Effectiveness of energy efficiency improvements in the context of energy subsidy policies

Abstract

Malaysia, as one of the top energy subsidizing countries, has announced to remove energy subsidies necessarily, not only to reduce energy consumption and the government budget deficit but also to improve overall efficiency and air quality. Therefore, this study evaluates the impacts of rationalizing energy subsidy and its energy efficiency improvement during 2010–2030 using a dynamic recursive computable general equilibrium model. Results revealed that reducing energy subsidies decreases energy consumption and emissions of all air pollutants. While the economic performance of the country improves in the long run due to stimulation in capital demand and investment, it reduces in the short run. Energy efficiency also improves by 1.1% and 2.3%, in the short run, in response to a reduction of 10% and 100% in energy subsidies, respectively. Energy efficiency improvements decrease the negative effects of pure subsidy policies on real GDP, trade, investment, and household consumption. The efficiency improvement policies also are effective in reducing more level of the rebound effect and lead to more energy saving in the economy, particularly in the petroleum products sector. The impacts on the rebound effect also differ across economic sectors. The results of this study provide new insights for energy subsidy policy and energy efficiency and suggest that additional tools and policies are required for improving the energy efficiency caused by phasing out energy subsidies.

Graphic abstract

Malaysia, as one of the top energy subsidized countries, attempts to reduce the level of energy subsidies over time and, consequently, decline the use of fossil fuels in the economy. Therefore, this study analyzes the impacts of different subsidy reform policy on energy efficiency and, consequently, on economic and environmental performance and rebound effect of Malaysia by a recursive dynamic computable general equilibrium model.

Appendix A: Model specification

Sets
i	Sectors	(1,2, …, 25)
f	Factors of production	(Labor, capital and energy)
h	Households	(Rural and urban)
br	Lending institutions	(Domestic, Foreign)
ie(i)	Export sectors
ien(i)	Non-export sectors
TP	Simulation experiments	(SAM2010, 2010 * 2030)
TFUT(TP)	Future Time Periods	(2010 * 2030)
T(TP)	Current experiment
P	Pollutants	(PM, SO2, NOx, CO, CH4,N2O,CO2)
E1(i)	Energy sectors	/ngs, col, mot, dis, ful, lpg, opt, ele/
FL(i)	Fuels sectors	/ngs, col, mot, dis, ful, opt, lpg/
EL(i)	Electricity sector	/eLe/
NEL(i)	Nonelectricity sectors	/ngs, col, mot, dis, ful, lpg, opt/
NG(I)	Natural	Gas/NGS/
PT(I)	Petroleum products	/mot, dis, ful, opt, lpg/
E2(i)	Non-energy sectors	/pad, fod, veg, fru, rub, pal, liv, frs, fis, oag, min, fdp, tex, ind, trn, fin, svc/Alias (i,j)
Lc(f)	Labor and capital
Alias		(E1,E1P)
Alias		(E2,E2P),(NG,NGP)
Alias		(F,FP),(FL,FLP)

Equations

	Price block equations
(1)	${\text{PM}}_{i} = {\text{PWM}_{i}} . \, \left( {1 + {\text{tm}}_{i} } \right).{\text{EXR}}$	Domestic prices of import goods
(2)	${\text{PE}}_{i} = {\text{PWE}}_{i} . \, \left( {1 - {\text{te}}_{i} } \right).{\text{EXR}}$	Domestic prices of export goods
(3)	${\text{PQ}}_{i} = \left( {{\text{PD}}_{i} .D_{i} + {\text{ PM}}_{i} .M_{i} } \right)/Q_{i}$	Average price of composite goods Q
(4)	${\text{PX}}_{i} = \left( {{\text{PD}}_{i} .D_{i} + {\text{ PE}}_{i} .E_{i} } \right)/X_{i}$	Average price of sectoral output X
(5)	${\text{PV}}_{i} = \frac{{\left[ {{\text{PX}}_{i} .X_{i} .(1 - ({\text{tx}}_{i} - {\text{subsh}}_{i} )) - \sum\limits_{j} {{\text{io}}_{ji} .X_{i} .} {\text{PQ}}_{i} } \right]}}{{{\text{KL}}_{i} }}$	Value added price equation included subsidies
(6)	${\text{PEKL}}_{i} = \left( {{\text{PEN}}_{i} .{\text{EN}}_{i} + {\text{PV}}_{i} .{\text{KL}}_{i} } \right)/{\text{EKL}}_{i}$	Price of factor of production (labor, capital and energy)
(6)	x ${\text{PEN}}_{i} = \left( {{\text{PELEC}}_{i} .{\text{ELEC}}_{i} + {\text{PFUL}}_{i} .{\text{FUL}}_{i} } \right)/{\text{EN}}_{i}$	Price of energy
(8)	${\text{PNEN}}_{i} = \sum\limits_{e2p} {{\text{ane}}_{e2p,i} .{\text{PQ}}_{e2p} }$	Price of non-energy commodities
(9)	PELECi = PQele	Price of Electricity
(10)	${\text{PK}}_{i} = \mathop \sum \limits_{j} {\text{ccmat}}_{ji} .{\text{PQ}}_{j}$	Capital prices equation
(11)	${\text{PINDEX}} = \mathop \sum \limits_{j} {\text{wtq}}_{i} .{\text{PQ}}_{i}$	Consumer price index
(12)	${\text{PINDOM}} = \mathop \sum \limits_{j} {\text{wtd}}_{i} .{\text{PD}}_{i}$	Domestic price index

