Determnng Demand for Energy Servces: Investgatng ncomedrven behavours Chantal Guertn* Subal C. Kumbhakar** Anantha K. Duraappah* *Internatonal Insttute for Sustanable Development **State Unversty of New York at Bnghamton
Determnng Demand for Energy Servces: Investgatng ncome-drven behavours Chantal Guertn*, Subal C. Kumbhakar**, Anantha K. Duraappah* *Internatonal Insttute for Sustanable Development **State Unversty of New York at Bnghamton
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Table of Contents Abstract... 1 1. Introducton... 2 2 Input and Output Energy... 3 2.1 Energy Content of the Utlty Consumpton... 4 2.2 Input and Output Prces... 5 3 A Bref Survey of Econometrc Models of Resdental Energy Demand... 5 3.1 Energy Servces, End Uses and Income Groups... 5 3.1.1 Demand for Energy Servces... 6 3.1.2 End Uses... 6 3.1.3 Income Groups... 7 3.2 Desgnng a Resdental Energy Demand Model... 8 3.2.1 Structural Form... 9 3.2.2 Energy Unts... 10 3.2.3 Effcency of Converson Technologes... 11 3.2.4 Average vs. Margnal Utlty Prces... 12 3.2.5 Varable Prce Elastctes...13 3.2.6 Fuel Substtuton... 13 4. Demand for Energy Servces Usng Fronter Analyss... 14 4.1 A Fronter Analyss to Determne Effcency... 15 4.2 Econometrc Model of Output Energy... 15 4.3 Econometrc Model of Input Energy... 18 4.4 Prce and Income Elastcty... 18 5. Data... 18 5.1 Descrpton of the Database... 18 5.2 Dsaggregaton of the Utlty Bll for Natural-gas-heated Houses... 20 5.3 Dsaggregaton of the Utlty Bll for Electrcty-heated Houses... 21 5.4 Determnaton of the Income Groups... 22 5.5 Analyss of the Database n Lght of Income Groups... 22 6 Results... 24 6.1 Results from the Fronter Analyss: Effcency of Furnaces and Water Heaters... 24 6.2 Estmaton of Energy Servces Demand... 25 6.2.1 Applances and Lghtng... 26 6.2.2 Water Heatng... 26 6.2.3 Space Heatng... 27 6.3 Results for Energy Servces Demand... 29 6.4 Results on Input Energy and Comparson wth Other Studes... 32 7 Polcy Implcatons... 35 7.1 Subsdes... 35 7.2 Targeted Subsdes: More Effcent Furnaces... 36 7.3 Targeted Subsdes: Utlty Prce... 36 7.4 Polcy Relevance to Inda... 36 8 Concluson... 37 8.1 Future Development n Econometrc Energy Demand Modellng... 38 9 Acknowledgements... 39 References... 40
Abstract Conventonal resdental energy demand models are concerned wth estmatng fuel use (for eample, gas, electrcty and ol) demand. In ths paper, we propose a resdental energy demand model that s based on the demand for energy servces, namely space heatng load, water heatng load, and applance and lghtng load. The model s developed usng Canadan household data. We estmate the demand for energy servces usng a twostep estmaton procedure. In the frst step we compute the effcences for furnaces and water heaters for each of the 440 households usng a determnstc fronter analyss. In the second step, the estmated furnace and water heater effcences are used to determne the demand for energy servces. Prce elastctes are epressed as a lnear functon of ncome to hghlght ncome-related behavour. Despte lmtatons wth the database, the results show a clear varaton n behavoural responses to changes n prce and n ncome across the ncome groups and energy servces. Low-ncome households are more responsve to prce and ncome changes than hgher-ncome households, whle all households are more responsve to prce changes than ncome changes. Space heatng load presents the strongest dstrbutonal effect wth a factor two between prce elastctes of the low- and hgh-ncome groups. Results also confrmed the rebound effect wth respect to the effcency of furnaces and water heaters. Ths effect s qute notceable wth furnace effcency. We used the rebound effect to desgn a polcy that could help lower-ncome groups cope wth ncreases n energy prces. January 24, 2003 1
1. Introducton Conventonal resdental energy demand models are concerned wth estmatng utlty (fuel) demand. However, fuel s not consumed for tself but for the servces t provdes. It s energy servces that people demand, not fuels. For eample, t s the desre to keep warm that people value and not the desre for a partcular fuel or energy. In ths paper, we propose a resdental energy demand model that s based on the demand for energy servces, namely space heatng load, water heatng load, and applance and lghtng load. We apply t to Canadan household data. Prce elastcty s a useful parameter that provdes nformaton on consumer behavour wth respect to changes n the prce of commodtes. However, unlke a majorty of models that looks at the prce elastcty of fuels, n ths paper we focus on the prce elastcty wth respect to energy servces and compare t wth the prce elastcty of utltes. Ths work s part of a broader research agenda. In 2001, the Internatonal Insttute for Sustanable Development, together wth The Energy Resources Insttute (TERI) n Inda, ntated research on the mpacts of clmate-change-drven energy polces on lowerncome groups. In ths phase of the project, the methodology for developng a resdental energy demand model was tested usng Canadan data. It s envsaged that the learnng acqured n ths eercse would prove useful n replcatng the methodology for Inda where data may not be so readly avalable and modfcatons may need to be made. Generally, lower-ncome Canadan households allocate a greater share of ther budget to energy epenses than hgher-ncome groups (see Table 1). It can therefore be antcpated that ncreases n energy prces caused by clmate-change-drven energy polces wll be borne dsproportonately by lower-ncome groups. However, the magntude of these mpacts on these groups has yet to be determned wthn an energy demand modellng framework. Table 1: Canadan Income Groups and ther Energy Ependtures n 2000. Electrcty Fuel Total Rato of Total Energy Income Group Ependture Ependture Ependture Ependtures to Total Range s s s Ependtures Low < $30,180 900 851 21,564 8% $30,180-964 47,166 Medum 1,089 4% $61,849 Hgh > $61,849 1,061 1,301 95,753 2% Source: Compled from Statstcs Canada (2001, 2002). In order to assess these mpacts, we modfed the MARKAL (MARKet ALlocaton) model (Fshbone and Ablock 1981) an energy plannng tool used to evaluate GHG emssons. MARKAL was developed n the late 1970s by member countres of the OECD under the gudance of the Internatonal Energy Agency (IEA) (Berger et al. 1992; Condevau-Lanloy and Fragnère 2000; Fshbone and Ablock 1981). It s now n use n 2 January 24, 2003
