraman ,
TSP
V. Acurio, F.
McIsaac, N. Pham,
CES, Paris I
I. Why is this
relationship
important ?
I.1. Kaya’s
equation
I. Why is this
relationship
important ?
I.2. Why is this
relationship
ignored ?
II. The empirical
estimation
II.1. A PMG
approach
II. The empirical
estimation
III. The Bayesian
estimation of a
DSGE model
Household
The stochastic
discount factor
Firms
◦
How Dependent is
Output Growth
from Primary
Energy ?
Gael Giraud
CNRS, PSE,
University Paris I
and
Z. Kahraman ,
TSP
V. Acurio, F.
McIsaac, N. Pham,
CES, Paris I
I. Why is this
relationship
important ?
I.1. Kaya’s
equation
I. Why is this
relationship
important ?
I.2. Why is this
relationship
ignored ?
II. The empirical
estimation
II.1. A PMG
approach
II. The empirical
estimation
III. The Bayesian
estimation of a
DSGE model
Household
The stochastic
discount factor
Firms
◦ The cost-share theorem
max
x
Y (x) − p · x (1)
How Dependent is
Output Growth
from Primary
Energy ?
Gael Giraud
CNRS, PSE,
University Paris I
and
Z. Kahraman ,
TSP
V. Acurio, F.
McIsaac, N. Pham,
CES, Paris I
I. Why is this
relationship
important ?
I.1. Kaya’s
equation
I. Why is this
relationship
important ?
I.2. Why is this
relationship
ignored ?
II. The empirical
estimation
II.1. A PMG
approach
II. The empirical
estimation
III. The Bayesian
estimation of a
DSGE model
Household
The stochastic
discount factor
Firms
◦ The cost-share theorem
max
x
Y (x) − p · x (1)
◦
εi :=
xi
Y (x)
×
∂Y
∂xi
(x) =
pi xi
p · x
(2)
How Dependent is
Output Growth
from Primary
Energy ?
Gael Giraud
CNRS, PSE,
University Paris I
and
Z. Kahraman ,
TSP
V. Acurio, F.
McIsaac, N. Pham,
CES, Paris I
I. Why is this
relationship
important ?
I.1. Kaya’s
equation
I. Why is this
relationship
important ?
I.2. Why is this
relationship
ignored ?
II. The empirical
estimation
II.1. A PMG
approach
II. The empirical
estimation
III. The Bayesian
estimation of a
DSGE model
Household
The stochastic
discount factor
Firms
◦
max
x
Y (x) − p · x s.t. f (x) = 0 (3)
f (·) : geological, technical, political... constraints.
How Dependent is
Output Growth
from Primary
Energy ?
Gael Giraud
CNRS, PSE,
University Paris I
and
Z. Kahraman ,
TSP
V. Acurio, F.
McIsaac, N. Pham,
CES, Paris I
I. Why is this
relationship
important ?
I.1. Kaya’s
equation
I. Why is this
relationship
important ?
I.2. Why is this
relationship
ignored ?
II. The empirical
estimation
II.1. A PMG
approach
II. The empirical
estimation
III. The Bayesian
estimation of a
DSGE model
Household
The stochastic
discount factor
Firms
◦
max
x
Y (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.
How Dependent is
Output Growth
from Primary
Energy ?
Gael Giraud
CNRS, PSE,
University Paris I
and
Z. Kahraman ,
TSP
V. Acurio, F.
McIsaac, N. Pham,
CES, Paris I
I. Why is this
relationship
important ?
I.1. Kaya’s
equation
I. Why is this
relationship
important ?
I.2. Why is this
relationship
ignored ?
II. The empirical
estimation
II.1. A PMG
approach
II. The empirical
estimation
III. The Bayesian
estimation of a
DSGE model
Household
The stochastic
discount factor
Firms
◦
max
x
Y (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 is
Output Growth
from Primary
Energy ?
Gael Giraud
CNRS, PSE,
University Paris I
and
Z. Kahraman ,
TSP
V. Acurio, F.
McIsaac, N. Pham,
CES, Paris I
I. Why is this
relationship
important ?
I.1. Kaya’s
equation
I. Why is this
relationship
important ?
I.2. Why is this
relationship
ignored ?
II. The empirical
estimation
II.1. A PMG
approach
II. The empirical
estimation
III. The Bayesian
estimation of a
DSGE model
Household
The stochastic
discount factor
Firms
II. The empirical estimation
II.1. A PMG approach
◦ Cointegration = Correlation.
How Dependent is
Output Growth
from Primary
Energy ?
Gael Giraud
CNRS, PSE,
University Paris I
and
Z. Kahraman ,
TSP
V. Acurio, F.
McIsaac, N. Pham,
CES, Paris I
I. Why is this
relationship
important ?
I.1. Kaya’s
equation
I. Why is this
relationship
important ?
I.2. Why is this
relationship
ignored ?
II. The empirical
estimation
II.1. A PMG
approach
II. The empirical
estimation
III. The Bayesian
estimation of a
DSGE model
Household
The stochastic
discount factor
Firms
◦
How Dependent is
Output Growth
from Primary
Energy ?
Gael Giraud
CNRS, PSE,
University Paris I
and
Z. Kahraman ,
TSP
V. Acurio, F.
McIsaac, N. Pham,
CES, Paris I
I. Why is this
relationship
important ?
I.1. Kaya’s
equation
I. Why is this
relationship
important ?
I.2. Why is this
relationship
ignored ?
II. The empirical
estimation
II.1. A PMG
approach
II. The empirical
estimation
III. The Bayesian
estimation of a
DSGE model
Household
The stochastic
discount factor
Firms
II. The empirical estimation
II.1. A PMG approach
From 1970 to 2011.
How Dependent is
Output Growth
from Primary
Energy ?
Gael Giraud
CNRS, PSE,
University Paris I
and
Z. Kahraman ,
TSP
V. Acurio, F.
McIsaac, N. Pham,
CES, Paris I
I. Why is this
relationship
important ?
I.1. Kaya’s
equation
I. Why is this
relationship
important ?
I.2. Why is this
relationship
ignored ?
II. The empirical
estimation
II.1. A PMG
approach
II. The empirical
estimation
III. The Bayesian
estimation of a
DSGE model
Household
The stochastic
discount factor
Firms
◦ 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 Development
Indicators.
- Gross Fixed Capital Formation (in 2000 U.S $) World Bank,
World Development Indicators.
- Population data - World Bank, World Development Indicators.
How Dependent is
Output Growth
from Primary
Energy ?
Gael Giraud
CNRS, PSE,
University Paris I
and
Z. Kahraman ,
TSP
V. Acurio, F.
McIsaac, N. Pham,
CES, Paris I
I. Why is this
relationship
important ?
I.1. Kaya’s
equation
I. Why is this
relationship
important ?
I.2. Why is this
relationship
ignored ?
II. The empirical
estimation
II.1. A PMG
approach
II. The empirical
estimation
III. The Bayesian
estimation of a
DSGE model
Household
The stochastic
discount factor
Firms
◦ The main equation:
ln GDPi,t = βi,0+βi,1 ln NRJi,t+βi,2 ln EFFi,t−1+βi,3 ln Ki,t+εi,t.
All the variables are per capita.
How Dependent is
Output Growth
from Primary
Energy ?
Gael Giraud
CNRS, PSE,
University Paris I
and
Z. Kahraman ,
TSP
V. Acurio, F.
McIsaac, N. Pham,
CES, Paris I
I. Why is this
relationship
important ?
I.1. Kaya’s
equation
I. Why is this
relationship
important ?
I.2. Why is this
relationship
ignored ?
II. The empirical
estimation
II.1. A PMG
approach
II. The empirical
estimation
III. The Bayesian
estimation of a
DSGE model
Household
The stochastic
discount factor
Firms
◦ The main equation:
ln GDPi,t = βi,0+βi,1 ln NRJi,t+βi,2 ln EFFi,t−1+βi,3 ln Ki,t+εi,t.
All the variables are per capita.
◦ Energy efficiency is lagged in order to avoid tautological
over-identification.
How Dependent is
Output Growth
from Primary
Energy ?
Gael Giraud
CNRS, PSE,
University Paris I
and
Z. Kahraman ,
TSP
V. Acurio, F.
McIsaac, N. Pham,
CES, Paris I
I. Why is this
relationship
important ?
I.1. Kaya’s
equation
I. Why is this
relationship
important ?
I.2. Why is this
relationship
ignored ?
II. The empirical
estimation
II.1. A PMG
approach
II. The empirical
estimation
III. The Bayesian
estimation of a
DSGE model
Household
The stochastic
discount factor
Firms
Is there a (hidden) long-run relationship ?
◦
How Dependent is
Output Growth
from Primary
Energy ?
Gael Giraud
CNRS, PSE,
University Paris I
and
Z. Kahraman ,
TSP
V. Acurio, F.
McIsaac, N. Pham,
CES, Paris I
I. Why is this
relationship
important ?
I.1. Kaya’s
equation
I. Why is this
relationship
important ?
I.2. Why is this
relationship
ignored ?
II. The empirical
estimation
II.1. A PMG
approach
II. The empirical
estimation
III. The Bayesian
estimation of a
DSGE model
Household
The stochastic
discount factor
Firms
Is there a (hidden) long-run relationship ?
◦
◦ Westerlund panel cointegration test also strongly reject the
(no-cointegration) null hypothesis.
How Dependent is
Output Growth
from Primary
Energy ?
Gael Giraud
CNRS, PSE,
University Paris I
and
Z. Kahraman ,
TSP
V. Acurio, F.
McIsaac, N. Pham,
CES, Paris I
I. Why is this
relationship
important ?
I.1. Kaya’s
equation
I. Why is this
relationship
important ?
I.2. Why is this
relationship
ignored ?
II. The empirical
estimation
II.1. A PMG
approach
II. The empirical
estimation
III. The Bayesian
estimation of a
DSGE model
Household
The stochastic
discount factor
Firms
Can we quantify this long-run relationship ?An ECM approach:
◦
How Dependent is
Output Growth
from Primary
Energy ?
Gael Giraud
CNRS, PSE,
University Paris I
and
Z. Kahraman ,
TSP
V. Acurio, F.
McIsaac, N. Pham,
CES, Paris I
I. Why is this
relationship
important ?
I.1. Kaya’s
equation
I. Why is this
relationship
important ?
