Monetary policy and energy price shocks

Bao Tan Huynh

doi:10.1515/bejm-2015-0113

Published by De Gruyter May 4, 2017

Monetary policy and energy price shocks

Bao Tan Huynh

From the journal The B.E. Journal of Macroeconomics

https://doi.org/10.1515/bejm-2015-0113

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Abstract

A New Keynesian framework with endogenous energy production is proposed to investigate the role of monetary policy in addressing disturbances in energy markets. The novelty of the model lies in the endogenous production of energy with convex costs, explicit modeling of goods with different degrees of energy-dependency and sectoral price rigidities. Our analyses prescribe the desirable monetary responses to four types of energy price shocks, highlighting the distinct characteristics of each shock and affirming the need for diverse policy considerations. We also found several points of divergence in relation to previous studies on addressing energy supply shocks. In addition, we shed light on the role of sectoral price rigidities in the shocks’ propagation.

Keywords: DSGE model; energy; energy price shock; monetary policy

JEL Classification: C68; E32; E52; Q43

Acknowledgements:

I sincerely thank Sungbae An for his invaluable guidance and endless patience.

A Appendices

A.1 Table of calibrated parameters

Table 7:

Calibrated parameters.

Parameter	Value	Description
β	0.99	Discount factor
φ	0.34	Share of consumption in household’s utility
α	0.2	Share of durables in household’s consumption
ρ	1 −1/0.99	Durables–nondurables CES parameter
δ_k	0.015	Capital depreciation rate
a₁	0.055	Param1 of durables depreciation function
a₂	0.3	Param2 of durables depreciation function
γ_e1	0.60	Capital share of energy production function
γ_d1	0.34	Capital share of durables production function
γ_n1	0.38	Capital share of nondurables production function
ω_k1	3	Param1 of capital adj. cost function
ω_k2	1	Param2 of capital adj. cost function
ω_d1	6	Param1 of durables adj. cost function
ω_d2	1	Param2 of durables adj. cost function
ω_B1	0.001	Param1 of portfolio adj. cost function
ω_B2	1	Param2 of portfolio adj. cost function
B¯	1.2	Bond target in PAC function
ω_e1	3.77	Param1 of energy convex cost function
ω_e2	2	Param2 of energy convex cost function
ϵ_d	5	Elasticity of substitution among varieties of durables
ϵ_n	5	Elasticity of substitution among varieties of nondurables
ϕ_d	46	Price adjustment cost parameter for durables
ϕ_n	46	Price adjustment cost parameter for nondurables
a	0.06	Energy intensity of durables
b	0.012	Energy intensity of capital
α_r	0.8	Lagged interest rate coefficient of the monetary rule
α_π	0.2	Inflation coefficient parameter of the monetary rule
α_y	0.09	Output coefficient parameter of the monetary rule
π¯	1	Steady-state gross inflation
g	0.18	Steady-steady share of government spending
τ_c	0.07	Steady-state consumption tax
τ_i	0.15	Steady-state income tax
τe,c	0.10	Steady-state energy tax on households
τe,f	0.10	Steady-state energy tax on producers
ρ_c	0.08	Lagged tax rate coefficient of the consumption tax rule
ρ_i	0.08	Lagged tax rate coefficient of the income tax rule
ρe,c	0.08	Lagged tax rate coefficient of the energy tax rule for consumers
ρe,f	0.08	Lagged tax rate coefficient of the energy tax rule for producers
ϕ_c	0.12	Bond coefficient of the consumption tax rule
ϕ_i	0.12	Bond coefficient of the income tax rule
ϕe,c	0.12	Bond coefficient of the energy tax rule for consumers
ϕe,f	0.12	Bond coefficient of the energy tax rule for producers
ρ_A1	0.95	Persistence of shock to energy suppy
ρ_e1	0.95	Persistence of TFP shock to non-energy producers
ρ_a	0.95	Persistence of shock to energy intensity of durables
ρ_b	0.95	Persistence of shock to energy intensity of capital
σe,t	0.021	Standard error of shock to energy supply
σA,t	0.0065	Standard error of TFP shock to non-energy producers
σa,t	0.0006	Standard error of shock to energy intensity of durables
σb,t	0.0012	Standard error of shock to energy intensity of capital

A.2 Equilibrium conditions

Household’s first order conditions

Euler equation for durables

(1−α)1−ρpd,tpn,tct−ρntρ−1(1+ωd1dt(dt+1−dtdt)ωd2)=βEα1−ρct+1−ρ(ut+1dt+1)ρ−1ut+1+βE(1−α)1−ρ(1+τc,t+1)pn,t+1ct+1−ρnt+1ρ−1[−ape,t+1(1+τe,c,t+1)ut+1+(1+τc,t+1)pd,t+1(1−δd,t+1+ωd1dt+2dt+12(dt+2−dt+1dt+1)ωd2)]