more than 35 countres (Condevau-Lanloy and Fragnère 2000). MARKAL s a demand-drven, mult-perod, partal equlbrum model. It s a dynamc optmzaton model that uses lnear programmng to fnd the optmal m of fuel and technologes to meet demand for energy servces, at least cost, over a pre-determned tme horzon, usually between 20 to 50 years. Some MARKAL models, lke the Canadan MARKAL- ED model, have demand endogenously determned through prce-elastc demand functons (Loulou and Lavgne 1995). The Canadan MARKAL-ED model requres prce elastctes on energy servces to determne the change n demand when there s a constrant on the system, such as a carbon constrant. Up to now, prce elastctes of resdental energy servces n Canada have been based on prce-elastctes of resdental utlty consumpton determned for Quebec and adapted to the MARKAL model usng epert judgment (Kanuda and Loulou 1999). In ths paper, we go one step further by estmatng prce elastctes of resdental energy servces for the three ncome groups usng a robust econometrc approach. 2. Input and Output Energy Resdental energy end-uses can be decomposed nto space heatng, water heatng, applance usage and lghtng. Demand for energy servces s also referred to as the load, and for the resdental sector, we have the space heatng load, the water heatng load, the applance load and the lghtng load. The load s gven n Joules (J). However, households purchase utltes such as klowatt-hours (kwh) of electrcty, ltres (l) of ol, cubc metres (m 3 ) of natural gas, etc. These utltes are typcally transformed nto energy servces (e.g., space heatng load, water heatng load, applance load and lghtng load) through converson technologes lke furnaces, space heaters and heat pumps (see Fgure 1). Converson technology INPUT ENERGY Utlty bll CONSUMPTION Effcency OUTPUT ENERGY Space heatng load Water heatng load Applance load Lghtng load ENERGY SERVICES NEEDS Fgure 1: Relatonshp between nput and output energy. January 24, 2003 3
The appellatons nput energy and output energy are gven wth respect to the converson technology. Input energy refers to the energy content of the utlty consumpton, whle output energy refers to the load. The relatonshp between nput energy and output energy, llustrated n Fgure 1, can be wrtten as follows: E OUT, j E IN, j = (1) λ k, j Where: E IN, j : s the energy content of the utlty consumpton j for provdng the energy servce or nput energy (n Joules); E, : s the energy servce or output energy (n Joules); and OUT j λ k, j : s the effcency of technology k for convertng the nput energy nto output energy for utlty j. Each converson technology s characterzed by ts effcency n convertng nput energy nto output energy. Typcal effcency values are less than one for space heaters usng natural gas and water heaters usng gas or electrcty. 2.1 Energy Content of the Utlty Consumpton The energy content of the utlty consumpton depends on the fuel type. Standard values for convertng the utlty consumpton nto ts energy content (or nput energy) are gven n Table 2. The energy content of utlty consumpton can therefore be epressed as follows: E j IN, j =C U j (2) Where: E IN, j : s the nput energy or energy content of the utlty consumpton j for provdng energy servce (J); U j : s the utlty consumpton j assocated wth energy servce (kwh, ltres, cubc metres, etc.); and C j : s the converson factor to establsh the energy content of utlty consumpton j gven n Table 2. Table 2: Energy Content of Dfferent Types of Fuels. Type of Fuel Basc Unt of Input Energy Energy Content Electrcty 1 kwh 3.6 MJ Natural gas 1 Cubc metre (m 3 ) 37.259 MJ Ol 1 Ltre (l) 38.524 MJ Propane 1 Ltre (l) 25.6 MJ Wood 1 tonne (t) 13956 MJ Source: NRCAN 1995. 4 January 24, 2003
2.2 Input and Output Prces The energy epenses of a sngle household for a gven energy servce reman the same whether you consder output energy or nput energy. We have: P IN, j EIN, j = POUT, j E (3) OUT, j Where: P IN, j OUT j : s the prce of nput energy for fuel consumpton j;and P, : s the prce of output energy for fuel consumpton j. The prce of output energy s not a real prce but s what people actually pay takng nto consderaton effcency of the converson technology. Substtutng the output energy epressed n Equaton (1) nto (3), the epresson of the output energy prce becomes: λ E P E (4) P OUT, j k, j IN, j = IN, j IN, j P OUT, j P = (5) λ IN, j k, j The prce of output energy s greater than the prce of nput energy by the same rato as energy lost n the converson process from nput to output energy. 3. A Bref Survey of Econometrc Models of Resdental Energy Demand We dd a lterature revew on two fronts. The frst nvolved a revew of studes lookng at energy servces, end uses and ncome groups. The second survey focused on the key varables used by the present cadre of models n the desgn of resdental energy demand models. 3.1 Energy Servces, End Uses and Income Groups Econometrc models of energy consumpton, as opposed to engneerng models, permt the determnaton of prce and ncome elastctes. Studes have nvestgated demand for output energy, the energy demand by end uses or the energy demand by dfferent household groups. None of these studes nvestgated all of these aspects at once as we dd. Our methodology models demand for output energy of end uses accordng to household ncome. We dscrmnate between energy servces and end uses. End uses refers to unbundled nput energy nto ts components (e.g., space heatng, water heatng, applances and lghtng) whle energy servces are the output energy of end uses (see Fgure 1 and Equaton 1). Ths secton revews the lterature on demand for energy servces, end uses and ncome groups. The revew s lmted to energy demand models developed usng mcrodata,.e., data at the household level. The revew shows that households respond dfferently to prce ncreases accordng to the type of end uses, and that ncome groups do show a January 24, 2003 5