Production and trade block equations

(13)	$X_{i} = {\text{tech}}_{i} .\alpha_{i}^{x} .{\text{EN}}_{i}^{{\alpha_{i}^{x} }} .{\text{KL}}_{i}^{{(1 - \alpha_{i}^{x} )}}$	Domestic production function
(14)	${\text{tech}}_{i} .{\text{PEKL}}_{i} .{\text{EN}}_{i} = X_{i} .{\text{PV}}_{i} .\alpha_{i}^{x}$	Value added function
(15)	${\text{NEN}}_{i} = {\text{amt}}_{i} .X_{i}$	Non-energy function
(16)	${\text{EN}}_{i} = \alpha_{i}^{{{\text{en}}}} .\left[ {\beta_{i}^{{{\text{en}}}} .{\text{FUL}}_{i}^{{{ - \rho_{i}{{\text{en}}}} }} + (1 - \beta_{i}^{{{\text{en}}}} ).{\text{ELEC}}_{i}^{{{ - \rho_{i}{{\text{en}}}} }} } \right]^{{ - \tfrac{1}{{\rho_{i}^{{{\text{en}}}} }}}}$	CES energy function
(17)	$\frac{{{\text{FUL}}_{i} }}{{{\text{ELEC}}_{i} }} = \left( {\frac{{{\text{PELEC}}_{i} }}{{{\text{PFUL}}_{i} }}.\frac{{\beta_{i}^{{{\text{en}}}} }}{{(1 - \beta_{i}^{{{\text{en}}}} )_{i} }}} \right)^{{\tfrac{1}{{1 + \beta_{i}^{{{\text{en}}}} }}}}$	F.O.C. of Energy Function
(18)	${\text{ELEC}}_{i} = \sum\limits_{{{\text{elp}}}} {{\text{io}}_{{{\text{elp}},i}} } .X_{i}$	Electricity function
(19)	${\text{FUL}}_{i} = \alpha_{i}^{{{\text{fl}}}} .\left[ {\beta_{i}^{{{\text{fl}}}} .{\text{PETROL}}_{i}^{{{ - \rho_{i}{{\text{fl}}}} }} + (1 - \beta_{i}^{{{\text{fp}}}} ).{\text{COALNGS}}_{i}^{{{ - \rho_{i}{{\text{fl}}}} }} } \right]^{{ - \tfrac{1}{{\rho_{i}^{{{\text{fl}}}} }}}}$	CES Fuels function
(20)	$\frac{{{\text{PETROLD}}_{i} }}{{{\text{COALNGAS}}_{i} }} = \left( {\frac{{{\text{PCOLNGS}}_{i} }}{{{\text{PPETROL}}_{i} }}.\frac{{\beta_{i}^{{{\text{fl}}}} }}{{(1 - \beta_{i}^{{{\text{fl}}}} )_{i} }}} \right)^{{\tfrac{1}{{1 + \beta_{i}^{{{\text{fl}}}} }}}}$	F.O.C. of Fuels Function
(21)	${\text{PETROLD}}_{j} = \alpha_{j}^{{{\text{pt}}}} \prod\limits_{pt} {({\text{PETROL}}_{{{\text{pt}},j}} )^{{\beta_{{{\text{pt}},j}} }} }$	Cobb–Douglas Petroleum products function
(22)	${\text{PETROL}}_{{{\text{pt}},j}} = \,\,\frac{{\beta_{{{\text{pt}},j}} .{\text{PPETROL}}_{j} .{\text{PETROLD}}_{j} }}{{{\text{PQ}}_{j} }}$	F.O.C. of Petroleum products function
(23)	${\text{COALNGS}}_{i} = \alpha_{i}^{{{\text{cong}}}} .\left[ {\beta_{i}^{{{\text{cong}}}} .{\text{COAL}}_{i}^{{{ - \rho_{i}{{\text{cong}}}} }} + (1 - \beta_{i}^{{{\text{cong}}}} ).{\text{NGASD}}_{i}^{{{ - \rho_{i}{{\text{cong}}}} }} } \right]^{{ - \tfrac{1}{{\rho_{i}^{{{\text{cong}}}} }}}}$	CES Coal and natural gas aggregate function
