how sensitive to time period sampling is the asymmetric price response specification in energy...
TRANSCRIPT
Energy Economics 40 (2013) 90–109
Contents lists available at ScienceDirect
Energy Economics
j ourna l homepage: www.e lsev ie r .com/ locate /eneco
How sensitive to time period sampling is the asymmetric priceresponse specification in energy demand modelling?
Yaw Osei Adofo a, Joanne Evans b,⁎, Lester Charles Hunt b
a Design Division of the Engineering Directorate, Electricity Company of Ghana Ltd., Ghanab Surrey Energy Economics Centre (SEEC), School of Economics, University of Surrey, Guildford GU2 7XH, Surrey, UK
⁎ Corresponding author.E-mail address: [email protected] (J. Evans).
1 The price decomposition method employed by Gatealso been used in a number of other papers, for ex(1992) and Dargay and Gately (1997) amongst others.
0140-9883/$ – see front matter © 2013 Elsevier B.V. Allhttp://dx.doi.org/10.1016/j.eneco.2013.05.015
a b s t r a c t
a r t i c l e i n f oArticle history:Received 2 August 2011Received in revised form 24 May 2013Accepted 28 May 2013Available online 14 June 2013
JEL classification:C23C52Q41
Keywords:Energy demand modellingAsymmetric price responsesStability of estimates
The purpose of this paper is to investigate the criticism that energy demand estimates based on a specificprice decomposition are sensitive to the chosen time period used for the estimation. To analyse this in asystematic way, different time series sample periods are constructed from annual data for 17 OECD countriescovering the overall period 1960 to 2008. The specific price decomposition under consideration, often used toestimate asymmetric price response models of energy demand, separates the impact of prices above theprevious maximum, of a price recovery below the previous maximum and of a price cut. Therefore, theanalysis does not just involve using different time periods; instead, for each time period investigated, anew dataset is constructed and for each dataset, the price variable is decomposed in this way. An energydemand relationship allowing for asymmetric price responses is therefore estimated for each differentsample period and the results suggest that recalculation of the decomposed price variables for each differentperiod does affect the stability of the estimated energy demand responses. In contrast, a similarly estimatedenergy demand relationship with symmetric price responses for each different sample period is found tohave less instability.
© 2013 Elsevier B.V. All rights reserved.
2
1. Introduction
In the face of the rising cost and growing demand for energy,concerns surrounding security of supply and challenging CO2 targets,appropriate energy policy depends upon reliable and stable models ofenergy demand. History suggests that periods of high energy pricesmight have a lasting, dampening effect on demand. For example,the high energy prices of the 1970s resulted in increases in efficiencydue to the installation of energy-saving technologies that remained inplace despite a return to lower prices. This being the case, it has beenargued that energy demand models with symmetric demand specifi-cations do not provide an adequate description of energy demand.Consequently, estimates of elasticities and forecasts based on suchmodels could be misleading (Dargay, 1992).
Various model specifications have been put forward. An oftenquoted example is Gately and Huntington (2002),1 which establishedthat energy demandmodel specifications which ignore the asymmetriceffects of prices on demand usually lead to an underestimation ofthe income elasticities and therefore to lower projections of energy
ly and Huntington (2002) hasample Dargay (1992), Gately
rights reserved.
demand and of carbon dioxide emissions. Griffin and Schulman(2005) criticised this particular asymmetric specification, arguing thatusing fixed-time effects to capture technical progress provided a bettermodel specification than using separate price decomposition compo-nents. Furthermore, according to Griffin and Schulman (2005) theasymmetric price model used by Gately and Huntington (2002) andothers “has the peculiarity of being dependent on the starting point ofthe data period so that parameter estimates are not robust acrossdifferent sample periods” (p. 1).
The focus of this paper is on this criticism of the dependence of theasymmetric price responses specification on the starting point andhence the time period over which the dataset is drawn. To achievethis, different time series sample periods are drawn from an annualpanel of 17 OECD countries covering the overall period 1960 to2008 for per capita energy consumption, per capita real income andreal energy prices.2 Given the price decomposition used by Gatelyand Huntington (2002) and others, which are required to estimate
This paper analyses the issues around the use of the specific price decompositionused by Gately and Huntington (2002) and criticised by Griffin and Schulman (2005)both of which, provided estimates of energy demand and oil demand relationships.Here only energy demand is considered given the methodological focus of the paperand space constraints. Nonetheless, it is worth noting that the volatility of internationaloil prices would generally be expected to be higher than average end-user energyprices.
91Y.O. Adofo et al. / Energy Economics 40 (2013) 90–109
specific asymmetric price response models, this does not just involveusing different time periods; instead, for each time period investigated,a new dataset is constructed. Moreover, for each period, the pricevariable is decomposed into the asymmetric components that separatelymeasure the impact of prices above the previous maximum (pmax forshort), a price recovery below the previous maximum (prec), and a pricecut (pcut).3 From this the effect of changing the start date for the construc-tion of the decomposed price variable on the stability of the estimatedprice and income elasticities of energy demand are observed.
The paper proceeds with a brief review of the literature inSection 2; a discussion of the data in Section 3 and the methodologyemployed for analysis in Section 4. The empirical results of theestimation of the demand responses for each of the generated sampleperiods are presented in Section 5, along with an analysis of theestimated coefficient series obtained. Section 6 summarises andconcludes.
4 Griffin and Schulman (2005) implicitly considered APR and fixed-time effects assubstitutes, but suggested that fixed-time effects are better proxies for what APR wereinitially proposed to tackle.
5 It is worth adding that Adeyemi and Hunt (2007) and Adeyemi et al. (2010) do notrule out such a constant change if it is what the data suggests. They argue that any gen-eral energy demand specification should initially include a general non-linear UEDT. Itis only if accepted by the data that a more restrictive version should be accepted.
6 These tests would give useful additional information on which to choose the pre-ferred model, however, arguably this should not be used blindly without recourse toeconomic theory and intuition. As Adeyemi and Hunt (2007) notes, the “chosen modelshould be the one that is accepted by the data while at the same time conforming to
2. Literature
Jones (1994) argues for a general model specification of energydemand that is “representative of the data generation process,capable of providing better estimates of the price and income elastic-ities needed for forecasting and policy analysis” (p. 252). One of themost important differences in energy consumption decisionscompared to other demand sectors of an economy is that it is closelylinked to the capital stock of energy-using equipment (Gately andHuntington, 2002). This is because each type of equipment embodiesa technology that specifies a given level of energy use per unit of theservices it produces thereby affecting the ability of energy users inresponding in the long-run to price variations. Consumers' responsetherefore becomes a trade-off between their anticipated energysavings and full opportunity cost of replacing the old equipmentwith new ones (Ryan and Plourde, 2002a).
The inclusion of technical change in energy demand models isassumed by Beenstock and Willcocks (1981) and Hunt et al. (2003a,2003b) to be primarily exogenous in nature, separate from theresponse to changing energy prices. Kouris (1983) argued thattechnical change is generally price induced; hence, in general itshould be captured via the price response (or elasticity) in energydemand models. More recently, Adeyemi et al. (2010) have arguedthat general energy demand specifications should allow for both.
Furthermore, given that some energy-saving technologies remainin place (such as loft insulation) despite falling prices, there is a goodreason to believe that high energy prices (such as those experiencedin the 1970s and early 1980s) had a lasting, dampening effect ondemand. Therefore, it has been argued by Dargay (1992), Dargayand Gately (1995), and others that symmetric energy demandfunctions (with or without an allowance for exogenous technicalchange) do not provide an adequate description of energy demand,likely making estimates of elasticities and forecasts based on suchmodels misleading; hence, their argument for the inclusion ofasymmetric price responses (APR). Energy demand models shouldtherefore arguably allow for both price-induced technical progressin an asymmetric way and exogenous technical progress. However,Hunt et al. (2003a, 2003b) argued that the exogenous componentshould be suitably flexible to capture not only technical progressbut also other non-systematic exogenous influences via what theycall an underlying energy demand trend (UEDT). In summary, themost general energy demand specification is one that allows for the ex-ogenous elements (via a flexible UEDT) andAPR (through a decomposedprice variable); thus allowing for the distinction between the exogenouseffects and the different induced effects of price shocks and rising andfalling energy prices (Adeyemi et al., 2010).
3 The way these are calculated is discussed below.
However, this approach has not always been adopted with somedebate in the literature as to how it might be achieved. By ignoringthe exogenous component, Gately and Huntington (2002) showed thatenergy demand responds differently to pmax, prec, and pcut (although asimilar asymmetry in income response was generally rejected). Griffinand Schulman (2005) suggested that the price decomposition approachused by Gately and Huntington (2002) is only a proxy for energy-savingtechnical progress and that a better alternative is to use fixed-time ef-fects (time dummies).4 However, Huntington (2006) rejects symmetry.By providing some coefficient restriction tests, not carried out by Griffinand Schulman (2005), Huntington (2006) demonstrates that both exog-enous and price-induced technological developments represented in amodel by fixed-time effects and APR (pmax, prec, and pcut) respectivelyhave a role (statistically) to play in understanding energy demand pat-terns. Adeyemi and Hunt (2007) corroborated this statistical findingfor the OECD industrial sector.