dfferent response to prce ncreases n ther utlty consumpton. We therefore antcpate that households wll respond dfferently across ncome groups and energy servces (or end uses). 3.1.1 Demand for Energy Servces Our lterature revew hghlghted only one study, based on household data, that dealt wth demand for energy servces. Schwarz and Taylor (1995) nvestgated the demand for comfort, epressed as the ndoor temperature, and evaluated the heatng energy load usng an engneerng epresson that s a functon of the dfference between ndoor and outdoor temperatures. Ther objectve was to relate the thermostat response to changes n nsulaton (Schwarz and Taylor 1995: 45). However, ther approach does not relate energy need to energy consumpton as defned by Equaton (1). At the sectoral (macro) level, McRae (1979) nvestgated the demand for output energy usng a two-stage analyss of demand for fuels that determnes the contrbuton of each fuel to the total demand for energy. To do ths, he frst converted physcal unts of fuel demand nto energy content (BTU) usng a standard converson factor. Then, he converted the nput energy (fuel demand epressed n BTU) nto output energy (BTU) usng publshed standard factors that capture the relatve effcency of converson from nput to output energy of dfferent fuels and converson technologes n the same end-use sector (McRae 1979: 204). However, the approach used by McRae s not satsfactory because each household s furnace and water heater typcally has a dfferent effcency. Varatons n effcency are eplaned not only by the technology used defned by the type of gnton devce used and fresh ar ntake but also by the frequency of servcng (Douthtt 1986; 1989). 3.1.2 End Uses There are more studes on energy demand by end uses (nput energy) than on demand for energy servces (output energy). The studes we revewed on energy servces focused on the demand for space heatng. Not surprsngly, these studes were performed usng data from northern countres where the greatest energy consumpton n the resdental sector s usually attrbutable to space heatng. Douthtt (1986) determned the combned demand for natural gas for resdental space heatng and water heatng n Canada. In that study, the fuel was not used for other usage ecept for space heatng and water heatng and therefore no unbundlng was needed (When a specfc fuel s only used for a gven end use, the unbundlng process s then smplfed. Otherwse, the process s a non-trval task and s prone to nduce errors). Douthtt (1989) determned the demand for space heatng of Canadan households. In that case, the unbundlng to determne specfcally the demand attrbutable to space heatng was not performed by the author but by the Department of Energy, Mnes and Resources (EMR) of Canada, and the unbundlng technque s not dsclosed. Haas and Bermayr (1997) developed an energy model for space heatng, hot water and electrc applances of Austran households. The authors present how they unbundled space heatng consumpton from water heatng consumpton when the same fuel s used n both. Ther technque s based on a smple lnear regresson of the monthly energy consumpton of 6 January 24, 2003
that fuel. Frst, they assume that monthly water heatng consumpton s constant and s therefore assocated to the constant parameter of the regresson. Then, they assume that the monthly space heatng consumpton s proportonal to heatng degree days of that month. In another study, Leth-Pethersen and Togeby (2001) nvestgated space heatng for apartment blocks n Denmark, heated wth ol or dstrct heatng. In ths study, no unbundlng was carred out. Klen (1988) nvestgated demand for space heatng by takng the dfference n utlty consumpton durng the heatng months and the months when no heatng s needed. Haas and Bermayr (1997) are the only authors that nvestgated energy demand of a range of end-uses wthn the same study, permttng a comparson of prce and ncome elastctes between end uses. Ther results show that households respond dfferently for dfferent end uses. 3.1.3 Income Groups A few studes have nvestgated prce and ncome elastctes for dfferent household groups and we present ther man results here. These studes show that dfferent ncome groups respond dfferently to prce ncreases. Lafrance and Perron (1994) report nterestng results by ncome groups but dd not publsh them, whle Donnelly and Desendorf (1985) ntroduced an aggregate energy demand wth a prce elastcty that vares wth the ncome, but dd not use t. Poyer and Wllams (1993) developed a model of total energy consumpton and reported long-term prce elastctes of -1.13 (Blacks); -0.46 (Latnos); and -2.45 (Majorty), and long-term ncome elastctes of 0.12 (Blacks); 0.23 (Latnos); and 0.16 (Majorty). Although Poyer et al. (1997) reported average energy and electrcty ependtures for poor and non-poor households wthn each household type, Mnorty and Majorty, they dd not apply ths dscrmnaton to ther results. The model developed by Poyer et al. (1997) does not provde prce and ncome elastctes but allows the determnaton of mpacts of prce changes on economc welfare of households. Baker et al. (1989) found that, on average, the hgher-ncome households are less responsve than low-ncome groups to changes n energy prces, whle ther estmaton of ncome elastctes based on mcrodata dd not show postve values for each sngle household (see Table 3). However, ncome elastctes tend to ncrease, on average, toward the lower-ncome households. January 24, 2003 7
Table 3: Prce and Income Elastctes: Source Baker et al. (1999). Elastcty All Households Income Level Low Hgh Gas-heated houses Income 0.115 0.139 0.012 Own prce 0.20-0.444-0.208 Electrcty-heated houses Income 0.131 0.177-0.172 Own prce -0.758-0.759-0.684 Contrary to ntuton, Nesbakken (1999), usng two sets of pooled data for 1993 1995, found that the Norwegan hgher-ncome group s more responsve to prce and ncome changes (see Table 4). Nesbakken (1999) advances the possblty that the lower-ncome group s already at a low level of energy consumpton and therefore cannot adjust ts consumpton to a prce ncrease wthout dscomfort.. Table 4: Prce and Income Elastctes: Source Nesbakken (1999) Elastcty All Households Income Level Below Average Above Average Short-run ncome 0.01 0.01 0.01 Long-run ncome 0.20 0.18 0.22 Short-run energy prce -0.50-0.33-0.66 3.2 Desgnng a Resdental Energy Demand Model The objectve of the eercse or study and the avalable data are the two key factors that determne the choce and/or desgn of the resdental energy demand model. Some authors argue that there s no consensus on the best way to epress energy demand (Poyer and Wllams 1993). We argue here that t s the objectves