(24)	$\frac{{{\text{COAL}}_{i} }}{{{\text{NGASD}}_{i} }} = \left( {\frac{{{\text{PNGAS}}_{i} }}{{{\text{PCOAL}}_{i} }}.\frac{{\beta_{i}^{{{\text{cong}}}} }}{{(1 - \beta_{i}^{{{\text{cong}}}} )_{i} }}} \right)^{{\tfrac{1}{{1 + \beta_{i}^{{{\text{cong}}}} }}}}$	F.O.C. of Coal and natural gas aggregate function
(25)	NGASDi = iongs,i.Xi	Natural gas function
(26)	COALi = iocol,i.Xi	Coal function
(27)	${\text{KL}}_{i} = \alpha_{i}^{{{\text{kl}}}} .\left[ {\sum\limits_{{{\text{lc}}}} {\beta_{{i,{\text{lc}}}}^{{{\text{kl}}}} .({\text{LCSC}}_{{i,{\text{lc}}}} )^{{{ - \rho_{i}{{\text{kl}}}} }} } } \right]^{{\tfrac{ - 1}{{\rho_{i}^{{{\text{kl}}}} }}}}$	labor and capital function
(28)	$\frac{{{\text{LCSC}}_{{i,{\text{lc}}}} }}{{{\text{KL}}_{i} }} = \left( {\frac{{\beta_{{i,{\text{lc}}}}^{{{\text{kl}}}} .{\text{PV}}_{i} }}{{(\alpha_{i}^{{{\text{kl}}}} )^{{{\rho_{i}{{\text{kl}}}} }} .{\text{PKL}}_{i} .{\text{PKLSEC}}_{{i,{\text{lc}}}} }}} \right)^{{\tfrac{1}{{1 + \rho_{i}^{{{\text{kl}}}} }}}}$	Labor and capital’ demand function
(29)	$X_{{{\text{ie}}}} = \propto_{{{\text{ie}}}}^{t} .\left[ {\beta_{{{\text{ie}}}}^{t} .E_{{{\text{ie}}}}^{{\rho_{{{\text{ie}}}}^{t} }} + \left( {1 - \beta_{{{\text{ie}}}}^{t} } \right).D_{{{\text{ie}}}}^{{\rho_{{{\text{ie}}}}^{t} }} } \right]^{{\frac{1}{{\rho_{{{\text{ie}}}}^{t} }}}} , \ldots X_{{{\text{ien}}}} = \, D_{{{\text{ien}}}}$	Producers’ transformation choice between domestic and export sales
(30)	$E_{{{\text{ie}}}} = D_{{{\text{ie}}}} .\left[ {\frac{{{\text{PE}}_{{{\text{ie}}}} }}{{{\text{PD}}_{{{\text{ie}}}} }}.\frac{{(1 - \propto_{{{\text{ie}}}}^{t} )}}{{ \propto_{{{\text{ie}}}}^{t} }}} \right]^{{\frac{1}{{( \propto_{{{\text{ie}}}}^{t} - 1)}}}} \quad {\text{or}}\quad E_{{{\text{ied}}}} = \gamma_{{{\text{ied}}}} .\left[ {\frac{{{\text{PWE}}_{{{\text{ied}}}} }}{{{\text{PWSe}}_{{{\text{ied}}}} }}} \right]^{{ - \rho_{{{\text{ied}}}} }}$ or	First-order condition of the CET function = Export demand
(31)	$Q_{{{\text{im}}}} = \propto_{{{\text{im}}}}^{c} .\left[ {\beta_{{{\text{im}}}}^{c} .M_{{{\text{im}}}}^{{ - \rho_{{{\text{im}}}}^{c} }} + (1 - \beta_{{{\text{im}}}}^{c} ).D_{{{\text{im}}}}^{{\rho_{{{\text{im}}}}^{c} }} } \right]^{{ - \frac{1}{{\rho_{{{\text{im}}}}^{c} }}}}$	Armington (CES) function
(32)	$M_{{{\text{im}}}} = D_{{{\text{im}}}} .\left[ {\frac{{{\text{PD}}_{{{\text{im}}}} }}{{{\text{PM}}_{{{\text{im}}}} }}.\frac{{\beta_{{{\text{im}}}}^{c} }}{{(1 - \beta_{{{\text{im}}}}^{c} )}}} \right]^{{\frac{1}{{(1 + \rho_{{{\text{im}}}}^{c} )}}}}$	First-order condition of the CET function

