Econometric Models for Major Residential Energy End-Uses

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    Canadian Residential Energy End-use Data and Analysis Centre

    CREEDAC

    CREEDAC, Dalhousie University5269 Morris Street, Halifax, Nova Scotia, Canada B3J 1B6Tel: (902) 494 6183 Fax: (902) 494 3165 E-mail:[email protected]://www.dal.ca/daltech/creedac

    Econometric Models for Major Residential Energy End-uses

    (CREEDAC-1999-04-05)

    Submitted to:Cristobal Miller

    Policy Development and Analysis DivisionEfficiency and Alternative Energy Branch

    Natural Resources Canada580 Booth Street

    Ottawa, OntarioCanadaK1A 0E4

    CREEDAC Project Team:Alan S. Fung

    Merih AydinalpV. Ismet Ugursal

    April 1999

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    Table of Contents

    TABLE OF CONTENTS ................................................................................................ 2

    LIST OF TABLES.......................................................................................................... 3

    LIST OF FIGURES ........................................................................................................ 5

    EXECUTIVE SUMMARY ............................................................................................. 6

    1. INTRODUCTION ...................................................................................................9

    2. REGRESSION MODEL........................................................................................ 11

    2.1 OVERVIEW ...................................................................................................... 112.2 GENERAL FORM OF THE MODEL EQUATIONS ........................................................ 122.3 DETERMINATION OF THE ELASTICITIES.................................................................. 142.4 MODEL EQUATIONS FOR DIFFERENT END-USES..................................................... 15

    2.4.1 Household Appliance model Equation ......................................................... 152.4.2 Space Heating Model equation .................................................................... 162.4.3 DHW Heating Model equation .................................................................... 162.4.4 Combined Space and DHW Heating model equation ..................................17

    3. DATA SET............................................................................................................18

    3.1 OVERVIEW .......................................................................................................... 183.2 PHYSICAL AND DEMOGRAPHIC CHARACTERISTICS OF HOUSEHOLDS .......................183.3 HOUSEHOLD APPLIANCE CHARACTERISTICS......................................................... 19

    3.4 WEATHER CHARACTERSITICS............................................................................... 203.5 HOUSEHOLD ENERGY CONSUMPTION DATA......................................................... 21

    3.5.1 Disaggregation of Energy Consumption data............................................... 223.5.1.1. Disaggregation of Energy Consumption in Natural Gas Heated Houses . 233.5.1.2. Disaggregation of Energy Consumption in All-Electric Houses.............. 24

    3.6 AVERAGE PROVINCIAL FUEL PRICE ..................................................................... 25

    4. RESULTS AND DISCUSSION.............................................................................27

    4.1 OVERVIEW .......................................................................................................... 274.2 HOUSEHOLD APPLIANCE ENERGY CONSUMPTION MODEL .................................... 294.3 SPACE HEATING ENERGY CONSUMPTION MODEL ................................................. 32

    4.4 DHW HEATING ENERGY CONSUMPTION MODEL ................................................. 344.5 COMBINED SPACE AND DHW HEATING ENERGY CONSUMPTION MODEL .............. 37

    5. CONCLUSION...................................................................................................... 64

    6. REFERENCES AND BIBLIOGRAPHY ............................................................... 66

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    List of Tables

    Table 1: Household End-use Energy Consumption Elasticities calculated using 20%significance criterion....................................................................................................... 8

    Table 2: List of model equations ................................................................................... 12

    Table 3: List of model equations developed................................................................... 12

    Table 4: Average Current and Lagged Provincial Fuel Prices ........................................ 26

    Table 5: Data Statistics for Appliance Energy Consumption Model for Natural GasHeated Households........................................................................................................ 40

    Table 6: Data Statistics for Appliance Energy Consumption Model for ElectricHeated Households........................................................................................................ 41

    Table 7: Appliance Energy Consumption Model Summary for Fossil FueledHouseholds ................................................................................................................... 42

    Table 8: Appliance Energy Consumption Model Summary for Electric HeatedHouseholds ................................................................................................................... 43

    Table 9: Appliance Energy Consumption Model Elasticities Estimates for NaturalGas Fueled Households................................................................................................. 44

    Table 10: Appliance Energy Consumption Model Elasticities Estimates for Electric

    Heated Households........................................................................................................ 45

    Table 11: Data Statistics for Natural Gas Space Heating Energy Consumption Modelin Natural Gas Heated Households ................................................................................ 46

    Table 12: Data Statistics for Electric Space Heating Energy Consumption Model inElectric Heated Households........................................................................................... 47

    Table 13: Natural Gas Space Heating Energy Consumption Model Summary forNatural Gas Fueled Households..................................................................................... 48

    Table 14: Electric Space Heating Energy Consumption Model Summary for ElectricHeated Households........................................................................................................ 49

    Table 15: Natural Gas Space Heating Energy Consumption Model ElasticitiesEstimates for Natural Gas Fueled Households ............................................................... 50

    Table 16: Electric Heating Energy Consumption Model Elasticities Estimates forElectric Heated Households........................................................................................... 51

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    Table 17: Data Statistics for Natural Gas DHW Heating Energy Consumption Modelin Natural Gas Heated Households ................................................................................ 52

    Table 18: Data Statistics for Electric DHW Heating Energy Consumption Model inElectric Heated Households........................................................................................... 53

    Table 19: Natural Gas DHW Heating Energy Consumption Model Summary forNatural Gas Fueled Households..................................................................................... 54

    Table 20: Electric DHW Heating Energy Consumption Model Summary for ElectricHeated Households........................................................................................................ 55

    Table 21: Natural Gas DHW Heating Energy Consumption Model ElasticitiesEstimates for Natural Gas Fueled Households ............................................................... 56

    Table 22: Electric DHW Heating Energy Consumption Model Elasticities Estimatesfor Electric Heated Households ..................................................................................... 57

    Table 23: Data Statistics for Natural Gas Space and DHW Heating EnergyConsumption Model in Natural Gas Heated Households ............................................... 58

    Table 24: Data Statistics for Electric Space and DHW Heating Energy ConsumptionModel in Electric Heated Households............................................................................ 59

    Table 25: Natural Gas Space and DHW Heating Energy Consumption ModelSummary for Natural Gas Fueled Households............................................................... 60

    Table 26: Electric Space and DHW Heating Energy Consumption Model Summaryfor Electric Heated Households ..................................................................................... 61

    Table 27: Natural Gas Space and DHW Heating Energy Consumption ModelElasticities Estimates for Natural Gas Fueled Households ............................................. 62

    Table 28: Electric Space and DHW Heating Energy Consumption Model ElasticitiesEstimates for Electric Heated Households ..................................................................... 63

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    List of Figures

    Figure 1: Typical monthly natural gas consumption in natural gas heated households.... 23

    Figure 2: Typical monthly electricity consumption in air-conditioned electric heatedhouses ........................................................................................................................... 24

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    EXECUTIVE SUMMARY

    A comprehensive econometric regression analysis was carried out on the three major

    components of the residential end-use energy consumption, namely space heating energyconsumption, domestic hot water (DHW) heating energy consumption and appliance

    energy consumption, to determine their long- and short-term price and income

    elasticities.

    The analysis was carried out on the 1993 Canadian housing stock. Three main data

    sources were utilized in the analysis: (1) Survey of Household Energy Use (SHEU,

    1993), (2) Energy billing records for a subset of SHEU data, and (3) Energy Statistics

    Handbook (Statistics Canada, 1998), Electric Power Statistics (Statistics Canada, 1992),

    and Canadian Economic Observer (Statistics Canada, 1998). SHEU provided most of the

    demographic and physical housing characteristics while its subset of billing records

    provided the total annual household fuel consumption data for both natural gas and

    electricity. Both current and lagged average provincial fuel prices were obtained and/or

    estimated using Statistics Canadas Energy Statistics Handbook, Electric Power

    Statistics, and Canadian Economic Observer.

    Log-linear variable price and variable income elasticity energy demand model, which

    was first proposed by Betancourt (1981) and later used by Donnelly and Diesendorf

    (1985) and Douthitt (1989), was adopted and modified to determine the price and income

    elasticities of the major components of the residential end-use energy consumption in

    natural gas and electric heated households. Model equations that incorporate

    demographics, weather and equipment characteristics as explanatory variables were

    developed, and price and income elasticities were derived from the model equations. The

    price, income and expenditure elasticities thus derived are presented in Table 1.

    Both the long- and the short-term own fuel price elasticities were found to have the

    expected negative sign, implying that fuel price has a negative effect on energy

    consumption (i.e. as fuel price increases, energy consumption decreases) for all types of

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    end-use energy consumption and fuel types. The magnitude of the short-term price

    elasticities were found to be significantly less than unity, indicating that the impact of

    price increase on end-use energy consumption was quite inelastic. The magnitude of the

    long-term price elasticities were found to be negative and above unity, indicating that in

    the long-term consumers would respond to a one percent increase in fuel price by

    reducing energy consumption by more than one percent.

    Income elasticity on end-use energy consumption was found to be statistically

    insignificant in most cases, and the ones that proved to be significant were very inelastic,

    i.e. the absolute magnitudes of the elasticities were very close zero. Household energy

    expenditure elasticities for all end-uses and fuel types proved to be positive indicating

    that the energy consumption for all three major residential end-uses (appliance, space

    heating and domestic hot water heating) behave like normal goods. All cross price effects

    were proved to be statistically significant with negative sign, except that for electric

    DHW heating which was insignificant. This indicated that consumers would have a

    similar response on energy demand to substitute price change as to own price change.