Euler equation for capital

pd,t(1+τc,t)pn,tct−ρntρ−1(1+ωk1kt(kt+1−dtkt)ωk2)=βEct+1−ρnt+1ρ−1(1+τc,t+1)pn,t+1[(1−τi,t+1)rt+1+pd,t+1(1−δk+ωk1kt+2kt+12(kt+2−kt+1kt+1)ωk2)]

Euler equation for bond

ct−ρntρ−1(1+τc,t)pn,t(1+ωB1(Bt+1−B¯)ωB2)=βE(1+Rt+1)ct+1−ρnt+1ρ−1(1+τc,t+1)pn,t+1

Intra-temporal nondurables-labor

(1−α)1−ρφ1−φ(1−ht)ct−ρntρ−1=(1+τc,t)pn,t(1−τi,t)wt

Intra-temporal nondurables-utilization

(1−α)1−ρα1−ρntρ−1(utdt)ρ−1=(1+τc,t)pn,ta(1+τe,c,t)pe,t+(1+τc,t)pd,tδd,t′

with

ct=[α1−ρ(utdt)ρ+(1−α)1−ρntρ]1/ρ

Budget constraint

(1+τe,c,t)pe,tautdt+(1+τc,t)pn,tnt+(1+τc,t)pd,tid,t+pd,tik,t+iB,t=(1−τi,t)(wtht+rtkt)+RtBt

Investment adjustment costs and variable depreciation

id,t=dt+1−(1−δd,t)dt+ωd11+ωd2(dt+1−dtdt)1+ωd2

ik,t=kt+1−(1−δk)kt+ωk11+ωk2(kt+1−ktkt)1+ωk2

iB,t=Bt+1−Bt+ωB11+ωB2(Bt+1−B¯)1+ωB2

δd,t=a1a2+1uta2+1

Sectors’ aggregate outputs

ye,t=exp(Ae,t)ke,tγehe,t1−γe

be,t=ωe1(1+ωe2)(ke,tγehe,t1−γe)1+ωe2

yi,t=exp(At)(ki,t)γi(hi,t)1−γi−χi

with i=d,n

Firms’ first order conditions

mci,texp(At)(1−γi)(ki,thi,t)γi=wtpi,t

1−γiγiki,thi,t=wtrt+bpe,t(1+τe,f,t)

pe,texp(Ae,t)γe(ke,the,t)γe−1=rt+be,tpe,t(1+τe,f,t)+ke,tpe,t(1+τe,f,t)be,t′he,t1−γeγeke,tγe−1

pe,texp(Ae,t)(1−γe)(ke,the,t)γe=wt+ke,tpe,t(1+τe,f,t)be,t′he,t−γe(1−γe)ke,tγe

Sectoral Phillips curves

π^i,t=βEt[π^i,t+1]+ϵi−1ϑimc^i,t

with i=d,n

Fiscal and monetary policies

Government budget constraint

τe,c,tpe,tautdt+τe,f,tpe,t(b(kd,t+kn,t)+be,tke,t)+τc,t(pn,tnt+pd,tid,t)+τi,t(rtkt+wtht)+iB,t=ptgtyt+RtBt

Tax rules

(38)log(τ(),tτ¯())=ρ()log(τ(),t−1τ¯())+ϕ()log(BtB¯)

with ()=(e,c),(e,f),c,i

Monetary policy function

Rt−R∗=αR(Rt−1−R∗)+απ(πt−π∗)+αy(yt−yt−1)+ϵr,t

Market clearing

kt=kd,t+kn,t+ke,t

ht=hd,t+hn,t+he,t

yd,t=id,t+ik,t+gd,t+ϑd2(πd,t−1)2yd,t

yn,t=nt+gn,t+ϑn2(πn,t−1)2yn,t

gtyt=[α1−ρgd,tρ+(1−α)1−ρgn,tρ]1/ρ

ptgtyt=pd,tgd,t+pn,tgn,t+pe,tagd,t

Aggregate price and aggregate value added

pt=[α(pd,t+ape,t)ρρ−1+(1−α)pn,tρρ−1]ρ−1ρ

ptyt=pd,tyd,t+pn,tyn,t+pe,tautdt

Exogenous shock process

At=ρAAt−1+ϵA,t

Ae,t=ρeAe,t−1+ϵe,t

gt=ρggt−1+ϵg,t

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Published Online: 2017-5-4

Monetary policy and energy price shocks

Abstract

Acknowledgements:

A Appendices

A.1 Table of calibrated parameters

A.2 Equilibrium conditions

References

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