ML19329E973

Residential Electricity Elasticities in Lower Peninsula of Mi, Vol 1,prepared for CPC & Detroit Edison Co

ML19329E973
Person / Time
Site:	Midland
Issue date:	07/31/1977
From:	Banks P, Campbell J, Knowles R EQUITABLE ENVIRONMENTAL HEALTH, INC. (SUBS. OF EQUITA
To:
References
NUDOCS 8006190749
Download: ML19329E973 (111)

Text

{{#Wiki_filter:3 m-rs [. i" >L 1 g _ ' "t [ sur se 1 i: l y. tk 1 so_ m xIc= 1

• /

REs:DE';*IAL ELECTRICIT ELASTICIIIES II g_ j ,; E m,Es re.: sLA 0F "IuiIGA:: R ,2 - s p letter u d C t' d 9-I- b- -{l e D l t j i [ S . c

t

n 1

i i -1, = NOTICE - l 1 THE ATTACHED FILES ARE OFFICIAL RECORDS OF THE i DIVISION OF DOCUVENT CONTROL THEY HAVE BEEN ! ! CHARGED TO YOU FOR A LlYlTED TIME PERIOD AND l j ! MUST BE RETURNED TO THE RECORDS F ACILITY j i BRANCH 016. PLEASE DO NOT SEND DOCUYENTS l CHARGED OUT THROUGH THE VAll l REYOVAL OF ANY j PAGE(S) FROY DOCUVENT FOR REPRODUCTION YUST BE REFERRED TO FILE PERSONNEL. d. -a DEADLINE RETURN DATE z a (i ( g3 ki', THIS DOCUMENT CONTNNS y W j .g s, 000R gua0TY m.) = u, '? y t Ts: g i ~ y ~ g C I _ RECORDS F ACILITY BR ANCH 1,.. !] , 9O ' {' l w s

r7

i..

1 RESIDENTIAL ELECTRICITY ELASTICITIES-IN THE LOWER PENINSULA 0F MICHIGAN VOLUME 1 . 4 Prepared For: Consumers Power Company and Detroit Edison Company Prepared By: Philip $. Banks John M. Campbell, Jr. Richard K. Knowles E. Kemp Prugh George S. Tolley, Consultant Economic Analysts Division of Equitable Environmental Health, Inc. 455 Fullerton Avenue Elmhurst, Illinois 60126 July 1977 A Subsidiary of The Equitable Life Assurance Society of the United States z

f*+

a

M CONTENTS

Page, t_.

LIST OF FIGURES iv LIST OF TABLES i V EXECUTIVE

SUMMARY

vi I INTRODUCTION 1 A. Purpose and Objectives 1 B. Meaning and Importance of Elasticity 2 C. Price Elasticity of Demand for Electricity 3 D. Rationale and Problems of Econometric Modeling 4 E. Approach and Organization 6 i f' II DEFINITION AND EXPLANATION OF THE ECONOMIC TERM " ELASTICITY" 7 1 A. Elasticity and Demand 8 B. Estimation Procedure 15 C. Policy Implications 17 III LITERATURE REVIEW 19 .A. Elasticity Estimates Obtained by Other Investigators 19 B. Summary of Procedures Employed in Past Studies 22 1. Type of Estimation Procedure 22 2. Unit of Observation 27 i 3. Form of Estimating Equation 30 C. Specification of Variables 30 1. Dependent Variables 31 p.. L_ 2. Price of Electricity 32 3. Income 35 7

l...

emimi. 1 -__..m _..--.-r-.-. p- --m.,..-,w ,.,,.....,w.,, 7 -

0 CONTENTS (Cont.) Pace 4. Competing Fuels 36 5. Housing Characteristics 38 6. Weather Variables 39 7. Appliance Saturation Levels 40 ~~ D. Summary 40 IV DATA 42. A. Data Expectations 43 B. Regional Data 44 1. Consumption, Revenue, and Average Price for the 45 Electricity Utilities .1, {.. 2. Inccme 46

r-3.