I.2. Why is this
relationship
ignored ?
II. The empirical
estimation
II.1. A PMG
approach
II. The empirical
estimation
III. The Bayesian
estimation of a
DSGE model
Household
The stochastic
discount factor
Firms
Is there a causality link ?
◦ Kraft & Kraft (1978), D. Stern (1993), Ozturk (2010), D. Stern
(2011)
Non-conclusive causal relationship between quantities
Except for Sweden over 1 century (Stern (2011)).
Strong relationship in terms of prices. (Cf. Hamilton...)
How Dependent is
Output Growth
from Primary
Energy ?
Gael Giraud
CNRS, PSE,
University Paris I
and
Z. Kahraman ,
TSP
V. Acurio, F.
McIsaac, N. Pham,
CES, Paris I
I. Why is this
relationship
important ?
I.1. Kaya’s
equation
I. Why is this
relationship
important ?
I.2. Why is this
relationship
ignored ?
II. The empirical
estimation
II.1. A PMG
approach
II. The empirical
estimation
III. The Bayesian
estimation of a
DSGE model
Household
The stochastic
discount factor
Firms
Is there a causality link ?
◦ Kraft & Kraft (1978), D. Stern (1993), Ozturk (2010), D. Stern
(2011)
Non-conclusive causal relationship between quantities
Except for Sweden over 1 century (Stern (2011)).
Strong relationship in terms of prices. (Cf. Hamilton...)
◦ Granger panel tests (valid since cointegration):
How Dependent is
Output Growth
from Primary
Energy ?
Gael Giraud
CNRS, PSE,
University Paris I
and
Z. Kahraman ,
TSP
V. Acurio, F.
McIsaac, N. Pham,
CES, Paris I
I. Why is this
relationship
important ?
I.1. Kaya’s
equation
I. Why is this
relationship
important ?
I.2. Why is this
relationship
ignored ?
II. The empirical
estimation
II.1. A PMG
approach
II. The empirical
estimation
III. The Bayesian
estimation of a
DSGE model
Household
The stochastic
discount factor
Firms
III. The Bayesian estimation of a DSGE model
We construct a New-Keynesian model with capital and oil in
the production function and consumption.
We observe impact of shocks in the economy, for instance,
shock in energy price, capital price shock or government
expenditure shock.
How Dependent is
Output Growth
from Primary
Energy ?
Gael Giraud
CNRS, PSE,
University Paris I
and
Z. Kahraman ,
TSP
V. Acurio, F.
McIsaac, N. Pham,
CES, Paris I
I. Why is this
relationship
important ?
I.1. Kaya’s
equation
I. Why is this
relationship
important ?
I.2. Why is this
relationship
ignored ?
II. The empirical
estimation
II.1. A PMG
approach
II. The empirical
estimation
III. The Bayesian
estimation of a
DSGE model
Household
The stochastic
discount factor
Firms
III. The Bayesian estimation of a DSGE model
Model
An open small economy
A representative agent invests, works and consumes - Final
consumption good and energy -
A continuum of competitive final good producers
Continuum of imperfectly competitive intermediate good
producers
Government rules fiscal policy and monetary policy
Energy is imported, i.e. no energy produced within the
country, with an exogenous price.
Exogenous process for the price of capital.
How Dependent is
Output Growth
from Primary
Energy ?
Gael Giraud
CNRS, PSE,
University Paris I
and
Z. Kahraman ,
TSP
V. Acurio, F.
McIsaac, N. Pham,
CES, Paris I
I. Why is this
relationship
important ?
I.1. Kaya’s
equation
I. Why is this
relationship
important ?
I.2. Why is this
relationship
ignored ?
II. The empirical
estimation
II.1. A PMG
approach
II. The empirical
estimation
III. The Bayesian
estimation of a
DSGE model
Household
The stochastic
discount factor
Firms
The Bayesian estimation of a DSGE model
Household
The problem of the representative household is
max E0
∞
t=0
βt
u(Ct, Lt) , 0 < β < 1,
subject to : Pe,tCe,t +
1
0
Pq,t(i)Cq,t(i)di + Pi,tIt + Bt + Tt
≤ (1 + it−1)Bt−1 + WtLt + Dt + rk
t Pk,tKt,
where
the consumption flow of household is defined as:
Ct := Θx Cx
e,tC1−x
q,t ,
Ce,t = h’s consumption of energy,
Cq,t :=
1
0
Cq,t(i)1− 1
ε di
ε
ε−1
is a CES index of domestic
goods (or Dixit-Stiglitz agregator),
x ∈ (0, 1) is the share of oil in consumption,
Θx := x−x
(1 − x)−(1−x)
.
How Dependent is
Output Growth
from Primary
Energy ?
Gael Giraud
CNRS, PSE,
University Paris I
and
Z. Kahraman ,
TSP
V. Acurio, F.
McIsaac, N. Pham,
CES, Paris I
I. Why is this
relationship
important ?
I.1. Kaya’s
equation
I. Why is this
relationship
important ?
I.2. Why is this
relationship
ignored ?
II. The empirical
estimation
II.1. A PMG
approach
II. The empirical
estimation
III. The Bayesian
estimation of a
DSGE model
Household
The stochastic
discount factor
Firms
The Bayesian estimation of a DSGE model
No Ponzi scheme
Transversality condition (no Ponzi scheme)
lim
k→∞
Et





Bt+k
t+k−1
s=0
(1 + is−1)





≥ 0, ∀t.
How Dependent is
Output Growth
from Primary
Energy ?
Gael Giraud
CNRS, PSE,
University Paris I
and
Z. Kahraman ,
TSP
V. Acurio, F.
McIsaac, N. Pham,
CES, Paris I
I. Why is this
relationship
important ?
I.1. Kaya’s
equation
I. Why is this
relationship
important ?
I.2. Why is this
relationship
ignored ?
II. The empirical
estimation
II.1. A PMG
approach
II. The empirical
estimation
III. The Bayesian
estimation of a
DSGE model
Household
The stochastic
discount factor
Firms
The Bayesian estimation of a DSGE model
Household’s optimal expenditure allocation
Household maximizes her consumption Ct under the budget
constraint : Pc,tCt = Pq,tCq,t + Pe,tCe,t, this yield to this optimal
allocation of expenditures:
Pq,tCq,t = (1 − x)Pc,tCt
Pe,tCe,t = xPc,tCt
Where : Pc,t = Px
e,tP
(1−x)
q,t is the CPI index.
How Dependent is
Output Growth
from Primary
Energy ?
Gael Giraud
CNRS, PSE,
University Paris I
and
Z. Kahraman ,
TSP
V. Acurio, F.
McIsaac, N. Pham,
CES, Paris I
I. Why is this
relationship
important ?
I.1. Kaya’s
equation
I. Why is this
relationship
important ?
I.2. Why is this
relationship
ignored ?
II. The empirical
estimation
II.1. A PMG
approach
II. The empirical
estimation
III. The Bayesian
estimation of a
DSGE model
Household
The stochastic
discount factor
Firms
The Bayesian estimation of a DSGE model
FOC of Household
Using the Lagrangian associated with the maximization problem of
the household one has the following conditions:
Marg. util. of cons. :
Ct : λt =
1
CtPc,t
The Labor supply :
Lt : λt =
Lφ
t
Wt
The Euler equation :
Bt : λt = βEt (1 + it)λt+1
The Fisher equation :
Kt+1 : λtPi,t = βEtλt+1 rk
t+1 + 1 − δ Pk,t+1.
How Dependent is
Output Growth
from Primary
Energy ?
Gael Giraud
CNRS, PSE,
University Paris I
and
Z. Kahraman ,
TSP
V. Acurio, F.
McIsaac, N. Pham,
CES, Paris I
I. Why is this
relationship
important ?
I.1. Kaya’s
equation
I. Why is this
relationship
important ?
I.2. Why is this
relationship
ignored ?
II. The empirical
estimation
II.1. A PMG
approach
II. The empirical
estimation
III. The Bayesian
estimation of a
DSGE model
Household
The stochastic
discount factor
Firms
The Bayesian estimation of a DSGE model
Stochastic 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,
1
1 + 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+1
s , then, dt,t+k :=
βk
uC (Ct+k , Lt+k )
uC (Ct, Lt)
Pc,t
Pc,t+k
.
How Dependent is
Output Growth
from Primary
Energy ?
Gael Giraud
CNRS, PSE,
University Paris I
and
Z. Kahraman ,
TSP
V. Acurio, F.
McIsaac, N. Pham,
CES, Paris I
I. Why is this
relationship
important ?
I.1. Kaya’s
equation
I. Why is this
relationship
important ?
I.2. Why is this
relationship
ignored ?
II. The empirical
estimation
II.1. A PMG
approach
II. The empirical
estimation
III. The Bayesian
estimation of a
DSGE model
Household
The stochastic
discount factor
Firms
The Bayesian estimation of a DSGE model
Final good producers
We 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
Qh
t =
[0,1]
Qh
t (i)
ε−1
ε di
ε
ε−1
ε denotes the elasticity of substitution across intermediate goods.
The higher ε, the smaller is the market power of each
intermediate-good producer.
Given all intermediate goods prices and the final good price, the
problem of final good firm is that
max
Yt (·)
Pq,tYt −
[0,1]
Pq,t(i)Yt(i)di
subject to : Yt =
[0,1]
Yt(i)
ε−1
ε di
ε
ε−1
How Dependent is
Output Growth
from Primary
Energy ?
Gael Giraud
CNRS, PSE,
University Paris I
and
Z. Kahraman ,
TSP
V. Acurio, F.
McIsaac, N. Pham,
CES, Paris I
I. Why is this
relationship
important ?
I.1. Kaya’s
equation
I. Why is this
relationship
important ?
I.2. Why is this
relationship
ignored ?
II. The empirical
estimation
II.1. A PMG
approach
II. The empirical
estimation
III. The Bayesian
estimation of a
DSGE model
Household
The stochastic
discount factor
Firms
The Bayesian estimation of a DSGE model
Final good producers (2)
The input demand functions associated with the problem are
Yt(i) =
Pq,t(i)
Pq,t
−ε
Yt
Note that the final good producer is in a perfect competition
drives 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
1
1−ε
How Dependent is
Output Growth
from Primary
Energy ?