sought, coupled wth the data avalable, that shape the energy demand model. For eample, n our case, we want to nvestgate the mpact clmate change mtgaton polces wll have on the demand for energy servces across ncome groups. We therefore need to have a model that captures the demand for energy servces and not the demand for fuels. There are a number of key questons that must be answered before an energy demand model s formulated and estmated. The modeller must choose the structural form of the demand functon jont-decson models, reduced-form models, condtonal-demand analyss or household producton functon and ts functonal form should t be lnear, sem-log or a double log. The net ssue to resolve s the unts of analyss for the energy demand model physcal vs. thermal vs. ependture. Prces also play a key role n determnng consumer behavour and t s mportant to make sure that they choose the rght fuel prce, whether t s the margnal or average prce, as well as the prce of the substtute. And last but not least, the epresson of elastctes, ether varable or a constant. Sectons 3.2.1 to 3.2.6 look at each of these key ssues, and also nvestgate the ssue of the effcency of the converson technology. 8 January 24, 2003
3.2.1 Structural Form We choose to consder energy models accordng to how energy s vewed at the household level. Demand for energy can ether be consdered as a fnal good or as an nput to the household producton functon. In the latter case, energy can be substtuted wth other household goods, whle n the former t s not. It s mportant to note that all models recognze that energy demand s a derved demand household purchase utltes for the servces they provde, not for the utltes by themselves. Resdental energy demand s determned by addng up the consumpton of each equpment (space heaters, water heaters, applances and lghtng), whch n turn s gven by the (nput) captal stock of equpment multpled by ts utlzaton rate. For a gven household, the resdental energy demand can be epressed as: = u A (6) E IN, j k, j k, j k Where: E, : s the energy consumpton of fuel j (nput energy); IN j u, : s the utlzaton rate of equpment k for fuel j; and k j A, : s the captal stock of equpment k that uses fuel j. k j The double nde of the utlzaton rate of the equpment allows for dual-fuel equpments such as electrcty-ol furnaces. Dependng on how Equaton (6) s solved, the energy demand model can be jontdecson models or dscrete-contnuous models, reduced-form models or condtonaldemand analyss. Equaton (6) can also be solved wthn the framework of the household producton functon. The jont-decson models or dscrete-contnuous models closely reflect energy demand as a jont decson of the choce of equpment (dscrete decson) and the utlzaton rate of the equpment (contnuous decson). In that case, the energy demand model s a twolevel model (Boh and Zmmerman, 1984): Aj = g( Pj, Ps, Pk, Y, X ) (7) u = f ( P, Y, Z) Where j A : j s the demand for equpment that uses fuel j; u : j s the utlzaton rate of equpment for fuel j; P j, P s : are the prce of the fuel j, and the prce of alternatve fuel s, respectvely; P : k s the prce of equpment k; Y : s the household ncome; and X, Z : are other soco-economc and structural varables (e.g., equpment and dwellng characterstcs). j January 24, 2003 9
Ths approach was used by Nesbakken (1999); Halvorsen and Larsen (2001); Dubn and McFadden (1984); Bernard et al. (1996); and Hausman (1979). However, ths approach s data ntensve and can be computer ntensve as well. Reduced-form models are also named condtonal-demand models because energy demand s condtonal on the stock of applances and/or technologes. Reduced-form models collapse the Equaton system (7) that descrbes the equpment stock and the utlzaton rate nto a sngle equaton (Boh and Zmmerman, 1984): E IN, j= h( Pj, Ps, Y, X, Z, Aj) (8) Prce of equpment s a determnant of the captal stock of equpment but not drectly of energy consumpton, and s therefore not ncluded n Equaton (8). Statc models assume the stock of applances s fed. Dynamc models are bult usng tme seres, but we dd not revew them specfcally. Ths approach has been wdely used over the years and for a varety of fuels (Branch 1993; Wlls 1981; Green et al. 1986; Mcklewrght 1989; Douthtt 1986 and 1989; Poyer et al. 1993 and 1997; Lee and Sngh 1994; Haas and Bermayr 1997; and Leth-Peterson and Togeby 2001). Condtonal analyss unbundles the energy demand nto unt energy consumpton (UEC) of a gven applance or end use. It s based on condtonal-demand models but condtonal analyss does not provde prce elastctes. It was ntroduced by Part and Part (1980) and used by Febg et al. (1991), Lafrance and Perron (1994) and Tedemann (1997). Energy demand can also be modelled wthn the framework of household producton functon. To enable the substtuton of energy wth non-energy goods, energy demand s epressed by an equaton, such as a reduced-form model, wthn a system of equatons that descrbes the household producton functon. Such models were used by Flag 1990, Klen (1988) and Qugley (1984). 3.2.2 Energy Unts When performng energy demand analyss smultaneously on dfferent fuels, the queston of the energy unts arses. Energy can ether be epressed n terms of physcal unts (klowatt-hours, ltres, etc.), monetary unts (ependture) or thermal unts (Joules or thermal equvalent unts such as ol equvalent). Thermal unts are based on the calorfc factor of the fuel,.e., the amount of energy released f t were burned wth perfect effcency (Turvey and Nobay 1965). Besdes electrcty, there s no sngle value for the energy content of carbon-based fuels. Furthermore, when aggregatng dfferent fuels usng tme seres data, Bernard et al. (1987) show that the total energy consumpton epressed n thermal unts can decrease over tme when, n realty, total energy consumpton does not (when epressed n other unts). Turvey and Nobay (1965) had shown a smlar effect. Turvey and Nobay (1965) argued that monetary unts, epressed through ependtures, should be used when aggregatng fuel consumpton of dfferent types to compare market shares. As they conclude: An economc phenomenon deserves an economc approach (Turvey and Nobay 1965: 791). 10 January 24, 2003