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    Table 1: Household End-use Energy Consumption Elasticities calculated using 20%

    significance criterion

    End-use Energy Consumption Elasticities All Natural Gas All Electric

    Heated Household Heated Household

    Appliance Energy Consumption

    Short-run Price Elasticity -0.341 -0.594 Long-run Price Elasticity -1.746 -1.208

    Income Elasticity 0.009 N/A

    Expenditure Elasticity 1.115 0.830

    Space Heating Energy Consumption

    Short-run Price Elasticity -0.246 -0.467

    Long-run Price Elasticity -0.904 -2.804

    Income Elasticity -0.005 N/A

    Expenditure Elasticity 1.791 1.755

    Cross Price Effect -0.793 -0.606

    DHW Heating Energy Consumption

    Short-run Price Elasticity -0.534 -0.548

    Long-run Price Elasticity -2.510 -1.213 Income Elasticity N/A 0.022

    Expenditure Elasticity 1.197 0.860

    Cross Price Effect -0.366 N/A

    Space + DHW Heating Energy Consumption

    Short-run Price Elasticity -0.303 -0.419

    Long-run Price Elasticity -1.036 -1.694

    Income Elasticity N/A N/A

    Expenditure Elasticity 1.733 1.292

    Cross Price Effect -0.701 -0.257

    Note: N/A indicates the variables are statistically not significant at 20% level

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    1. INTRODUCTION

    In 1996 the end-use energy consumption in Canada was about 7630 PJ (NRCan, 1998),

    making Canada one of the highest per capita energy consumers in the world. The carbondioxide emission associated with this energy consumption was about 416 Mt. Mostly

    owing to its northerly location and the prevalence of single family housing, residential

    energy consumption was about 1450 PJ, representing 19% of the total energy

    consumption in Canada. The carbon dioxide emission associated with the residential

    energy consumption was about 72 Mt.

    With the Kyoto Protocol signed in December 1997, developed countries committed to

    legally binding greenhouse gas (GHG) emission reductions of at least five percent by

    2008 to 2012. Canada promised a six percent reduction below 1990 emission levels by

    2010. Canada's commitment represents a reduction in greenhouse gas emissions of at

    least 19 percent below what they would be without the agreement. To meet this

    challenging commitment, Canada has to evaluate and exploit every feasible measure to

    reduce the energy consumption and GHG emissions while maintaining its economic

    growth.

    Residential energy consumption in Canada is primarily for space heating (61%), followed

    by domestic hot water heating (21%), appliances and lights (17%), and finally, cooling,

    which is negligibly small (0.4%) (NRCan, 1998). End-use energy consumption in the

    residential sector could be reduced by improving the building envelope characteristics

    (better insulation, better windows and doors, tighter buildings), and by using higher

    efficiency lighting, appliances, domestic hot water (DHW) heating and space heating,

    ventilating and air-conditioning (HVAC) equipment. Reducing the end-use energy

    consumption and switching to less carbon-intensive fuels for space and domestic hot

    water heating would result in reduced carbon dioxide emissions from the residential

    sector. However, the energy consumption pattern of consumers is a result of many

    complex and interrelated socioeconomic and technical factors as well as consumers

    energy conservation consciousness. Thus, an effective and efficient energy conservation

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    policy requires accurate and comprehensive estimates of residential energy demand

    parameters. These parameter estimates are among the most important inputs into

    informed policy decisions. In turn, accurate estimation of energy demand parameters

    requires realistic modeling of the consumers energy demand behavior, detailed data on

    energy consumption, and careful treatment of any econometric problems created by the

    model and the data used.

    In this report, econometric residential end-use energy models are developed to identify

    income and price elasticities of major residential energy end-uses.Using the models, the

    impact of various socioeconomic and physical housing characteristics on the residential

    energy consumption in Canada are also evaluated. In addition, some conclusions are

    made regarding possible strategies for reducing energy consumption from the residential

    sector.

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    2. REGRESSION MODEL

    2.1 OVERVIEW

    The objective of this study is to develop price and income elasticities for energy demand

    in the Canadian residential sector. The analytical approach is based primarily on the work

    done by Betancourt (1981), Donnelly and Diesendorf (1985) and Douthitt (1989). Ideally,

    the analysis should provide both price and income elasticities of energy demand for each

    of the three major residential energy end-uses; namely, space heating, domestic hot water

    heating, and appliance energy end-uses.

    It is expected that each one of the three major residential energy end-uses poses a distinct

    consumption profile for different fuel types and equipment characteristics. Consequently,

    each different end-use is expected to have a distinct demand equation based on the fuel

    type and equipment characteristic. Thus, three sets of model equations are developed

    here: (i) appliance, (ii) space heating, (iii) DHW heating. Additionally, a fourth set of

    model equations are developed for combined space and DHW heating since these two

    end-uses generally utilize the same fuel.

    The major fuel types considered in this study are natural gas, electricity and oil. Thus, a

    set of four equations (one for each end use; i.e. appliance, space heating, DHW heating,

    combined space and DHW heating) were to be developed for each of the three fuel types

    as shown in Table 2.However, as it is explained in Section 3.5, the number of oil heated

    households in the database is not sufficient to conduct a statistical analysis; therefore, oil

    is not included in the analysis. On the other hand, two sets of equations would be needed

    for households heated with electricity: (i) all-electric households in regions where naturalgas is available, and (ii) all-electric households in regions where natural gas is not

    available. However, it is not possible to categorize the households in the database

    according to this criterion because the exact locations of the houses are not known,

    consequently, availability of natural gas is not known either. Therefore, a single set of

    equations were developed for all of the electric heated households.

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    To facilitate the evaluation of long-term price elasticity as suggested by Poyer and

    Williams (1993), a set of model equations were developed by excluding the lagged fuel

    price from the variable list used in the regressions. The long-term price elasticities can be

    estimated by dividing the short-term estimates by unit minus the estimated coefficient of

    the lagged variable.

    In conclusion, a total of 16 model equations were developed as shown in Table 3.

    Table 2: List of model equations

    End-use Energy Electric Heated Natural Gas

    Consumption Model Households Heated Households

    Appliances

    DHW HeatingSpace Heating

    Combined Space & DHW Heating

    Table 3: List of model equations developed

    Electric Heated Natural Gas Heated

    End-use Energy House holds House holds

    Consumption Model Model I Model II Model I Model II

    (No Lag) (with Lag) (No Lag) (with Lag)

    Appliances

    DHW Heating

    Space Heating

    Combined Space & DHW Heating

    2.2 GENERAL FORM OF THE MODEL EQUATIONS

    The general stochastic econometric variable elasticity demand model, first proposed by

    Betancourt (1981) and later modified by Donnelly and Diesendorf (1985) to yield unitlessmeasures of elasticity, is given in Equation (1):

    n5432mm a

    n

    a

    k

    a

    j

    aaXa

    i0i XPPEYPaQ = (1)

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    where Qi= Total end-use energy consumption (GJ or kWh)

    a0,a1, . an= Variable coefficients

    Y = Household income ($)

    E = Total expenditure on fuel or energy ($)

    Piand Pi,-1 = Average current and lagged chosen fuel prices ($/GJ)

    Pj, Pk= Substitute fuel prices ($/GJ)

    Xn= Other socioeconomic and engineering variables

    Xm= Other socioeconomic and engineering variables

    Vector for other variables Xn and Xm includes all other pertinent variables. These are

    given below categorized in groups of related parameters (units given in parentheses):

    1) Structural Variables:

    Number of floors (-): STOREY

    Total Heated floor area (m2): AREA

    Basement area (m2): BASE

    Number of windows (-): WIN

    Number of doors (-): DOOR

    Number of skylights (-): SKY

    2) Weather and Temperature for space heating:

    Average indoor temperature (C): TEMP

    Average heating degree days (C-day): HDD

    3) Human Capital Factors:

    Household size (no. of people): HHS

    Overall heating equipment efficiency (%): EFF

    Total appliance energy consumption (GJ): APP

    4) Domestic Hot Water Heating:

    Number of aerators and low-flow shower heads (-): AERATOR

    Average ground temperature (C): GT

    Hot water tank size (liters): TANK

    Presence of tank insulation (0 or 1): INSUL

    5) Cooling:

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    Central air-conditioning usage in the cooling season (% of time):

    AC_USAGE

    Average cooling degree days (C-day): CDD

    6) Appliances:

    Dishwasher load (no. of loads/year): DW

    Clothes washer load (no. of loads/year): WA

    Clothes dryer load (no. of loads/year): DRY

    Cooking range/oven age (years): RANGE_A

    Presence of cooktop (0 or 1): COOKTOP

    Freezer age (years): FREEZER_A

    Freezer size (ft3): FREEZER_S

    First frost-free fridge age (years): FF1_A

    First frost-free fridge size (ft3): FF1_S

    First non frost-free fridge age (years): NFF1_A

    First non frost-free fridge size (ft3): NFF1_S

    Second frost-free fridge age (years): FF2_A

    Second frost-free fridge size (ft3): FF2_S

    Second non frost-free fridge age (years): NFF2_A

    Second non frost-free fridge size (ft

    3

    ): NFF2_SNumber of light bulbs (-): LIGHT

    Presence of furnace fan (0 or 1): FFAN

    2.3 DETERMINATION OF THE ELASTICITIES

    Variable coefficients in the general model equation can be determined by multi-variate

    linear regression conducted on the available data once Equation (1) is transformed by

    taking the natural logarithm of both sides:

    )Xln(a)Pln(a)Pln(a)Eln(a)Yln(a)Pln(XaA)Qln( nnk5j432imm0i ++++++= (2)

    Once the variable coefficients are determined, the price and income (and other

    parameters) elasticities on energy demand can be determined using the classical

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    economic elasticity definition. The general and price elasticities derived from Equation

    (1) can be expressed as:

    Q

    X

    X

    Q

    X

    X

    Q

    Q

    EX

    =

    = (3)

    mmP XaQ

    P

    P

    Q

    P

    P

    Q

    QE =

    =

    = (3a)

    Since the general elasticity, shown in equation (3), provides the measure of percent

    change in Q for one percent change in X, it is a unitless measure of elasticity. On the

    other hand, Equation (3a) does not provide such a unitless measure of elasticity as in

    Equation (3), since it has the unit of parameter Xm. Thus, it is necessary to transform the

    exponent variable, Xm, in Equation (3a) into a unitless variable. The method of

    transforming the exponent variables by dividing them by their corresponding standard

    deviations, as proposed by Donnelly and Diesendorf (1985), is used in this study.