Gael Giraud
CNRS, PSE,
University Paris I
and
Z. Kahraman ,
TSP
V. Acurio, F.
McIsaac, N. Pham,
CES, Paris I
I. Why is this
relationship
important ?
I.1. Kaya’s
equation
I. Why is this
relationship
important ?
I.2. Why is this
relationship
ignored ?
II. The empirical
estimation
II.1. A PMG
approach
II. The empirical
estimation
III. The Bayesian
estimation of a
DSGE model
Household
The stochastic
discount factor
Firms
The Bayesian estimation of a DSGE model
Intermediate good firms
By contrast with final-good producing firm, the intermediate-good
producing ones live in a imperfectly competitive environment.
We consider the following production function
Cobb-Douglas:
Qt(i) = AtEt(i)αm
Lt(i)αn
Kt(i)αk
αm, αl , αk ≥ 0, αm + αl + αk ≤ 1
How Dependent is
Output Growth
from Primary
Energy ?
Gael Giraud
CNRS, PSE,
University Paris I
and
Z. Kahraman ,
TSP
V. Acurio, F.
McIsaac, N. Pham,
CES, Paris I
I. Why is this
relationship
important ?
I.1. Kaya’s
equation
I. Why is this
relationship
important ?
I.2. Why is this
relationship
ignored ?
II. The empirical
estimation
II.1. A PMG
approach
II. The empirical
estimation
III. The Bayesian
estimation of a
DSGE model
Household
The stochastic
discount factor
Firms
The Bayesian estimation of a DSGE model
The strategy of firm i
The strategy of firm 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.
Choose price Pq,t(i) to maximize her utility. We are going to
consider two cases: flexible price and Calvo price setting.
How Dependent is
Output Growth
from Primary
Energy ?
Gael Giraud
CNRS, PSE,
University Paris I
and
Z. Kahraman ,
TSP
V. Acurio, F.
McIsaac, N. Pham,
CES, Paris I
I. Why is this
relationship
important ?
I.1. Kaya’s
equation
I. Why is this
relationship
important ?
I.2. Why is this
relationship
ignored ?
II. The empirical
estimation
II.1. A PMG
approach
II. The empirical
estimation
III. The Bayesian
estimation of a
DSGE model
Household
The stochastic
discount factor
Firms
The Bayesian estimation of a DSGE model
Firms minimize cost function
the problem of firm i is
minimize cost: Pe,tEt(i) + WtLt(i) + rk
t Pi,tKt(i)
subject to Et(i), Lt(i), Kt(i) ≥ 0,
F(Et(i), Lt(i), Kt(i)) ≥ Qt(i)
How Dependent is
Output Growth
from Primary
Energy ?
Gael Giraud
CNRS, PSE,
University Paris I
and
Z. Kahraman ,
TSP
V. Acurio, F.
McIsaac, N. Pham,
CES, Paris I
I. Why is this
relationship
important ?
I.1. Kaya’s
equation
I. Why is this
relationship
important ?
I.2. Why is this
relationship
ignored ?
II. The empirical
estimation
II.1. A PMG
approach
II. The empirical
estimation
III. The Bayesian
estimation of a
DSGE model
Household
The stochastic
discount factor
Firms
The Bayesian estimation of a DSGE model
Example with Coob Douglas function
Cobb-Douglas:
Qt(i) = AtEt(i)αm
Lt(i)αn
Kt(i)αk
αm, αn, αk ≥ 0, αm + αn + αk ≤ 1
Then the first-order conditions:
Et(i) : Pe,t = λt(i)αeAtEαe −1
t Lt(i)αl Kt(i)αk
Lt(i) : Wt = λt(i)αl AtEt(i)αe
Lt(i)αl −1
Kt(i)αk
Kt(i) : rk
t Pq,t = λt(i)αk AtEt(i)αe
Lt(i)αl Kt(i)αk −1
.
By rewriting the system:
λt(i)Qt(i) =
WtLt(i)
αn
=
rk
t Kt(i)Pq,t
αk
=
Et(i)Pe,t
αe
.
How Dependent is
Output Growth
from Primary
Energy ?
Gael Giraud
CNRS, PSE,
University Paris I
and
Z. Kahraman ,
TSP
V. Acurio, F.
McIsaac, N. Pham,
CES, Paris I
I. Why is this
relationship
important ?
I.1. Kaya’s
equation
I. Why is this
relationship
important ?
I.2. Why is this
relationship
ignored ?
II. The empirical
estimation
II.1. A PMG
approach
II. The empirical
estimation
III. The Bayesian
estimation of a
DSGE model
Household
The stochastic
discount factor
Firms
The Bayesian estimation of a DSGE model
Cobb-Douglas production function
Cobb-Douglas:
Qt(i) = AtEt(i)αm
Lt(i)αn
Kt(i)αk
αm, αn, αk ≥ 0, αm + αn + αk ≤ 1
Denote Ft :=
Atααe
e ααn
n α
αk
k
Pαe
e,t W αn
t (rk
t Pi,t)αk
−1
αe +αn+α
k
, then
cost function: cost(Qt(i)) = (αe + αn + αk )FtQt(i)
1
αe +αn+α
k ,
marginal cost: mct(i) := λt(i) = FtQt(i)
1
αe +αn+α
k
−1
How Dependent is
Output Growth
from Primary
Energy ?
Gael Giraud
CNRS, PSE,
University Paris I
and
Z. Kahraman ,
TSP
V. Acurio, F.
McIsaac, N. Pham,
CES, Paris I
I. Why is this
relationship
important ?
I.1. Kaya’s
equation
I. Why is this
relationship
important ?
I.2. Why is this
relationship
ignored ?
II. The empirical
estimation
II.1. A PMG
approach
II. The empirical
estimation
III. The Bayesian
estimation of a
DSGE model
Household
The stochastic
discount factor
Firms
The Bayesian estimation of a DSGE model
Cobb-Douglas production function
Cobb-Douglas:
Qt(i) = AtEt(i)αm
Lt(i)αn
Kt(i)αk
αm, αn, αk ≥ 0, αm + αn + αk ≤ 1
Denote Ft :=
Atααe
e ααn
n α
αk
k
Pαe
e,t W αn
t (rk
t Pi,t)αk
−1
αe +αn+α
k
, then
cost function: cost(Qt(i)) = (αe + αn + αk )FtQt(i)
1
αe +αn+α
k ,
marginal cost: mct(i) := λt(i) = FtQt(i)
1
αe +αn+α
k
−1
Now, firm i chooses price Pq,t(i) to maximize her utility. We are
going to consider two cases: flexible price and Calvo price setting.
How Dependent is
Output Growth
from Primary
Energy ?
Gael Giraud
CNRS, PSE,
University Paris I
and
Z. Kahraman ,
TSP
V. Acurio, F.
McIsaac, N. Pham,
CES, Paris I
I. Why is this
relationship
important ?
I.1. Kaya’s
equation
I. Why is this
relationship
important ?
I.2. Why is this
relationship
ignored ?
II. The empirical
estimation
II.1. A PMG
approach
II. The empirical
estimation
III. The Bayesian
estimation of a
DSGE model
Household
The stochastic
discount factor
Firms
The Bayesian estimation of a DSGE model
Flexible prices (1)
At each date t, firm i’s problem is
max
Pq,t (i)
Pq,t(i)Qt(i) − cost(Qt(i))
subject to Qt(i) =
Pq,t(i)
Pq,t
−ε
Qt.
Note that this problem does not depend on i, consequently its
solution 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−ε
di
1
1−ε
, we
have Pq,t(i) = Pq,t for every i.
How Dependent is
Output Growth
from Primary
Energy ?
Gael Giraud
CNRS, PSE,
University Paris I
and
Z. Kahraman ,
TSP
V. Acurio, F.
McIsaac, N. Pham,
CES, Paris I
I. Why is this
relationship
important ?
I.1. Kaya’s
equation
I. Why is this
relationship
important ?
I.2. Why is this
relationship
ignored ?
II. The empirical
estimation
II.1. A PMG
approach
II. The empirical
estimation
III. The Bayesian
estimation of a
DSGE model
Household
The stochastic
discount factor
Firms
The Bayesian estimation of a DSGE model
Flexible prices (2)
FOC of P∗
q,t gives
P∗
q,t =
ε
ε − 1
mc∗
t ,
where
mc∗
t := FtQ
1
αe +αn+α
k
−1
t ,
Ft :=
Atααe
e ααn
n α
αk
k
Pαe
e,t W αn
t (rk
t Pi,t)αk
−1
αe +αn+α
k
.
ε
ε−1 is the price markup, greater than 1 similar as a tax, note
than when ε → +∞ this markup is 1.
How Dependent is
Output Growth
from Primary
Energy ?
Gael Giraud
CNRS, PSE,
University Paris I
and
Z. Kahraman ,
TSP
V. Acurio, F.
McIsaac, N. Pham,
CES, Paris I
I. Why is this
relationship
important ?
I.1. Kaya’s
equation
I. Why is this
relationship
important ?
I.2. Why is this
relationship
ignored ?
II. The empirical
estimation
II.1. A PMG
approach
II. The empirical
estimation
III. The Bayesian
estimation of a
DSGE model
Household
The stochastic
discount factor
Firms
The Bayesian estimation of a DSGE model
Calvo setting (1)
Assumption
Calvo price setting
A 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) = Po
q,t(i).
We have "Aggregate Price Relationship"
Pq,t =
[0,1]
Pq,t(i)1−ε
di
1
1−ε
= θP1−ε
q,t−1 + (1 − θ)(Po
q,t)1−ε
1
1−ε
.
How Dependent is
Output Growth
from Primary
Energy ?
Gael Giraud
CNRS, PSE,
University Paris I
and
Z. Kahraman ,
TSP
V. Acurio, F.
McIsaac, N. Pham,
CES, Paris I
I. Why is this
relationship
important ?
I.1. Kaya’s
equation
I. Why is this
relationship
important ?
I.2. Why is this
relationship
ignored ?
II. The empirical
estimation
II.1. A PMG
approach
II. The empirical
estimation
III. The Bayesian
estimation of a
DSGE model
Household
The stochastic
discount factor
Firms
The Bayesian estimation of a DSGE model
Calvo setting (2)
At date t, denote Qt,t+k (i) be the output at date t + k for firm i
that last reset its price in period t. Firm i’s problem is
max
Pq,t (i)
Et
∞
k=0
θk
dt,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
−ε
Qt+k , ∀k ≥ 0.