Income and saving block equations

(33)	${\text{YF}}_{f} = \mathop \sum \limits_{i} {\text{WF}}_{f} .{\text{FDSC}}_{if} .{\text{wfdist}}_{if}$	Factors income
(34)	${\text{YCOMP}} = {\text{YF}}_{{{\text{capi}}}} {-}{\text{EXR.REPAT}} + {\text{INTERS}}_{{{\text{comp}}}}$	Companies income
(35)	$\begin{aligned} {\text{YH}} _{h} & = \mathop \sum \limits_{f} {\text{hhdis}}_{hf} .{\text{YF}}_{f} + {\text{ gtrn}}_{h} .{\text{ GOVTRN}} + {\text{ctrn}}_{h} .{\text{ YCOMP}}. \\ & \quad \left( {1 - {\text{ctax}}} \right).\left( {1 - {\text{csav}}} \right) + {\text{sfin}}_{h} .{\text{FACTIN.EXR}} \\ \end{aligned}$	Households income
(36)	${\text{TARIFF}} = \mathop \sum \limits_{i} {\text{pwm}}_{i} .{\text{M}}_{i} .{\text{tm}}_{i} .{\text{ EXR}}$	Tariffs
(37)	${\text{INTAX}} = \mathop \sum \limits_{i} {\text{PX}}_{i} .{\text{X}}_{i} .{\text{tx}}_{i}$	Indirect taxes
(38)	${\text{HHTAX}} = \mathop \sum \limits_{{\text{h}}} {\text{YH}}_{{\text{h}}} .\tau_{{\text{h}}}^{{\text{h}}}$	Household income taxes
(39)	${\text{ COMTAX }} = {\text{ctax }}.{\text{YCOMP}}$	Company taxes
(40)	${\text{EXPTAX}} = \mathop \sum \limits_{{{\text{ie}}}} {\text{pwe}}_{{{\text{ie}}}} .{\text{E}}_{{{\text{ie}}}} .(1 - te_{{{\text{ie}}}} ).{\text{EXR}}$	Export taxes
(41)	${\text{GR}} = {\text{TARIFF}} + {\text{INDTAX}} + {\text{HHTAX}} + {\text{EXPTAX}} + {\text{COMTAX}}$	Government revenues
(42)	${\text{HHSAV}} = \mathop \sum \limits_{{\text{h}}} {\text{YH}}_{{\text{h}}} .(1 - {\text{th}}_{{\text{h}}} ).{\text{mps}}_{{\text{h}}}$	Household savings
(43)	${\text{COMSAV}} = {\text{YCOMP}}.\left( {1 - {\text{ctax}}} \right).{\text{csav}}$	Company savings
(44)	${\text{SAVING}} = {\text{HHSAV}} + {\text{GOVSAV}} + {\text{COMSAV}} - {\text{CURACT}}{\text{. EXR}}$	Total savings
(45)	${\text{TSUB}} = \sum\limits_{i} {{\text{SUB}}_{i} }$