Marginal Price of Electricity 47 l 4. Alternative Fuel Prices 51 5. Weather Data ' !.\\ 54 6. Housing Characteristics 55 7. Appliance Saturation Levels 57 8. Cost of Living Deflaters 58 f- ~ C. Company Level Data 58 f D. Individual Customer Data 59 .L E. Special Problem Areas and Alternative Data Sources 62 ?L V ESTIMATION OF DEMAND 64 J-A. Time Series Estimation of Demand 64 1. Regional-level Estimation of Demand 64 a. Initial Estimation Efforts 64 b. Addition of Housing Characteristics 65 '. l _ amme 11 r- ~

CONTENTS (Cont.) Page c. Inclusion of Additional Alternative Fuel 65 Price Data d. Inclusion of Appliance Saturation Levels 66 e. Lagged Independent Variables 67 f. Weather Variables 67 g. Electricity Price - Marginal 67 2. Company Level Demand Estimation 68 B. Combined Cross-Section/ Time Series Estimation Of Demand 70 C. Cross Section Estimation of Demand 73 1. Regional Cross Section Work 73 2. Individual Customer Cross Section Estimation of Demand 75 [' VI ANALYSIS 80

i A.

Cross Section Analysis 84 B. Time Series Analysis 90 GLOSSARY 96 REFERENCES 99 APPENDIX A - LITERATURE REVIEW APPENDIX B - DERIVATION OF WEIGHTS FOR AGGREGATION OF COUNTY DATA TO THE DIVISIONAL LEVEL APPENDIX C - DOCUMENTATION OF DEVELOPMENT OF REGIONAL DATA BASE FROM RAW DATA SOURCES APPENDIX D - DATA LISTING APPENDIX E - REGIONAL TIME SERIES REGRESSIONS i_ APPENDIX F - COMPANY LEVEL TIME SERIES

u.

APPENDIX G - REGIONAL CROSS SECTION MODEL APPENDIX H - COMBINED CROSS-SECTION/ TIME SERIES ANALYSIS APPENDIX I - INDIVIDUAL CUSTOMER CROSS SECTION REGRESSIONS APPENDIX J - APPLIANCE SATURATION REGRESSIONS iii

LIST OF FIGURES Page II-1 Example of a Demand Curve 9 ~ II-2 Shift in Demand Curve 11 II-3 Calculation of Elasticity 14

P V-1 Degree Day Correlation, Detroit City Airport 72

. l VI-1 Typical Patterns of Observed Market Quantities 81 and Prices i VI-2 Elasticity Estimation with Properly Identified 82 Demand Curve VI-3 Elasticity Estimation with Improperly Identified 83 Demand Curve VI-4 Estimating Block Structure " Elasticity" 85

r i

L.., e a e E I o ' r 4.. t u e T e ^%** 4 C c4-jy /

LIST OF TABLES Page III-1 Summary of Selected Previous Elasticity Studies 20 IV-1 Marginal Prices for Electricity, Consumers Power 49 i ~' Company IV-2 Marginal Prices for Electricity, Detroit Edison 50 Company IV-3 Sources for Natural Gas Data Within Detroit 53 Edison Service Area IV-4 Sources for Heating Degree-Day Data Within 56 Detroit Edison Service Area IV-5 Weighting Factors for Company Level Gas Prices 60 V-1 Regional Time-Series Modei 69 V-2 Comparison of Weather Related Variables for 71 Detroit Edison V-3 Individual Customer Results Which Do Not Include 76 . Appliance Variables or a Price Variable V-4 Individual Customer Results Including Appliance 77 Variables But Not a Price Variable V-5 Individual Customer Results Including An Average 78 Price Variable and No Specific Appliance Variable 't V-6 Individual Customer Results Including An Average 79 Price Variable and Appliance Variables VI-1 Consumption Analysis by Income Group 88 VI-2 Calculated " Elasticity" Estimates from the 89 Individual Customer Data VI-3 Derivation of Weights for Use in Aggregating Regional 93 Data VI-4 Service Area Elasticity Estimates 94 1 6 c, v

,~. EXECUTIVE

SUMMARY

The analysis presented here involves a rather straightforward applica-tion of modern econometric methods. It is distinguished from previous studies of the elasticity of demand for electricity, first by the fact that .s it deals specifically with the areas served by the two client companies ~ and with the regions into which their service areas are sub-divided, and second, by the fact that it has involved the investigation of a larger number of variables as determinants of electricity consumption than any previous study of which we're aware. ~ The purpose of the study was to determine what the actual historical experience of these two ctmpanies can tell us about the elasticity of demand in their service araas -- i.e., about the degree to which rate changes have caused changes in the consumption of electricity -- and what basis it 1 thus provides for predicting the effects of proposed rate changes. Some 50 variables were investigated as determinants of demand with the potential for explaining variations in consumption that might otherwise be associated with, and attributed. to, differences in residential rates. This investigation utilized cross-sectional analysis, concerned with the effects of differences existing at given points of time, as well as time-l l series analysis, which is concerned with the effects of changes occurring over time. The econometric models that provided the best estimates (i.e., estimates of consumption that most closely fit the actual historical ievels) { i Vi r-t... ~