Note that this problem does not depend on i, hence its solution
Pq,t(i) also, we write
Pq,t(i) = Po
q,t
How Dependent is
Output Growth
from Primary
Energy ?
Gael Giraud
CNRS, PSE,
University Paris I
and
Z. Kahraman ,
TSP
V. Acurio, F.
McIsaac, N. Pham,
CES, Paris I
I. Why is this
relationship
important ?
I.1. Kaya’s
equation
I. Why is this
relationship
important ?
I.2. Why is this
relationship
ignored ?
II. The empirical
estimation
II.1. A PMG
approach
II. The empirical
estimation
III. The Bayesian
estimation of a
DSGE model
Household
The stochastic
discount factor
Firms
The Bayesian estimation of a DSGE model
Calvo setting (3)
FOC for Po
q,t,
Et
∞
k=0
θk
dt,t+k Qo
t,t+k Po
q,t − Mp
mco
t,t+k = 0,
where mco
t,t+k := Ft+k (Qo
t,t+k )
1
αe +α
l
+α
k
−1
, and
Qo
t,t+k =
Po
q,t
Pq,t+k
−ε
Qt+k for every k ≥ 0.
How Dependent is
Output Growth
from Primary
Energy ?
Gael Giraud
CNRS, PSE,
University Paris I
and
Z. Kahraman ,
TSP
V. Acurio, F.
McIsaac, N. Pham,
CES, Paris I
I. Why is this
relationship
important ?
I.1. Kaya’s
equation
I. Why is this
relationship
important ?
I.2. Why is this
relationship
ignored ?
II. The empirical
estimation
II.1. A PMG
approach
II. The empirical
estimation
III. The Bayesian
estimation of a
DSGE model
Household
The stochastic
discount factor
Firms
Denote
Ao
t := Et
∞
k=0
θk
dt,t+k Qo
t,t+k ,
Bo
t := Et
∞
k=0
θk
dt,t+k Qo
t,t+k mco
t,t+k .
We have
Po
q,tAo
t = Mp
Bo
t ,
Ao
t := Qo
t,t + θEtdt,t+1Ao
t+1,
Bo
t := Qo
t,tmco
t,t + θEtdt,t+1Bo
t+1.
How Dependent is
Output Growth
from Primary
Energy ?
Gael Giraud
CNRS, PSE,
University Paris I
and
Z. Kahraman ,
TSP
V. Acurio, F.
McIsaac, N. Pham,
CES, Paris I
I. Why is this
relationship
important ?
I.1. Kaya’s
equation
I. Why is this
relationship
important ?
I.2. Why is this
relationship
ignored ?
II. The empirical
estimation
II.1. A PMG
approach
II. The empirical
estimation
III. The Bayesian
estimation of a
DSGE model
Household
The stochastic
discount factor
Firms
The Bayesian estimation of a DSGE model
Monetary policy
Denote Πq,t :=
Pq,t
Pq,t−1
.
The Central Bank sets the nominal short-term interest rate
it + 1 =
1
β
× Πq,t
φπ
×
Py,tYt
Py Y
φy
Where Y denotes the steady state value of nominal GDP implied
by the model and Py is the steady state of the GDP deflator.
How Dependent is
Output Growth
from Primary
Energy ?
Gael Giraud
CNRS, PSE,
University Paris I
and
Z. Kahraman ,
TSP
V. Acurio, F.
McIsaac, N. Pham,
CES, Paris I
I. Why is this
relationship
important ?
I.1. Kaya’s
equation
I. Why is this
relationship
important ?
I.2. Why is this
relationship
ignored ?
II. The empirical
estimation
II.1. A PMG
approach
II. The empirical
estimation
III. The Bayesian
estimation of a
DSGE model
Household
The stochastic
discount factor
Firms
The Bayesian estimation of a DSGE model
Government 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) + εg
t ,
Where ωQ denotes the steady state share of government spending
in output.
How Dependent is
Output Growth
from Primary
Energy ?
Gael Giraud
CNRS, PSE,
University Paris I
and
Z. Kahraman ,
TSP
V. Acurio, F.
McIsaac, N. Pham,
CES, Paris I
I. Why is this
relationship
important ?
I.1. Kaya’s
equation
I. Why is this
relationship
important ?
I.2. Why is this
relationship
ignored ?
II. The empirical
estimation
II.1. A PMG
approach
II. The empirical
estimation
III. The Bayesian
estimation of a
DSGE model
Household
The stochastic
discount factor
Firms
The Bayesian estimation of a DSGE model
Definition 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 equilibrium
Pc,tCt + Pi,tIt + Gt = Pq,tQt − Pe,tEt.
(iii) Government budget constraint
(1 + it−1)Bt−1 + Gt = Bt + Tt,
How Dependent is
Output Growth
from Primary
Energy ?
Gael Giraud
CNRS, PSE,
University Paris I
and
Z. Kahraman ,
TSP
V. Acurio, F.
McIsaac, N. Pham,
CES, Paris I
I. Why is this
relationship
important ?
I.1. Kaya’s
equation
I. Why is this
relationship
important ?
I.2. Why is this
relationship
ignored ?
II. The empirical
estimation
II.1. A PMG
approach
II. The empirical
estimation
III. The Bayesian
estimation of a
DSGE model
Household
The stochastic
discount factor
Firms
The Bayesian estimation of a DSGE model
Equilibrium (2)
(iv) The production function
[0,1]
Pq,t(i)
Pq,t
−ε
αe +α
l
+α
k di
αe +αl +αk
Qt = AtEαe
t L
αl
t K
αk
t .
In Calvo setting :
Define vt := [0,1]
Pq,t (i)
Pq,t
−ε
αe +α
l
+α
k
di. Then we have
vt = θΠε
q,tvt−1 + (1 − θ)
Po
q,t
Pq,t
−ε
(iv) The marginal cost of firms.
How Dependent is
Output Growth
from Primary
Energy ?
Gael Giraud
CNRS, PSE,
University Paris I
and
Z. Kahraman ,
TSP
V. Acurio, F.
McIsaac, N. Pham,
CES, Paris I
I. Why is this
relationship
important ?
I.1. Kaya’s
equation
I. Why is this
relationship
important ?
I.2. Why is this
relationship
ignored ?
II. The empirical
estimation
II.1. A PMG
approach
II. The empirical
estimation
III. The Bayesian
estimation of a
DSGE model
Household
The stochastic
discount factor
Firms
The Bayesian estimation of a DSGE model
Shocks
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 is
Output Growth
from Primary
Energy ?
Gael Giraud
CNRS, PSE,
University Paris I
and
Z. Kahraman ,
TSP
V. Acurio, F.
McIsaac, N. Pham,
CES, Paris I
I. Why is this
relationship
important ?
I.1. Kaya’s
equation
I. Why is this
relationship
important ?
I.2. Why is this
relationship
ignored ?
II. The empirical
estimation
II.1. A PMG
approach
II. The empirical
estimation
III. The Bayesian
estimation of a
DSGE model
Household
The stochastic
discount factor
Firms
III. The Bayesian estimation approach
III. Estimating the parameters
◦ Estimating the parameters of a New-Keynesian DSGE model
US: 1984 Q1 - 2007Q1. αe= Oil input elasticity.

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

  • 1. How Dependent is Output Growth from Primary Energy ? Gael Giraud CNRS, PSE, University Paris I and Z. Kahraman , TSP V. Acurio, F. McIsaac, N. Pham, CES, Paris I I. Why is this relationship important ? I.1. Kaya’s equation I. Why is this relationship important ? I.2. Why is this relationship ignored ? II. The empirical estimation II.1. A PMG approach II. The empirical estimation III. The Bayesian estimation of a DSGE model Household The stochastic discount factor Firms How Dependent is Output Growth from Primary Energy ? Gael Giraud CNRS, PSE, University Paris I and Z. Kahraman , TSP V. Acurio, F. McIsaac, N. Pham, CES, Paris I March 6, 2014
  • 2. How Dependent is Output Growth from Primary Energy ? Gael Giraud CNRS, PSE, University Paris I and Z. Kahraman , TSP V. Acurio, F. McIsaac, N. Pham, CES, Paris I I. Why is this relationship important ? I.1. Kaya’s equation I. Why is this relationship important ? I.2. Why is this relationship ignored ? II. The empirical estimation II.1. A PMG approach II. The empirical estimation III. The Bayesian estimation of a DSGE model Household The stochastic discount factor Firms 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.
  • 3. How Dependent is Output Growth from Primary Energy ? Gael Giraud CNRS, PSE, University Paris I and Z. Kahraman , TSP V. Acurio, F. McIsaac, N. Pham, CES, Paris I I. Why is this relationship important ? I.1. Kaya’s equation I. Why is this relationship important ? I.2. Why is this relationship ignored ? II. The empirical estimation II.1. A PMG approach II. The empirical estimation III. The Bayesian estimation of a DSGE model Household The stochastic discount factor Firms ◦ Source : OECD.
  • 4. How Dependent is Output Growth from Primary Energy ? Gael Giraud CNRS, PSE, University Paris I and Z. Kahraman , TSP V. Acurio, F. McIsaac, N. Pham, CES, Paris I I. Why is this relationship important ? I.1. Kaya’s equation I. Why is this relationship important ? I.2. Why is this relationship ignored ? II. The empirical estimation II.1. A PMG approach II. The empirical estimation III. The Bayesian estimation of a DSGE model Household The stochastic discount factor Firms ◦ Source : OECD.
  • 5. How Dependent is Output Growth from Primary Energy ? Gael Giraud CNRS, PSE, University Paris I and Z. Kahraman , TSP V. Acurio, F. McIsaac, N. Pham, CES, Paris I I. Why is this relationship important ? I.1. Kaya’s equation I. Why is this relationship important ? I.2. Why is this relationship ignored ? II. The empirical estimation II.1. A PMG approach II. The empirical estimation III. The Bayesian estimation of a DSGE model Household The stochastic discount factor Firms ◦ ∆ Y Pop = ∆ E Pop × Y E . ∆ Y Pop := growth of GDP per capita. ∆ E Pop := growth of energy consumption per capita. ∆Y E := growth of energy efficiency.
