Goals Model Household Firms Government Estimation Impulse Response Functions Energy and Capital in a New-Keynesian Framework Verónica Acurio Vásconez, Gaël Giraud, Florent Mc Isaac, Ngoc Sang Pham CES, PSE, University Paris I March 27, 2014
Goals Model Household Firms Government Estimation Impulse Response Functions Outline Goals Model Household Firms The Final Good Firm Intermediate Good Firms Government GDP and GDP Deflator Estimation Setting Estimation Results Impulse Response Functions
Goals Model Household Firms Government Estimation Impulse Response Functions Outline Goals Model Household Firms Government Estimation Impulse Response Functions
Goals Model Household Firms Government Estimation Impulse Response Functions Goals • This paper constructs a New-Keynesian model with oil in the production function and in consumption. • The model’s parameters are estimated using Bayesian techniques. • We observe the impact of the oil shock in this economy.
Goals Model Household Firms Government Estimation Impulse Response Functions Outline Goals Model Household Firms Government Estimation Impulse Response Functions
Goals Model Household Firms Government Estimation Impulse Response Functions Model Structure Domestic Economy
Goals Model Household Firms Government Estimation Impulse Response Functions Model Structure Domestic Economy Final Good Firm Household
Goals Model Household Firms Government Estimation Impulse Response Functions Model Structure Domestic Economy Final Good Firm l.s taxes invests Household works consumes
Goals Model Household Firms Government Estimation Impulse Response Functions Model Structure Domestic Economy Final Good Firm l.s taxes invests bonds capital Household works consumes
Goals Model Household Firms Government Estimation Impulse Response Functions Model Structure Domestic Economy Final Good Firm l.s taxes invests bonds capital Household works consumes Final Goods Energy
Goals Model Household Firms Government Estimation Impulse Response Functions Model Structure Domestic Economy Final Good Firm l.s taxes invests bonds capital Household works consumes produces Final Goods Energy
Goals Model Household Firms Government Estimation Impulse Response Functions Model Structure Domestic Economy Final Good Firm l.s taxes invests bonds Intermediate Firms capital Household works consumes produces Final Goods Energy
Goals Model Household Firms Government Estimation Impulse Response Functions Model Structure Domestic Economy Final Good Firm l.s taxes invests bonds Intermediate Firms capital Household works exo p. consumes Energy Labor Capital produces Final Goods Energy
Goals Model Household Firms Government Estimation Impulse Response Functions Model Structure Domestic Economy Final Good Firm l.s taxes invests bonds profits Intermediate Firms capital Household works exo p. consumes Energy Labor Capital produces Final Goods Energy
Goals Model Household Firms Government Estimation Impulse Response Functions Model Structure Domestic Economy Final Good Firm l.s taxes invests bonds profits Intermediate Firms capital Household works exo p. consumes Energy Labor Capital produces exo p. Final Goods Energy Foreign exogenous price
Goals Model Household Firms Government Estimation Impulse Response Functions Model Structure Government Domestic Economy Final Good Firm Taylor l.s taxes invests bonds profits Intermediate Firms capital Household works exo p. consumes Energy Labor Capital produces exo p. Final Goods Energy Foreign exogenous price
Goals Model Household Firms Government Estimation Impulse Response Functions Outline Goals Model Household Firms Government Estimation Impulse Response Functions
Goals Model Household Firms Government Estimation Impulse Response Functions Household Problem � ∞ � � β t U ( C t , L t ) max E 0 , 0 < β < 1 t = 0 s. t P e , t C e , t + P q , t C q , t + P k , t I t + B t + T t ≤ ( 1 + i t − 1 ) B t − 1 + W t L t + D t + r k t P k , t K t
Goals Model Household Firms Government Estimation Impulse Response Functions Household Problem Θ x := x − x ( 1 − x ) − ( 1 − x ) � ∞ � e , t C 1 − x � β t U ( C t , L t ) C t := Θ x C x max E 0 , 0 < β < 1 q , t t = 0 s. t P e , t C e , t + P q , t C q , t + P k , t I t + B t + T t ≤ ( 1 + i t − 1 ) B t − 1 + W t L t + D t + r k t P k , t K t