    2.4 MODEL EQUATIONS FOR DIFFERENT END-USES

    To identify the variables to be included in the model equations and the final form of the

    model equations, various model equations were tested. As a result of these tests, the

    variables and the form of the equations were determined.

    The resulting equations are presented below.

    2.4.1 HOUSEHOLD APPLIANCE MODEL EQUATION

    The model equation for appliance end-use energy consumption is given in Equation (4).

    There is no substitute price in the equation because electricity is predominantly the only

    fuel choice for appliances.

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    n109

    87654321,i1

    a

    n

    aa

    aaaa)HHSa()GTaHDDaPa(

    i0i

    XBASEAREA

    STOREYTEMPEFFEYPaQ ++

    =(4)

    where variables Xnfor appliance energy consumption model are:

    FFANaCOOKTOPaa

    CDDaaA_2NFFa

    A_1NFFaA_2FFaA_1FFa

    A_FREEZERaaaaa

    n

    13n12n11n

    10n9n8n

    7n6n5n

    4n3n2n1nn

    eeLIGHT

    USAGE_ACA_RANGES_2NFF

    S_1NFFS_2FFS_1FF

    S_FREEZERDRYWADWX =

    (4a)

    2.4.2 SPACE HEATING MODEL EQUATION

    The model equation for space heating end-use energy consumption is given in Equation

    (5). The appliance energy consumption variable, APP is a proxy for internal heat gain.

    n121110

    987654321,i1

    a

    n

    aa

    s

    a

    aaaaa)HHSa()GTaHDDaPa(

    i0i

    XAPPPBASE

    AREASTOREYTEMPEFFEYPaQ ++

    =(5)

    where variables Xnfor space heating energy consumption model are:

    3n2n1nn aaaan WINSKYDOORX = (5a)

    2.4.3 DHW HEATING MODEL EQUATION

    The model equation for space heating end-use energy consumption is given in Equation

    (6):

    n1110

    987654321,i1

    a

    n

    a

    s

    a

    aaaaa)HHSa()GTaHDDaPa(

    i0i

    XPBASEAREASTOREYTEMPEFFEYPaQ

    ++=

    (6)

    where variables Xnfor DHW heating energy consumption model are:

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    INSULaaaaaa

    n5n4n3n2n1nn eWADWAERATORTANKX = (6a)

    2.4.4 COMBINED SPACE AND DHW HEATING MODEL EQUATION

    The model equation for combined space heating and DHW heating end-use energy

    consumption is given in Equation (7)

    n1211109

    87654321,i1

    a

    n

    aa

    s

    aa

    aaaa)HHSa()GTaHDDaPa(

    i0i

    XAPPPBASEAREA

    STOREYTEMPEFFEYPaQ ++=

    (7)

    where variables Xn for combined space and DHW heating energy consumption model

    are:

    INSULaa

    aaaaaaa

    n

    8n7n

    6n5n4n3n2n1nn

    eWA

    DWAERATORTANKWINSKYDOORX =(7a)

    The equation contains only one substitute price and several building and DHW heating

    equipment specific parameters. There is only one substitute price in the model equation

    because most homeowners have only one alternative fuel choice.1

    1Only 31 households out of a total of 320 electric heated households have natural gas

    available in their areas. Thus, the only alternative fuel choice for these electric heatedhouseholds is fuel oil. Most of the natural gas heated households are located in regionswhere oil is not a major player in residential home heating market due to significantlylower price of natural gas compared to oil.

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    3. DATA SET

    3.1 OVERVIEW

    To construct the necessary data set for the development of the econometric model, three

    main sources of data were used in this study: (i) Survey of Household Energy Use

    (SHEU, 1993), (ii) Energy billing records for a subset of SHEU data, and (iii) Energy

    Statistics Handbook (Statistics Canada, 1998), Electric Power Statistics (Statistics

    Canada, 1992), and Canadian Economic Observer (Statistics Canada, 1998).

    SHEU (1993) contains comprehensive data physical and demographic data on 10,982

    households across Canada. 8,767 of these 10,982 records are for low-rise single family

    dwellings. These include single detached and attached dwellings. The energy billing data

    for about 3,000 of the 8,767 single family dwellings are also available from a SHUE data

    file. Since this study focuses on low-rise dwellings, physical, demographic and energy

    billing data from these 3000 households were used here.

    Both current and lagged average provincial fuel prices were obtained and/or estimated

    using the Energy Statistics Handbook, Electric Power Statistics, and Canadian Economic

    Observer published by Statistics Canada.

    3.2 PHYSICAL AND DEMOGRAPHIC CHARACTERISTICS OFHOUSEHOLDS

    The values for most of the variables used in the parameter vector Xnof the models given

    in Equations (4) - (7) were obtained directly or indirectly from the SHEU data as given

    below (the column numbers refer to the SHEU micro-data file):

    1) Structural Variables:Number of floors/storeys: Column 181.

    Total heated area: Column 189 (mean value of each category is use).

    Basement area: Column 192 (mean value of each category is used).

    Number of windows: Column 231, 232, 234, 235, 237, 238, 240, 241.

    Number of doors: Column 210, 211, 213, 214, 216, 218.

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    Number of skylights: Column 227, 228, 229.

    2) Weather and Temperature:

    Average indoor temperature: Column 178, 179, 180.

    3) Human Capital Factors:

    Household size: Column 8.

    Household income: Column 355 (mean value of each category is used).

    Overall heating equipment efficiency: Column 142: (mean value of each

    category is used. 100%, 150%, and 250% are assigned for electric

    resistance, air-source heat pump, and water/ground source heat pump

    heated households, respectively.)

    4) Domestic Hot Water Heating:

    Number of aerators and low-flow shower heads: Column 327, 329.

    Hot water tank size: Column 323.

    Presence of DHW tank insulation: Column 324.

    3.3 HOUSEHOLD APPLIANCE CHARACTERISTICS

    In order to capture the effect of appliance stock holding, its characteristics and usage on

    energy demand, data on major household appliances were included in the appliance

    energy demand equation. The following data from SHEU were used:

    1) Dishwasher:

    Number of loads: Column 75 (value is multiplied by 52 to obtain number

    of loads/year).

    2) Clothes washer:

    Number of loads: Column 100, 101 (values are multiplied by 26 and

    added to obtain number of loads/year).

    3) Clothes dryer:

    Number of loads: Column 114, 115 (values are multiplied by 26 and

    added to obtain number of loads/year).

    4) Freezer:

    Age of freezer: Column 79 (mean value of each category is used).

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    Size of freezer: Column 83 (mean value of each category is used).

    5) First Refrigerator:

    Age of Refrigerator: Column 42 (mean value of each category is used).

    Size of Refrigerator: Column 46 (mean value of each category is used).

    Frost free or manual defrosted: Column 48.

    6) Second Refrigerator:

    Age of Refrigerator: Column 43 (mean value of each category is used).

    Size of Refrigerator: Column 47 (mean value of each category is used).

    Frost free or manual defrosted: Column 49.

    7) Cooking equipment:

    Electric range/oven age: Column 56 (mean value of each category is

    used).

    Presence of electric cooktop: Column 53.

    8) Lighting:

    Number of light bulbs: Column 331, 332, 334, 335, 345, 346, 347.

    9) Furnace fan:

    Presence of furnace fan: Column 138.

    10)Central air conditioning:

    Central air-conditioning usage: Column 300: assign 0, 25, 50, 75, and 100

    percent usage to response 1 to 5, respectively.

    3.4 WEATHER CHARACTERSITICS

    Weather plays a major role on overall residential energy consumption. Ideally, both long-

    term average and temporal heating degree-days (HDD) should be included in the model

    development. Long-term average heating degree-days would be expected to have an

    influence on price elasticity since consumers are likely to be energy conscious in colder

    climates due to high energy expenditures. On the other hand, temporal heating degree-

    days mainly influence the temporal space heating energy consumption because of its

    direct influence on the amount of heat loss through the building envelope.

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    It was decided not to include the temporal heating degree-days in this study because of

    the time and cost associated in obtaining temporal degree-day information.

    Cooling degree-days have an effect on air-conditioning energy consumption, therefore

    long-term average cooling degree-days were used in the model.

    3.5 HOUSEHOLD ENERGY CONSUMPTION DATA

    To formulate the energy demand model equations, actual data on overall as well as

    disaggregated end-use energy consumption for houses are needed. A subset of SHEU

    database contains one year of energy consumption billing records from utility companies.

    There are a total of 133, 972, and 1424 households with oil, natural gas, and electricitybilling records, respectively.

    To ensure data quality, a number of data screenings were performed. The following

    procedures were employed to screen the data:

    No household was accepted if supplemental space heating is different from the main

    space heating fuel. For example, if wood or propane was indicated as the

    supplemental space heating fuel in a natural gas/electric/oil heated house, then thishousehold was rejected.

    Only households that use the same fuel for both space and DHW heating were

    accepted because the number of households in the database that use different fuels for

    space and DHW heating is 18, which is not sufficient to conduct a statistical analysis.

    Only households with complete twelve month fuel billing records were accepted. This

    was essential for disaggregating the space heating energy consumption from DHW

    heating energy consumption for fossil fuel heated houses, and for disaagregating the

    space heating energy consumption from other end-uses in electrically heated houses.

    After applying this screening process, only 22 oil, 249 natural gas, and 320 electric

    heated households were left to be used in the analysis.