  • 6. How Dependent is Output Growth from Primary Energy ? Gael Giraud CNRS, PSE, University Paris I and Z. Kahraman , TSP V. Acurio, F. McIsaac, N. Pham, CES, Paris I I. Why is this relationship important ? I.1. Kaya’s equation I. Why is this relationship important ? I.2. Why is this relationship ignored ? II. The empirical estimation II.1. A PMG approach II. The empirical estimation III. The Bayesian estimation of a DSGE model Household The stochastic discount factor Firms ◦ ∆ Y Pop = ∆ E Pop × Y E . ∆ Y Pop := growth of GDP per capita. ∆ E Pop := growth of energy consumption per capita. ∆Y E := growth of energy efficiency. ◦ Taking the log... ∆ ln Y Pop = ∆ ln E Pop + ∆ ln Y E .
  • 7. How Dependent is Output Growth from Primary Energy ? Gael Giraud CNRS, PSE, University Paris I and Z. Kahraman , TSP V. Acurio, F. McIsaac, N. Pham, CES, Paris I I. Why is this relationship important ? I.1. Kaya’s equation I. Why is this relationship important ? I.2. Why is this relationship ignored ? II. The empirical estimation II.1. A PMG approach II. The empirical estimation III. The Bayesian estimation of a DSGE model Household The stochastic discount factor Firms ◦ The relationship in terms of per capita quantities : Source : BP statistical review, 2012, Shilling et al. 1977, EIA, 2012, et Banque Mondiale (PIB), 2012.
  • 8. How Dependent is Output Growth from Primary Energy ? Gael Giraud CNRS, PSE, University Paris I and Z. Kahraman , TSP V. Acurio, F. McIsaac, N. Pham, CES, Paris I I. Why is this relationship important ? I.1. Kaya’s equation I. Why is this relationship important ? I.2. Why is this relationship ignored ? II. The empirical estimation II.1. A PMG approach II. The empirical estimation III. The Bayesian estimation of a DSGE model Household The stochastic discount factor Firms ◦ 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.
  • 9. How Dependent is Output Growth from Primary Energy ? Gael Giraud CNRS, PSE, University Paris I and Z. Kahraman , TSP V. Acurio, F. McIsaac, N. Pham, CES, Paris I I. Why is this relationship important ? I.1. Kaya’s equation I. Why is this relationship important ? I.2. Why is this relationship ignored ? II. The empirical estimation II.1. A PMG approach II. The empirical estimation III. The Bayesian estimation of a DSGE model Household The stochastic discount factor Firms ◦ 1965-1981 : world average 3.5% = 2.5% + 1%
  • 10. How Dependent is Output Growth from Primary Energy ? Gael Giraud CNRS, PSE, University Paris I and Z. Kahraman , TSP V. Acurio, F. McIsaac, N. Pham, CES, Paris I I. Why is this relationship important ? I.1. Kaya’s equation I. Why is this relationship important ? I.2. Why is this relationship ignored ? II. The empirical estimation II.1. A PMG approach II. The empirical estimation III. The Bayesian estimation of a DSGE model Household The stochastic discount factor Firms ◦◦ 1965-1981 : world average 3.5% = 2.5% + 1% ◦ 1981-2013 : world average 1.5% = 0.5% + 1%
  • 11. How Dependent is Output Growth from Primary Energy ? Gael Giraud CNRS, PSE, University Paris I and Z. Kahraman , TSP V. Acurio, F. McIsaac, N. Pham, CES, Paris I I. Why is this relationship important ? I.1. Kaya’s equation I. Why is this relationship important ? I.2. Why is this relationship ignored ? II. The empirical estimation II.1. A PMG approach II. The empirical estimation III. The Bayesian estimation of a DSGE model Household The stochastic discount factor Firms ◦◦ 1965-1981 : world average 3.5% = 2.5% + 1% ◦ 1981-2013 : world average 1.5% = 0.5% + 1% ◦ Japan : 2000-2013 : 0% = 0% + 0%...
  • 12. How Dependent is Output Growth from Primary Energy ? Gael Giraud CNRS, PSE, University Paris I and Z. Kahraman , TSP V. Acurio, F. McIsaac, N. Pham, CES, Paris I I. Why is this relationship important ? I.1. Kaya’s equation I. Why is this relationship important ? I.2. Why is this relationship ignored ? II. The empirical estimation II.1. A PMG approach II. The empirical estimation III. The Bayesian estimation of a DSGE model Household The stochastic discount factor Firms ◦◦ 1965-1981 : world average 3.5% = 2.5% + 1% ◦ 1981-2013 : world average 1.5% = 0.5% + 1% ◦ Japan : 2000-2013 : 0% = 0% + 0%...
  • 13. How Dependent is Output Growth from Primary Energy ? Gael Giraud CNRS, PSE, University Paris I and Z. Kahraman , TSP V. Acurio, F. McIsaac, N. Pham, CES, Paris I I. Why is this relationship important ? I.1. Kaya’s equation I. Why is this relationship important ? I.2. Why is this relationship ignored ? II. The empirical estimation II.1. A PMG approach II. The empirical estimation III. The Bayesian estimation of a DSGE model Household The stochastic discount factor Firms ◦◦
  • 14. How Dependent is Output Growth from Primary Energy ? Gael Giraud CNRS, PSE, University Paris I and Z. Kahraman , TSP V. Acurio, F. McIsaac, N. Pham, CES, Paris I I. Why is this relationship important ? I.1. Kaya’s equation I. Why is this relationship important ? I.2. Why is this relationship ignored ? II. The empirical estimation II.1. A PMG approach II. The empirical estimation III. The Bayesian estimation of a DSGE model Household The stochastic discount factor Firms ◦
  • 15. How Dependent is Output Growth from Primary Energy ? Gael Giraud CNRS, PSE, University Paris I and Z. Kahraman , TSP V. Acurio, F. McIsaac, N. Pham, CES, Paris I I. Why is this relationship important ? I.1. Kaya’s equation I. Why is this relationship important ? I.2. Why is this relationship ignored ? II. The empirical estimation II.1. A PMG approach II. The empirical estimation III. The Bayesian estimation of a DSGE model Household The stochastic discount factor Firms ◦
  • 16. How Dependent is Output Growth from Primary Energy ? Gael Giraud CNRS, PSE, University Paris I and Z. Kahraman , TSP V. Acurio, F. McIsaac, N. Pham, CES, Paris I I. Why is this relationship important ? I.1. Kaya’s equation I. Why is this relationship important ? I.2. Why is this relationship ignored ? II. The empirical estimation II.1. A PMG approach II. The empirical estimation III. The Bayesian estimation of a DSGE model Household The stochastic discount factor Firms ◦
  • 17. How Dependent is Output Growth from Primary Energy ? Gael Giraud CNRS, PSE, University Paris I and Z. Kahraman , TSP V. Acurio, F. McIsaac, N. Pham, CES, Paris I I. Why is this relationship important ? I.1. Kaya’s equation I. Why is this relationship important ? I.2. Why is this relationship ignored ? II. The empirical estimation II.1. A PMG approach II. The empirical estimation III. The Bayesian estimation of a DSGE model Household The stochastic discount factor Firms ◦
  • 18. How Dependent is Output Growth from Primary Energy ? Gael Giraud CNRS, PSE, University Paris I and Z. Kahraman , TSP V. Acurio, F. McIsaac, N. Pham, CES, Paris I I. Why is this relationship important ? I.1. Kaya’s equation I. Why is this relationship important ? I.2. Why is this relationship ignored ? II. The empirical estimation II.1. A PMG approach II. The empirical estimation III. The Bayesian estimation of a DSGE model Household The stochastic discount factor Firms I. Why is this relationship important ? I.2. Why is this relationship ignored ? ◦ No such obvious relation in terms of energy prices.
  • 19. How Dependent is Output Growth from Primary Energy ? Gael Giraud CNRS, PSE, University Paris I and Z. Kahraman , TSP V. Acurio, F. McIsaac, N. Pham, CES, Paris I I. Why is this relationship important ? I.1. Kaya’s equation I. Why is this relationship important ? I.2. Why is this relationship ignored ? II. The empirical estimation II.1. A PMG approach II. The empirical estimation III. The Bayesian estimation of a DSGE model Household The stochastic discount factor Firms ◦
  • 20. How Dependent is Output Growth from Primary Energy ? Gael Giraud CNRS, PSE, University Paris I and Z. Kahraman , TSP V. Acurio, F. McIsaac, N. Pham, CES, Paris I I. Why is this relationship important ? I.1. Kaya’s equation I. Why is this relationship important ? I.2. Why is this relationship ignored ? II. The empirical estimation II.1. A PMG approach II. The empirical estimation III. The Bayesian estimation of a DSGE model Household The stochastic discount factor Firms ◦ The cost-share theorem max x Y (x) − p · x (1)
  • 21. How Dependent is Output Growth from Primary Energy ? Gael Giraud CNRS, PSE, University Paris I and Z. Kahraman , TSP V. Acurio, F. McIsaac, N. Pham, CES, Paris I I. Why is this relationship important ? I.1. Kaya’s equation I. Why is this relationship important ? I.2. Why is this relationship ignored ? II. The empirical estimation II.1. A PMG approach II. The empirical estimation III. The Bayesian estimation of a DSGE model Household The stochastic discount factor Firms ◦ The cost-share theorem max x Y (x) − p · x (1) ◦ εi := xi Y (x) × ∂Y ∂xi (x) = pi xi p · x (2)
  • 22. How Dependent is Output Growth from Primary Energy ? Gael Giraud CNRS, PSE, University Paris I and Z. Kahraman , TSP V. Acurio, F. McIsaac, N. Pham, CES, Paris I I. Why is this relationship important ? I.1. Kaya’s equation I. Why is this relationship important ? I.2. Why is this relationship ignored ? II. The empirical estimation II.1. A PMG approach II. The empirical estimation III. The Bayesian estimation of a DSGE model Household The stochastic discount factor Firms ◦ max x Y (x) − p · x s.t. f (x) = 0 (3) f (·) : geological, technical, political... constraints.
  • 23. How Dependent is Output Growth from Primary Energy ? Gael Giraud CNRS, PSE, University Paris I and Z. Kahraman , TSP V. Acurio, F. McIsaac, N. Pham, CES, Paris I I. Why is this relationship important ? I.1. Kaya’s equation I. Why is this relationship important ? I.2. Why is this relationship ignored ? II. The empirical estimation II.1. A PMG approach II. The empirical estimation III. The Bayesian estimation of a DSGE model Household The stochastic discount factor Firms ◦ max x Y (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.