Despite this, there is still argument in the literature about the useof APR vis-à-vis time dummies (or UEDT) in panel data estimation.According to Dargay and Gately (2010), the Griffin and Schulman(2005) approach produces coefficients that are constant acrosscountries for a given year and can vary over time in an “unstructuredmanner” (p. 6276). This is in contrast to the view of Adeyemi andHunt (2007) and Adeyemi et al. (2010) who argue that it is wrongto assume that the UEDT will be represented by a constant changeover time given that technical progress and other exogenousfactors are unlikely to change in such a way. Therefore, according toAdeyemi and Hunt (2007) and Adeyemi et al. (2010) when estimat-ing panel energy demand models the time dummies suggested byGriffin and Schulman (2005) should be included and the estimatedcoefficients are very likely to be non-linear with periods when theyare increasing or decreasing—i.e. they are likely to vary in an ‘unstruc-tured manner’.5
In addition, Dargay and Gately (2010) show that for G7 OECDcountries' per capita oil demand there is a strong negative correla-tion between the fixed time effects and pmax arguing that demandreductions were likely to have been pmax induced; reflecting eitherendogenous technical change or fuel switching not reversed byprice cuts. Dargay and Gately (2010) argue that the fixed timeeffects (the time dummies coefficients) “tell us nothing about thedeterminants of demand changes, in either the past or the future”(p. 6276). In summary, according to Dargay and Gately (2010)given the time dummies are not independent of prices (at leastnot pmax) they do not help explain demand and could be measur-ing anything. Unfortunately, Dargay and Gately (2010) do notreport the tests undertaken by Huntington (2006) and Adeyemiet al. (2010) which would at least give a statistical basis to helpdetermine whether there is a role for the time dummies and/orAPR.6
The above highlights the issues around the way technical progress(and other exogenous factors) might be incorporated in energydemand models be it exogenously via the UEDT or endogenously
economic theory—but this should be estimated and tested rather than imposed atthe outset” (p. 707).
0
20
40
60
80
100
120
140
1861
1864
1867
1870
1873
1876
1879
1882
1885
1888
1891
1894
1897
1900
1903
1906
1909
1912
1915
1918
1921
1924
1927
1930
1933
1936
1939
1942
1945
1948
1951
1954
1957
1960
1963
1966
1969
1972
1975
1978
1981
1984
1987
1990
1993
1996
1999
2002
2005
2008
2011
Fig. 1. Crude oil prices 1861–2011 (US$2011 per barrel).Source: BP, 2012.
92 Y.O. Adofo et al. / Energy Economics 40 (2013) 90–109
via the pmax, prec, and pcut version of APR.7 Consequently, in order tofocus on the main criticism that estimated APR based on the pmax,prec, and pcut decomposition depend upon the starting point andhence time period over which the dataset is drawn (discussed furtherbelow), models that include and exclude time dummies both withAPR are estimated (as explained in Section 4).
As highlighted one of the biggest criticisms of research thatinclude APR based on the pmax, prec, and Pcut decomposition is theirdependence on the starting point of the dataset and the implicitassumption that energy consumers have very long memories whenthere is a sustained period of falling prices (or prices rising and fallingbelow the previous maximum). However, given that the decomposi-tion approach is based on technical progress being price inducedand the inclusion of pmax arguably reflects that when price was at itsmaximum, the induced efficiency change (such as the installation ofloft insulation) continues to impact on energy consumption decisions.Despite this, the decomposed series are conditional on the timeperiod over which the data is drawn. A price increase can thereforebe identified as pmax in one dataset but as prec in another dataset.This therefore raises questions as to the robustness of the estimatesobtained for different estimation sample periods, meaning that therelative importance of the three decomposed price variables appearhighly sensitive to the time period sampled (Griffin and Schulman,
7 It is worth noting that these are not the only criticisms of previous energy demandresearch that has incorporated APR. Adeyemi and Hunt (2007) suggest that in countrypanel data models a model specification that assumes that the slope and time coeffi-cients are constant across the various countries is unrealistic in light of differentsocio-economic and institutional patterns and could lead to conflicting statistical andeconomic estimates. Moreover, they argue that the imposition of the same pattern ofthe UEDT, proxied by the fixed-time effects in the panel data context, is likely to betoo restrictive. Adeyemi and Hunt (2007) also suggest that there might be problemswith assuming a Koyck lag structure when modelling energy demand as used by Gatelyand Huntington amongst others. These are all issues that warrant further investigation,however, in order to focus on the specific pmax, prec, and pcut decomposition issue, theseare not considered here.
2005). Indeed, as Fig. 1 shows, when considering real internationaloil prices back to 1861 the highest price was in 1864 so that if thisprice series were decomposed into pmax, prec, and pcut then themaximum price, pmax, would have been constant since 1864 withincreases in the 1970s early 1980s and the mid to late 2000s deemedmerely as a price recovery, prec.8 For the shorter data period, begin-ning in 1960 which is used in this paper the countries can be splitinto two groups. For nine of the 17 countries (Group A) the real ener-gy price generally falls from the start of the period until the late1970s/early 1980s; consequently the first notable jump in pmax isaround this time (see Figs. 2a and 3a). For the nine countries inGroup A this suggests that the energy crisis of the early 1970s repre-sented just a price recovery, prec. Yet, as Fig. 4a shows, if the datastarts in 1970 then the early 1970s is seen as a maximum price,pmax for the nine Group A countries. Conversely, for the other eightcounties (Group B) the early 1970s is seen as being a maximumprice, pmax whether the data starts in 1960 or 1970 (see Figs. 2b, 3band 4b).
This begs the question of exactly what is pmax attempting to mea-sure. The idea that it measures price shocks (based on a rise in the realprice of energy above the previous maximum) is appealing in princi-ple. However, can it be right that in one sample period the early 1970senergy price hike is seen as a shock when in others it is not? Since ev-erything that is known about that period suggests that it definitelywas a shock. Moreover, it begs the additional question of how reliableand useful are estimated energy demand models based on the pmax,prec, and pcut decomposition if events such as the early 1970s oilprice shock are (arbitrarily) classified according to when the dataperiod starts. This is what this paper attempts to explore.9
8 We are grateful to an anonymous referee for suggesting the inclusion of Figs. 1–4.9 It is worth highlighting that the focus here is the consideration of the specific pmax,
prec, and pcut decomposition used by Dargay and Gately (1995), Gately and Huntington(2002), etc. that is dependent upon the starting point of the data; however, this is notthe only decomposition, as discussed further in the Summary and conclusion section.
0
20
40
60
80
100
120
140
160
1960
1962
1964
1966
1968
1970
1972
1974
1976
1978
1980
1982
1984
1986
1988
1990
1992
1994
1996
1998
2000
2002
2004
2006
2008
France Greece Ireland Italy Japan
Netherlands Portugal Sweden Switzerland
0
20
40
60
80
100
120
140
160
1960
1962
1964
1966
1968
1970
1972
1974
1976
1978
1980
1982
1984
1986
1988
1990
1992
1994
1996
1998
2000
2002
2004
2006
2008
Austria Belgium Canada Denmark Norway Spain UK USA
Group A
Group B
Fig. 2. Real end-user energy price indices p (2005 = 100) 1960–2008.
93Y.O. Adofo et al. / Energy Economics 40 (2013) 90–109
In summary, although the APR model based on the pmax, prec, andpcut decomposition has been widely used in estimating energydemand models, there are a number of criticisms of the approach.This paper therefore focuses on the key concern, that the estimatesare dependent on the start date of the sample. In particular, varioussamples with different start and/or end dates are used to estimatemodels with APR based on the pmax, prec, and pcut decomposition inorder to examine the impact on the stability of the estimated energydemand responses.
10 This source was used in a similar way by Prosser (1985) and Adeyemi et al. (2010).
3. Data
Data for 17 OECD countries (Austria, Belgium, Canada, Denmark,France, Greece, Ireland, Italy, Japan, The Netherlands, Norway, Portugal,Spain, Sweden, Switzerland, the UK and the US) are employed in this
study. Per capita energy and per capita income for each country arecalculated from data on aggregate energy consumption (ktoe) andGDP (billions 2000 US$ using PPP) and population from the IEA energystatistics database (www.iea.org) covering the period 1960 to 2008. Thereal price index (2000 = 100) series is obtained by splicing two series1960–1980 (1972 = 100) and 1978–2008 (2000 = 100) togetherusing the ratio from the overlap year 1978. The 1978 to 2008 energyprices are from the IEA database while energy prices from 1960 to1980 came from an alternative source using each country's data ascaptured in Baade (1981), determined by weighting household andindustrial gas, coal and electricity as well as diesel and kerosene bytheir fuel consumption shares.10 The final panel data used is the natural
3.6
3.8
4
4.2
4.4
4.6
4.8
5
5.2
1960
1962
1964
1966
1968
1970
1972
1974
1976
1978
1980
1982
1984
1986
1988
1990
1992
1994
1996
1998
2000
2002
2004
2006
2008
France Greece Ireland Italy Japan
Netherlands Portugal Sweden Switzerland
3.6
3.8
4
4.2
4.4
4.6
4.8
5
5.2
1960
1962
1964
1966
1968
1970
1972
1974
1976
1978
1980
1982
1984
1986
1988
1990
1992
1994
1996
1998
2000
2002
2004
2006
2008
Austria Belgium Canada Denmark Norway Spain UK USA
Group A
Group B
Fig. 3. Maximum historical real end-user energy price pmax (natural logs) for samples starting in 1960. (Base year 2005).
94 Y.O. Adofo et al. / Energy Economics 40 (2013) 90–109
logarithm forms of the per capita energy (E), per capita income (Y) andreal energy price index (P).
The different sample periods for the estimation are obtained bydrawing, from the 1960 to 2008 panel data, samples with differentstarting years from 1960 up to and including 1987 and for each sam-ple re-calculating the decomposed price components, pmax, prec, andpcut. (Using periods with starting years spanning 1960 to 1987 shouldcapture the oil price increases, and by extension energy prices, of the1970s and the low prices of the 1960s and mid-1980s to see how thestarting year of a drawn dataset affects the stability of the estimatedelasticities, whether it be high or low.) However, this can be done intwo ways giving two types of datasets: one with fixed degrees offreedom [hereafter fixed-df] and one with varying degrees of freedom
[hereafter varying-df]. The essence of generating these two datasets isto help identify any possible effect that the loss of degrees of freedom,in the different sample periods forming the varying-df dataset, has onthe stability of the estimated energy demand response. The construc-tion of these two possible datasets is as follows:
• Varying-df: The original 1960–2008 panel data is re-constructedby changing the starting years consecutively from 1960 to 1987,but maintaining the final year, 2008, for each sample period(i.e. 1960–2008, 1961–2008 and so on until 1987–2008) but eachtime re-calculating the decomposed price data.
