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Energy demand elasticities and weather worldwide
Tarek Atallah, KAPSARC
Simona Bigerna, University of Perugia
Carlo Andrea Bollino, University of Perugia and KAPSARC
33rd USAEE North-American Conference
Pittsburgh, 25 - 28 October 2015
The aim of the paper
provide theoretical and empirical evidence of energy demand
elasticity
taking explicitly into account capital stock effects and a newly
constructed measure of weather impact based on geo-located
heating and cooling degree-days
energy demand function for the most important 117 countries in
the world, representing more than 95% of the world population, for
the period 1978-2012
This is a novelty in the literature, for number of countries and
for estimation of climate effect.
Outline
Introduction
Model
Dataset
Results
Conclusions
Introduction
many empirical studies on energy demand in the literature are based on the single
demand estimation, which assumes a partial equilibrium viewpoint, neglecting the
simultaneity of the consumer decision process.
Causal relationship between energy and GDP (Coers and Sanders, 2012;
Salamaliki and Venetis 2013; Lee and Mei-Se, 2010; Steinbucks and Neuhoff,
2014; Adeyemi and Hunt, 2007; Beaver and Huntington, 2003).
Residential electricity demand in a household production model (Willett, K. and
Naghshpour S., 1987; Flaig, 1990)
Impact of energy efficiency (Hunt and Ryan, 2014)
Impact of weather on short term and long term residential demand (Bašta and
Heòlman, 2013; Auffhammer and Mansur, 2014).
Introduction
We improve the existing literature in three ways.
1 We improve the simple single equation approach existing in the energy and
electricity market literature
2 we present estimates of price and income elasticities of the household sector for
the largest number of countries for which coherent data are available worldwide.
(Previous studies have analyzed mainly the OECD countries (Lee and Chiu, 2010)
or specific emerging countries (e.g.: Filippini and Pachauri, 2004, for India ).
3 We incorporate explicitly capital stock and climatic effects in the demand system
in a theoretically plausible fashion.
(New dataset of specific measures of heating and cooling degree-days (Atallah et
al., 2015).
Model
Multi-stage
model
Model
Multi-stage model
First stage
C=C(pe,py,Z, Φ, U) = min [ pe e + py y │ U(e,y,Z, Φ) ]
(1)
Second stage
Ce = Ce(pe1, pe2, Φ, Ue)
(2)
U=V(pe, py, Z, Φ, C)
(3)
Ue=V((pe1, pe2, Φ, Ce)
gk= - ∂V/∂pk/∂V/∂C = gk(py, pe, Z, Φ, C) where k= y, e
ej= - ∂Ve/∂pj/∂Ve/∂Ce = ej(pe1, pe2, Φ, Ce ,)
where j= 1,2
(4)
(5)
(6)
Model
Conditional expenditure and price elasticities, at the first stage:
ηk = (∂gk/∂C)(C/gk)
(7)
ε(k)(s) = (∂gk/∂ps)(ps/Gk)
(8)
for ∀ k,s ∈ [y,e].
and at the second stage:
ηi(k) = (∂ei(k)/∂Ck)(Ck/ei(k))
(9)
εij(k) = (∂ei(k)/∂pj(k))(pj(k)/ei(k))
(10)
where ei(k) is the quantity and pj(k) is the price of elementary good in the group k: i ∈ k,
for ∀ i,j ∈ [k] and k = [e].
Uconditional elasticities from conditional ones (Edgerton, 1997, Deaton and
Muellbauer, 1980):
ηi = ηi(k) ηk
εij = δks εij(k) + ηi(k) wi(k) ( δks + ε(k)(s) )
(11)
(12)
Model
We incorporate committed quantites, capital stock
climate variables with translating method at country level
The functional form for demand functions is GAI: Generalized Almost Ideal demand
system, which is a generalization by Bollino (1987) of a model by Deaton and
Muellbauer (1980).
In the first stage:
gk = fk + C*/pk [αk + ∑s βks ln(ps) + γc ln(C*/P*) + ζk Z]
(19)
where k=y,e and fk are committed quantity parameters, αk are constants, βks are price
coefficients, γk are total expenditure coefficient, ζk are capital stock coefficients, φk are
weather coefficients,and wk are group budget shares.
C* as the supernumerary expenditure:
C* = c – (∑s fs ps )
(20)
P* a price aggregator (Stone index):
P* = ∑s ws ln(ps)
(21)
Model
In the second stage:
ei = fi + Ce*/pi [αi + ∑j βij ln(pej) + γi ln(Cy*/Py*)+ ζk Z ]
Ce* = Ce – (∑fj pej)
Pe* = ∑i wki ln(pei)
(22)
(23)
(24)
where i=1,2 and fi, αi, βij, γi, ζk, φk, wki, Cye* and Pe* have the same interpretation at the
elementary level.
In order to include the climate effect into the demand system we assume a translating
procedure, which entails to define:
fi = fi(Φ)
Notice that in the quantity expenditure space, translating has the effect to shift the
Engel curve (Bollino et al. 2000).