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    The data set of 22 samples for oil heated houses is unacceptably low to carry out a

    meaningful statistical analysis with a high number of explanatory variables. Moreover, an

    inspection of these 22 household files revealed that all are from one province. This

    renders the fuel price invariant in all of these 22 households, making the regression

    process on oil heated households even more pointless. Thus, oil heated households are

    not included in this work.

    3.5.1 DISAGGREGATION OF ENERGY CONSUMPTION DATA

    To formulate the energy demand model equations, it is necessary to disaggregate the

    energy consumption data obtained from energy bills into three major components, i.e.

    space heating, DHW heating and appliances energy consumption. To accomplish this, it

    is commonly assumed that that there is no space heating requirement during the summer

    months of July and August. Thus, the energy consumption in these two months can be

    assumed to be for DHW heating and appliances (including lighting) only (see Figure 1).

    Furthermore, it is assumed that the energy consumption for DHW heating and appliances

    is independent of the time of the year (i.e. constant over the whole year). This second

    assumption is clearly questionable since water supply temperature, daylight hours, indoor

    temperature, etc. all have impact on DHW and appliance energy consumption. However,

    in the absence of disaggregated data, the inaccuracy involved with this assumption is

    tolerated.

    The disaggregation of the energy consumption data was accomplished as described

    below.

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    Typical Monthly Household Natural Gas Consumption

    Profile

    Jan Feb Mar Apr May June July Aug Sept Oct Nov Dec

    Month

    Figure 1: Typical monthly natural gas consumption in natural gas heated households

    3.5.1.1. Disaggregation of Energy Consumption in Natural Gas Heated Houses

    Appliance energy consumption: The total annual appliance energy consumption is

    available from the total annual electricity billing.

    DHW heating energy consumption: The average monthly natural gas consumption for

    DHW heating was estimated from the natural gas billings for July and August.

    Space heating energy consumption: The annual space heating energy consumption is

    estimated by subtracting the estimated DHW heating energy consumption from the total

    annual natural gas billing record.

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    3.5.1.2. Disaggregation of Energy Consumption in All-Electric Houses

    Appliance and DHW heating energy consumption: The average monthly electrical

    consumption for appliances and DHW heating (combined) was estimated from the

    electricity billings for July and August. In air-conditioned households, July and August

    energy consumption includes electricity consumption for air-conditioning (see Figure 2).

    Therefore, in air-conditioned houses, data from shoulder months of June and September

    were used to represent the average monthly electrical consumption for appliances and

    DHW heating.

    Typical Monthly Household Electricity Consumption

    Profile

    0

    500

    1000

    1500

    2000

    2500

    3000

    Jan Feb Mar Apr May June July Aug Sept Oct Nov Dec

    Month

    E

    lectricityConsumption(kWh)

    Figure 2: Typical monthly electricity consumption in air-conditioned electric heatedhouses

    To disaggregate the electrical energy consumption for DHW heating and appliances, the

    following approach was used:

    It was assumed that the average ratio of appliance energy consumption to that of DHW

    heating energy load is constant in all houses. The average efficiency of natural gas heated

    DHW heaters is 55%. The ratio of appliance energy consumption to DHW heating energy

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    load in natural gas heated houses was calculated using this average efficiency and the

    estimated appliance and DHW heating consumption values as follows:

    nconsumptio

    DHWloadAPP

    DHW55.0

    mptionnergyConsuApplianceER =

    (8)

    This ratio was found to be 1.51. The average efficiency of electrically heated DHW

    heaters is 83%. Thus, using the ratio calculated using Equation 8 and this average

    efficiency, the ratio of electricity consumption of appliances to the electricity

    consumption for DHW heating was calculated as follows:

    25.1)51.1)(83.0(DHW

    mptionnergyConsuApplianceE

    nconsumptio

    == (9)

    Using this ratio, the total energy consumption for appliances and DHW heating was

    disaggregated into its two components.

    Space heating energy consumption: The annual space heating energy consumption is

    estimated by subtracting the estimated appliance and DHW heating energy consumption

    from the total annual electricity billing records.

    3.6 AVERAGE PROVINCIAL FUEL PRICE

    It was not possible to obtain the actual fuel price, tax, rate structure, and basic service

    charge information for each household in the database since the exact location of the

    households is not available; therefore, average provincial fuel prices were used in this

    study.

    Average provincial natural gas prices for residential uses were obtained directly from

    Statistics Canadas Energy Statistics Handbook (1998). Since electricity prices are not

    given in Energy Statistics Handbook, electricity price data were estimated using data

    obtained from Electric Power Statistics (1992) multiplied by the consumers price index

    from Canadian Economic Observer (1998). The average current and lagged provincial

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    fuel prices used in this study are presented in Table 4. The total household energy

    expenditure for each household was calculated using the billing records and the average

    provincial fuel prices.

    Table 4: Average Current and Lagged Provincial Fuel Prices

    Lagged Price Current Price

    Province Electricity Natural gas Oil Electricity Natural gas Oil

    (cents/kWh) (cents/m^3) (cents/liter) (cents/kWh) (cents/m^3) (cents/liter)

    NFLD 4.70 N/A 39.70 4.71 N/A 39.60

    PEI 11.70 N/A 35.50 11.69 N/A 36.00

    NS 7.70 N/A 36.50 7.69 N/A 36.50

    NB 5.60 N/A 38.20 5.79 N/A 38.70

    QUE 4.80 28.07 37.70 4.87 28.12 37.00

    ON 7.00 20.60 36.40 7.47 20.99 38.00

    MAN 4.70 20.04 41.00 4.73 20.70 42.50

    SAS 5.90 15.90 36.10 6.24 16.49 35.70AB 5.20 12.67 N/A 5.37 14.59 N/A

    BC 4.60 19.06 40.40 4.78 19.75 41.40

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    4. RESULTS AND DISCUSSION

    4.1 OVERVIEW

    Eight end-use energy consumption models were developed and analyzed. These are:

    - For households heated with natural gas:

    . Space heating energy consumption,

    . Appliance energy consumption,

    . DHW heating energy consumption,

    . Combined space heating and DHW heating energy consumption;

    - For households heated with electricity:

    . Space heating energy consumption,

    . Appliance energy consumption,

    . DHW heating energy consumption,

    . Combined space heating and DHW heating energy consumption.

    To facilitate the evaluation of long-term price elasticity suggested by Poyer and Williams

    (1993), another eight sets of model regressions without lagged price (Pi,-1) variables were

    also performed. These eight sets of model equations were denoted as Model I while the

    set of model equations with lagged fuel prices are denoted as Model II.

    All of the regression analyses were performed using Version 9 of SPSS (1998) computer

    statistical software package. For each model equation analysis, two statistical analyses

    were run using SPSS:

    (i) "As Entered": The first scenario was run using the As Entered feature of SPSS

    to determine the coefficients of all of the entered variables regardless of their

    statistical significance. The results of this scenario are denoted as As Entered in

    the summary tables 7, 8, 13, 14, 19, 20, 25, and 26.

    (ii) "Backward Elimination": The second scenario was run using Backward

    elimination" feature of SPSS to determine the coefficients of the variables with

    the 20 percent significance level option. This relatively high significance level

    option of 20 percent was used for the backward elimination method to ensure that

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    most of the important variables (such as the lagged price, substitute price, and

    income) were included in the final model equations so that price and income

    elasticities as well as cross-price effects on end-use energy consumption can be

    identified. It was however found that most of these variables are statistically

    significant at or below 5 percent significance level. The results of this second

    scenario were denoted as Up to 20 Percent in the summary tables 7, 8, 13, 14,

    19, 20, 25, and 26.

    The statistics on the variables used in each one of the energy end-use model equation are

    presented in Tables 5, 6, 11, 12, 17, 18, 23, and 24. The coefficients of the variables, the

    t-statistics and the R2values are presented in Tables 7, 8, 13, 14, 19, 20, 25, and 26. The

    estimated short-term and long-term price elasticities, income elasticities, and cross-price

    effects are presented in Tables 9, 10, 15, 16, 21, 22, 27, and 28. To represent price

    elasticities for households that face average, higher than average, and lower than average

    initial fuel prices, price elasticities were estimated at (i) sample mean, (ii) sample mean

    plus its standard deviation, and (iii) sample mean minus its standard deviation,

    respectively.

    At up to 20 percent significance level, the adjusted R2 values (i.e. goodness of fit) range

    from 0.376 to 0.987. All R2 values are above 0.64 except that for natural gas DHW

    heating, which has an adjusted R2 of 0.376. The adjusted R2values are surprisingly high

    for combined space and DHW heating energy consumption models. The adjusted R2

    values are 0.949 and 0.987 for natural gas and electric heated households, respectively.

    These adjusted R2values are much higher than those reported by Douthitt (1989) for a

    similar study of the Canadian housing stock. This could be attributed to the fact that

    estimated, instead of actual, household space heating energy consumption data were used

    in his analyses.

    Some interesting observations can be made from comparisons of the data sets of natural

    gas heated and electric heated households:

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    - Natural gas heated households, in general, consume more energy for all end-uses,

    including electric appliances (higher energy consumption for both space and DHW

    heating energy end-uses is to be expected since natural gas has lower overall fuel

    utilization efficiency),

    - On average, natural gas heated households have higher household income and bigger

    home.

    - Natural gas heated households experience colder climate (higher heating degree-days)

    in winter and warmer climate (higher cooling degree-days) in summer.

    - Indoor temperature setpoint in natural gas heated households is higher than those of

    electric heated households.

    - Natural gas heated households have a greater number of light bulbs.

    4.2 HOUSEHOLD APPLIANCE ENERGY CONSUMPTION MODEL

    Results from the appliance end-use energy consumption model are presented in Tables 5

    to 10. The discussion of the results here is limited to the results for the "up to 20%"

    significance level.