• Fixed-df: In order to identify any possible effect of loss of degreesof freedom for the different estimation periods constructed above,
3.6
3.8
4
4.2
4.4
4.6
4.8
5
5.2
1970
1972
1974
1976
1978
1980
1982
1984
1986
1988
1990
1992
1994
1996
1998
2000
2002
2004
2006
2008
France Greece Ireland Italy Japan
Netherlands Portugal Sweden Switzerland
3.6
3.8
4
4.2
4.4
4.6
4.8
5
5.2
1970
1971
1972
1973
1974
1975
1976
1977
1978
1979
1980
1981
1982
1983
1984
1985
1986
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007
2008
Austria Belgium Canada Denmark Norway Spain UK USA
Group A
Group B
Fig. 4. Maximum historical real end-user energy price pmax (natural logs) for samples starting in 1970. (Base year 2005).
95Y.O. Adofo et al. / Energy Economics 40 (2013) 90–109
another set of sampling periods are constructed but with a fixed22 years included in each sample period.11 So similar to thevarying-df version, the original 1960–2008 panel data isre-constructed by changing the starting years consecutively from1960 to 1987, but with the 22 year period fixed so that the final yearvaries (i.e. 1960–1981, 1961–1982 and so on until 1987–2008) 12
and again re-calculating the decomposed price data for each sample.
11 22 years were chosen in order to ensure that most of the sample periods includedperiods of rising and low oil prices. Although the 22 year estimation period might ap-pear arbitrary and/or short, the use of panel data for 17 countries over a 22-year periodstill provides a total of 357 observations for estimation after allowing for the elimina-tion of one year for each country due to the one year lag in the model.12 Similar to the varying-df the 1960 to 1987 starting dates are chosen in order tocapture the periods of rising and low oil prices.
Hence, there is a fixed-df and a varying-df dataset of estimationperiods that are applied to the models described in the next sectionin order to analyse the stability of the estimated coefficients.13
4. Methodology
The exposition of the estimated models is based on Adeyemi andHunt's (2007) re-statement of the Gately and Huntington (2002)and Griffin and Schulman (2005) methodology. From a Koyckmodel, a general symmetric model is specified whereby the natural
13 Although this is analogous to undertaking ‘recursive estimation’ and ‘rolling win-dow’ estimation, it is more comprehensive given a new dataset is constructed for eachnew time period considered.
96 Y.O. Adofo et al. / Energy Economics 40 (2013) 90–109
logarithm of per capita energy consumption (et) is dependent on thenatural logarithm of real income per capita (yt) and a distributed lagof the past natural logarithm of the real price of energy (pt). This ismathematically represented as follows:
et ¼ f yt ;γ Lð Þpt½ � ð1Þwhere L is the lag operator.
Assuming a linear specification and that the lag distributionon prices follows a geometric lag distribution, Eq. (1) can be written as:
et ¼ α þ βyt þγpt
1−λLþ μ t ð2Þ
where μt is the random error term assumed to be N(0, σt2).
Eq. (2) can further be transformed by the lag operator, L toobtain:
et ¼ ψþ β yt−λyt−1ð Þ þ γpt þ λet−1 þ εt ð3Þ
where ψ = α(1 − λ) and εt = μt − λμt − 1.However, given that a panel data of OECD countries is used, like
Gately and Huntington (2002), Eq. (3) is re-written in a panel contextand augmented with country dummies in order to allow for a differ-ent constant for each country, i, (the fixed effects approach) as givenby:
eit ¼ ψþ β yit−λyit−1ð Þ þ γpit þ λeit−1 þ δiDi þ εit ð4Þ
where εit = μit − λμit − 114 and δi represent the differential constants
for the individual countries relative to the base constant ψwith all theother parameters assumed to be constant across countries. Eq. (4)constitutes the general conventional symmetric price specificationenergy demand model using a Koyck-lag equation. In order to intro-duce APR into the initial model the price variable is decomposed asfollows:
pt ¼ pmax þ prec þ pcut ð5Þ
where pmax,t = max(p1, …,pt), representing the log of the maximum
historical price prec;t ¼ ∑tt¼1 maxf0;ðpt−pt−1Þ− pmax;t−pmax;t−1
� �g,representing the cumulative sub-maximum increases in thelogarithm of price, monotonically non-decreasing, prec,t ≥ 0
pcut;t ¼ ∑tt¼1 min 0;ðpt−pt−1
n �− pmax;t−pmax;t−1
� �g, increases in
the logarithm of maximum historical price, monotonicallynon-decreasing, pmax,t ≥ 0.15
The asymmetric model specification used by Gately andHuntington (2002), excluding the income asymmetry,16 is obtained
14 Gately and Huntington assumed in its preferred model specification that εit is notautocorrelated but independently and normally distributed, thus ignoring the first or-der moving average, MA(1) structure that comes about from the Koyck derivation(Adeyemi and Hunt, 2007). This issue also warrants further investigation.15 Gately and Huntington (2002) include p1 in their decomposition as follows:pt =p1 + pmax + prec + pcut, where the components are defined as follows:p1 =logarithm of price in the starting year, t = 1 pmax;t ¼∑t
t¼1 max p1;…; ptð Þ−max p1;…; pt−1ð Þf g; representing cumulative increases inthe logarithm of maximum historical price, monotonically non-decreasing,pmax,t ≥ 0. prec and pcut have the same definition as those in the text above.This is slightly different to the decomposition used here given the focus onthe effect of using samples with different starting years. The alternative wasused in order to eliminate any influence on the estimated base constant term.The base constant term in Gately and Huntington (2002) is α(1 − λ) + γp1but for the specification used here it is α(1 − λ) as in Eq. (4)). It is importantto note however that the estimated income and price elasticities are the sameirrespective of which decomposition is used.16 Gately and Huntington (2002) included asymmetric income responses in theirmodel, but in general the statistical test for symmetry was not significant, indicatingthat income is symmetric and not asymmetric. The specified model therefore assumessymmetric income responses as used by Griffin and Schulman (2005).
by substituting Eq. (5) into Eq. (4) and simplifying further to getwhat Adeyemi and Hunt (2007) refer to as Model I:
eit ¼ ψþ β yit−λyit−1ð Þ þ γmpmax;it þ γrprec;it þ γcpcut;it þ λeit−1
þ δiDi þ εit ð6Þ
where ψ and εit are as originally defined.In setting up their model, Griffin and Schulman (2005) included a
variable zt in Eq. (1) to represent a technical index for energyefficiency. The revised equation therefore becomes:
et ¼ f yt ;γ Lð Þpt ; zt½ �: ð7Þ
When written in log-linear form this becomes
et ¼ α þ βyt þγpt
1−λLþ θzt þ μ t ð8Þ
and transforming by the lag operator, L and simplifying further yields:
eit ¼ ψþ β yit−λyit−1ð Þ þ γpit þ λeit−1 þ θ zt−λzt−1ð Þ þ εit : ð9Þ
Since zt is unobservable, Griffin and Schulman (2005) replacedθ(zt − λzt − 1) in Eq. (9) above with the simpler time dummies inthe panel context to obtain Eq. (10) below; getting, what Adeyemiand Hunt (2007) refer to as, Model II:
eit ¼ ψþ β yit−λyit−1ð Þ þ γpit þ λeit−1 þ δiDi þ θtDt þ εit ð10Þ
where θt represents the differential time dummy coefficients for eachyear of the sample period relative to the base, ψ.
In order to compare their model with that of Gately andHuntington (2002), Griffin and Schulman (2005) also introducedtime dummies into Eq. (6),17 giving, what Adeyemi and Hunt(2007) refer to as, Model III:
eit ¼ ψþ β yit−λyit−1ð Þ þ γmaxpmax;it þ γrecprec;it þ γcutpcut;itþ λeit−1 þ δiDi þ θtDt þ εit : ð11Þ
In summary, the restricted models given by Eq. (6) and Eq. (10)and the unrestricted model given by Eq. (11) represent Models I, IIand III respectively and can be used to estimate the coefficients ofenergy demand. Following Huntington (2006), simple F-tests oflinear restrictions can be applied to test the restriction of imposingsymmetry when moving from Model III to Model II (i.e. to testH0 : γmax = γrec = γcut) and the restriction of removing the timedummies when moving from Model III to Model I (i.e. to testH0 : θt = 0) in order to attempt to find the ‘preferred specification’.(These tests were also explored by Adeyemi et al., 2010.)
In an attempt to provide empirical evidence to justify the criticismthat specifications with APR, via the pmax, prec, and pcut decompositiontechnique, are conditional on the time period over which the data isdrawn, Griffin and Schulman (2005) did partially consider the stabil-ity hypothesis using two sample periods one for 1970–1996 and onefor 1960–1999. However, this did not fully address the issue andarguably a more systematic approach of investigating the stability ofthe estimated coefficients for different sample periods over time isappropriate. The more systematic approach employed in this paperis therefore achieved by initially estimating Models I and III usingthe different sample periods of the varying-df and the fixed-df
17 Griffin and Schulman (2005) argue that this is to capture exogenous energy savingtechnical progress; however, there is not a consensus view that this is in fact the case,see Dargay and Gately (2010) for example.
97Y.O. Adofo et al. / Energy Economics 40 (2013) 90–109
datasets. This allows the stability (or otherwise) of the estimatedenergy demand responses to be observed across the different sampleperiods. These are then compared to the estimates of the symmetricalModel II where any instability of the estimates is due purely to thedifferent sample periods, not because of the need to re-calculate thedecomposed price data over the different periods (as is necessaryfor the asymmetrical Models I and III).18 In addition, the Huntington(2006) tests outlined above for the different sample periods are alsoundertaken to assess their stability (or otherwise). The results ofthis exercise are discussed in the next section.
5. Results
The results from estimating Models I and III using the differentsample periods for the varying-df and fixed-df versions of the dataare presented in Figs. 5–8.19 Figs. 5 and 6 present the results ofthe models with APR but without time dummies (i.e. Model I, theGately and Huntington, 2002 approach) for varying-df and fixed-dfrespectively. Figs. 7 and 8 present the results of the models withAPR but with time dummies (i.e. Model III, the Griffin andSchulman, 2005/Huntington, 2006 approach) for varying-df andfixed-df respectively. For all four figures: a, presents incomeresponse; b presents the pmax, response; c, presents the prec response;and d, presents the pcut response.