Expenditure block equations

(46)	${\text{ THCON}}_{{\text{h}}} = \mathop \sum \limits_{i} \left[ {{\text{hhclesi}}_{{i,{\text{h}}}} .{\text{YH}}_{{\text{h}}} .\left( {1 - {\text{mps}}_{{\text{h}}} } \right).\left( {1 - \tau_{h} } \right)} \right]$	Total household consumption
(47)	${\text{HDM}}_{{{\text{h}},i}} \, = \, \frac{{C\_\min_{{{\text{h}},i}} .{\text{PQ}}_{i} + \, \gamma_{{{\text{h}},i}} .\left[ {{\text{THCON}}_{{\text{h}}} - \sum\limits_{i} {C\_\min_{{{\text{h}},i}} } .{\text{PQ}}_{i} } \right]}}{{{\text{PQ}}_{i} }}$	Demand for commodities by households
(48)	${\text{GD}}_{i} = {\text{ggs}}_{i} .{\text{GOVCON}}$	Government demand
(49)	${\text{STK}}_{i} = {\text{inv}}_{i} . \, X_{i}$	Demand for new inventories
(50)	${\text{FXDINV}} = {\text{INVEST}} - \mathop \sum \limits_{i} {\text{PQ}}_{i} .{\text{STK}}_{i}$	Total nominal fixed investment
(51)	${\text{DK}}_{i} = \frac{{{\text{zz}}_{i} .{\text{FXDINV}}}}{{\mathop \sum \nolimits_{j} {\text{ccmat}}_{ji} .{\text{PQ}}_{j} }}$	Investment allocation
(52)	${\text{ID}}_{i} = \mathop \sum \limits_{j} {\text{ccmat}}_{ij} .{\text{DK}}_{j}$	Demand for investment goods
(53)	${\text{GDPVA}} = \mathop \sum \limits_{i} {\text{PV}}_{i} .V_{i} + {\text{INDTAX}} + {\text{TARIFF}} + {\text{EXPTAX - TSUB}}$	Nominal GDP
(54)	${\text{REGDP}} = \mathop \sum \limits_{i} \left( {{\text{THCON}}_{i} + {\text{GD}}_{i} + {\text{ID}}_{i} + {\text{STK}}_{i} + \mathop \sum \limits_{{{\text{ie}}}} E_{{{\text{ie}}}} - \mathop \sum \limits_{{{\text{im}}}} (1 - {\text{tmreal}}_{{{\text{im}}}} ).M_{{{\text{im}}}} } \right)$	Real GDP
(55)	$Z_{h} = \, \sum\limits_{j} {C\_{\text{MIN}}_{hj} } .{\text{PQ}}_{j}$	Poverty line

Constraints block equations

(56)	$Q_{i} = {\text{INTM}}_{i} + {\text{THCON}}_{i} + {\text{GD}}_{i} + {\text{ID}}_{i} + {\text{STK}}_{i }$	Product market equilibrium
(57)	$\mathop \sum \limits_{i} {\text{FDSC}}_{if} = {\text{FS}}_{f}$	Factor market equilibrium
(58)	${\text{CURACT}} = \mathop \sum \limits_{{{\text{im}}}} {\text{pwm}}_{{{\text{im}}}} .M_{{{\text{im}}}} .{\text{EXR}} + \mathop \sum \limits_{{{\text{ie}}}} {\text{PWE}}_{{{\text{ie}}}} .(1 - {\text{te}}_{{{\text{ie}}}} ).E_{{{\text{ie}}}} .{\text{EXR}}$	Market-clearing in the foreign exchange market
(59)	${\text{GOVSAV}} = {\text{GR}} - \mathop \sum \limits_{i} {\text{PQ}}_{i} .{\text{GD}}_{i} - {\text{EXR}}{\text{.INTERS}}_{{{\text{br}}}} - {\text{INTERS}}_{{{\text{comp}}}} - {\text{GOVTRN}} - {\text{TSUB}}$	Government budget balance
(60)	${\text{SAVING}} = {\text{INVEST}}$	Saving and investment balance

Air pollutant function

(61)	CO2fl,p = EMISSIONfl,p.FULfl

Dynamic section of the model

(62)	${\text{FS}}_{f} = {\text{FS}}_{f} + \sum\limits_{i} {{\text{ID}}_{i} } .{\text{fr}}\_{\text{inv}}$	Here f = capital
(63)	${\text{FS}}_{f} = {\text{FS}}_{f} .(1 + G)$	Here f = labor and G (population growth rate) = 2%
(64)	CURACT = CURACT. (1 + G)	G = 2%