were the regional time-series models showing electricity consumption as a function of the following 9 variables: Marginal Electricity Price Marginal Natural Gas Price Fuel Oil Price - Per Capita Income Percent Multi-unit Housing Percent Urbanization Heating Degree Days Previous Period Consumption Consumer Price Index (used as a deflater) As shown in the table below, the price coefficients for the two ((' companies are in close agreement, and well within the range that would be expected for measures of price elasticity. -They also lie at the mid-point ( of the range of estimates that other studies have made of short-run price eYasticity. For these reasons, it would be tempting to interpret the price coefficients -- as other studies have interpretted them -- _as ' measures of price elasticity. But the insights provided by the regional analysis i argue against that interpretation. l l SHORT-RUN PRICE COEFFfCIENTS* (Commonly Regarded as Measures of Price Elasticity) DETROIT CONSUMERS EDISON POWER i~ REGIONS 1.owest .046 .062 Highest .229 .255 (I, SERVICE AREA .16 .20

• Derived from the time-series analysis vii

-The coefficients for the individual regions vary too widely to be consistent, as measures of elasticity, either with one another, with the . l company averages, or with the industry's experience with revenues. The analysis clearly demonstrates that the experience of these two companies provides little insight into the effects of rate changes, and is dominated instead by the effect that varying consumption has on the marginal and average prices paid for electricity, and by the growth that has occurred during a period of inflation (which is conventionally and necessarily treated as a decline in the "real" price of electricity, but can hardly

~

be said to have caused the growth in consumption). The extremely low income coefficients and related estimates of income elasticity would further suggest that too much of the variation in consump-tion has been attributed to price. This tends to be confirmed by the ( substantial increase in income coefficients that result from deleting the price variable. To the degree that econometric models accurately capture the price-consumption relationships that have been dominant in the case of these two companies, their price coefficients cannot be logically construed as measures of price. elasticity -- however conventional it may be to do so, and however valid it may be in othLr cases. They cannot in other words, provide a valid basis for predicting the effacts of proposed rate changes. tied M me e a viii

---

,mz.

r- ,--y-ge n-- g y

1 I. INTRODUCTION A. PURPOSE AND OBJECTIVES The study presented here was prompted by the need to better understand the relationship existing between the price and consumption of electricity in the Lower Peninsula of Michigan, in order to anticipate the effects of proposed rate changes. The specific objectives of the study are first to determine'the i qucnticative relationship that has prevailed historically between residen-tia: rates and consumption, and then to assess the degree to which that ~ relationship can serve as a basis for predicting the effects of price changes -- or, in other words, for estimating the elasticity of demand with respect to price. Since the basic aim of the interested parties is to predict future. i effects on the basis of cast experience, the purpose of the study could be said to be simply to provide the estimates of price elasticities on which such predictions could be based, with consideration given to the price elasticities within usage blocks (e.g., less than 500 kWh monthly, 500 to 1000 kWh, and more than 1000 kWh). However, a concern for objec-tivity argues that the purpose of the study itself is more correctly seen as being to determine whether that can be done and, if so, with what degree of confidence -- and to provide estimates of elasticity only insofar as the analysis shows them to be logically supportable. The first objective, then, is to develop the econometric models that { most accurately capture the quantitative relationship that has prev. ed historically between the price and consumption of electricity, in the areas t. i L,