    All economic factors used in the models proved to be statistically significant except the

    lagged price in the electricity heated household model. Appliance energy consumption

    proved to be positively related to household energy expenditure and income, and

    negatively related to price and heating degree-days. Other appliance variables that proved

    to be significant are dishwasher load, clothes dryer load, refrigerators, and air

    conditioning usage. As expected, all of these variables, except the first non frost-free

    refrigerator, are positively related to energy consumption. This could be attributed to the

    fact that non frost-free refrigerators consume less energy than their frost-free counterparts

    since they do not employ defrost-cycles.

    As expected, both estimated short- and long-term price elasticities were negative. The

    short- and long-term elasticities, evaluated at the sample mean, were found to be 0.341

    and 1.746 for natural gas heated households, and 0 .594 and 1.208 for electric heated

    households, respectively. Natural gas heated households respond to price changes less

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    than the electric heated households in the short-term. This trend is reversed in the long-

    term price responses. Since electric heated households face higher fuel prices and have

    higher household energy expenditures, in the short- term they are expected to respond to

    price changes more than natural gas heated households. The elastic nature of the long-

    term price elasticities indicate that consumers tend to become more energy conscious if

    they are faced with long-term price increases. The higher long-term price elasticity for

    the natural gas heated households may indicate that these households would consider

    switching to natural gas fueled appliances (such as gas cooktop/oven/range and dryer) if

    they faced long-term electricity price increases.

    Household energy expenditure elasticities were found to be significant and positive,

    indicting that appliance energy consumption behaves as a normal good. However, the

    magnitude was greater for natural gas heated households (1.115 versus 0.83.)

    Income elasticities were found to be significant only for natural gas heated households.

    The income elasticity for this group of households was positive and very inelastic at

    0.009.

    The final econometric model equations for appliance end-use energy consumption for

    both natural gas and electric heated households at 20 percent significance level are

    presented in Equations 10 to 13.

    Natural gas heated household without lagged fuel price:

    na

    n

    2E81.91E93.11E73.3

    1E68.9)HHS3E75.5()GT2E75.8HHD1E12.1(

    ii

    XBASESTOREYTEMP

    EYP98.40Q

    =

    (10)

    where variables Xnfor appliance energy consumption model are:

    FFAN1E39.31E18.1CDD5E33.7

    A_1NFF3E59.12E40.32E26.1a

    n

    eLIGHTUSAGE_AC

    S_1NFFDRYDWX n

    =

    (10a)

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    Natural gas heated household with lagged fuel price:

    n

    1,i

    a

    n

    2E68.81E64.1

    E12.1)HHS3E54.3()HHD2E05.2P2E76.5(

    ii

    XBASESTOREY

    EYP92.7Q

    =(11)

    where variables Xnfor appliance energy consumption model are:

    2E91.7CDD5E33.5A_1NFF3E32.2

    A_2FF3E45.12E70.22E00.1a

    n

    LIGHTUSAGE_ACS_1NFF

    S_2FFDRYDWX n

    =

    (11a)

    Electric heated household without lagged fuel price:

    na

    n

    2E86.61E29.11E12.4

    1E30.8)HHS3E27.9()GT2E28.4HHD2E73.4(

    ii

    XBASESTOREYEFF

    EYP23.8Q

    =

    (12)

    where variables Xnfor appliance energy consumption model are:

    A_2NFF3E68.1

    A_1NFF3E53.22E13.22E53.1a

    n

    S_2NFF

    S_1NFFDRYDWX n

    =

    (12a)

    Electric heated household with lagged fuel price:

    na

    n

    2E86.61E29.11E12.4

    1E30.8)HHS3E27.9()GT2E28.4HHD2E73.4(

    ii

    XBASESTOREYEFF

    EYP23.8Q

    =

    (13)

    where variables Xnfor appliance energy consumption model are:

    A_2NFF3E68.1

    A_1NFF3E53.22E13.22E53.1a

    n

    S_2NFF

    S_1NFFDRYDWX n

    =

    (13a)

    4.3 SPACE HEATING ENERGY CONSUMPTION MODEL

    The results for the space heating end-use energy consumption model are presented in

    Tables 11 to 16. Major economic factors, such as substitute and lagged prices, income,

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    and household energy expenditure, proved to be statistically significant. However,

    substitute fuel price for electric heated households was not significant. This could

    partially be explained by the fact that oil is not truly an alternative fuel for electricity due

    to its higher capital requirement, marginally lower price (in most provinces), and

    inconvenience. Space heating energy consumption is positively related to household

    energy expenditure, house area, and heating degree-days, and negatively related to lagged

    price, income, and total household appliance consumption. Other housing variables

    proved to be significant are number of storeys, total heated area, total basement area,

    number of doors, windows, and skylights. As to be expected, variables such as number of

    doors, windows, and skylights, are positively related to space heating energy

    consumption since these house features provide less thermal resistance against heat loss

    than solid wall assemblies. Also as expected, both average ground temperature and total

    appliance energy consumption variables proved to be negatively related to space heating

    energy consumption. This can be explained by the fact that higher ground temperature

    reduces heat loss through basement while higher total appliance energy consumption

    increases the amount of internal heat gain in the house, lowering its overall space heating

    requirement. Space heating equipment efficiency variables in both cases are found to be

    not significant statistically.

    As expected, both estimated short- and long-term price elasticities are negative. The

    short- and long-term elasticities, evaluated at sample mean, were found to be 0.246 and

    0.904 for natural gas heated households, and 0.467 and 2.804 for electric heated

    households, respectively. Natural gas heated households respond to fuel price changes

    less than electric heated households in both the short- and the long-term. Since electric

    heated households face higher fuel prices and have higher household energy expenditure,

    they were expected to respond to price changes more than natural gas heated households

    in the short-term. The very elastic nature of the long-term price elasticities in electric

    heated households indicate that consumers tend to become extremely energy conscious if

    they are faced with long-term price increases; or, they may supplement their space

    heating energy requirements with a less expensive fuel such as wood.

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    Household energy expenditure elasticities are found to be significant and positive,

    indicting that appliance energy consumption behaves like normal goods. However, the

    magnitude is larger for natural gas heated households (1.791 versus 1.755).

    Income elasticities are found only to be significant for natural gas heated households. The

    income elasticity for this group of households is positive and very inelastic at 0.005.

    Cross-price effects for both natural gas and electricity space heating energy consumption

    are statistically significant and negative. The cross-price effect coefficient values are

    estimated to be 0.793 and 0.606 for natural gas and electricity, respectively. For every

    percent increase in electricity price, there would be a 0.793 percent decrease in natural

    gas space heating energy consumption. Similarly, for every percent increase in oil price,

    there would be a 0.606 percent decrease in electricity space heating energy consumption.

    The final econometric model equations for space heating end-use energy consumption for

    both natural gas and electric heated households at 20 percent significance level are

    presented in Equations 14 to 17.

    Natural gas heated household without lagged fuel price:

    na

    n

    1E4.91E2.8

    s

    2E2.32E5.9

    2E3.8E8.1)HHS3E6.1()GT2E1.5HHD2E5.3(

    ii

    XAPPPBASEAREA

    STOREYEYP15.0Q

    =

    (14)

    where variables Xnfor space heating energy consumption model are:

    2E5.3a

    n WINXn = (14a)

    Natural gas heated household with lagged fuel price:

    n

    1,i

    a

    n

    1E2.91E9.7

    s

    2E1.32E0.92E2.8

    E8.1)HHS3E0.2()HHD2E1.1P2E7.5(

    ii

    XAPPPBASEAREASTOREY

    EYP069.0Q

    + =(15)

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    where variables Xnfor space heating energy consumption model are:

    2E7.4a

    n WINXn = (15a)

    Electric heated household without lagged fuel price:

    na

    n

    1E7.71E1.7

    s

    2E4.42E0.6

    1E1.1E7.1)GT1E5.1HHD1E3.1(

    ii

    XAPPPAREASTOREY

    TEMPEP0011.0Q

    =

    (16)

    where variables Xnfor space heating energy consumption model are:

    2E0.31E3.1a

    n WINSKYXn = (16a)

    Electric heated household with lagged fuel price:

    n

    1,i

    a

    n

    1E9.71E1.6

    s

    2E2.6

    1E0.1E8.1)GT2E5.2P2E0.4(

    ii

    XAPPPSTOREY

    TEMPEP019.0Q

    =(17)

    where variables Xnfor space heating energy consumption model are:

    2E7.92E0.3a

    n SKYDOORXn = (17a)

    4.4 DHW HEATING ENERGY CONSUMPTION MODEL

    The results for DHW heating end-use energy consumption models are presented in

    Tables 17 to 22. Major economic factors, such as substitute and lagged prices, income,

    and household energy expenditure proved to be statistically significant. Similar to the

    space heating energy consumption model, the substitute fuel price for electric heated

    households is insignificant. DHW heating energy consumption is positively related to

    household energy expenditure and household income, and negatively related to lagged

    price. Other DHW related variables that proved to be significant are DHW tank size,

    ground temperature, and number of dishwasher loads. As expected, the ground

    temperature is negatively related to DHW heating energy consumption.

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    Again, both estimated short and long-term price elasticities proved to be negative. The

    short- and long-term elasticities, evaluated at sample mean, are 0.534 and -2.510 for

    natural gas heated households, and 0.548 and 1.213 for electric heated households,

    respectively. Natural gas heated households respond to fuel price changes less than

    electric heated households in the long-term, whereas for the short-term, for every percent

    increase in DHW fuel price, there would be a about half of a percent decrease in energy

    consumption for both natural gas and electric heated households. The very large

    magnitude of long-term fuel price elasticity for natural gas heated households may

    indicate that consumers are very sensitive to fuel price on DHW heating energy

    consumption.

    Household energy expenditure elasticities are significant and positive, indicting that

    appliance energy consumption behaves like a normal good. However, the magnitude is

    larger for natural gas heated households (1.197 versus 0.860.)

    Income elasticities only significant for electric heated households. The income elasticity

    for this group of households is positive and very inelastic at 0.022.