Goals Model Household Firms Government Estimation Impulse Response Functions Household Problem Θ x := x − x ( 1 − x ) − ( 1 − x ) � ∞ � e , t C 1 − x � β t U ( C t , L t ) C t := Θ x C x max E 0 , 0 < β < 1 q , t t = 0 s. t U ( C t , L t ) = log ( C t ) − L 1 + φ P e , t C e , t + P q , t C q , t + P k , t I t + B t + T t t 1 + φ ≤ ( 1 + i t − 1 ) B t − 1 + W t L t + D t + r k t P k , t K t
Goals Model Household Firms Government Estimation Impulse Response Functions Household Problem Θ x := x − x ( 1 − x ) − ( 1 − x ) � ∞ � e , t C 1 − x � β t U ( C t , L t ) C t := Θ x C x max E 0 , 0 < β < 1 q , t t = 0 s. t U ( C t , L t ) = log ( C t ) − L 1 + φ P e , t C e , t + P q , t C q , t + P k , t I t + B t + T t t 1 + φ ≤ ( 1 + i t − 1 ) B t − 1 + W t L t + D t + r k t P k , t K t ǫ �� 1 � ǫ − 1 0 C q , t ( i ) 1 − 1 ǫ di C q , t :=
Goals Model Household Firms Government Estimation Impulse Response Functions Household Problem Θ x := x − x ( 1 − x ) − ( 1 − x ) � ∞ � e , t C 1 − x � β t U ( C t , L t ) C t := Θ x C x max E 0 , 0 < β < 1 q , t t = 0 s. t U ( C t , L t ) = log ( C t ) − L 1 + φ P e , t C e , t + P q , t C q , t + P k , t I t + B t + T t t 1 + φ ≤ ( 1 + i t − 1 ) B t − 1 + W t L t + D t + r k t P k , t K t I t := K t + 1 − ( 1 − δ ) K t ǫ �� 1 � ǫ − 1 0 C q , t ( i ) 1 − 1 ǫ di C q , t :=
Goals Model Household Firms Government Estimation Impulse Response Functions Optimization Household’s Optimal Expenditure Allocation
Goals Model Household Firms Government Estimation Impulse Response Functions Optimization Household’s Optimal Expenditure Allocation C q , t , C e , t P c , t C t max s. t P c , t C t = P e , t C e , t + P q , t C q , t e , t C 1 − x C t = Θ x C x q , t
Goals Model Household Firms Government Estimation Impulse Response Functions Optimization Household’s Optimal Expenditure Allocation P q , t C q , t = ( 1 − x ) P c , t C t C q , t , C e , t P c , t C t max P e , t C e , t = xP c , t C t e , t P ( 1 − x ) P c , t = P x q , t s. t P c , t C t = P e , t C e , t + P q , t C q , t e , t C 1 − x C t = Θ x C x q , t
Goals Model Household Firms Government Estimation Impulse Response Functions Outline Goals Model Household Firms The Final Good Firm Intermediate Good Firms Government Estimation Impulse Response Functions
Goals Model Household Firms Government Estimation Impulse Response Functions Final Good Producers Final Good Firm
Goals Model Household Firms Government Estimation Impulse Response Functions Final Good Producers Intermediate Good i ∈ [ 0 , 1 ] Final Good Firm
Goals Model Household Firms Government Estimation Impulse Response Functions Final Good Producers Intermediate Good i ∈ [ 0 , 1 ] Final Good Firm ǫ �� 1 � ǫ − 1 ǫ − 1 ǫ di Q t = 0 Q t ( i )
Goals Model Household Firms Government Estimation Impulse Response Functions Final Good Producers Intermediate Good i ∈ [ 0 , 1 ] Final Good Firm ǫ : the elasticity of substitution ǫ �� 1 � ǫ − 1 ǫ − 1 ǫ di Q t = 0 Q t ( i ) among intermediate goods
Goals Model Household Firms Government Estimation Impulse Response Functions Final Good Producer Problem Final Good Firm Profit Optimization � − ǫ � P q , t ( i ) Q t ( i ) = Q t � 1 P q , t i demand max Q t ( i ) P q , t Q t − 0 P q , t ( i ) Q t ( i ) di 1 �� 1 � e 1 − ǫ c i 0 P q , t ( i ) 1 − ǫ di r P q , t = p d o o g l a n fi s. t ǫ �� 1 ǫ − 1 � ǫ − 1 ǫ di Q t = 0 Q t ( i )
Goals Model Household Firms Government Estimation Impulse Response Functions Intermediate Good Firms Intermediate Firms
Goals Model Household Firms Government Estimation Impulse Response Functions Intermediate Good Firms Intermediate Firms Q t ( i ) = A t E t ( i ) α e L t ( i ) α ℓ K t ( i ) α k α e , α ℓ , α k ≥ 0 , α e + α ℓ + α k ≤ 1
Goals Model Household Firms Government Estimation Impulse Response Functions Intermediate Good Firms Intermediate Firms Q t ( i ) = A t E t ( i ) α e L t ( i ) α ℓ K t ( i ) α k α e , α ℓ , α k ≥ 0 , α e + α ℓ + α k ≤ 1 strategy of firm i : Marginal cost pricing behavior FOC Given: P e , t , P k , t , W t and Q t ( i ) Choses: E t ( i ) , L t ( i ) and K t ( i )
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