For Model I using both the varying-df and fixed-df samples,(Figs. 5a and 6a) it can be seen that income is always significantlydifferent from zero. For Model I, using varying-df (Fig. 5b, c, andd) all the asymmetric price components are significantly differentfrom zero other than for a couple of periods in the early tomid-1980s. However, for the fixed-df samples for Model I (Fig. 6b,c and d) the asymmetric price components are often not signifi-cantly different from zero.20 For Model III it can be seen that in-come is always significantly different from zero (Figs. 7a and 8a)while the asymmetric price components are often not significantlydifferent from zero (Figs. 7b–d and 8b–d). Furthermore, althoughthe instability of all the estimated coefficients (Figs. 5–8) is not asbig as expected a-priori, there appears to be a relatively largevariation.
To explore the stability further (and compare across models anddifferent data samples) Fig. 9 presents the estimated income coeffi-cients across all models and datasets (including Model II21). Thisshows that Model I, for both varying-df and fixed-df, shows thegreatest variation. This is also illustrated in Table 1 showing that theincome elasticity estimates ranges from 0.3 to 0.7 for varying-df andfrom 0.3 to 0.8 for fixed-df, however for Model III the variation isless, 0.3 to 0.5 for both varying-df and fixed-df. The range for ModelII is similar to Model III; 0.4 to 0.5 for both varying-df and fixed-df.However, the degree of variation is slightly less. The Coefficient ofVariation (CoV) for Model III is 8% for varying-df and 13% forfixed-df compared to the 6% for varying-df and 11% for fixed-dffor Model II; both of which are less than Model I, the CoV being20% for varying-df and 27% for fixed-df. This is further seen in
18 In other words, investigating the stability of Model II is no different to investigatingthe stability of the estimates in any model using ‘recursive’ or ‘rolling window’ estima-tion given a new dataset does not need to be constructed. In contrast, as already stated,investigation of the stability of Models I and III does require the construction of a newdataset for each period but is still similar to ‘recursive’ or ‘rolling window’ estimation.19 Note, that given the Koyck lag structure the first observation is lost from eachdataset. Therefore, the x-axis on these charts refers to the ‘estimation periods’ notthe ‘dataset periods’.20 The spikes in the estimated pmax, coefficients for the data period starting 1980(Figs. 5b, 6b, 7b, and 8b) might be due to the second oil price shock which was initiatedby the 1979 Iranian revolution, which was further worsened by the Iran–Iraq War inSeptember 1980.21 The values of the coefficients and their associated 95% confidence intervals forModel II are given in Fig. A1 (for varying-df) and Fig. A2 (for fixed-df) in Appendix A.
Fig. 9, which also illustrates the similarity between estimated in-come coefficients from Model III and Model II. In fact, the ModelIII and Model II estimates are very similar for the varying-dfand the fixed-df, suggesting that when time dummies are includ-ed, the estimated income coefficient does not noticeably varywhether the price variable is decomposed or not. In summary,it would appear that the different sample periods do impact on thestability of the estimated income coefficient, with the variation general-ly being greater than the normal time series variation found forModel II,nevertheless, the impact appears to be less when time dummies areincluded.
Fig. 10 presents the estimated price coefficients across allmodels and datasets including Model II (Fig. 10a presents thepmax, coefficients from Models I and III; Fig. 10b the prec coefficientsfrom Models I and III; Fig. 10c the pcut coefficients from Models Iand III; and Fig. 10d the p coefficients from Model II). This suggeststhat the variation is greater for the decomposed price coefficientsin Models I and III than the price coefficients in Model II. This isalso illustrated in Table 1 where for the ranges of the price coeffi-cient estimates for Model II and the CoV are on the whole lowerthan that for the decomposed price coefficients and the CoV inModels I and III. Again this would appear to indicate that the var-iation in estimated decomposed price coefficients in Models I andIII is generally greater than the normal time series variationfound in Model II.
Fig. 11 illustrates the results from testing for symmetry in bothModels I and Model III (i.e. testing H0 : γmax = γrec = γcut).Fig. 11a shows that for the varying-df estimates of Model Ithe null hypothesis of symmetry is generally rejected for the earlierdata periods starting before 1970 (when, as seen in the Introductionsection, the early 1970s energy crisis is regarded as just a pricerecovery for nine of the 17 countries in the sample). However, forthe dataset starting from 1970 onwards in the majority of cases,the null hypothesis of symmetry cannot be rejected for Model I;which is similar to the results to the fixed-df results for all theperiods. For Model III however, shown in Fig. 11b, in almost allcases for all periods the null hypothesis of symmetry cannot berejected; suggesting that Model II is favoured (statistically) toModel III. A result that is very stable across all estimation periodsconsidered.
For completeness, the tests of omitting the time dummies(i.e. testing H0 : θt = 0) were conducted and in all cases for ModelsII and III using both varying-df and fixed-df the null hypothesis wasrejected (with a probability of 0.00). Fig. 12a and b shows that forModel III the estimated coefficients for the time dummies are stableacross the different estimation periods for both the varying-df andfixed-df. Moreover, these are very similar to those obtained for Model IIshown in Fig. 12c and d; however, the spread of the estimated timedummy coefficients for Model III appears slightly wider than that forModel II.22
Finally, it is interesting to see the relationship between the coeffi-cients of pmax, prec, and pcut over the different estimation periods(shown in Fig. 13). It is expected a-priori that in absolute terms theestimated pmax elasticity would be greater than or equal to theestimated prec elasticity which in turn would be greater than orequal to the estimated pcut elasticity (i.e.
∧γmax
�� ��≥∧γrec
�� ��≥∧γcut
�� ��). Orgenerally the estimated coefficient for pmax should be less than theestimated coefficient for prec which in turn should be less than orequal to the estimated pcut coefficient. However, Fig. 13 shows that
22 Following a suggestion from an anonymous referee, Appendix B presents the UScorrelation coefficients for the estimated time dummy coefficients and pmax, and theestimated time dummy coefficients and energy demand, given the Dargay and Gately(2010) argument that a ‘strong’ negative and positive correlation respectively, effec-tively renders the time dummies redundant. However, as Fig. A3 in Appendix B illus-trates, this does not appear to be the case for the US.
0
0.2
0.4
0.6
0.8
1
1.219
61 -
200
819
62 -
200
819
63 -
200
819
64 -
200
819
65 -
200
819
66 -
200
819
67 -
200
819
68 -
200
819
69 -
200
819
70 -
200
819
71 -
200
819
72 -
200
819
73 -
200
819
74 -
200
819
75 -
200
819
76 -
200
819
77 -
200
819
78 -
200
819
79 -
200
819
80 -
200
819
81 -
200
819
82 -
200
819
83 -
200
819
84 -
200
819
85 -
200
819
86 -
200
819
87 -
200
819
88 -
200
8
-0.25
-0.2
-0.15
-0.1
-0.05
0
0.05
0.1
0.15
0.2
0.25
0.3
1961
- 2
008
1962
- 2
008
1963
- 2
008
1964
- 2
008
1965
- 2
008
1966
- 2
008
1967
- 2
008
1968
- 2
008
1969
- 2
008
1970
- 2
008
1971
- 2
008
1972
- 2
008
1973
- 2
008
1974
- 2
008
1975
- 2
008
1976
- 2
008
1977
- 2
008
1978
- 2
008
1979
- 2
008
1980
- 2
008
1981
- 2
008
1982
- 2
008
1983
- 2
008
1984
- 2
008
1985
- 2
008
1986
- 2
008
1987
- 2
008
1988
- 2
008
-0.2
-0.15
-0.1
-0.05
0
0.05
0.1
1961
- 2
008
1962
- 2
008
1963
- 2
008
1964
- 2
008
1965
- 2
008
1966
- 2
008
1967
- 2
008
1968
- 2
008
1969
- 2
008
1970
- 2
008
1971
- 2
008
1972
- 2
008
1973
- 2
008
1974
- 2
008
1975
- 2
008
1976
- 2
008
1977
- 2
008
1978
- 2
008
1979
- 2
008
1980
- 2
008
1981
- 2
008
1982
- 2
008
1983
- 2
008
1984
- 2
008
1985
- 2
008
1986
- 2
008
1987
- 2
008
1988
- 2
008 -0.3
-0.25
-0.2
-0.15
-0.1
-0.05
0
0.05
0.1
1961
- 2
008
1962
- 2
008
1963
- 2
008
1964
- 2
008
1965
- 2
008
1966
- 2
008
1967
- 2
008
1968
- 2
008
1969
- 2
008
1970
- 2
008
1971
- 2
008
1972
- 2
008
1973
- 2
008
1974
- 2
008
1975
- 2
008
1976
- 2
008
1977
- 2
008
1978
- 2
008
1979
- 2
008
1980
- 2
008
1981
- 2
008
1982
- 2
008
1983
- 2
008
1984
- 2
008
1985
- 2
008
1986
- 2
008
1987
- 2
008
1988
- 2
008
a) Income Coefficient Series
c) Coefficient of Price Recovery Series
b) Coefficient of Maximum Historical Price Series
d) Coefficient of Price Cut Series
Fig. 5. Model I, APR without time dummies with varying-df. Note: Measures are estimated elasticities and the upper and lower bounds are 95% confidence intervals. The x-axis refers to the ‘estimation periods’ rather than the ‘datasetperiods’.