Ths dffculty dsappears when analyzng a sngle fuel. Many econometrc analyss of energy demand have been carred out n physcal unts (Bernard et al. 1996, Branch 1993, Douthtt 1986, Halvorsen and Larsen 2001, Wlls 1981). When aggregatng dfferent fuels, some authors used kwh equvalents (Dubn and McFadden 1984, Leth-Petersen and Togeby 2001), energy content (Douthtt 1986, Douthtt 1989, Poyer and Wllams 1993, Poyer et al. 1997), or used monetary unts (Mcklewrght 1989, Qugley 1984). Green constructed energy consumpton by dvdng ependtures by prce (Green et al. 1986). Once agan, the selecton of unts to carry an energy demand analyss s condtonal on the avalablty of the data and the objectve of the study. 3.2.3 Effcency of Converson Technologes Although effcency s one of the key factors that determne utlty consumpton (Douthtt 1986, 1989) as shown n Equaton (1), t s seldom taken nto consderaton n an energy demand model. Models n whch effcences of the converson technology were consdered are all space heatng demand models, although water heatng s also condtoned by the effcency of the water heater. Douthtt (1986, 1989) determned the demand for space heatng of Canadan households. In 1986, he used a proy for the furnace effcency. If the furnace had been replaced or servced n the current year, then the value of the dummy varable would be one. Otherwse, t would be zero. Haas and Bermayr (1997) developed an energy model for energy end uses of Austran households that ncluded the effcency of the furnace. Because the same converson technology not only provdes space heatng but also hot water, Haas and Bermayr ncluded the effcency value of the space heatng equpment n ther energy demand model for hot water. Leth-Pethersen and Togeby (2001) nvestgated space heatng n apartment blocks of Denmark whose energy model s condtonal on the energy carrer type (ol or dstrct heatng). The coeffcent of the energy carrer type parameter s epressed as the sum of an average value (over all apartment buldngs) and an unobserved random component that allows for specfc effcency levels of heatng systems. The effcency of converson technologes can lead to a rebound effect that was frst dentfed by Khazzoom (1980). The rebound effect can be descrbed as an ncrease n demand for energy servces that s caused by effcency mprovement, thus reducng conservaton gans (Khazzoom 1980; Haas and Bermayr 1997; and Schwarz and Taylor 1995). Ths effect s also called the feedback effect or takeback effect. A typcal eample to llustrate the rebound effect s car travel demand that s usually epressed n passenger-mle. If a car s effcency doubles, one would thnk that half as much fuel s necessary to meet the car travel demand, as Equaton (1) shows. A parallel (and also vald) approach s to consder that you can now travel twce as far for the same cost as before whch s equvalent to sayng that the prce of gas has halved (Khazzoom 1987). If the prce elastcty n car travel s non-zero, meanng that the car owner responds to a prce change, then hs demand n car travel wll ncrease. An ncreased effcency can therefore ncrease the demand n output energy! The same logc can be appled to space heatng and hot water. If the effcency of the furnace ncreases, the household may January 24, 2003 11
ncrease ts average ndoor temperature. The household can now ncrease ts ndoor temperature wthout ncreasng ts utlty bll when comparng wth the heatng costs before changng the furnace. Schwarz and Taylor (1995) showed that mproved nsulaton leads to hgher ndoor temperature settng across varous clmates and house szes. Berndt and Watkns (1986) overlooked the rebound effect n ther study. They made a plea for prce and ncome elastctes to be determned on fuel consumpton (nput energy) rather than on the energy load or requrement (output energy). Ther man argument s that econometrc analyss of nput energy captures the effect of the converson technology (and hence ts effcency), but not output energy. We show below that output energy can also capture the effcency of the converson technology. Let us start wth the epresson of output energy wrtten as follows: E OUT, k, j = uk, jwk, j (9) whch s derved from comparng Equaton (6) to (1). Accordng to Berndt and Watkns (1986), the only way to capture the mpact of the converson technology effcency s to model energy demand usng nput energy. Clearly, ths comes from the fact that the utlzaton rate, as epressed by Equaton (7), does not depend on effcency. We argue otherwse. From the descrpton of Khazzoom (1980) and results from Schwarz and Taylor (1995) already dscussed above, one would rather epress the utlzaton rate as: uk, j = g( Pj, Y, Z, λk, j ) (10) Ths equaton epresses the level of usage of a technology and how the effcency of the converson technology can nfluence t. In partcular, the above epresson permts the rebound effect. Smlarly, one could also wrte: uk, j = g( POUT, k, j, Y, Z) (11) where the utlzaton rate depends on the output prce. In ths approach, the effcency of the converson technology s taken nto account n the defnton of the output prce. 3.2.4 Average vs. Margnal Utlty Prces Authors have nvarably used average or margnal utlty prces n ther energy demand models. Supporters of margnal and average prces have developed ther own set of arguments. Standard economc theory s developed on margnal prcng and, as such, most econometrc models of energy demand are based on margnal utlty prcng. Margnal utlty prces were used by Douthtt (1986, 1989), Hausman (1979) and Wlls (1981). A small number of authors dd look at margnal prcng under a mult-block tarff. Under an ncreasng mult-block tarff, average and margnal prces ncrease wth ncreasng utlty consumpton. Taylor (1975) had recommended usage of margnal prces n conjuncton wth average prces n an energy demand model. Nordn (1976) modfed Taylor s approach and showed that margnal prces should be used n conjuncton wth a lump sum payment before purchasng all utlty unts at the margnal prce. Later, Barnes (1982) operatonalzed Nordn s approach. The procedure was appled by Douthtt (1986, 1989). 12 January 24, 2003