  • 24. How Dependent is Output Growth from Primary Energy ? Gael Giraud CNRS, PSE, University Paris I and Z. Kahraman , TSP V. Acurio, F. McIsaac, N. Pham, CES, Paris I I. Why is this relationship important ? I.1. Kaya’s equation I. Why is this relationship important ? I.2. Why is this relationship ignored ? II. The empirical estimation II.1. A PMG approach II. The empirical estimation III. The Bayesian estimation of a DSGE model Household The stochastic discount factor Firms ◦ max x Y (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.
  • 25. How Dependent is Output Growth from Primary Energy ? Gael Giraud CNRS, PSE, University Paris I and Z. Kahraman , TSP V. Acurio, F. McIsaac, N. Pham, CES, Paris I I. Why is this relationship important ? I.1. Kaya’s equation I. Why is this relationship important ? I.2. Why is this relationship ignored ? II. The empirical estimation II.1. A PMG approach II. The empirical estimation III. The Bayesian estimation of a DSGE model Household The stochastic discount factor Firms II. The empirical estimation II.1. A PMG approach ◦ Cointegration = Correlation.
  • 26. How Dependent is Output Growth from Primary Energy ? Gael Giraud CNRS, PSE, University Paris I and Z. Kahraman , TSP V. Acurio, F. McIsaac, N. Pham, CES, Paris I I. Why is this relationship important ? I.1. Kaya’s equation I. Why is this relationship important ? I.2. Why is this relationship ignored ? II. The empirical estimation II.1. A PMG approach II. The empirical estimation III. The Bayesian estimation of a DSGE model Household The stochastic discount factor Firms ◦
  • 27. How Dependent is Output Growth from Primary Energy ? Gael Giraud CNRS, PSE, University Paris I and Z. Kahraman , TSP V. Acurio, F. McIsaac, N. Pham, CES, Paris I I. Why is this relationship important ? I.1. Kaya’s equation I. Why is this relationship important ? I.2. Why is this relationship ignored ? II. The empirical estimation II.1. A PMG approach II. The empirical estimation III. The Bayesian estimation of a DSGE model Household The stochastic discount factor Firms II. The empirical estimation II.1. A PMG approach From 1970 to 2011.
  • 28. How Dependent is Output Growth from Primary Energy ? Gael Giraud CNRS, PSE, University Paris I and Z. Kahraman , TSP V. Acurio, F. McIsaac, N. Pham, CES, Paris I I. Why is this relationship important ? I.1. Kaya’s equation I. Why is this relationship important ? I.2. Why is this relationship ignored ? II. The empirical estimation II.1. A PMG approach II. The empirical estimation III. The Bayesian estimation of a DSGE model Household The stochastic discount factor Firms ◦ 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 Development Indicators. - Gross Fixed Capital Formation (in 2000 U.S $) World Bank, World Development Indicators. - Population data - World Bank, World Development Indicators.
  • 29. How Dependent is Output Growth from Primary Energy ? Gael Giraud CNRS, PSE, University Paris I and Z. Kahraman , TSP V. Acurio, F. McIsaac, N. Pham, CES, Paris I I. Why is this relationship important ? I.1. Kaya’s equation I. Why is this relationship important ? I.2. Why is this relationship ignored ? II. The empirical estimation II.1. A PMG approach II. The empirical estimation III. The Bayesian estimation of a DSGE model Household The stochastic discount factor Firms ◦ The main equation: ln GDPi,t = βi,0+βi,1 ln NRJi,t+βi,2 ln EFFi,t−1+βi,3 ln Ki,t+εi,t. All the variables are per capita.
  • 30. How Dependent is Output Growth from Primary Energy ? Gael Giraud CNRS, PSE, University Paris I and Z. Kahraman , TSP V. Acurio, F. McIsaac, N. Pham, CES, Paris I I. Why is this relationship important ? I.1. Kaya’s equation I. Why is this relationship important ? I.2. Why is this relationship ignored ? II. The empirical estimation II.1. A PMG approach II. The empirical estimation III. The Bayesian estimation of a DSGE model Household The stochastic discount factor Firms ◦ The main equation: ln GDPi,t = βi,0+βi,1 ln NRJi,t+βi,2 ln EFFi,t−1+βi,3 ln Ki,t+εi,t. All the variables are per capita. ◦ Energy efficiency is lagged in order to avoid tautological over-identification.
  • 31. How Dependent is Output Growth from Primary Energy ? Gael Giraud CNRS, PSE, University Paris I and Z. Kahraman , TSP V. Acurio, F. McIsaac, N. Pham, CES, Paris I I. Why is this relationship important ? I.1. Kaya’s equation I. Why is this relationship important ? I.2. Why is this relationship ignored ? II. The empirical estimation II.1. A PMG approach II. The empirical estimation III. The Bayesian estimation of a DSGE model Household The stochastic discount factor Firms Is there a (hidden) long-run relationship ? ◦
  • 32. How Dependent is Output Growth from Primary Energy ? Gael Giraud CNRS, PSE, University Paris I and Z. Kahraman , TSP V. Acurio, F. McIsaac, N. Pham, CES, Paris I I. Why is this relationship important ? I.1. Kaya’s equation I. Why is this relationship important ? I.2. Why is this relationship ignored ? II. The empirical estimation II.1. A PMG approach II. The empirical estimation III. The Bayesian estimation of a DSGE model Household The stochastic discount factor Firms Is there a (hidden) long-run relationship ? ◦ ◦ Westerlund panel cointegration test also strongly reject the (no-cointegration) null hypothesis.
  • 33. How Dependent is Output Growth from Primary Energy ? Gael Giraud CNRS, PSE, University Paris I and Z. Kahraman , TSP V. Acurio, F. McIsaac, N. Pham, CES, Paris I I. Why is this relationship important ? I.1. Kaya’s equation I. Why is this relationship important ? I.2. Why is this relationship ignored ? II. The empirical estimation II.1. A PMG approach II. The empirical estimation III. The Bayesian estimation of a DSGE model Household The stochastic discount factor Firms Can we quantify this long-run relationship ?An ECM approach: ◦
  • 34. How Dependent is Output Growth from Primary Energy ? Gael Giraud CNRS, PSE, University Paris I and Z. Kahraman , TSP V. Acurio, F. McIsaac, N. Pham, CES, Paris I I. Why is this relationship important ? I.1. Kaya’s equation I. Why is this relationship important ? I.2. Why is this relationship ignored ? II. The empirical estimation II.1. A PMG approach II. The empirical estimation III. The Bayesian estimation of a DSGE model Household The stochastic discount factor Firms Is there a causality link ? ◦ Kraft & Kraft (1978), D. Stern (1993), Ozturk (2010), D. Stern (2011) Non-conclusive causal relationship between quantities Except for Sweden over 1 century (Stern (2011)). Strong relationship in terms of prices. (Cf. Hamilton...)
  • 35. How Dependent is Output Growth from Primary Energy ? Gael Giraud CNRS, PSE, University Paris I and Z. Kahraman , TSP V. Acurio, F. McIsaac, N. Pham, CES, Paris I I. Why is this relationship important ? I.1. Kaya’s equation I. Why is this relationship important ? I.2. Why is this relationship ignored ? II. The empirical estimation II.1. A PMG approach II. The empirical estimation III. The Bayesian estimation of a DSGE model Household The stochastic discount factor Firms Is there a causality link ? ◦ Kraft & Kraft (1978), D. Stern (1993), Ozturk (2010), D. Stern (2011) Non-conclusive causal relationship between quantities Except for Sweden over 1 century (Stern (2011)). Strong relationship in terms of prices. (Cf. Hamilton...) ◦ Granger panel tests (valid since cointegration):
  • 36. How Dependent is Output Growth from Primary Energy ? Gael Giraud CNRS, PSE, University Paris I and Z. Kahraman , TSP V. Acurio, F. McIsaac, N. Pham, CES, Paris I I. Why is this relationship important ? I.1. Kaya’s equation I. Why is this relationship important ? I.2. Why is this relationship ignored ? II. The empirical estimation II.1. A PMG approach II. The empirical estimation III. The Bayesian estimation of a DSGE model Household The stochastic discount factor Firms III. The Bayesian estimation of a DSGE model We construct a New-Keynesian model with capital and oil in the production function and consumption. We observe impact of shocks in the economy, for instance, shock in energy price, capital price shock or government expenditure shock.
  • 37. How Dependent is Output Growth from Primary Energy ? Gael Giraud CNRS, PSE, University Paris I and Z. Kahraman , TSP V. Acurio, F. McIsaac, N. Pham, CES, Paris I I. Why is this relationship important ? I.1. Kaya’s equation I. Why is this relationship important ? I.2. Why is this relationship ignored ? II. The empirical estimation II.1. A PMG approach II. The empirical estimation III. The Bayesian estimation of a DSGE model Household The stochastic discount factor Firms III. The Bayesian estimation of a DSGE model Model An open small economy A representative agent invests, works and consumes - Final consumption good and energy - A continuum of competitive final good producers Continuum of imperfectly competitive intermediate good producers Government rules fiscal policy and monetary policy Energy is imported, i.e. no energy produced within the country, with an exogenous price. Exogenous process for the price of capital.
  • 38. How Dependent is Output Growth from Primary Energy ? Gael Giraud CNRS, PSE, University Paris I and Z. Kahraman , TSP V. Acurio, F. McIsaac, N. Pham, CES, Paris I I. Why is this relationship important ? I.1. Kaya’s equation I. Why is this relationship important ? I.2. Why is this relationship ignored ? II. The empirical estimation II.1. A PMG approach II. The empirical estimation III. The Bayesian estimation of a DSGE model Household The stochastic discount factor Firms The Bayesian estimation of a DSGE model Household The problem of the representative household is max E0 ∞ t=0 βt u(Ct, Lt) , 0 < β < 1, subject to : Pe,tCe,t + 1 0 Pq,t(i)Cq,t(i)di + Pi,tIt + Bt + Tt ≤ (1 + it−1)Bt−1 + WtLt + Dt + rk t Pk,tKt, where the consumption flow of household is defined as: Ct := Θx Cx e,tC1−x q,t , Ce,t = h’s consumption of energy, Cq,t := 1 0 Cq,t(i)1− 1 ε di ε ε−1 is a CES index of domestic goods (or Dixit-Stiglitz agregator), x ∈ (0, 1) is the share of oil in consumption, Θx := x−x (1 − x)−(1−x) .