    The cross-price effect for natural gas DHW heating energy consumption is statistically

    significant and negative. The cross-price effect coefficient value is 0.366 for natural gas

    heated DHW, which means that for every percent increase in electricity price (substituted

    price for natural gas), there would be a 0.366 percent decrease in natural gas DHW

    heating energy consumption.

    The final econometric model equations for DHW heating end-use energy consumption

    for both natural gas and electric heated households at 20 percent significance level are

    presented in Equations 18 to 21.

    Natural gas heated household without lagged fuel price:

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    na

    n

    1E66.4

    s

    1E83.4E18.1)GT2E78.6HHD2E02.7(

    ii

    XP

    TEMPEP08.1Q

    =

    (18)

    where variables Xnfor DHW heating energy consumption model are:

    1E01.6a

    n TANKXn = (18a)

    Natural gas heated household with lagged fuel price:

    n1,i a

    n

    1E66.3

    s

    1E82.4E20.1)P2E91.7(

    ii XPTEMPEP23.0Q = (19)

    where variables Xnfor DHW heating energy consumption model are:1E65.5a

    n TANKXn = (19a)

    Electric heated household without lagged fuel price:

    na

    n

    1E06.1

    1E60.8)HHS3E70.9()GT2E84.4HHD2E24.5(

    ii

    XSTOREY

    EYP12.0Q

    =

    (20)

    where variables Xnfor DHW heating energy consumption model are:

    2E51.1a

    n DWXn = (20a)

    Electric heated household with lagged fuel price:

    na

    n

    1E06.1

    1E60.8)HHS3E70.9()GT2E84.4HHD2E24.5(

    ii

    XSTOREY

    EYP12.0Q

    =

    (21)

    where variables Xnfor DHW heating energy consumption model are:

    2E51.1a

    n DWXn = (21a)

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    4.5 COMBINED SPACE AND DHW HEATING ENERGYCONSUMPTION MODEL

    The results for combined space and DHW heating end-use energy consumption models

    are presented in Tables 23 to 28. Major economic factors, such as substitute and lagged

    prices, and household energy expenditure, proved to be statistically significant. However,

    income effects in both cases are not significant. For natural gas heated households, the

    combined space and DHW heating energy consumption is positively related to household

    energy expenditure, total heated area, heating degree-days, number of windows, DHW

    tank size, and number of clothes washer loads are negatively related to lagged price,

    substitute price, total household appliance consumption, and extra DHW tank insulation.

    On the other hand, the combined space and DHW heating energy consumption is

    positively related to household energy expenditure, indoor temperature, and number ofstoreys, and negatively related to lagged price, substitute price, number of doors, number

    of windows, number of clothes washer loads, and total household appliance energy

    consumption.

    As expected, both estimated short- and long-term price elasticities are negative. The short

    and long-term elasticities, evaluated at sample mean, were found to be 0.303 and 1.036

    for natural gas heated households, and 0.419 and 1 .694 for electric heated households,

    respectively. Natural gas heated households respond to fuel price changes less than

    electric heated households in both short- and long-term. Similar to the space heating

    energy consumption case, electric heated households face higher fuel prices and have

    higher household energy expenditures; therefore, they are expected to respond to price

    changes more than natural gas heated households in the short-term. The very elastic

    nature of the long-term price elasticities in the electric heated households indicate that

    consumers would tend to become extremely energy conscious if they are faced with long-

    term price increases.

    Household energy expenditure elasticities are significant and positive, indicting that

    appliance energy consumption behaves like normal goods. The magnitude for natural gas

    heated households is larger than that for electric heated households (1.733 versus 1.292).

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    Income elasticities are statistically insignificant for both natural gas and electric heated

    households.

    Cross-price effects for both natural gas and electricity combined space and DHW heating

    energy consumption are statistically significant and negative. The cross-price effect

    coefficients are 0.701 and 0.257 for natural gas and electricity, respectively. This

    indicates that for every percent increase in electricity price, there would be a 0.701

    percent decrease in natural gas consumption. Similarly, for every percent increase in oil

    price, there would be a 0.257 percent decrease in electricity consumption.

    The adjusted R2 values for combined space and DHW energy consumption are quite

    highat 0.987 and 0.949 for natural gas and electricity, respectively.

    The final econometric model equations for combined space heating end-use energy

    consumption for both natural gas and electric heated households at 20 percent

    significance level are presented in Equations 22 to 25.

    Natural gas heated household without lagged fuel price:

    na

    n

    1E41.81E42.7

    s

    2E93.2

    2E87.31E03.1

    E73.1)HHS3E13.1()GT2E44.7HHD2E02.6(

    ii

    XAPPPAREA

    STOREYTEMP

    EYP25.0Q

    =

    (22)

    where variables Xnfor space and DHW heating energy consumption model are:

    2E38.51E07.1a

    n TANKSKYXn = (22a)

    Natural gas heated household with lagged fuel price:

    n

    1,i

    a

    n

    1E30.81E01.7

    s

    2E06.32E23.3

    1E04.1E73.1)HHD2E04.1P2E48.5(

    ii

    XAPPPAREASTOREY

    TEMPEP1.0Q

    + =(23)

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    where variables Xnfor space and DHW heating energy consumption model are:

    INSUL2E03.33E01.7

    2E13.62E61.11E08.1a

    n

    eWA

    TANKWINSKYX n

    =

    (23a)

    Electric heated household without lagged fuel price:

    na

    n

    E96.21E85.4

    s

    2E26.32E20.4

    2E59.7E29.1)HHS4E82.8()GT2E84.9HHD2E33.8(

    ii

    XAPPPAREASTOREY

    TEMPEYP6.0Q

    =

    (24)

    where variables Xnfor space and DHW heating energy consumption model are:

    2E65.12E88.1a

    n DWAERATORXn = (24a)

    Electric heated household with lagged fuel price:

    n

    1,i

    a

    n

    1E98.21E57.2

    s

    2E33.3

    2E64.4E29.1)GT2E08.2HHD3E11.9P2E05.3(

    ii

    XAPPPSTOREY

    TEMPEP078.0Q

    =(25)

    where variables Xnfor space and DHW heating energy consumption model are:

    3E68.32E50.12E40.1a

    n WAWINDOORXn = (25a)

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    Table 5: Data Statistics for Appliance Energy Consumption Model for Natural Gas Heated Households

    Variables Name Count Max Min Average Median StDev 25 Percentile 75 Percentile

    App E Con (kWh) Q 271 39688.0 3901.0 10207.4 8956.0 5145.3 6716.0 11645.5

    Energy Exp. ($) EXP 271 2864.6 699.3 1282.4 1199.8 398.3 1008.2 1461.0

    Income ($) IN 230 100000.0 6000.0 47467.4 45000.0 25198.9 27500.0 70000.0

    HHSize HHS 271 8.0 1.0 3.1 3.0 1.3 2.0 4.0

    Old price ($/GJ) P-1 271 32.5 12.8 16.2 15.6 5.0 13.1 16.4Price ($/GJ) P 271 32.5 13.1 16.7 16.1 5.0 13.1 17.3

    HDD (C-day) HDD 271 6562.0 3007.0 5513.4 5889.0 734.1 5345.0 5920.0

    GdTemp (C) GT 271 12.3 4.8 6.4 6.1 1.8 4.8 6.6

    SHEff (%) EFF 271 77.5 57.5 63.3 64.0 6.6 57.5 64.0

    Temp (C) TEMP 271 23.3 15.0 19.8 20.0 1.5 19.0 21.0

    No. of Storey STOREY 271 3.0 1.0 1.3 1.0 0.4 1.0 1.5

    Hted Area (m^2) AREA 271 278.7 46.5 124.0 116.1 45.4 116.1 118.4

    BsmtSize (m^2) BASE 271 223.0 1.3 96.3 97.5 32.5 77.4 111.5

    DW-Total DW 271 780.0 0.0 174.6 156.0 189.0 0.0 312.0

    Wash-Total WA 271 780.0 0.0 308.9 260.0 192.3 156.0 455.0

    Dryer-Total DRY 271 780.0 0.0 268.1 208.0 190.5 130.0 364.0

    Age-free FREEZER-A 271 28.0 0.0 12.4 13.0 9.1 4.0 18.0

    Size-free (ft^3) FREEZER-S 271 25.0 0.0 13.4 16.0 6.9 11.0 16.0

    FF-1-Age FF1-A 271 23.0 0.0 8.2 9.0 6.4 2.0 13.0

    FF-1-Size (ft^3) FF1-S 271 22.0 0.0 14.8 15.0 6.0 15.0 19.0

    NFF-1-Age NFF1-A 271 23.0 0.0 1.9 0.0 5.7 0.0 0.0NFF-1-Size (ft^3) NFF1-S 271 19.0 0.0 1.6 0.0 4.8 0.0 0.0

    FF-2-Age FF2-A 271 23.0 0.0 2.0 0.0 5.6 0.0 0.0

    FF-2-Size (ft^3) FF2-S 271 22.0 0.0 1.9 0.0 5.2 0.0 0.0

    NFF-2-Age NFF2-A 271 23.0 0.0 3.9 0.0 7.8 0.0 0.0

    NFF-2-Size (ft^3) NFF2-S 271 19.0 0.0 2.7 0.0 5.4 0.0 0.0

    Range Age RANGE-A 271 23.0 0.0 10.4 9.0 6.7 5.0 13.0

    Cooktop (0/1) COOKTOP 271 1.0 0.0 0.0 0.0 0.2 0.0 0.0

    CDD (C) CDD 271 238.0 19.0 140.8 155.0 57.2 94.0 189.0

    AC usage (%) AC-USAGE 271 100.0 0.0 17.4 0.0 25.8 0.0 25.0

    Light LIGHT 271 132.0 10.0 40.1 37.0 19.0 27.5 49.0

    Ffan (0/1) FFAN 271 1.0 0.0 1.0 1.0 0.1 1.0 1.0

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    Table 6: Data Statistics for Appliance Energy Consumption Model for Electric Heated Households