98Y.O
.Adofo
etal./
EnergyEconom
ics40
(2013)90
–109
0
0.2
0.4
0.6
0.8
1
1.219
62 -
198
219
63 -
198
319
64 -
198
419
65 -
198
519
66 -
198
619
67 -
198
719
68 -
198
819
69 -
198
919
70 -
199
019
71 -
199
119
72 -
199
219
73 -
199
319
74 -
199
419
75 -
199
519
76 -
199
619
77 -
199
719
78 -
199
819
79 -
199
919
80 -
200
019
81 -
200
119
82 -
200
219
83 -
200
319
84 -
200
419
85 -
200
519
86 -
200
619
87 -
200
719
88 -
200
8 -0.25
-0.2
-0.15
-0.1
-0.05
0
0.05
0.1
0.15
0.2
0.25
0.3
1961
- 1
981
1962
- 1
982
1963
- 1
983
1964
- 1
984
1965
- 1
985
1966
- 1
986
1967
- 1
987
1968
- 1
988
1969
- 1
989
1970
- 1
990
1971
- 1
991
1972
- 1
992
1973
- 1
993
1974
- 1
994
1975
- 1
995
1976
- 1
996
1977
- 1
997
1978
- 1
998
1979
- 1
999
1980
- 2
000
1981
- 2
001
1982
- 2
002
1983
- 2
003
1984
- 2
004
1985
- 2
005
1986
- 2
006
1987
- 2
007
1988
- 2
008
-0.2
-0.15
-0.1
-0.05
0
0.05
0.1
1961
- 1
981
1961
- 1
981
1962
- 1
982
1963
- 1
983
1964
- 1
984
1965
- 1
985
1966
- 1
986
1967
- 1
987
1968
- 1
988
1969
- 1
989
1970
- 1
990
1971
- 1
991
1972
- 1
992
1973
- 1
993
1974
- 1
994
1975
- 1
995
1976
- 1
996
1977
- 1
997
1978
- 1
998
1979
- 1
999
1980
- 2
000
1981
- 2
001
1982
- 2
002
1983
- 2
003
1984
- 2
004
1985
- 2
005
1986
- 2
006
1987
- 2
007
1988
- 2
008
-0.3
-0.25
-0.2
-0.15
-0.1
-0.05
0
0.05
0.1
1961
- 1
981
1962
- 1
982
1963
- 1
983
1964
- 1
984
1965
- 1
985
1966
- 1
986
1967
- 1
987
1968
- 1
988
1969
- 1
989
1970
- 1
990
1971
- 1
991
1972
- 1
992
1973
- 1
993
1974
- 1
994
1975
- 1
995
1976
- 1
996
1977
- 1
997
1978
- 1
998
1979
- 1
999
1980
- 2
000
1981
- 2
001
1982
- 2
002
1983
- 2
003
1984
- 2
004
1985
- 2
005
1986
- 2
006
1987
- 2
007
1988
- 2
008
a) Income Coefficient Series b) Coefficient of Maximum Historical Price Series
c) Coefficient of Price Recovery Series d) Coefficient of Price Cut Series
Fig. 6. Model I, APR without time dummies with fixed-df. Note: Measures are estimated elasticities and the upper and lower bounds are 95% confidence intervals. The x-axis refers to the ‘estimation periods’ rather than the ‘dataset periods’.
99Y.O
.Adofo
etal./
EnergyEconom
ics40
(2013)90
–109
0
0.2
0.4
0.6
0.8
1
1.2 a) Income Coefficient Series b) Coefficient of Maximum Historical Price Series
c) Coefficient of Price Recovery Series d) Coefficient of Price Cut Series
1961
- 2
008
1962
- 2
008
1963
- 2
008
1964
- 2
008
1965
- 2
008
1966
- 2
008
1967
- 2
008
1968
- 2
008
1969
- 2
008
1970
- 2
008
1971
- 2
008
1972
- 2
008
1973
- 2
008
1974
- 2
008
1975
- 2
008
1976
- 2
008
1977
- 2
008
1978
- 2
008
1979
- 2
008
1980
- 2
008
1981
- 2
008
1982
- 2
008
1983
- 2
008
1984
- 2
008
1985
- 2
008
1986
- 2
008
1987
- 2
008
1988
- 2
008
-0.25
-0.2
-0.15
-0.1
-0.05
0
0.05
0.1
0.15
0.2
0.25
0.3
1961
- 2
008
1962
- 2
008
1963
- 2
008
1964
- 2
008
1965
- 2
008
1966
- 2
008
1967
- 2
008
1968
- 2
008
1969
- 2
008
1970
- 2
008
1971
- 2
008
1972
- 2
008
1973
- 2
008
1974
- 2
008
1975
- 2
008
1976
- 2
008
1977
- 2
008
1978
- 2
008
1979
- 2
008
1980
- 2
008
1981
- 2
008
1982
- 2
008
1983
- 2
008
1984
- 2
008
1985
- 2
008
1986
- 2
008
1987
- 2
008
1988
- 2
008
-0.2
-0.15
-0.1
-0.05
0
0.05
0.1
1961
- 2
008
1962
- 2
008
1963
- 2
008
1964
- 2
008
1965
- 2
008
1966
- 2
008
1967
- 2
008
1968
- 2
008
1969
- 2
008
1970
- 2
008
1971
- 2
008
1972
- 2
008
1973
- 2
008
1974
- 2
008
1975
- 2
008
1976
- 2
008
1977
- 2
008
1978
- 2
008
1979
- 2
008
1980
- 2
008
1981
- 2
008
1982
- 2
008
1983
- 2
008
1984
- 2
008
1985
- 2
008
1986
- 2
008
1987
- 2
008
1988
- 2
008
-0.3
-0.25
-0.2
-0.15
-0.1
-0.05
0
0.05
0.1
1961
- 2
008
1962
- 2
008
1963
- 2
008
1964
- 2
008
1965
- 2
008
1966
- 2
008
1967
- 2
008
1968
- 2
008
1969
- 2
008
1970
- 2
008
1971
- 2
008
1972
- 2
008
1973
- 2
008
1974
- 2
008
1975
- 2
008
1976
- 2
008
1977
- 2
008
1978
- 2
008
1979
- 2
008
1980
- 2
008
1981
- 2
008
1982
- 2
008
1983
- 2
008
1984
- 2
008
1985
- 2
008
1986
- 2
008
1987
- 2
008
1988
- 2
008
Fig. 7.Model III, APR with time dummies with varying-df. Note: Measures are estimated elasticities and the upper and lower bounds are 95% confidence intervals. The x-axis refers to the ‘estimation periods’ rather than the ‘dataset periods’.
100Y.O
.Adofo
etal./
EnergyEconom
ics40
(2013)90
–109
0
0.2
0.4
0.6
0.8
1
1.219
61 -
198
119
62 -
198
219
63 -
198
319
64 -
198
419
65 -
198
519
66 -
198
619
67 -
198
719
68 -
198
819
69 -
198
919
70 -
199
019
71 -
199
119
72 -
199
219
73 -
199
319
74 -
199
419
75 -
199
519
76 -
199
619
77 -
199
719
78 -
199
819
79 -
199
919
80 -
200
019
81 -
200
119
82 -
200
219
83 -
200
319
84 -
200
419
85 -
200
519
86 -
200
619
87 -
200
719
88 -
200
8 -0.25
-0.2
-0.15
-0.1
-0.05
0
0.05
0.1
0.15
0.2
0.25
0.3
1961
- 1
981
1962
- 1
982
1963
- 1
983
1964
- 1
984
1965
- 1
985
1966
- 1
986
1967
- 1
987
1968
- 1
988
1969
- 1
989
1970
- 1
990
1971
- 1
991
1972
- 1
992
1973
- 1
993
1974
- 1
994
1975
- 1
995
1976
- 1
996
1977
- 1
997
1978
- 1
998
1979
- 1
999
1980
- 2
000
1981
- 2
001
1982
- 2
002
1983
- 2
003
1984
- 2
004
1985
- 2
005
1986
- 2
006
1987
- 2
007
1988
- 2
008
-0.2
-0.15
-0.1
-0.05
0
0.05
0.1 c) Coefficient of Price Recovery Series d) Coefficient of Price Cut Series
a) Income Coefficient Series b) Coefficient of Maximum Historical Price Series19
61 -
198
119
62 -
198
219
63 -
198
319
64 -
198
419
65 -
198
519
66 -
198
619
67 -
198
719
68 -
198
819
69 -
198
919
70 -
199
019
71 -
199
119
72 -
199
219
73 -
199
319
74 -
199
419
75 -
199
519
76 -
199
619
77 -
199
719
78 -
199
819
79 -
199
919
80 -
200
019
81 -
200
119
82 -
200
219
83 -
200
319
84 -
200
419
85 -
200
519
86 -
200
619
87 -
200
719
88 -
200
8 -0.3
-0.25
-0.2
-0.15
-0.1
-0.05
0
0.05
0.1
1961
- 1
981
1962
- 1
982
1963
- 1
983
1964
- 1
984
1965
- 1
985
1966
- 1
986
1967
- 1
987
1968
- 1
988
1969
- 1
989
1970
- 1
990
1971
- 1
991
1972
- 1
992
1973
- 1
993
1974
- 1
994
1975
- 1
995
1976
- 1
996
1977
- 1
997
1978
- 1
998
1979
- 1
999
1980
- 2
000
1981
- 2
001
1982
- 2
002
1983
- 2
003
1984
- 2
004
1985
- 2
005
1986
- 2
006
1987
- 2
007
1988
- 2
008
Fig. 8. Model III, APR with Time Dummies with Fixed-df. Note: Measures are estimated elasticities and the upper and lower bounds are 95% confidence intervals. The x-axis refers to the ‘estimation periods’ rather than the ‘dataset periods’.
101Y.O
.Adofo
etal./
EnergyEconom
ics40
(2013)90
–109
0.25
0.35
0.45
0.55
0.65
0.75
0.85
0.95
1988
Model I, APR without Time Dummies with Varying - df Model I, APR without Time Dummies with Fixed - df
Model II, with Varying - df Model II, with Fixed - df
Model III, APR with Time Dummies with Varying - df Model III, APR with Time Dummies with Fixed - df
1961
1962
1963
1964
1965
1966
1967
1968
1969
1970
1971
1972
1973
1974
1975
1976
1977
1978
1979
1980
1981
1982
1983
1984
1985
1986
1987
Fig. 9. Comparison of estimated income coefficient forModels I, II, III. Note: To allow for a comparison the x-axis refers to the start of the ‘estimation periods’ rather than the start of the ‘datasetperiods’. Therefore, for estimates with varying-df the end date of each of the series estimates is 2008 as in Fig. 5, whereas for estimates with fixed-df the end date varies as in Fig. 6.