However, some authors argue that consumers facng utlty blls react not to the margnal prce of utltes but to ther bll as a whole, and thus to the average prce of the bll (Branch 1993 and Green et al. 1986). Average utlty prces were used by Branch (1993), Green et al. (1986) and Nesbakken (1999). For convenent reasons, average prces substtute for margnal prces (Garca-Cerutt 2000 and Douthtt 1989 for ol), whle others used consumer or retaled prce nde (Baker et al. 1989 and Mcklewrght 1989). Green et al. (1986) used lagged average prces to avod smultanety and dentfcaton problems. In that case, he had already used current average prces to determne the quantty of electrcty and natural gas demanded by dvdng utlty ependtures by average utlty prce. 3.2.5 Varable Prce Elastctes Most resdental energy demand models are based on constant prce elastctes. However, Betancourt (1981) ntroduced varable prce elastctes n resdental energy demand modellng. He nvestgated four models of varable elastctes, one of whch was dependent on prevous electrcty prces, heatng degree-days and coolng degree-days. Betancourt s calculaton of varable prce elastcty was later corrected by Donnelly and Desendorf (1985) who demonstrated that prces need to be normalzed when usng a prce elastcty functon of lagged prce. Although Donnelly and Desendorf (1985) ntroduced prce elastctes as a functon of ncome, they have not tested t n ther emprcal eample on Australan data. Snce then, varable elastctes have been used n resdental energy demand by varous authors. Mcklewrght (1989) allowed prce and ncome elastctes to depend on whether central heatng s present and how t s powered, whle the effect of ncome s n addton allowed to vary wth housng tenure (mortgage pad, free rent, tenant, etc.). Wlls (1981) showed that prce elastcty (electrcty) ncreases wth the sze of owned applance stock. Douthtt (1989) determned that consumers facng hgher than average fuel prces present a greater responsveness to prce changes than consumers facng lower than average fuel prces. Poyer and Wllams (1993) use the prce elastcty specfcaton as n Betancourt (1981), and showed that prce elastctes vary wth coolng and heatng degree-days. Furthermore, they also showed that ncome elastcty s a functon of household sze. 3.2.6 Fuel Substtuton Some energy models nclude the prce of one or many substtute fuel(s). It was not possble to do so n our model because our database s not homogeneous wth respect to the avalablty of gas. There are some regons n Canada, especally n the eastern provnces, where natural gas s not avalable. Ths s usually crcumvented by specfyng an energy model for each case, one electrcty demand model for regons where gas s avalable and one where gas s not avalable (Douthtt 1989). January 24, 2003 13
4. Demand for Energy Servces Usng Fronter Analyss The challenge we faced was to develop a methodology that could estmate prce elastctes across ncome groups on output energy, but wth only data on nput energy avalable. Surveys track nput energy, not output energy. Furthermore, the crtcal data for movng from nput energy to output energy s through the converson technologes and ther respectve effcences. However, these data are not relable for two reasons. Frst, effcency was surveyed for the furnace only, and second, each household reported what they thought the effcency of ther furnace was by selectng an effcency range. To crcumvent unrelable effcency values of furnaces and unobserved values for water heaters, we developed a methodology based on a two-step process. The frst step determnes the effcency of gas furnaces and electrc and gas hot water heaters usng the determnstc fronter analyss descrbed below. The second step then goes on to use a standard econometrc regresson eercse but usng the effcency values from the frst step. The methodology we develop here to model energy demand servces has the followng key features: 1) It models demand for energy servces space heatng, hot water, and a combnaton of applances and lghtng usng a double log statc reduced form. 2) It uses thermal unts (Joules) because our database contans data on energy consumpton, not on energy ependtures. Because we are not usng tme seres data but cross-sectonal data, the dffculty noted n the prevous secton does not apply to our work. 3) It eplctly consders effcency of furnaces and water heaters. 4) It determnes these effcences usng a determnstc fronter analyss. In our energy model, the effcency of the converson technology s ncorporated n the epresson of the output energy by multplyng nput energy values by the effcency of the converson technology, because output energy values are unobserved. By dong so, our approach s consstent consderng the feedback effect of effcency on demand for energy servces. 5) It used average provncal utlty prces because we cannot assocate a specfc prcng schedule to each household, as the eact locaton of each household was not publc nformaton. In some Canadan provnces, prcng schedules can vary from one regon to another or from one localty to another. 6) It does not use prces of substtute energy sources because, n some provnces, the two stuatons co-est,.e., gas s avalable n some regons wthn a gven provnce whle t s not n others, and our database does not dscrmnate at the regonal level. 7) It epresses prce elastcty as a lnear functon of ncome. We wll determne f dfferent ncome groups show dfferent responses to prce changes. 14 January 24, 2003
4.1 A Fronter Analyss to Determne Effcency The effcency s gven by the followng equaton, whch follows from Equaton (1): ln λ = ln E OUT, ln EIN, (12) The output energy s smaller than or, at the lmt, equal to the nput energy. Therefore, ln λ k 0. The effcency s determned by mnmzng the dfference between the output energy and the nput energy for each household : 2 Mn ln E ln E λ, a0, a1, Λ subject to: defnng: ( OUT, IN, ) ln E OUT, ln E IN, E OUT, > 0 (13) λ > 0 ln λ = ln E OUT, ln EIN, where output energy s gven by Equatons (14) and (15) and the nput energy s data. A non-lnear optmzaton program (GAMS) s used to solve the problem n whch the coeffcents of the output energy and the effcency values are smultaneously estmated for a gven energy servce. We do not solve for the effcency for applances and lghtng servces and electrc space heaters as these are assumed to be 100 per cent. Instead we only solve for effcency of water heaters (electrcty and natural gas) and natural gas space heaters. The system s frst solved for hot water. Output energy s gven by Equaton (15), nput energy s gven by the bllng data (dsaggregated and converted nto Joules) and the prce of output energy s substtuted wth Equaton (5). Then the system s solved for space heatng servces substtutng Equaton (14) for output energy and agan Equaton (5) for the prce of output energy, and usng the correspondng bllng data for nput energy. In ths way, we estmated the effcency value for each household n our dataset that s needed for the second step whereby, we estmate the actual energy servce demand equaton. 