    Variable Name Count Max Min Average Median StDev 25 Percentile 75 Percentile

    App E Con (kWh) Q 320 19423.7 1599.7 6783.6 6403.3 2699.0 4809.1 8291.5

    Energy Exp. ($) EXP 320 3246.8 490.6 1535.9 1487.2 447.4 1244.0 1806.1

    Income ($) IN 263 100000.0 6000.0 40667.3 37500.0 24397.7 22500.0 55000.0

    HHSize HHS 320 9.0 1.0 3.0 3.0 1.3 2.0 4.0

    Old price ($/GJ) P-1 320 32.5 12.8 15.1 15.6 1.8 15.6 15.6

    Price ($/GJ) P 320 32.5 13.1 15.5 16.1 1.9 16.1 16.1

    HDD (C-day) HDD 320 7930.0 3007.0 5077.2 4771.0 904.4 4709.0 4884.0

    GdTemp (C) GT 320 11.3 2.7 7.3 7.7 1.4 7.6 7.7

    SHEff (%) EFF 305 250.0 100.0 101.1 100.0 10.3 100.0 100.0

    Temp (C) TEMP 320 25.0 15.0 19.1 19.7 2.1 17.7 20.7

    No. of Storey STOREY 320 3.0 1.0 1.3 1.0 0.4 1.0 1.5

    Hted Area (m^2) AREA 320 278.7 46.5 116.4 116.1 46.2 74.3 118.4

    BsmtSize (m^2) BASE 320 278.7 13.4 94.9 98.0 33.5 74.3 116.1

    DW-Total DW 320 780.0 0.0 102.1 0.0 148.7 0.0 208.0

    Wash-Total WA 320 780.0 0.0 340.4 312.0 218.2 156.0 546.0

    Dryer-Total DRY 320 780.0 0.0 248.4 195.0 183.5 104.0 364.0

    Age-free FREEZER-A 320 28.0 0.0 9.4 9.0 7.9 1.0 13.0

    Size-free (ft^3) FREEZER-S 320 25.0 0.0 12.6 16.0 7.7 11.0 16.0

    FF-1-Age FF1-A 320 23.0 0.0 7.5 6.5 6.0 2.0 10.8

    FF-1-Size (ft^3) FF1-S 320 22.0 0.0 14.4 15.0 6.2 15.0 19.0

    NFF-1-Age NFF1-A 320 23.0 0.0 1.6 0.0 4.6 0.0 0.0

    NFF-1-Size (ft^3) NFF1-S 320 19.0 0.0 1.9 0.0 5.1 0.0 0.0

    FF-2-Age FF2-A 320 23.0 0.0 0.8 0.0 3.6 0.0 0.0

    FF-2-Size (ft^3) FF2-S 320 19.0 0.0 0.7 0.0 3.2 0.0 0.0

    NFF-2-Age NFF2-A 320 23.0 0.0 1.8 0.0 5.5 0.0 0.0

    NFF-2-Size (ft^3) NFF2-S 320 15.0 0.0 1.3 0.0 3.9 0.0 0.0

    Range Age RANGE-A 320 23.0 0.0 9.0 9.0 7.0 3.8 13.0

    Cooktop (0/1) COOKTOP 320 1.0 0.0 0.1 0.0 0.3 0.0 0.0

    CDD (C) CDD 320 189.0 19.0 108.6 125.0 39.1 97.0 138.0

    AC usage (%) AC-USAGE 320 100.0 0.0 1.0 0.0 7.8 0.0 0.0

    Light LIGHT 320 109.0 5.0 32.7 30.0 16.5 20.0 43.0

    Ffan (0/1) FFAN 320 1.0 0.0 0.9 1.0 0.3 1.0 1.0

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    Table 7: Appliance Energy Consumption Model Summary for Fossil Fueled Households

    Model Coefficients and t Values

    Without Lagged Fuel Price With Lagged Fuel Price

    Variable Name Variable Variable Description As "ENTER Upto 20% As "ENTER" Upto 20%

    Unit Coeff t Coeff t Coeff t Coeff t

    LN_CON (kWh) Ln (Appliance Con.)

    LN_EXP ($) Ln (Household energy exp) 9.77E-01 13.81 9.68E-01 14.62 1.13E+00 16.24 1.12E+00 17.39

    LN_EFF (-) Ln (Heating equipment efficiency) -1.13E-01 -0.63 -2.00E-02 -0.12LN_TEMP (C) Ln (Indoor temp.) 2.64E-01 1.25 3.73E-01 1.84 4.72E-02 0.24

    LN_STORE (-) Ln (No. of storey) -1.79E-01 -2.66 -1.93E-01 -3.15 -1.47E-01 -2.35 -1.64E-01 -2.94

    LN_AREA (m^3) Ln (Heated area) -2.58E-02 -0.38 -4.86E-02 -0.78

    LN_BASE (m^3) Ln (Basement area) -9.69E-02 -2.37 -9.81E-02 -2.60 -7.43E-02 -1.96 -8.68E-02 -2.52

    LN_DW_L (-) Ln (No. of dish washer load) -1.10E-02 -1.48 -1.26E-02 -1.75 -8.39E-03 -1.23 -1.00E-02 -1.55

    LN_WA_L (-) Ln (No. of clothes washer load) -1.62E-02 -0.67 -5.88E-03 -0.26

    LN_DRY_L (-) Ln (No. of clothes dryer load) 4.23E-02 2.11 3.40E-02 2.16 2.88E-02 1.55 2.70E-02 1.87

    LN_LIGHT ($) Ln (No of light blubs) 1.12E-01 2.52 1.18E-01 2.80 8.12E-02 1.97 7.91E-02 2.06

    HDD_LN_P ($/GJ) HDD*Ln (Price) -1.08E-01 -12.13 -1.12E-01 -12.81 -1.79E-02 -1.07 -2.05E-02 -3.49

    GT_LN_P ($/GJ) Ground Temp*LN (Price) -8.30E-02 -9.49 -8.75E-02 10.37 4.05E-03 0.25

    HHS_LN_I ($) Household size*Ln (Income) 5.65E-03 3.07 5.75E-03 3.31 3.72E-03 2.17 3.54E-03 2.22

    A_N_S_FR (ft^3) Freezer Age*Ln (Size) -4.47E-05 -0.06 -4.45E-04 -0.69

    ALN_S_F1 (ft^3) First Frostfree Fridge Age* Ln(Size) -1.47E-03 -1.28 -9.35E-04 -0.88

    ALN_SN1 (ft^3) First non-Frostfree Fridge Age* Ln(Size) -2.70E-03 -1.97 -1.59E-03 -1.44 -3.19E-03 -2.52 -2.32E-03 -2.31

    ALN_S_F2 (ft^3) Second Frostfree Fridge Age* Ln(Size) 1.94E-03 1.67 1.92E-03 1.79 1.45E-03 1.46

    ALN_SN2 (ft^3) Second non-Frostfree Fridge Age* Ln(Size) 8.51E-04 0.93 8.15E-04 0.96

    CDD_LN_U (%) CDD*Ln (A/C Usage) 6.59E-05 3.19 7.33E-05 3.70 4.99E-05 2.60 5.33E-05 2.90CT_I (-) Cooktop Indicator (0 or 1) 9.95E-02 1.07 1.18E-01 1.38

    FAN_I (-) Furance Fan Indicator (0 or 1) 3.51E-01 1.39 3.39E-01 1.36 1.25E-01 0.53

    LN_RAN_A (-) Ln (Range/oven age) 3.32E-02 1.40 3.10E-02 1.42

    OP_LN_P ($/GJ) Lag. Price * Ln (Price) -5.75E-02 -6.21 -5.76E-02 -13.39

    CONSTANT 4.452 3.797 3.713 4.525 1.828 1.577 2.070 4.537

    R-SQUARE 0.706 0.696 0.753 0.746

    ADJ. R-SQUARE 0.675 0.678 0.725 0.732

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    Table 8: Appliance Energy Consumption Model Summary for Electric Heated Households

    Model Coefficients and t Values

    Without Lagged Fuel Price With Lagged Fuel Price

    Variable Name Variable Variable Description As "ENTER Upto 20% As "ENTER" Upto 20%

    Unit Coeff t Coeff t Coeff t Coeff t

    LN_CON (kWh) Ln (Appliance Con.)LN_EXP ($) Ln (Household energy exp) 7.97E-01 12.65 8.30E-01 14.54 7.96E-01 12.61 8.30E-01 14.54

    LN_EFF (-) Ln (Heating equipment efficiency) 3.65E-01 1.08 4.12E-01 1.77 3.62E-01 1.07 4.12E-01 1.77

    LN_TEMP (C) Ln (Indoor temp.) 1.63E-01 1.16 1.62E-01 1.15

    LN_STORE (-) Ln (No. of storey) -1.34E-01 -2.00 -1.29E-01 -2.19 -1.34E-01 -2.00 -1.29E-01 -2.19

    LN_AREA (m^3) Ln (Heated area) 4.01E-02 0.71 4.16E-02 0.73

    LN_BASE (m^3) Ln (Basement area) -8.99E-02 -1.74 -6.86E-02 -1.63 -8.82E-02 -1.70 -6.86E-02 -1.63

    LN_DW_L (-) Ln (No. of dish washer load) 1.27E-02 1.70 1.53E-02 2.34 1.23E-02 1.64 1.53E-02 2.34

    LN_WA_L (-) Ln (No. of clothes washer load) 8.49E-03 0.51 7.80E-03 0.46

    LN_DRY_L (-) Ln (No. of clothes dryer load) 1.94E-02 1.37 2.13E-02 1.80 1.93E-02 1.36 2.13E-02 1.80