Dataset
Demand system for 117 countries, period 1978-2012
GDP and household consumption expenditure in real terms
GDP and consumption deflators, according to the NIA
Household sectors include residential and commercial final energy usage.
Total final energy consumption, electricity and gas quantities, prices and
exchange rates are computed taking specific information from national
statistical sources in addition to IEA’s energy balances (2014), Enerdata and
Thomson’s Reuters DataStream.
All prices are computed in constant 2005 dollars per tons of oil equivalent (toe)
using World Bank’s GDP deflator.
In some very limited cases, mainly emerging economies, we also relied on local
online publications (newspapers and magazines) to report changes in energy
prices due to regulatory change in the administration of prices.
Capital stock variables are computed as index values, considering the
aggregated time series of internet penetration, cellular phones diffusion and
other proxies, scaled by the population size of the country.
Dataset
Climate variables are computed according to the original methodology
explained in Atallah et al. (2015).
Missing climate data for Cyprus, Malta, Luxembourg, Oman and Qatar were
generated using Wolfram Alfa online computational platform.
The initial dataset included 186 countries for the period 1978-2012.
Due to data limitations, we disregarded some countries while others were
retained with a shorter times span than 1978-2012.
No country was reported having fewer than eight consecutive observations
with 70+ countries having more than 20 observations.
Our current definition of OECD excludes Iceland and Israel; OPEC excludes Iraq
while South and Central America exclude the Guyanas and some Caribbean
islands.
This leads to a matrix with a total of 2007 usable observations for our current
estimation out of an original dataset of 8370 observations.
Dataset
Figure 2 – Funnell distribution of shares in the two-stage allocation of household consumption for
the year 2009
Results
We have estimated the general model GAI which includes the stock and the
weather effect form and have imposed and tested six restrictions that are
nested in the general model (R1, R2, R3 R4, R5 and R6).
We have also estimated three restricted versions of the GAI demand system,
namely using the simple Cobb-Douglas (CD), the Linear Expenditure System
(LES) and the original (AI).
R1 imposes zero committed quantities
R2 allows to test the GAI functional form versus the LES
R3 imposes zero assumptions to the capital stock parameter
R4 imposes zero restriction to the weather variables
R5 imposes zero cross price effects
R6 imposes in the second stage that demand is exogenous (test the validity of
the multi-stage assumption)
Results
Results
Results – estimated elasticities – first stage
Results – estimated conditonal elasticities - second stage
Results – estimated unconditonal elasticities - second stage
Results –First stage elasticities
Income elasticities show that composite goods and energy are necessary goods
or luxury
The energy category is a necessity, with an income elasticity clearly below unity
The composite good price elasticity is around -0.9 – -1.0 for most countries
The energy price elasticity is on average around -0.19
We share the common notion of price inelasticity with most of the literature
(e.g.: Krishnamurthy et al., 2015; Karim and Brännlund, 2013)
The energy elasticity to the capital stock is positive, implying that an increase in
capital formation, ceteris paribus, has a positive effect on energy demand
The energy elasticity to the weather variables is positive, implying that an
increase in degree-days, ceteris paribus, has a positive effect on energy
demand.
The elasticity to Cooling is about triple than the elasticity to Heating
Results –Second stage elasticities
Natural gas is a necessity and electricity is a luxury good
(This may be further reinforced by the fact that natural gas as a commodity is
used for basic heating needs and the fact that many emerging countries have
access to cheap gas (e.g. Former Eastern Bloc).
electricity price elasticity are approximately in the – 0.1 and -0.2 range for most
countries.
elasticity to the capital stock is negative for electricity and positive for gas,
electricity elasticity to cooling degree days, although positive, is inversely
correlated to GDP per capita
(efficiency is certainly higher in higher income countries)
“other energy” elasticity to heating degree days is positive and more so for cold
and richer countries
(attitude toward a comfortable lifestyle is rooted in those affluent countries)
Results – GDP and second stage elasticities
demand price elasticities
Results – GDP and second stage elasticities
Electricity demand elasticities to cooling and heating degree-days
Results – GDP and second stage elasticities
«other energy» demand elasticities to cooling and heating degree-days
Conclusions
We are the first to estimate a two stage consumer demand structure for the allocation
of a composite good and energy at the first stage and electricity and other energy
sources, at the second stage, for 117 countries, for the period 1978-2012, with capital
stock and climate country-specific effects.
we obtain new empirical results in the literature
energy consumption is inelastic with a price elasticity of about -0.2.
electricity price elasticity are approximately in the – 0.1 and -0.2 range for most
countries.
differentiation between the perceived value of electricity and natural gas, the latter
being considered as a more essential good.
cooling degree-days’ elasticities are inversely correlated to the per capita income, in
the case of electricity consumption, reflecting a higher efficiency pattern in advanced
economies.
The validity of the multi-stage system confirms that the single equation estimations
are distorted