4.2 Econometrc Model of Output Energy Our econometrc model of output energy s based on a reduced-form model. The functonal form we chose s the double log because t allows drect readng of prce. Income elastctes have a more comple epresson because prce elastctes also vary accordng to ncome. For smplcty reasons, and to be consstent wth the dsaggregaton of the bllng data by energy servces, the energy servces related to applances and lghtng have been combned nto a sngle energy servce. The equatons below show the varables that are selected n the fnal model where only the statstcally sgnfcant parameters are kept. We ddn t nclude lagged prces because January 24, 2003 15
the smple correlaton coeffcent between prce and ts lag s found to be 0.997 (that s lkely to cause a severe multcollnearty problem). ln E ln E ln E SH OUT, HW OUT, AL OUT, where: : = a SH 0 SH b1 + 1+ ep( b + c + d + d + e + = a SH 1 SH 1 f SH 4 SH + SH 1 HW 0 + c + d + e WH 1 HW 1 HW 1 f HW SH SH ( a + a lny ) 1 ln A ln N Do SH ln E SH 3 ln HDD ln λ + d HW OUT, HW b1 + 1+ ep( b + = a AL 0 + c I + d + e AL 1 + + 3 Y ) + c SH 2 + d + SH 5 SH 2 H f B SH 2 lnt ln N ln P + d SH 3 W ln E HW HW ( a + a lny ) 1 lnt ln A lnc I lnλ AL Fz 1 A Tk HW HW 3 + d + e 3 + b Y ) HW 2 HW 2 N A HW 2 ln N AL AL ( a + a lny ) AL b1 + 1+ ep( b HB 2 R 1 + c AL 3 AL 4 + d + e N AL 2 I 3 DW N AL Ck 2 FF + b Y ) + e AL 2 + c AL 3 S AL 6 + d OUT, ln N + d AL OUT, ln P AL 3 + d ln P SH 6 HW 3 S OUT, ln HHS N OUT, ln HHS Dr N ln N NFF L N N + e Sk Dw I + d AL Ac 4 HW 4 + e N Wa I AL FuF 5 ndees the energy servce. SH: space heatng, HW: hot water, AL: applances and lghtng; E OUT, : s the output energy of energy servce for household n Joules; a j,, e j : are the coeffcents j for the energy servce ; P OUT, : s the prce of output energy that provdes energy servce n the current year, t; Y : s the ncome of household ; (14) (15) (16) 16 January 24, 2003
HHS : s the household sze of household ; HDD : s the average heatng degree-days of the provnce where household s located; T : s the average ndoor temperature for household ; Gd T : s the average ground temperature of the provnce where household s located; A : s the floor area of house ; B : s the basement area of house ; B H : s the heated basement area of house ; HB I : s the heated basement nde of house (1=yes; 0=no); S N : s the number of storeys n house ; Do N : s the number of doors n house ; W N : s the number of wndows n house ; Sk N : s the number of sky wndows n house ; Dw N : s the number of dshwasher loads for household ; Wa N : s the number of washer loads for household ; Dr N : s the number of dryer loads for household ; A N : s the number of aerators n house ; Fz I : s the freezer nde for house (1=yes; 0=no); FF N : s the number of frost-free refrgerators n house (1=yes; 0=no); NFF N : s the number of non-frost-free refrgerators n house (1=yes; 0=no); R A : s the age of the range n house ; L N : s the number of lght bulbs n house ; T I : s the hot water tank nsulaton nde for house (1=yes; 0=no); Ck I : s the cooktop nde for house (1=yes; 0=no); Ac I : s the ar condtonng nde for house (1=yes; 0=no); FuF I : s the furnace fan nde for house (1=yes; 0=no); and λ : s the effcency of the furnace (=SH) or of the water heater (=WH). The ncluson of water heatng, applances and lghtng nto the epresson for space heatng translates the heat ganed through loss mechansms from water heatng, applances and lghtng. As a consequence, the epressons of output energy for hot January 24, 2003 17
water, applances and lghtng must be solved before the output energy for space heatng can be estmated. The prce of output energy can be epressed n terms of nput energy and s gven by Equaton (5). We obtan a system of equatons that can be solved one at a tme, where the equaton for space heatng s solved last. 4.3 Econometrc Model of Input Energy The analytcal epressons for nput and output energy are the same, ecept for the prce of energy. The epressons of nput energy (space heatng, water heatng, and applances and lghtng) are the same as gven by Equatons (14) to (16) where nput energy s used nstead of the output energy. However, the hot water consumpton and the applance and lghtng consumpton do not contrbute to nput energy, only output energy, and the correspondng parameter coeffcents were set to zero. 4.4 Prce and Income Elastcty Prce elastctes are computed from the formula ln E / ln P OUT Out for = space heatng (SH), hot water (HW), and applance and lghtng (AL) n Equatons (14) to (16). Prce elastctes are thus smply the coeffcent of the prce parameter. Prce elastcty s gven by: ε P, = a1 + a3 lny (17) where ε s the prce elastcty of energy servce and for household. P, The epresson of prce elastcty s a lnear functon of ncome. Prce elastcty s determned for each household, accordng to ts level of ncome and, as a result, all households wth the same ncome level wll share the same prce elastcty. Smlarly, ncome elastctes are computed from the formula ln E OUT / lny for = space heatng (SH), hot water (HW), and applance and lghtng (AL) n Equatons (14) to (16). 5. Data 5.1 Descrpton of the Database The Canadan Resdental Energy End-use Data and Analyss Centre (CREEDAC), based at Dalhouse Unversty at the tme of ths study, provded the database on behalf of Statstcs Canada. Ths database s a combnaton of four sources of data: the 1993 Survey of Household Energy Use (SHEU 1993); the Energy Statstcs Handbook publshed by Statstcs Canada; the Electrc Power Statstcs; and the Canadan Economc Observer (CREEDAC 1999). The SHEU 1993, carred out by Statstcs Canada, contans demographc and dwellng data on 10,982 Canadan households (CREEDAC 1999). Access to actual energy meterng was granted through respondent s permsson. The other three data sources, the 18 January 24, 2003