    LN_LIGHT ($) Ln (No of light blubs) 5.28E-03 0.14 5.59E-03 0.14

    HDD_LN_P ($/GJ) HDD*Ln (Price) -4.04E-02 -2.18 -4.73E-02 -2.72 -3.26E-02 -1.18 -4.73E-02 -2.72

    GT_LN_P ($/GJ) Ground Temp*LN (Price) -3.69E-02 -2.46 -4.28E-02 -3.03 -2.95E-02 -1.20 -4.28E-02 -3.03

    HHS_LN_I ($) Household size*Ln (Income) 9.23E-03 5.22 9.27E-03 5.78 9.28E-03 5.23 9.27E-03 5.78

    A_N_S_FR (ft^3) Freezer Age*Ln (Size) -1.76E-04 -0.24 -1.78E-04 -0.24

    ALN_S_F1 (ft^3) First Frostfree Fridge Age* Ln(Size) 6.00E-04 0.53 5.79E-04 0.51

    ALN_SN1 (ft^3) First non-Frostfree Fridge Age* Ln(Size) -2.28E-03 -1.47 -2.53E-03 -1.90 -2.27E-03 -1.47 -2.53E-03 -1.90

    ALN_S_F2 (ft^3) Second Frostfree Fridge Age* Ln(Size) 1.59E-04 0.10 2.09E-04 0.13ALN_SN2 (ft^3) Second non-Frostfree Fridge Age* Ln(Size) 1.59E-03 1.22 1.68E-03 1.47 1.60E-03 1.22 1.68E-03 1.47

    CDD_LN_U (%) CDD*Ln (A/C Usage) 3.42E-05 0.23 3.48E-05 0.23

    CT_I (-) Cooktop Indicator (0 or 1) 9.81E-02 1.48 9.71E-02 1.46

    FAN_I (-) Furance Fan Indicator (0 or 1) 3.79E-03 0.08 3.14E-03 0.07

    LN_RAN_A (-) Ln (Range/oven age) 1.55E-02 0.73 1.53E-02 0.72

    OP_LN_P ($/GJ) Lag. Price * Ln (Price) -2.41E-03 -0.38

    CONSTANT 1.710 1.037 2.108 1.794 1.551 0.910 2.108 1.794

    R-SQUARE 0.671 0.665 0.672 0.665

    ADJ. R-SQUARE 0.641 0.650 0.640 0.650

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    Table 9: Appliance Energy Consumption Model Elasticities Estimates for Natural Gas Fueled Households

    Model I (w/o lagged) Model II (w/ lagged)

    As Entered 20% As Entered 20%

    Variable Coeff

    Lagged Price -5.747E-02 -5.756E-02

    HDD -1.080E-01 -1.120E-01 -1.794E-02 -2.050E-02GT -8.303E-02 -8.749E-02 4.048E-03 0.000E+00

    HHS 5.645E-03 5.746E-03 3.720E-03 3.539E-03

    Variable mean

    Lagged Price (mean) 3.255 3.255

    Lagged Price (mean+StDev) 4.255 4.255

    Lagged Price (mean-StDev) 2.255 2.255

    HDD 7.511 7.511 7.511 7.511

    GT 3.527 3.527 3.527 3.527

    HHS 2.433 2.433 2.433 2.433

    EXP 1282.418 1282.418 1282.418 1282.418

    CON 10207.354 10207.354 10207.354 10207.354

    Own Price Elasticity at Mean

    Short-run Price Elasticity -1.104 -1.150 -0.308 -0.341

    Long-run Price Elasticity -1.594 -1.746

    Own Price Elasticity at Mean+StDev

    Short-run Price Elasticity -1.104 -1.150 -0.365 -0.399

    Long-run Price Elasticity -1.739 -1.913

    Own Price Elasticity at Mean-StDev

    Short-run Price Elasticity -1.104 -1.150 -0.250 -0.284

    Long-run Price Elasticity -1.472 -1.605

    Income Elasticity 0.009 0.009

    Expenditure Elasticity 0.977 0.968 1.130 1.115

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    Table 10: Appliance Energy Consumption Model Elasticities Estimates for Electric Heated Households

    Model I (w/o lagged) Model II (w/ lagged)

    As Entered 20% As Entered 20%

    Variable Coeff

    Lagged Price*P -2.413E-03 0.000E+00

    HDD*P -4.041E-02 -4.729E-02 -3.261E-02 -4.729E-02GT*P -3.692E-02 -4.278E-02 -2.950E-02 -4.278E-02

    HHS*IN 9.228E-03 9.274E-03 9.282E-03 9.274E-03

    Variable mean

    Lagged Price (mean) 8.490 8.490

    Lagged Price (mean+StDev) 9.490 9.490

    Lagged Price (mean-StDev) 7.490 7.490

    HDD 5.614 5.614 5.614 5.614

    GT 5.253 5.253 5.253 5.253

    HHS 2.253 2.253 2.253 2.253

    EXP 1535.903 1535.903 1535.903 1535.903

    CON 6783.606 6783.606 6783.606 6783.606

    Own Price Elasticity at Mean

    Short-run Price Elasticity -0.421 -0.490 -0.430 -0.594

    Long-run Price Elasticity -0.739 -1.208

    Own Price Elasticity at Mean+StDev

    Short-run Price Elasticity -0.421 -0.490 -0.433 -0.594

    Long-run Price Elasticity -0.742 -1.208

    Own Price Elasticity at Mean-StDev

    Short-run Price Elasticity -0.421 -0.490 -0.250 -0.594

    Long-run Price Elasticity -0.561 -1.208

    Income Elasticity 0.021

    Expenditure Elasticity 0.797 0.830 0.796 0.830

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    Table 11: Data Statistics for Natural Gas Space Heating Energy Consumption Model in Natural Gas Heated Households

    Variables Name Count Max Min Average Median StDev 25 Percentile 75 Percentile

    SpHt+DHW E Con Q 226.0 181.4 20.6 92.8 87.4 27.8 73.6 108.0

    Income IN 190.0 100000.0 6000.0 45144.7 45000.0 24379.3 27500.0 55000.0

    HHSize HHS 226.0 7.0 1.0 3.2 3.0 1.2 2.0 4.0

    Old Price ($/GJ) P-1 226.0 5.5 3.4 4.7 4.3 0.7 4.3 5.4Price ($/GJ) P 226.0 5.6 3.9 4.9 4.4 0.6 4.4 5.6

    Price-s ($/GJ) Ps 226.0 20.8 13.1 15.7 17.3 2.3 13.1 17.3

    Energy Exp. ($) EXP 226.0 2499.0 699.3 1190.3 1160.3 288.8 984.0 1336.5

    HDD (C) HDD 226.0 6562.0 3962.0 5740.8 5889.0 476.8 5889.0 5920.0

    GdTemp (C) GT 226.0 11.1 4.8 5.9 6.1 1.2 4.8 6.1

    SHEff (%) EFF 226.0 77.5 57.5 62.5 64.0 6.3 57.5 64.0

    Temp (C) TEMP 226.0 23.3 15.0 19.9 20.0 1.5 19.0 21.0

    No.Storey STOREY 226.0 2.5 1.0 1.2 1.0 0.4 1.0 1.5

    Hted Area (m^2) AREA 226.0 278.7 46.5 117.5 116.1 40.1 74.3 116.1

    BsmtSize (m^2) BASE 226.0 223.0 1.3 93.9 93.6 31.3 74.3 111.5

    Total Door DOOR 226.0 7.0 1.0 2.6 2.0 0.9 2.0 3.0

    Total Sky SKY 8.0 4.0 1.0 1.6 1.0 1.1 1.0 2.0

    Total Win WIN 224.0 38.0 3.0 11.2 10.0 5.3 7.8 14.0

    App E Con. APP 226.0 98.5 14.0 35.1 32.3 14.4 25.1 39.8

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    Table 12: Data Statistics for Electric Space Heating Energy Consumption Model in Electric Heated Households

    Variables Name Count Max Min Average Median StDev 25 Percentile 75 Percentile

    SpHt+DHW E Con Q 320.0 148.1 8.7 56.0 53.2 21.0 41.8 67.0

    Income IN 263.0 100000.0 6000.0 40667.3 37500.0 24397.7 22500.0 55000.0

    HHSize HHS 320.0 9.0 1.0 3.0 3.0 1.3 2.0 4.0

    Old Price ($/GJ) P-1 320.0 32.5 12.8 15.1 15.6 1.8 15.6 15.6Price ($/GJ) P 320.0 32.5 13.1 15.5 16.1 1.9 16.1 16.1

    Price-s ($/GJ) Ps 320.0 11.0 7.3 10.1 10.0 0.7 10.0 10.0

    Energy Exp. ($) EXP 320.0 3246.8 490.6 1535.9 1487.2 447.4 1244.0 1806.1

    HDD (C) HDD 320.0 7930.0 3007.0 5077.2 4771.0 904.4 4709.0 4884.0

    GdTemp (C) GT 320.0 11.3 2.7 7.3 7.7 1.4 7.6 7.7

    SHEff (%) EFF 305.0 250.0 100.0 101.1 100.0 10.3 100.0 100.0

    Temp (C) TEMP 320.0 25.0 15.0 19.1 19.7 2.1 17.7 20.7

    No.Storey STOREY 320.0 3.0 1.0 1.3 1.0 0.4 1.0 1.5

    Hted Area (m^2) AREA 320.0 278.7 46.5 116.4 116.1 46.2 74.3 118.4

    BsmtSize (m^2) BASE 320.0 278.7 13.4 94.9 98.0 33.5 74.3 116.1

    Total Door DOOR 310.0 11.0 1.0 2.7 2.0 1.1 2.0 3.0

    Total Sky SKY 7.0 4.0 1.0 2.1 2.0 0.9 2.0 2.0

    Total Win WIN 311.0 40.0 2.0 10.7 10.0 4.3 8.0 13.0

    App E Con. APP 320.0 69.9 5.8 24.4 23.1 9.7 17.3 29.8

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