Table 1Summary of estimated income and price coefficients.
Model I Model III Model II
Varying-df Fixed-df Varying-df Fixed-df Varying-df Fixed-df
Income coefficient (y):Min 0.30 0.28 0.31 0.32 0.36 0.36Max 0.66 0.84 0.47 0.54 0.49 0.54Mean 0.54 0.64 0.42 0.46 0.44 0.46Median 0.60 0.72 0.43 0.45 0.44 0.46SD 0.11 0.17 0.04 0.06 0.03 0.05CoV 20% 27% 8% 13% 6% 11%
Maximum historical price coefficient (pmax): γmax
Min −0.08 −0.11 −0.03 −0.09Max 0.00 0.16 0.00 0.04Mean −0.05 −0.06 −0.01 −0.03Median −0.05 −0.08 −0.01 −0.03D 0.01 0.06 0.01 0.02CoV 28% 101% 63% 71%
Price recovery coefficient (prec): γrec
Min −0.10 −0.13 −0.06 −0.10Max −0.04 −0.01 −0.01 0.00Mean −0.07 −0.06 −0.02 −0.04Median −0.07 −0.05 −0.02 −0.04SD 0.01 0.04 0.01 0.03CoV 16% 65% 50% 60%
Price cut coefficient (pcut): γcut
Min −0.14 −0.17 −0.12 −0.12Max −0.02 0.00 −0.02 −0.02Mean −0.05 −0.07 −0.04 −0.06Median −0.05 −0.05 −0.04 −0.05SD 0.02 0.05 0.02 0.03CoV 43% 69% 49% 48%
Price coefficient (p): γMin −0.06 −0.08Max −0.02 −0.02Mean −0.03 −0.04Median −0.02 −0.04SD 0.01 0.02CoV 37% 39%
102 Y.O. Adofo et al. / Energy Economics 40 (2013) 90–109
this is rarely the case for both Model I and Model III for bothvarying-df and fixed-df.23
6. Summary and conclusion
The price decomposition that separately measure the impact ofprices above the previous maximum, a price recovery below the pre-vious maximum and a price cut when modelling energy demand hasbeen criticised as being sensitive to the time period sampled. Thispaper analyses this criticism in a systematic way by reconstructionof the price decomposition terms (pmax, prec, and pcut) for variousdata periods and estimating the Gately and Huntington (2002)and Griffin and Schulman (2005) models for each sample period.Although the variation is not as great as expected a-priori, the param-eter estimates for the different sample periods do vary somewhat forthe asymmetric models, whereas the parameter estimates do notvary so much for the symmetric model without a decomposed pricevariable; thus suggesting that the symmetric model is likely to givemore stable results. The analysis presented here therefore givessupport to the argument put forward by Griffin and Schulman(2005). Furthermore, this general observation applies when theUEDT, via the time dummies, is included or not; therefore givingsupport to the argument put forward by Adeyemi and Hunt (2007)and Adeyemi et al. (2010) that any general energy demand specifi-cations should allow for both endogenous price effects and anexogenous UEDT.
In summary, the key conclusion is that when using the pmax, prec,and pcut decomposition the starting point of the dataset used for
23 Following another suggestion from an anonymous referee, Appendix C presentsthe results of an exercise to isolate the income coefficient from the estimated pmax, prec,and pcut coefficients to see if this might be a cause of the variation in the estimated pmax,prec, and pcut coefficients. However, as Fig. A4 in Appendix C illustrates, the variation inthe estimated pmax, prec, and pcut coefficients does not change dramatically, being sim-ilar to that in Fig. 13.
-0.2
-0.15
-0.1
-0.05
0
0.05
0.1
0.15
0.2a) Coefficient of Maximum Historical Price Series b) Coefficient of Price Recovery Series
c) Coefficient of Price Cut Series d) Model II Coefficient of Price Series
1961
- 2
008
1962
- 2
008
1963
- 2
008
1964
- 2
008
1965
- 2
008
1966
- 2
008
1967
- 2
008
1968
- 2
008
1969
- 2
008
1970
- 2
008
1971
- 2
008
1972
- 2
008
1973
- 2
008
1974
- 2
008
1975
- 2
008
1976
- 2
008
1977
- 2
008
1978
- 2
008
1979
- 2
008
1980
- 2
008
1981
- 2
008
1982
- 2
008
1983
- 2
008
1984
- 2
008
1985
- 2
008
1986
- 2
008
1987
- 2
008
1988
- 2
008
Model I, APR without Time Dummies with Varying-df
Model I, APR without Time Dummies with Fixed-df
Model III, APR with Time Dummies with Varying-df
Model III, APR with Time Dummies with Fixed-df
-0.2
-0.15
-0.1
-0.05
0
0.05
0.1
0.15
0.2
1961
- 2
008
1962
- 2
008
1963
- 2
008
1964
- 2
008
1965
- 2
008
1966
- 2
008
1967
- 2
008
1968
- 2
008
1969
- 2
008
1970
- 2
008
1971
- 2
008
1972
- 2
008
1973
- 2
008
1974
- 2
008
1975
- 2
008
1976
- 2
008
1977
- 2
008
1978
- 2
008
1979
- 2
008
1980
- 2
008
1981
- 2
008
1982
- 2
008
1983
- 2
008
1984
- 2
008
1985
- 2
008
1986
- 2
008
1987
- 2
008
1988
- 2
008
Model I, APR without Time Dummies with Varying-df
Model I, APR without Time Dummies with Fixed-df
Model III, APR with Time Dummies with Varying-df
Model III, APR with Time Dummies with Fixed-df
-0.2
-0.15
-0.1
-0.05
0
0.05
0.1
0.15
0.2
1961
- 2
008
1962
- 2
008
1963
- 2
008
1964
- 2
008
1965
- 2
008
1966
- 2
008
1967
- 2
008
1968
- 2
008
1969
- 2
008
1970
- 2
008
1971
- 2
008
1972
- 2
008
1973
- 2
008
1974
- 2
008
1975
- 2
008
1976
- 2
008
1977
- 2
008
1978
- 2
008
1979
- 2
008
1980
- 2
008
1981
- 2
008
1982
- 2
008
1983
- 2
008
1984
- 2
008
1985
- 2
008
1986
- 2
008
1987
- 2
008
1988
- 2
008
Model I, APR without Time Dummies with Varying-df
Model I, APR without Time Dummies with Fixed-df
Model III, APR with Time Dummies with Varying-df
Model III, APR with Time Dummies with Fixed-df
-0.2
-0.15
-0.1
-0.05
0
0.05
0.1
0.15
0.2
1961
- 2
008
1962
- 2
008
1963
- 2
008
1964
- 2
008
1965
- 2
008
1966
- 2
008
1967
- 2
008
1968
- 2
008
1969
- 2
008
1970
- 2
008
1971
- 2
008
1972
- 2
008
1973
- 2
008
1974
- 2
008
1975
- 2
008
1976
- 2
008
1977
- 2
008
1978
- 2
008
1979
- 2
008
1980
- 2
008
1981
- 2
008
1982
- 2
008
1983
- 2
008
1984
- 2
008
1985
- 2
008
1986
- 2
008
1987
- 2
008
1988
- 2
008
Model II Price Elasticity Varying-df
Model II Price Elasticity Fixed-df
Fig. 10. Comparison of estimated price coefficient for Models I, II, III. Note: The x-axis refers to the ‘estimation periods’ rather than the ‘dataset periods’.
103Y.O
.Adofo
etal./
EnergyEconom
ics40
(2013)90
–109
1988
1961
1962
1963
1964
1965
1966
1967
1968
1969
1970
1971
1972
1973
1974
1975
1976
1977
1978
1979
1980
1981
1982
1983
1984
1985
1986
1987
Probability Values (Model I, Varying df) Probability Values (Model I, Fixed df)
1988
1961
1962
1963
1964
1965
1966
1967
1968
1969
1970
1971
1972
1973
1974
1975
1976
1977
1978
1979
1980
1981
1982
1983
1984
1985
1986
1987
Probability Values (Model III Varying df) Probability Values (Model III, Fixed df)
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
a
b
Fig. 11. Probabilities from Symmetry tests III (H0 : γmax = γrec = γcut) Note: Horizontal lines show the 5% and 10% probabilities respectively. To allow for a comparison the x-axisrefers to the start of the ‘estimation periods’ rather than the start of the ‘dataset periods’. Therefore, for estimates with varying-df the end date of each of the series estimates is 2008as in Fig. 5, whereas for estimates with fixed-df the end date of each of the series varies as in Fig. 6.
104 Y.O. Adofo et al. / Energy Economics 40 (2013) 90–109
analysis does matter given the impact on the stability of the priceelasticity estimates. This suggests two possibilities; either, i) thestarting point of the data needs to be carefully chosen to ensure anappropriate pmax value, or, ii) an alternative type of decompositionis utilised when trying to estimate asymmetric price elasticities of de-mand. The problem with i) is that however carefully the startingpoint is chosen it will always be subject to the criticism that thechoice is arbitrary leaving suspicion about the reliability of theestimated elasticities, given that there is always the risk that adifferent choice would have likely resulted in different estimates.This suggests that ii), using a more appropriate price decomposi-tion that does not suffer from the starting point problem of thepmax, prec, and pcut decomposition, might be the more fruitful wayto proceed.
This all points to two lines of future enquiry: Firstly, in order toinvestigate the robustness of the results presented here, similaranalysis should be conducted using different datasets with differentcountries and/or more specific energy fuel such as oil. It would beinteresting to see the exercise repeated for different panel datasetsto ascertain whether there is a dataset for which the resultsfound here do not hold, such as that used in Dargay and Gately(2010). This would also allow a further comparison with Gately andHuntington (2002), and Griffin and Schulman (2005) who bothestimated energy and oil demand relationships; in particular, itwould be an interesting exercise given that international oil priceswould generally be expected to be more volatile than average end-user energy prices.