Energy Statstcs Handbook; Electrc Power Statstcs; and the Canadan Economc Observer, were used to comple provncal (average) energy prces for electrcty, natural gas and ol n 1993 and 1992. Long-term heatng degree-days were suppled by CREEDAC. The database we receved s a subset of the SHEU 1993. It only contaned data on lowrse sngle famly dwellngs, ncludng sngle detached and attached dwellngs, that accepted to dsclose ther annual energy bllng over the year 1993 and that use the same fuel for space heatng and water heatng (CREEDAC 1999). There are 8,767 low-rse sngle-famly dwellngs n SHEU 1993, out of whch some 2,529 accepted to dsclose ther annual utlty consumpton. CREEDAC removed the followng households: (1) households wth ncomplete energy bllng,.e., for less than 12 months; (2) households that do not use the same fuel for supplemental and man space heatng when supplemental space heatng s used; and (3) households that do not use the same fuel for space heatng and water heatng. Twenty-two ol-, 249 natural-gas- and 320 electrcheated households passed the screenng process. Fnally, CREEDAC removed the 22 olheated households because they were from the same provnce. That left 569 households n the sub-dataset we receved. We then appled our own screenng process to remove households wth mssng data entres. Because the dataset was gettng smaller rather rapdly, we changed the entres related to refrgerators and freezers. In the CREEDAC sub-dataset, the age and sze of the frst two refrgerators and the age and sze of the freezer are gven. These entres are not always complete and many parameters were mssng. Some respondents had entered the second refrgerator wthout specfyng the frst refrgerator, or they had gven the age of the freezer but not ts sze. Therefore, to reduce the number of household entres to be removed, we determned for each entry the number of frost-free refrgerators, non-frostfree refrgerators and freezers. The other mssng parameters that resulted n dscardng households were the number of doors and wndows and the gross ncome. The fnal dataset we used had 440 households 188 natural-gas-heated households and 252 electrcty-heated households from seven provnces (Newfoundland, New Brunswck, Ontaro, Mantoba, Saskatchewan, Alberta and Brtsh Columba). There were no household entres from Prnce Edward Island, Nova Scota and Quebec. The fnal dataset we used for our analyss has the followng varables: household nde; space and water heatng fuel; household gross ncome (md-value of a range); energy consumpton for space heatng n Joules (constructed from bllng data); energy consumpton for hot water n Joules (constructed from bllng data); energy consumpton for applances and lghtng n Joules (constructed from bllng data); provncal average of electrcty prce n 1993 and 1992 ($/Joules); provncal average of natural gas prce n 1993 and 1992 ($/Joules); household sze; ground temperature; heatng degree days; average ndoor temperature durng the heatng season (constructed); number of storeys; heated floor area; number of doors; number of wndows; number of skylghts; number of frost-free refrgerators; number of non-frost-free refrgerators; number of freezers; age of stove or oven; presence of electrc cooktop; presence of ar condtoner (constructed); number of lghts; presence of furnace fan; annual number of dryer loads (constructed); January 24, 2003 19
annual number of annual dshwasher loads (constructed); annual number of annual washer loads (constructed); capacty of hot water tank; presence of hot water tank nsulaton and number of aerators and low-flow shower heads. It also had the effcency of the space heatng equpment (md-value of a range). As noted above, some of the varables n the database we receved were constructed (CREEDAC 1999). The utlty consumpton by end-use has already been converted nto ther energy content usng the values gven n Table 2. Utlty prces were also converted nto prces per Joule usng Table 2. Furthermore, the bllng data have already been dsaggregated nto space heatng, domestc hot water, and applances and lghtng. However, we re-dd the dsaggregaton of the bllng data for electrcty-heated houses nto end uses usng a methodology that nduced a varaton n the rato of applances and lghtng consumpton to hot water consumpton. Ths s the subject of Secton 5.3. Average ndoor temperature durng the heatng season s obtaned by tme-averagng the temperature settng n the daytme (6 a.m. 6 p.m.), evenng (6 p.m. 10 p.m.) and nght (10 p.m. 6 a.m.). In the database we receved, data were gven on the usage of ar condtoners (number of hours). It soon became evdent that these data were not correct. We therefore transformed the data nto an nde dentfyng the presence of ar condtoners. Weekly number of dryer and washer loads was for summer and wnter. Annual values were obtaned by addng wnter and summer values after havng multpled each one by 26 weeks. The weekly dshwasher loads were transformed nto annual dshwasher loads by multplyng the weekly value by 52. As stated earler, the number of frost-free and non-frost-free refrgerators was constructed from the database we receved. The SHEU93 does provde effcency values, but only for furnaces. However, effcency values of furnaces are not relable because surveyed households were asked to select a range of effcency wthn whch they thnk ther furnace les. As a result, the fnal dataset contans no data on effcency of furnaces and water heaters. 5.2 Dsaggregaton of the Utlty Bll for Natural-gas-heated Houses The dsaggregaton of the bllng data of houses heated wth natural gas was straghtforward because the houses found n ths category use natural gas for space heatng and for hot water. The electrcty bll drectly corresponds to applances and lghtng. Durng the summer months (July and August), space heatng s usually not requred. As such, the average consumpton of July and August provdes the average consumpton to supply the hot water throughout the year. Space heatng s thus taken as the remander of the natural gas bll once the yearly consumpton for hot water s subtracted from t. 5.3 Dsaggregaton of the Utlty Bll for Electrcty-heated Houses In electrcty-heated houses, electrcty supples all three energy servces: space heatng, hot water, and applances and lghtng. Whle the dsaggregaton of the electrcty bll nto space heatng was straghtforward, t was not such a straghtforward eercse to dscrmnate between hot water and applances and lghtng. 20 January 24, 2003