g served by the two client companies. The second objective is to critically assess the degree to which the price coefficients of those models reflect the causal relationship that would make them logically valid as estimates of elastic! i, and thus as a basis for predicting the effects of rate changes. B. MEANING AND IMPORTANCE OF ELASTICITY Contrary to the impressions sometimes encountered, pr' ice elasticity is basically a simple concept, and one of great practical importance. It has to do with the extent to which price changes cause changes in the quan-- tity demanded, and thus with the way in which revenues respond to price variations. The causal relationship needs to be stressed; elasticity is concerned with changes in quantity demanded that are caused by changes in price -- not those which are merely associated with price variations. ~ Demand is said to be elastic when price changes cause proportionately larger percentage changes in the quantity demanded, or consumed. In this case, since quantity demanded varies inversely with price, total revenue is increased by lowering price and decreased by raising price. Demand is inelastic, by definition, if price changes result in pro-portinately smaller percentage variations in consumption. In this case, because of the inverse relation of price and quantity (i.e., the negative l slope of demand functions), revenue varies directly -- though not pro-portinately -- with price, being increased by ' price hikes and reduced by m. j ~t price cuts. l ~~ Technically, the price elasticity of demand is defined as the ratio of t, _] percentage change in quantity to percentage change in price. Demand is said m: LI n, mes I ..y-..,-._,.--_.~.,,.-..7- .,y,.. m. .,,, ~,.v* .. -..v.-,.. c,.3,-,.,mc..,. ,, -..my,w -.,,y

3 to be elastic if the elasticity (this ratio) is greater than one, and in-elastic if it's less than one. The inverse relation of price and quantity gives this ratio negative values, and introduces an element of confusion in speaking of numbers that are greater or less than minu's one. " Greater than one" is understood to refer to a negative number larger than one; "less than one" is understood to refer to a negative number smaller than one -- i.e., a number between zero and minus one. As a first approximation, elasticity may be thought of as being ~~ determined by the slope of the demand curve, with steeply inclined curves being less elastic than flatter, more gradually inclined demand curves. f However, since elasticity is a ratio of percentage changes, all demand functions -- even those whose slope is constant -- are elastic in the higher price ranges and inelastic in the lower price ranges. The point is that we cannot refer simply to phs elasticity of demand for a good; we must speak of_,its elasticity at (or near) a given price. The two exceptions are the cases of vertical and horizontal demand curves, the fonaer having an .asticity of zero at all prices, and the latter having infinite elasticity at all quanticies. C. PRICE ELASTICITY OF DEMAND FOR ELECTRICITY ~ I_ The experience of the industry, and of consumers as well as the producers, t amply demonstrates that the demand for electricity is inelastic with respect to price. That is, consumers do not, as a group, curtail their use of electricity enough to offset rate hikes, or increase it enough to offset the effects of rate reductions. In other words, the consumers' bills and the producers' revenues rise when rates are increased and fall if rates are cut. 7 u_ l n-4

4

c.

Our purpose then, it not to determine whether the demand for electricity is elastic or inelastic, but to determine how close we can get to specifying, 4 numerically, where the elasticity lies within the inelastic range. The definition of elasticity, and the related general insights gained from the industry's experience, provide an important objective standard against which numerical estimates of elasticity may be judged. o L, D. RATIONALE AND PROBLEMS OF ECONOMETRIC MODELING As already noted, the basic aim of econometric anlaysis is to quantify the relationships existing between variables that are related by logic. The point to be stressed is that the independent variables are chosen because of theoretical, or logical, reasons to regard them as determinants of consumption, and not simply because a strong statistical association can be 3hown to exist. Statistical methods are used only to estimate the quantitative importance of the relationships, though this may-in some cases be viewed as testing the hypothesis that a relation exists. Price is included among the independent variables for a special reason, a' course -- not because it's presumed to be a major detenninant of consumption (in this case, it isn't), but because the effect of price, k however small, is the issue that the study is concerned with. The identification of one variable as a determinant of another obviously implies a theory of causation. Changes in the determinant (e.g., population ,[ or income) are presumed to cause changes in the dependent variable (in this case, consumption), while the reverse causal relationship is presumed not to exist. i

Lj

'f i -t-O e-g- + re -eece s --- i-- w-+,ym-- +m-e s-w -w--- +--*,sw+e w --e.- p +cw-t-r-e.-twe--+w y p- --e-r-err

• +--wDem,-m+e-e-wyf w

-wrw-ee-- c.e#-- -y--

~ 5 There's a certain tendency to assume implicitly that this simple causal theory applies to price once it's been included aaong the determinants of ~- consumption, and to forget that the causal relationship between these two variables is known to be far more complex, even in the general case. Quantity demanded is known to be affected by price, and the analysis of elasticity is concerned with.that effect. But this is easily confused with the effects that changing demand is known to have on price -- a very different phenomenon involving a shift of the demand function as a result of changes in population, incomes, tastes, prices and availability of competing and complementary goods, and so on. The causal relationship between price and quantity demanded is the reverse of that between demand and price; shifts in demand cause changes in price, while changes in price cause changes in the quantity demanded. And while quantity demanded varies inversely with price, price is commonly said to vary directly with demand -- though it's more correctly seen to vary either directly or inversely with demand (or not at all), depending on the slope of the supply function. To complicate matters still further, individual customers of the two client companies have faced declining supply functions until recently, and that relationship is dominant in the experience and data available for this analysis -- though rate structures have changed, and t the hope is that past experience can provide insights into the effects of future changes. U l' m -_w e