  • 39. How Dependent is Output Growth from Primary Energy ? Gael Giraud CNRS, PSE, University Paris I and Z. Kahraman , TSP V. Acurio, F. McIsaac, N. Pham, CES, Paris I I. Why is this relationship important ? I.1. Kaya’s equation I. Why is this relationship important ? I.2. Why is this relationship ignored ? II. The empirical estimation II.1. A PMG approach II. The empirical estimation III. The Bayesian estimation of a DSGE model Household The stochastic discount factor Firms The Bayesian estimation of a DSGE model No Ponzi scheme Transversality condition (no Ponzi scheme) lim k→∞ Et      Bt+k t+k−1 s=0 (1 + is−1)      ≥ 0, ∀t.
  • 40. How Dependent is Output Growth from Primary Energy ? Gael Giraud CNRS, PSE, University Paris I and Z. Kahraman , TSP V. Acurio, F. McIsaac, N. Pham, CES, Paris I I. Why is this relationship important ? I.1. Kaya’s equation I. Why is this relationship important ? I.2. Why is this relationship ignored ? II. The empirical estimation II.1. A PMG approach II. The empirical estimation III. The Bayesian estimation of a DSGE model Household The stochastic discount factor Firms The Bayesian estimation of a DSGE model Household’s optimal expenditure allocation Household maximizes her consumption Ct under the budget constraint : Pc,tCt = Pq,tCq,t + Pe,tCe,t, this yield to this optimal allocation of expenditures: Pq,tCq,t = (1 − x)Pc,tCt Pe,tCe,t = xPc,tCt Where : Pc,t = Px e,tP (1−x) q,t is the CPI index.
  • 41. How Dependent is Output Growth from Primary Energy ? Gael Giraud CNRS, PSE, University Paris I and Z. Kahraman , TSP V. Acurio, F. McIsaac, N. Pham, CES, Paris I I. Why is this relationship important ? I.1. Kaya’s equation I. Why is this relationship important ? I.2. Why is this relationship ignored ? II. The empirical estimation II.1. A PMG approach II. The empirical estimation III. The Bayesian estimation of a DSGE model Household The stochastic discount factor Firms The Bayesian estimation of a DSGE model FOC of Household Using the Lagrangian associated with the maximization problem of the household one has the following conditions: Marg. util. of cons. : Ct : λt = 1 CtPc,t The Labor supply : Lt : λt = Lφ t Wt The Euler equation : Bt : λt = βEt (1 + it)λt+1 The Fisher equation : Kt+1 : λtPi,t = βEtλt+1 rk t+1 + 1 − δ Pk,t+1.
  • 42. How Dependent is Output Growth from Primary Energy ? Gael Giraud CNRS, PSE, University Paris I and Z. Kahraman , TSP V. Acurio, F. McIsaac, N. Pham, CES, Paris I I. Why is this relationship important ? I.1. Kaya’s equation I. Why is this relationship important ? I.2. Why is this relationship ignored ? II. The empirical estimation II.1. A PMG approach II. The empirical estimation III. The Bayesian estimation of a DSGE model Household The stochastic discount factor Firms The Bayesian estimation of a DSGE model Stochastic 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, 1 1 + 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+1 s , then, dt,t+k := βk uC (Ct+k , Lt+k ) uC (Ct, Lt) Pc,t Pc,t+k .
  • 43. How Dependent is Output Growth from Primary Energy ? Gael Giraud CNRS, PSE, University Paris I and Z. Kahraman , TSP V. Acurio, F. McIsaac, N. Pham, CES, Paris I I. Why is this relationship important ? I.1. Kaya’s equation I. Why is this relationship important ? I.2. Why is this relationship ignored ? II. The empirical estimation II.1. A PMG approach II. The empirical estimation III. The Bayesian estimation of a DSGE model Household The stochastic discount factor Firms The Bayesian estimation of a DSGE model Final good producers We 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 Qh t = [0,1] Qh t (i) ε−1 ε di ε ε−1 ε denotes the elasticity of substitution across intermediate goods. The higher ε, the smaller is the market power of each intermediate-good producer. Given all intermediate goods prices and the final good price, the problem of final good firm is that max Yt (·) Pq,tYt − [0,1] Pq,t(i)Yt(i)di subject to : Yt = [0,1] Yt(i) ε−1 ε di ε ε−1
  • 44. How Dependent is Output Growth from Primary Energy ? Gael Giraud CNRS, PSE, University Paris I and Z. Kahraman , TSP V. Acurio, F. McIsaac, N. Pham, CES, Paris I I. Why is this relationship important ? I.1. Kaya’s equation I. Why is this relationship important ? I.2. Why is this relationship ignored ? II. The empirical estimation II.1. A PMG approach II. The empirical estimation III. The Bayesian estimation of a DSGE model Household The stochastic discount factor Firms The Bayesian estimation of a DSGE model Final good producers (2) The input demand functions associated with the problem are Yt(i) = Pq,t(i) Pq,t −ε Yt Note that the final good producer is in a perfect competition drives 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 1 1−ε
  • 45. How Dependent is Output Growth from Primary Energy ? Gael Giraud CNRS, PSE, University Paris I and Z. Kahraman , TSP V. Acurio, F. McIsaac, N. Pham, CES, Paris I I. Why is this relationship important ? I.1. Kaya’s equation I. Why is this relationship important ? I.2. Why is this relationship ignored ? II. The empirical estimation II.1. A PMG approach II. The empirical estimation III. The Bayesian estimation of a DSGE model Household The stochastic discount factor Firms The Bayesian estimation of a DSGE model Intermediate good firms By contrast with final-good producing firm, the intermediate-good producing ones live in a imperfectly competitive environment. We consider the following production function Cobb-Douglas: Qt(i) = AtEt(i)αm Lt(i)αn Kt(i)αk αm, αl , αk ≥ 0, αm + αl + αk ≤ 1
  • 46. How Dependent is Output Growth from Primary Energy ? Gael Giraud CNRS, PSE, University Paris I and Z. Kahraman , TSP V. Acurio, F. McIsaac, N. Pham, CES, Paris I I. Why is this relationship important ? I.1. Kaya’s equation I. Why is this relationship important ? I.2. Why is this relationship ignored ? II. The empirical estimation II.1. A PMG approach II. The empirical estimation III. The Bayesian estimation of a DSGE model Household The stochastic discount factor Firms The Bayesian estimation of a DSGE model The strategy of firm i The strategy of firm 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. Choose price Pq,t(i) to maximize her utility. We are going to consider two cases: flexible price and Calvo price setting.
  • 47. How Dependent is Output Growth from Primary Energy ? Gael Giraud CNRS, PSE, University Paris I and Z. Kahraman , TSP V. Acurio, F. McIsaac, N. Pham, CES, Paris I I. Why is this relationship important ? I.1. Kaya’s equation I. Why is this relationship important ? I.2. Why is this relationship ignored ? II. The empirical estimation II.1. A PMG approach II. The empirical estimation III. The Bayesian estimation of a DSGE model Household The stochastic discount factor Firms The Bayesian estimation of a DSGE model Firms minimize cost function the problem of firm i is minimize cost: Pe,tEt(i) + WtLt(i) + rk t Pi,tKt(i) subject to Et(i), Lt(i), Kt(i) ≥ 0, F(Et(i), Lt(i), Kt(i)) ≥ Qt(i)
  • 48. How Dependent is Output Growth from Primary Energy ? Gael Giraud CNRS, PSE, University Paris I and Z. Kahraman , TSP V. Acurio, F. McIsaac, N. Pham, CES, Paris I I. Why is this relationship important ? I.1. Kaya’s equation I. Why is this relationship important ? I.2. Why is this relationship ignored ? II. The empirical estimation II.1. A PMG approach II. The empirical estimation III. The Bayesian estimation of a DSGE model Household The stochastic discount factor Firms The Bayesian estimation of a DSGE model Example with Coob Douglas function Cobb-Douglas: Qt(i) = AtEt(i)αm Lt(i)αn Kt(i)αk αm, αn, αk ≥ 0, αm + αn + αk ≤ 1 Then the first-order conditions: Et(i) : Pe,t = λt(i)αeAtEαe −1 t Lt(i)αl Kt(i)αk Lt(i) : Wt = λt(i)αl AtEt(i)αe Lt(i)αl −1 Kt(i)αk Kt(i) : rk t Pq,t = λt(i)αk AtEt(i)αe Lt(i)αl Kt(i)αk −1 . By rewriting the system: λt(i)Qt(i) = WtLt(i) αn = rk t Kt(i)Pq,t αk = Et(i)Pe,t αe .
  • 49. How Dependent is Output Growth from Primary Energy ? Gael Giraud CNRS, PSE, University Paris I and Z. Kahraman , TSP V. Acurio, F. McIsaac, N. Pham, CES, Paris I I. Why is this relationship important ? I.1. Kaya’s equation I. Why is this relationship important ? I.2. Why is this relationship ignored ? II. The empirical estimation II.1. A PMG approach II. The empirical estimation III. The Bayesian estimation of a DSGE model Household The stochastic discount factor Firms The Bayesian estimation of a DSGE model Cobb-Douglas production function Cobb-Douglas: Qt(i) = AtEt(i)αm Lt(i)αn Kt(i)αk αm, αn, αk ≥ 0, αm + αn + αk ≤ 1 Denote Ft := Atααe e ααn n α αk k Pαe e,t W αn t (rk t Pi,t)αk −1 αe +αn+α k , then cost function: cost(Qt(i)) = (αe + αn + αk )FtQt(i) 1 αe +αn+α k , marginal cost: mct(i) := λt(i) = FtQt(i) 1 αe +αn+α k −1
  • 50. How Dependent is Output Growth from Primary Energy ? Gael Giraud CNRS, PSE, University Paris I and Z. Kahraman , TSP V. Acurio, F. McIsaac, N. Pham, CES, Paris I I. Why is this relationship important ? I.1. Kaya’s equation I. Why is this relationship important ? I.2. Why is this relationship ignored ? II. The empirical estimation II.1. A PMG approach II. The empirical estimation III. The Bayesian estimation of a DSGE model Household The stochastic discount factor Firms The Bayesian estimation of a DSGE model Cobb-Douglas production function Cobb-Douglas: Qt(i) = AtEt(i)αm Lt(i)αn Kt(i)αk αm, αn, αk ≥ 0, αm + αn + αk ≤ 1 Denote Ft := Atααe e ααn n α αk k Pαe e,t W αn t (rk t Pi,t)αk −1 αe +αn+α k , then cost function: cost(Qt(i)) = (αe + αn + αk )FtQt(i) 1 αe +αn+α k , marginal cost: mct(i) := λt(i) = FtQt(i) 1 αe +αn+α k −1 Now, firm i chooses price Pq,t(i) to maximize her utility. We are going to consider two cases: flexible price and Calvo price setting.