Secondly, it would also be useful to explore alternative pricedecompositions that would not be dependent upon the startingpoint of the data like the pmax, prec, and pcut version employed in thisanalysis. Hence, further work should conduct a similar exercise tothat here, but with alternative price decompositions such as thosesuggested by Ryan and Plourde (2002b) and Frondel and Vance(2013) (both of which do not require a new dataset to be constructedfor each period). This would help to uncover whether, on the groundsof stability, the symmetric model is or is not preferred to the asym-metric model (both with and without an exogenous UEDT). A fullerunderstanding of the robustness of the results presented here withrespect to the dataset and price decomposition would help ascertainwhether the symmetric model is more stable and hence preferredper se. Or whether in fact there is a more appropriate alternativeenergy price decomposition that is better at capturing APR—thusproducing more stable and reliable estimates than the symmetricmodel.
Acknowledgements
This work builds upon and extends the work undertaken in Adofo(2009). We gratefully acknowledge the financial support provided bythe Electricity Company of Ghana Ltd. We are also grateful to twoanonymous referees for their comments and suggestions that havehelped to significantly improve the paper. Nevertheless, the viewsexpressed in this paper are those of the authors alone and we are,of course, responsible for all errors and omissions.
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
0.08
1961
1963
1965
1967
1969
1971
1973
1975
1977
1979
1981
1983
1985
1987
1989
1991
1993
1995
1997
1999
2001
2003
2005
2007
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
1961
1963
1965
1967
1969
1971
1973
1975
1977
1979
1981
1983
1985
1987
1989
1991
1993
1995
1997
1999
2001
2003
2005
2007
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
1961
1963
1965
1967
1969
1971
1973
1975
1977
1979
1981
1983
1985
1987
1989
1991
1993
1995
1997
1999
2001
2003
2005
2007
-0.06
-0.04
-0.02
0
0.02
0.04
0.06
1961
1963
1965
1967
1969
1971
1973
1975
1977
1979
1981
1983
1985
1987
1989
1991
1993
1995
1997
1999
2001
2003
2005
2007
a) Model III with Varying-df b) Model III with Fixed-df
c) Model II with Varying-df d) Model II with Fixed-df
Fig. 12. Time dummy coefficients. Note: Unlike other charts in this paper, the years on the x-axis refer to the year of the estimated time dummy coefficients.
105Y.O
.Adofo
etal./
EnergyEconom
ics40
(2013)90
–109
-0.2
-0.15
-0.1
-0.05
0
0.05
0.1
0.15
0.219
61 -
200
819
62 -
200
819
63 -
200
819
64 -
200
819
65 -
200
819
66 -
200
819
67 -
200
819
68 -
200
819
69 -
200
819
70 -
200
819
71 -
200
819
72 -
200
819
73 -
200
819
74 -
200
819
75 -
200
819
76 -
200
819
77 -
200
819
78 -
200
819
79 -
200
819
80 -
200
819
81 -
200
819
82 -
200
819
83 -
200
819
84 -
200
819
85 -
200
819
86 -
200
819
87 -
200
819
88 -
200
8
pmax prec pcut
-0.2
-0.15
-0.1
-0.05
0
0.05
0.1
0.15
0.2
1961
- 1
981
1962
- 1
982
1963
- 1
983
1964
- 1
984
1965
- 1
985
1966
- 1
986
1967
- 1
987
1968
- 1
988
1969
- 1
989
1970
- 1
990
1971
- 1
991
1972
- 1
992
1973
- 1
993
1974
- 1
994
1975
- 1
995
1976
- 1
996
1977
- 1
997
1978
- 1
998
1979
- 1
999
1980
- 2
000
1981
- 2
001
1982
- 2
002
1983
- 2
003
1984
- 2
004
1985
- 2
005
1986
- 2
006
1987
- 2
007
1988
- 2
008
pmax prec pcut
-0.2
-0.15
-0.1
-0.05
0
0.05
0.1
0.15
0.2
1961
- 2
008
1962
- 2
008
1963
- 2
008
1964
- 2
008
1965
- 2
008
1966
- 2
008
1967
- 2
008
1968
- 2
008
1969
- 2
008
1970
- 2
008
1971
- 2
008
1972
- 2
008
1973
- 2
008
1974
- 2
008
1975
- 2
008
1976
- 2
008
1977
- 2
008
1978
- 2
008
1979
- 2
008
1980
- 2
008
1981
- 2
008
1982
- 2
008
1983
- 2
008
1984
- 2
008
1985
- 2
008
1986
- 2
008
1987
- 2
008
1988
- 2
008
pmax prec pcut
-0.2
-0.15
-0.1
-0.05
0
0.05
0.1
0.15
0.2
1961
- 1
981
1962
- 1
982
1963
- 1
983
1964
- 1
984
1965
- 1
985
1966
- 1
986
1967
- 1
987
1968
- 1
988
1969
- 1
989
1970
- 1
990
1971
- 1
991
1972
- 1
992
1973
- 1
993
1974
- 1
994
1975
- 1
995
1976
- 1
996
1977
- 1
997
1978
- 1
998
1979
- 1
999
1980
- 2
000
1981
- 2
001
1982
- 2
002
1983
- 2
003
1984
- 2
004
1985
- 2
005
1986
- 2
006
1987
- 2
007
1988
- 2
008
pmax prec pcut
a) Model I APR without Time Dummies with Varying-df b) Model I APR without Time Dummies with Fixed-df
c) Model III APR with Time Dummies with Varying-df d) Model III APR with Time Dummies with Fixed-df
Fig. 13. Price coefficient comparisons. Note: The x-axis refers to the ‘estimation periods’ rather than the ‘dataset periods’.
106Y.O
.Adofo
etal./
EnergyEconom
ics40
(2013)90
–109
a
0
0.2
0.4
0.6
0.8
1
1.219
61 -
200
8
1962
- 2
008
1963
- 2
008
1964
- 2
008
1965
- 2
008
1966
- 2
008
1967
- 2
008
1968
- 2
008
1969
- 2
008
1970
- 2
008
1971
- 2
008
1972
- 2
008
1973
- 2
008
1974
- 2
008
1975
- 2
008
1976
- 2
008
1977
- 2
008
1978
- 2
008
1979
- 2
008
1980
- 2
008
1981
- 2
008
1982
- 2
008
1983
- 2
008
1984
- 2
008
1985
- 2
008
1986
- 2
008
1987
- 2
008
1988
- 2
008
b
-0.2
-0.15
-0.1
-0.05
0
0.05
0.1
0.15
0.2
1961
- 2
008
1962
- 2
008
1963
- 2
008
1964
- 2
008
1965
- 2
008
1966
- 2
008
1967
- 2
008
1968
- 2
008
1969
- 2
008
1970
- 2
008
1971
- 2
008
1972
- 2
008
1973
- 2
008
1974
- 2
008
1975
- 2
008
1976
- 2
008
1977
- 2
008
1978
- 2
008
1979
- 2
008
1980
- 2
008
1981
- 2
008
1982
- 2
008
1983
- 2
008
1984
- 2
008
1985
- 2
008
1986
- 2
008
1987
- 2
008
1988
- 2
008
Fig. A1. Model II, symmetric price response with time dummies with varying-df(coefficients and 95% confidence intervals). a: income. b: price.Note: The x-axis refers to the ‘estimation periods’ rather than the ‘dataset periods’.
a
0
0.2
0.4
0.6
0.8
1
1.2
1961
- 1
981
1962
- 1
982
1963
- 1
983
1964
- 1
984
1965
- 1
985
1966
- 1
986
1967
- 1
987
1968
- 1
988
1969
- 1
989
1970
- 1
990
1971
- 1
991
1972
- 1
992
1973
- 1
993
1974
- 1
994
1975
- 1
995
1976
- 1
996
1977
- 1
997
1978
- 1
998
1979
- 1
999
1980
- 2
000
1981
- 2
001
1982
- 2
002
1983
- 2
003
1984
- 2
004
1985
- 2
005
1986
- 2
006
1987
- 2
007
1988
- 2
008
b
-0.2
-0.15
-0.1
-0.05
0
0.05
0.1
0.15
0.2
1961
- 1
981
1962
- 1
982
1963
- 1
983
1964
- 1
984
1965
- 1
985
1966
- 1
986
1967
- 1
987
1968
- 1
988
1969
- 1
989
1970
- 1
990
1971
- 1
991
1972
- 1
992
1973
- 1
993
1974
- 1
994
1975
- 1
995
1976
- 1
996
1977
- 1
997
1978
- 1
998
1979
- 1
999
1980
- 2
000
1981
- 2
001
1982
- 2
002
1983
- 2
003
1984
- 2
004
1985
- 2
005
1986
- 2
006
1987
- 2
007
1988
- 2
008
Fig. A2. Model II, symmetric price response with time dummies with fixed-df(coefficients and 95% confidence intervals). a: income. b: price.Note: The x-axis refers to the ‘estimation periods’ rather than the ‘dataset periods’.
107Y.O. Adofo et al. / Energy Economics 40 (2013) 90–109
Appendix A. Model II results
The results from estimating Model II using the different sampleperiods for the varying-df and fixed-df versions of the data arepresented in Figs. A1 and A2; i.e. the results for the symmetricmodel with time dummies (the Griffin and Schulman, 2005approach). These show that the coefficients for both the estimatedprice and income response are relatively stable.
Appendix B. The correlation between pmax and the estimated timedummy coefficients and energy consumption
As mentioned in the Introduction section, Dargay and Gately(2010) argue that the time dummies do not help explain demandand give no information about the determinants of energy demandchanges. They argue that a strong negative correlation between theestimated time dummy coefficients and pmax (−0.91 for G7 per capitaoil demand in their case) means that demand reductions are most-ly induced by pmax and therefore the time dummy coefficients donot “reflect either endogenous technical change or fuel-switchingthat was not reversed by price cuts” (p. 6277). Dargay and Gately(2010) also argue that there is a strong positive correlationbetween the estimated time dummy coefficients and energy de-mand (+0.75 for G7 per capita oil demand in their case) sothat higher time dummy coefficients are associated with higherenergy demand and lower time dummy coefficients with lowerenergy demand. Thus, in their view, the estimated time dummy
coefficients provide no information about what drives energydemand.