6 Apart from the common confusion between changes in demand and chacqas in quantity demanded, a serious potential exists for confusing the supply functions -- which in this case have had the negative slope more '~ canmonly associated with demand -- with the demand functions whose slopes we're endeavoring to measure. The effort to distinguish between these various effects. which are 't so easily (and so commonly) confused, constitutes a major part of this study. E. APPROACH AND ORtiANIZATION Section II provides an expanded discussion dealing with the concepts I cf demand and elasticity, and with the problems and procedures relating to their measurement. ~ Section III is a rather brief summary of the literature ~ pertaining q to previous studies of price elasticity, which was reviewed in some depth for the insights that it had to offer. ' L_ Section IV is concerned with the data on which the analysis rests and the problems involved in its collection and interpretation. Section V deals with the development of the econometric models and the estimation of demand on regional, company-wide, and individual customer basis. Section VI summarizes the analysis of the findings and presents the conclusions to be drawn from them. L;

en t_

-.m4,.- ,,e,r ,.,.,,., -., - ~ -wy ,.-- ~ ~ s,+- -r--,

b 7 II. DEFINITION AND EXPLANATION OF THE ECONOMIC TERM " ELASTICITY" ~ The phrases " elasticity of demand" or " demand elasticity" are widely I" used in many contexts; however, real understanding of what is meant by these .w-phrases is often missing. The purpose of this section is to explain the ~ i_ concept of elasticity to eliminate any basic misunderstand 1ngs that may exist, and then go on to a more in-depth analysis which demonstrates the underlying consumer behavior assumptions from which elasticities can be derived. I Elasticity of demand is defined as the percentage change in quantity demanded divided by the percentage change in price when the prics change is smaZZ. This concept is a measure of the responsiveness of the quantity de-manded to changes in the price of a good. A primary use of elasticity measures ~ is to indicate whether or not revenues will rise or fall in response to a price change. Elasticities are classified as elastic or inelastic on the basis of their effect on total revenues. An inelastic value is less than 1, and indicates a price increase will increase total revenues. An elastic value, one which is greater than 1, implies total revenues will decrease with a price increase. An elasticity of exactly one is called a unity elas- -L ticity, and indicates a price change will have no effect on total revenues. At this point it is worthwhile to point out the difference between the definition of a quantity and the quantitative estimation of that quantity. Clearly, these two things are different, one being an estimate of the other. .c I b_ . f' 1. Leftwich, "The Price System and Resource Allocation". l; \\ f ud ,9 =+e g-y, -r-i---i3 e,n- -,r---,y--- y-<y-w--grgy----,-y

---

y-gr+%i,--~+--py-ewwor-

~ pig w ' gr+,-e-g,--- g g-gwwt --s--9-, g-op-g-w--**wyg ---g-e we gy w y7 gy--- w--v----vyw-ey-

R i'!. ] But in elasticity scudies this distinction is obscured by the second layer of estimating that is occurring. The obvious estimation is statistical in i nature where coefficients represent inexact estimates. But what is not so widely appreciated is that these coefficients, even if they were exactly ~ measured, are still only theoretical estimates of elasticity. Starting with the concept of elasticity and then assuming a general functional form for numerical analyses still involves an estimation. The difference is that this is a theoretical estimation whereas the more readily understood statistical estimation is numerical in nature. If these points are kept in mind the later sections in this report can be properly interpreted. The remainder ~ of this section is devoted to an in-depth analysis which elucidates the I[, assumptions made in economics that allow the derivation of an elasticity. A. ELASTICITY AND DEMAND { Before proceeding directly into the conept of elasticity, it is useful ~ to introduce the idea of demand as economists use it. Demand is defined as L, a schedule that shows the alternative quantities of a good (or service) that a consumer is willing to buy at various prices. The important thing L-is that all factors except the prica of the good under consideration are considered to be held constant. This is the famous ceteris paribus or "other L things equal" condition. I' L M9 - g. ~