  • 51. How Dependent is Output Growth from Primary Energy ? Gael Giraud CNRS, PSE, University Paris I and Z. Kahraman , TSP V. Acurio, F. McIsaac, N. Pham, CES, Paris I I. Why is this relationship important ? I.1. Kaya’s equation I. Why is this relationship important ? I.2. Why is this relationship ignored ? II. The empirical estimation II.1. A PMG approach II. The empirical estimation III. The Bayesian estimation of a DSGE model Household The stochastic discount factor Firms The Bayesian estimation of a DSGE model Flexible prices (1) At each date t, firm i’s problem is max Pq,t (i) Pq,t(i)Qt(i) − cost(Qt(i)) subject to Qt(i) = Pq,t(i) Pq,t −ε Qt. Note that this problem does not depend on i, consequently its solution 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−ε di 1 1−ε , we have Pq,t(i) = Pq,t for every i.
  • 52. How Dependent is Output Growth from Primary Energy ? Gael Giraud CNRS, PSE, University Paris I and Z. Kahraman , TSP V. Acurio, F. McIsaac, N. Pham, CES, Paris I I. Why is this relationship important ? I.1. Kaya’s equation I. Why is this relationship important ? I.2. Why is this relationship ignored ? II. The empirical estimation II.1. A PMG approach II. The empirical estimation III. The Bayesian estimation of a DSGE model Household The stochastic discount factor Firms The Bayesian estimation of a DSGE model Flexible prices (2) FOC of P∗ q,t gives P∗ q,t = ε ε − 1 mc∗ t , where mc∗ t := FtQ 1 αe +αn+α k −1 t , Ft := Atααe e ααn n α αk k Pαe e,t W αn t (rk t Pi,t)αk −1 αe +αn+α k . ε ε−1 is the price markup, greater than 1 similar as a tax, note than when ε → +∞ this markup is 1.
  • 53. How Dependent is Output Growth from Primary Energy ? Gael Giraud CNRS, PSE, University Paris I and Z. Kahraman , TSP V. Acurio, F. McIsaac, N. Pham, CES, Paris I I. Why is this relationship important ? I.1. Kaya’s equation I. Why is this relationship important ? I.2. Why is this relationship ignored ? II. The empirical estimation II.1. A PMG approach II. The empirical estimation III. The Bayesian estimation of a DSGE model Household The stochastic discount factor Firms The Bayesian estimation of a DSGE model Calvo setting (1) Assumption Calvo price setting A 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) = Po q,t(i). We have "Aggregate Price Relationship" Pq,t = [0,1] Pq,t(i)1−ε di 1 1−ε = θP1−ε q,t−1 + (1 − θ)(Po q,t)1−ε 1 1−ε .
  • 54. How Dependent is Output Growth from Primary Energy ? Gael Giraud CNRS, PSE, University Paris I and Z. Kahraman , TSP V. Acurio, F. McIsaac, N. Pham, CES, Paris I I. Why is this relationship important ? I.1. Kaya’s equation I. Why is this relationship important ? I.2. Why is this relationship ignored ? II. The empirical estimation II.1. A PMG approach II. The empirical estimation III. The Bayesian estimation of a DSGE model Household The stochastic discount factor Firms The Bayesian estimation of a DSGE model Calvo setting (2) At date t, denote Qt,t+k (i) be the output at date t + k for firm i that last reset its price in period t. Firm i’s problem is max Pq,t (i) Et ∞ k=0 θk dt,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 −ε Qt+k , ∀k ≥ 0. Note that this problem does not depend on i, hence its solution Pq,t(i) also, we write Pq,t(i) = Po q,t
  • 55. How Dependent is Output Growth from Primary Energy ? Gael Giraud CNRS, PSE, University Paris I and Z. Kahraman , TSP V. Acurio, F. McIsaac, N. Pham, CES, Paris I I. Why is this relationship important ? I.1. Kaya’s equation I. Why is this relationship important ? I.2. Why is this relationship ignored ? II. The empirical estimation II.1. A PMG approach II. The empirical estimation III. The Bayesian estimation of a DSGE model Household The stochastic discount factor Firms The Bayesian estimation of a DSGE model Calvo setting (3) FOC for Po q,t, Et ∞ k=0 θk dt,t+k Qo t,t+k Po q,t − Mp mco t,t+k = 0, where mco t,t+k := Ft+k (Qo t,t+k ) 1 αe +α l +α k −1 , and Qo t,t+k = Po q,t Pq,t+k −ε Qt+k for every k ≥ 0.
  • 56. How Dependent is Output Growth from Primary Energy ? Gael Giraud CNRS, PSE, University Paris I and Z. Kahraman , TSP V. Acurio, F. McIsaac, N. Pham, CES, Paris I I. Why is this relationship important ? I.1. Kaya’s equation I. Why is this relationship important ? I.2. Why is this relationship ignored ? II. The empirical estimation II.1. A PMG approach II. The empirical estimation III. The Bayesian estimation of a DSGE model Household The stochastic discount factor Firms Denote Ao t := Et ∞ k=0 θk dt,t+k Qo t,t+k , Bo t := Et ∞ k=0 θk dt,t+k Qo t,t+k mco t,t+k . We have Po q,tAo t = Mp Bo t , Ao t := Qo t,t + θEtdt,t+1Ao t+1, Bo t := Qo t,tmco t,t + θEtdt,t+1Bo t+1.
  • 57. How Dependent is Output Growth from Primary Energy ? Gael Giraud CNRS, PSE, University Paris I and Z. Kahraman , TSP V. Acurio, F. McIsaac, N. Pham, CES, Paris I I. Why is this relationship important ? I.1. Kaya’s equation I. Why is this relationship important ? I.2. Why is this relationship ignored ? II. The empirical estimation II.1. A PMG approach II. The empirical estimation III. The Bayesian estimation of a DSGE model Household The stochastic discount factor Firms The Bayesian estimation of a DSGE model Monetary policy Denote Πq,t := Pq,t Pq,t−1 . The Central Bank sets the nominal short-term interest rate it + 1 = 1 β × Πq,t φπ × Py,tYt Py Y φy Where Y denotes the steady state value of nominal GDP implied by the model and Py is the steady state of the GDP deflator.
  • 58. How Dependent is Output Growth from Primary Energy ? Gael Giraud CNRS, PSE, University Paris I and Z. Kahraman , TSP V. Acurio, F. McIsaac, N. Pham, CES, Paris I I. Why is this relationship important ? I.1. Kaya’s equation I. Why is this relationship important ? I.2. Why is this relationship ignored ? II. The empirical estimation II.1. A PMG approach II. The empirical estimation III. The Bayesian estimation of a DSGE model Household The stochastic discount factor Firms The Bayesian estimation of a DSGE model Government 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) + εg t , Where ωQ denotes the steady state share of government spending in output.
  • 59. How Dependent is Output Growth from Primary Energy ? Gael Giraud CNRS, PSE, University Paris I and Z. Kahraman , TSP V. Acurio, F. McIsaac, N. Pham, CES, Paris I I. Why is this relationship important ? I.1. Kaya’s equation I. Why is this relationship important ? I.2. Why is this relationship ignored ? II. The empirical estimation II.1. A PMG approach II. The empirical estimation III. The Bayesian estimation of a DSGE model Household The stochastic discount factor Firms The Bayesian estimation of a DSGE model Definition 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 equilibrium Pc,tCt + Pi,tIt + Gt = Pq,tQt − Pe,tEt. (iii) Government budget constraint (1 + it−1)Bt−1 + Gt = Bt + Tt,
  • 60. How Dependent is Output Growth from Primary Energy ? Gael Giraud CNRS, PSE, University Paris I and Z. Kahraman , TSP V. Acurio, F. McIsaac, N. Pham, CES, Paris I I. Why is this relationship important ? I.1. Kaya’s equation I. Why is this relationship important ? I.2. Why is this relationship ignored ? II. The empirical estimation II.1. A PMG approach II. The empirical estimation III. The Bayesian estimation of a DSGE model Household The stochastic discount factor Firms The Bayesian estimation of a DSGE model Equilibrium (2) (iv) The production function [0,1] Pq,t(i) Pq,t −ε αe +α l +α k di αe +αl +αk Qt = AtEαe t L αl t K αk t . In Calvo setting : Define vt := [0,1] Pq,t (i) Pq,t −ε αe +α l +α k di. Then we have vt = θΠε q,tvt−1 + (1 − θ) Po q,t Pq,t −ε (iv) The marginal cost of firms.
  • 61. How Dependent is Output Growth from Primary Energy ? Gael Giraud CNRS, PSE, University Paris I and Z. Kahraman , TSP V. Acurio, F. McIsaac, N. Pham, CES, Paris I I. Why is this relationship important ? I.1. Kaya’s equation I. Why is this relationship important ? I.2. Why is this relationship ignored ? II. The empirical estimation II.1. A PMG approach II. The empirical estimation III. The Bayesian estimation of a DSGE model Household The stochastic discount factor Firms The Bayesian estimation of a DSGE model Shocks 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
  • 62. How Dependent is Output Growth from Primary Energy ? Gael Giraud CNRS, PSE, University Paris I and Z. Kahraman , TSP V. Acurio, F. McIsaac, N. Pham, CES, Paris I I. Why is this relationship important ? I.1. Kaya’s equation I. Why is this relationship important ? I.2. Why is this relationship ignored ? II. The empirical estimation II.1. A PMG approach II. The empirical estimation III. The Bayesian estimation of a DSGE model Household The stochastic discount factor Firms III. The Bayesian estimation approach III. Estimating the parameters ◦ Estimating the parameters of a New-Keynesian DSGE model US: 1984 Q1 - 2007Q1. αe= Oil input elasticity.