List of variables and their definition

Variables	Definition	Variables	Definition
EXR	Exchange rate	${\text{PKLSEC}}_{{i,{\text{lc}}}}$	Factor price sectoral proportionality ratios
PDi	Domestic prices	YFi	Factor income
PEi	Domestic price of exports	THCONi	Final demand for private consumption
PINDEX	Consumption price index	CORSAV	Corporate savings
PINDOM	Domestic price level	CORTAX	Corporate taxes
PKi	Price of composite capital good	GOVSAV	Government savings
PMi	Domestic price of imports	GOVTRN	Government transfers
PQi	Price of composite goods	GR	Government revenue
PVi	Value added price by sector	HHSAV	Total household savings
PWEi	World price of exports	IDi	Final demand for productive investment
PXi	Average output price by sector	INDTAX	Indirect tax revenue
PENi	Energy prices by sector	ioi,j	Intermediates uses coefficients
PNENi	Non-Energy prices by sector	INVEST	Total investment
PEKLi	Energy, capital and labor prices	mpsh	Marginal to save by household type
PELECi	Electricity prices	RGDP	Real GDP
PFULi	Fuels prices	SAVING	Total savings
PPETROLi	Petroleum products price	STKi	Inventory investment by sector
Di	Domestic sales of domestic output	TARIFF	Tariff revenue
Ei	Exports by sector	HHTAX	Household tax revenue
Mi	Imports by sector	REMIT	Remittance from abroad
Qi	Composite goods supply	FACTIN	Interest from abroad
Xi	Domestic output by sector	CURACT	Current account
FSf	Factor supply	BORROWbr	Current borrowing
LCSCi,f	Factor demand by sector	INTERSbr	Interest payments on foreign debt
PKLlc	Average capital and labor price	Tech	Efficiency parameter
C_mini,h	Minimum consumption	EN	Energy demand
THCONh	Total household consumption	NEN	Non-Energy demand
Z h	Poverty line in household h	ELEC	Electricity demand
HDMh,c	Demand for commodities	FUL	Fuels demand
SUB	Government subsidy to Enterprises	COALNGS	Coal and natural gas demand
TSUB	Total subsidies	PETROLD	Petroleum products demand
DKi	Vol. of investment by destination	PETROLpt,j	Sectoral petroleum demand by sector
EXPTAX	Export tax revenue	COALNGS	Aggregate coal and natural gas demand
FXDINV	Fixed capital investment	COAL	Coal demand
GDi	Final demand for govt. consumption	NGASD	Natural gas demand
GDPVA	Value added in market prices: GDP	COALNGS	Coal and natural gas demand
GOVCON	Total volume of govt. consumption	PCOAL	Coal price

List of parameters and their definition

Parameters and scalars	Definition	Parameters and scalars	Definition
CSAV	Saving rate for corporations	$\beta_{i}^{c}$	Armington function share parameter
CTAX	Tax rate for corporate income	SUMSH	Sum of share correction parameter
CTRNh	Share of distributed corporate income	SUMHSHh	Sum of share for h consumption shares
DEVBUD	Development budget as reported by government	SUMCCSHi	Sum of share for ccmat and 10 tables
GGi	Government consumption shares	tmreali	Real tariff rate
GTRNh	Share of government subsidies	WTDi	Domestic price index weights
INVi	Ratio of inventory investment to gross output	WTQi	Composite price index weights
$\rho_{i}^{c}$	Armington function exponent	${\text{io}}_{i,j}$	Input–output coefficients
$\rho_{i}^{e}$	Export demand price elasticity	ROUTIN	Government routine expenditures
$\rho_{i}^{t}$	CET function exponent	TXi	Indirect tax rates
$\rho_{i}^{v}$	Value added function exponent	TVAi	Value added tax rates (indirect plus export)
$\propto_{i}^{c}$	Armington function shift parameter	TMi	Tariff rates on imports
$\propto_{i}^{t}$	CET function shift parameter	THh	Income tax rate by household type
$\propto_{i}^{\nu }$	Value added function shift parameter	SFINh	Share of foreign income for each household
$\propto_{i}^{x}$	Production function shift parameter	ZZi	Shares of investment by sector of destination
$\beta_{i}^{t}$	CET function share parameter	TEi	Export duty rates
$\beta_{i,f}^{x}$	Production function share parameter	$\alpha_{i}$	Utility function exponent
$\alpha_{i}^{{{\text{en}}}}$	Shift parameter of energy function	$\alpha_{i}^{{{\text{kl}}}}$	Shift parameter of KL function
$\beta_{i}^{{{\text{en}}}}$	Share parameter of energy function	$\beta_{i}^{{{\text{kl}}}}$	Share parameter of KL function
$\rho_{i}^{{{\text{en}}}}$	Substitution elasticity of energy function	$\rho_{i}^{{{\text{kl}}}}$	Substitution elasticity of KL function
$\alpha_{i}^{{{\text{fl}}}}$	Shift parameter of fuel function
$\beta_{i}^{{{\text{fl}}}}$	Share parameter of fuel function
$\rho_{i}^{{{\text{fl}}}}$	Substitution elasticity of fuel function