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- 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.

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