This is explored further for one of the larger countries in thepanel used here, the US. Fig. A3 presents the correlation coeffi-cients between the estimated time dummy coefficients and a)pmax and b) energy demand; for Model III and Model II for bothvarying-df and fixed-df for all the different estimation periodsused in this analysis. These show that in general the ‘strong’ corre-lations predicted by Dargay and Gately (2010) do not appear forthe US.
Appendix C. Results from holding income elasticity constant
The income coefficients shown in Fig. 9 (which might be expectedto be relatively insensitive to the data period used) could be affectedby its interaction with the price coefficients—whose sensitivity isbeing investigated; an exercise was therefore undertaken to see ifthis is the case. The income elasticity was therefore assumed to beequal to 0.5 in Models I and II for both varying-df and fixed-df andthe pmax, prec, and pcut coefficients re-estimated accordingly. The ideabeing that this isolates the income coefficient from the price coeffi-cients, thus preventing the income coefficient from possibly varyingimplausibly as the coefficients are re‐estimated when different dataperiods are used using the non-linear least squares method. The resultsfrom this exercise are shown in Fig. A4 and it can be seen that thisappears to not be the reason for the variation in the estimated pmax,prec, and pcut coefficients, given the variation shown in Fig. A4 is similarto that shown in Fig. 13.
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
1961
1962
1963
1964
1965
1966
1967
1968
1969
1970
1971
1972
1973
1974
1975
1976
1977
1978
1979
1980
1981
1982
1983
1984
1985
1986
1987
1988
Model II Varying df Model II Fixed df Model III with Varying df Model III Fixed df
b
a
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
1961
1962
1963
1964
1965
1966
1967
1968
1969
1970
1971
1972
1973
1974
1975
1976
1977
1978
1979
1980
1981
1982
1983
1984
1985
1986
1987
1988
Model II Varying df Model II Fixed df Model III with Varying df Model III Fixed df
Fig. A3. Correlation coefficients—US. a: pmax and time dummy coefficients. b: energy and time dummy coefficients. Note: To allow for a comparison the x-axis refers to the start ofthe ‘estimation periods’ rather than the start of the ‘dataset periods’. Therefore, for the correlation coefficients with varying-df the end date of each of the series estimates is 2008 asin Fig. 5, whereas for the correlation coefficients with fixed-df the end date of each of the series estimates varies as in Fig. 6.
a
-0.2-0.15-0.1
-0.050
0.050.1
0.150.2
1961
- 2
008
1962
- 2
008
1963
- 2
008
1964
- 2
008
1965
- 2
008
1966
- 2
008
1967
- 2
008
1968
- 2
008
1969
- 2
008
1970
- 2
008
1971
- 2
008
1972
- 2
008
1973
- 2
008
1974
- 2
008
1975
- 2
008
1976
- 2
008
1977
- 2
008
1978
- 2
008
1979
- 2
008
1980
- 2
008
1981
- 2
008
1982
- 2
008
1983
- 2
008
1984
- 2
008
1985
- 2
008
1986
- 2
008
1987
- 2
008
1988
- 2
008
Pmax Prec Pcut b
-0.2-0.15-0.1
-0.050
0.050.1
0.150.2
1961
- 1
981
1962
- 1
982
1963
- 1
983
1964
- 1
984
1965
- 1
985
1966
- 1
986
1967
- 1
987
1968
- 1
988
1969
- 1
989
1970
- 1
990
1971
- 1
991
1972
- 1
992
1973
- 1
993
1974
- 1
994
1975
- 1
995
1976
- 1
996
1977
- 1
997
1978
- 1
998
1979
- 1
999
1980
- 2
000
1981
- 2
001
1982
- 2
002
1983
- 2
003
1984
- 2
004
1985
- 2
005
1986
- 2
006
1987
- 2
007
1988
- 2
008
Pmax Prec Pcut
c
-0.2
-0.15
-0.1
-0.05
0
0.05
0.1
0.15
0.2
1961
- 2
008
1962
- 2
008
1963
- 2
008
1964
- 2
008
1965
- 2
008
1966
- 2
008
1967
- 2
008
1968
- 2
008
1969
- 2
008
1970
- 2
008
1971
- 2
008
1972
- 2
008
1973
- 2
008
1974
- 2
008
1975
- 2
008
1976
- 2
008
1977
- 2
008
1978
- 2
008
1979
- 2
008
1980
- 2
008
1981
- 2
008
1982
- 2
008
1983
- 2
008
1984
- 2
008
1985
- 2
008
1986
- 2
008
1987
- 2
008
1988
- 2
008
Pmax Prec Pcut d
-0.2
-0.15
-0.1
-0.05
0
0.05
0.1
0.15
0.2
1961
- 1
981
1962
- 1
982
1963
- 1
983
1964
- 1
984
1965
- 1
985
1966
- 1
986
1967
- 1
987
1968
- 1
988
1969
- 1
989
1970
- 1
990
1971
- 1
991
1972
- 1
992
1973
- 1
993
1974
- 1
994
1975
- 1
995
1976
- 1
996
1977
- 1
997
1978
- 1
998
1979
- 1
999
1980
- 2
000
1981
- 2
001
1982
- 2
002
1983
- 2
003
1984
- 2
004
1985
- 2
005
1986
- 2
006
1987
- 2
007
1988
- 2
008
Pmax Prec Pcut
Fig. A4. Price coefficients when the income coefficient is assumed to be 0.5. a: Model I APR without time dummies with varying-df. b: Model I APR without time dummies withfixed-df. c: Model III APR with time dummies with varying-df. d: Model III APR with time dummies with fixed-df.Note: The x-axis refers to the ‘estimation periods’ rather than the ‘dataset periods’.
108 Y.O. Adofo et al. / Energy Economics 40 (2013) 90–109
109Y.O. Adofo et al. / Energy Economics 40 (2013) 90–109
Appendix D. Supplementary data
Supplementary data to this article can be found online at http://dx.doi.org/10.1016/j.eneco.2013.05.015.
References
Adeyemi, O.I., Hunt, L.C., 2007. Modelling OECD industrial energy demand: asymmetricprice responses and energy-saving technical change. Energy Econ. 29 (4), 693–709.
Adeyemi, O.I., Broadstock, D.C., Chitnis, M., Hunt, L.C., Judge, G., 2010. Asymmetric priceresponses and the underlying energy demand trend: are they substitutes or com-plements? Evidence frommodelling OECD aggregate energy demand. Energy Econ.32 (5), 1157–1164.
Adofo, Y.O., 2009. Price Decomposition and Its Effect on the Stability of Elasticities ofEnergy Demand for Different Estimation Periods. University of Surrey, UK(Unpublished MSc Dissertation).
Baade, P., 1981. International energy evaluation system: international energy prices:1955–1980. Information Administration, US Department of Energy Report, SR/STID/81-21, Washington, DC, USA..
Beenstock, M., Willcocks, P., 1981. Energy consumption and economic activity inindustrialised countries. Energy Econ. 3 (4), 225–232.
BP, 2012. Statistical Review of World Energy 2012. (Retrieved 10 November 2012 fromwww.bp.com/statisticalreview/).
Dargay, J.M., 1992. The irreversible effects of high oil prices: empirical evidence forthe demand for motor fuels in France, Germany and the UK. In: Hawdon, D.(Ed.), Energy Demand: Evidence and Expectations. Surrey University Press,Guildford, UK, pp. 165–182.
Dargay, J.M., Gately, D., 1995. The imperfect price-reversibility of non-transport oildemand in the OECD. Energy Econ. 17 (1), 59–71.
Dargay, J.M., Gately, D., 1997. The demand for transportation fuels: imperfect pricereversibility? Transp. Res. B 31 (1), 71–82.
Dargay, J.M., Gately, D., 2010. World oil demand's shift toward faster growing and lessprice-responsive products and regions. Energy Policy 38, 6261–6277.
Frondel, M., Vance, C., 2013. Re-identifying the rebound: what about asymmetry?Energy J. 34 (4), 43–54.
Gately, D., 1992. Imperfect price-reversibility of U.S. gasoline demand: asymmetricresponses to price increases and decreases. Energy J. 13 (4), 179–207.
Gately, D., Huntington, H.G., 2002. The asymmetric effects of changes in price andincome on energy and oil demand. Energy J. 23 (1), 19–55.
Griffin, J.M., Schulman, C.T., 2005. Price asymmetry in energy demand models: a proxyfor energy-saving technical change? Energy J. 26 (2), 1–21.
Hunt, L.C., Judge, G., Ninomiya, Y., 2003a. Underlying trends and seasonality in UKenergy demand: a sectoral analysis. Energy Econ. 25 (1), 93–118.
Hunt, L.C., Judge, G., Ninomiya, Y., 2003b. Modelling underlying energy demand trendschapter 9. In: Hunt, L.C. (Ed.), Energy in Competitive Market: Essays in Honour ofColin Robinson. Edward Elgar, UK, pp. 140–174.
Huntington, H., 2006. A note on price asymmetry as induced technical change. Energy J.27 (3), 1–7.
Jones, C.T., 1994. Accounting for technical progress in aggregate energy demand.Energy Econ. 16 (4), 245–252.
Kouris, G., 1983. Fuel consumption for road transport in the USA. Energy Econ. 5, 89–99.Prosser, R.D., 1985. Demand elasticities in OECD: dynamic aspects. Energy Econ. 7 (1), 9–12.Ryan, D.L., Plourde, A., 2002a. Smaller and smaller? The price responsiveness of non-
transport oil demand. Q Rev Econ Finance 42, 285–317.Ryan, D.L., Plourde, A., 2002b. Thanks for thememories: oil price decomposition and ener-
gy demand asymmetries. 25th Annual IAEE International Conference, Aberdeen.