9 Thus, graphic portrayal of a demand schedule would appear as in Figure II-1 below: ? Price p p -t I I I I I i i ~ l l d i-t 1 0 0 1 2 Quantity Figure II-1 Example of a demand curve At price P, a consumer desires to buy the quantity Q ; likewise, at 1 1 price P, he wishes to buy the quantity Q. If price were to change in a 2 2 given period from P to P in another period, an economist would say that t 2 the quantity demanded has increased from Q to Q

• 1 2

g The underlying behavioral model behind the above downward sloping demand schedule is called utility maximization theory. This theory assumes that L consumers purchase goods and services because of the utility derived from r-them. Since most goods have positive prices (i.e., are not " free goods") L V L. e e6 ~. - ,g ,e-s-~ ,y w--w-r,, ,e e m ,,,a

10 m e-i.. and all consumers have some sort of a budgetary constraint, a methcd must 2 be derived such that a consumer can rationally allocate his expencitures on the goods and services so as to maximize his total utility. As is shown in elementary microeconomics textbooks if a consumer allocates his purchase such that the marginal utility (MU) per dollar spent for all goods and t services are equal, then his total satisfaction or utility is maximized. Expressed in a simple mathmematical relationship, the rule (considering only three goods) is as follows: MU MU MU x= z P ~1 P x y z Now, if a consumer is in equilibrium (i.e., the above condition holds) and the price of X falls, then the following obtains: MU MU MU x > y, z x y z The consumer then has the incentive to buy more of good X since its marginal utility per dollar spent is greater than that for the other two goods. There-fore, a price decrease will result in a change in quantity demanded as illus-trated in Figure II-1. On the other hand, when economists speak of a change in demand, they are referring to a shift in the entire demand schedule as illustrated in Figure II-2 below: a. L M 7- ~- ,m ,,~- a ,,--.v---,,-,., n, 4 ~

11 Price d d' r-p l l ~ l I I i ri l l I I I I l I ~~r-I I l i I d' t I i l i i 9 0 Quantity 1 2 Figure II-2. Shift in demand curve. I L-Here, the shift in the demand schedule from dd to d'd' represents a change in demand. This shift is caused by a change in one (or more) of the factors previously held constant. Thus, a change in income, tastes, or price (s) of another good could cause such a change, but not a change in the price of the good under consideration. Note that, with this shift or change in demand, i l, the quantity demanded at a given price P has increased from Q to Q

• 1 2

To aid in the descriptive process when discussing changes in quantity demanded and changes in demand, economists developed the concept of elasticity. Basically, elasticity is intended as an indicator of the responsiveness of L.. quantities demanded to changes in prices or income. Economists generally i L define three elasticities: own price, cross price, and income. In each case, the elasticity is defined as the percentage change in quantity divided by the '~ percentage change in price or income. v i +,,,..,

12 .s Own-price elasticity is defined as the percentage change in the quantity demanded of good X divided by the percentage change in the price of good X. ~ This type of change is illustrated in Figure II-1. Since demand curves slope downward from left to right, the range of possible own-price elasticities is -- to 0. The range from -- to -1 is defined as elastic; the range from -1 to 0 as inelastic; and if the coefficient is calculated as -1, demand is r-defined as being of unitary elasticity. Cross-price elasticity is defined as the percentage change in quantity demanded of good X divided by the percentage change in the price of good Y. } This type of change is presented in Figure II-2, where a change in the price of good Y has resulted in a shift in the entire demand schedule for good X. d Since-the demand schedule for good X can shift either to the right or left with a change in the price of good Y, the possible range for the cross-price ,\\ elasticity is -- to t=. Goods that have negative cross-price elasticities are defined as complementary goods, meaning they tend to be consumed together or jointly. Tennis racquets and tennis balls are complementary goods. On the other hand, goods that have positive cross elasticities are defined as substitute goods. Gas and electricity are considered to be substitute goods, Finally, income elasticity is defined as the percentage change in quan-t tity demanded of good X divided by the percentage change in income. Figure II-2 can also illustrate the change in quantity demanded of good X associated l t_ with a change in income. Since consumption of a good may either increase i,, or decrease with an increase in income, the range for income elasticities L-is -- to t=. A good with a negative income elasticity is defined as an ' 7~ inferior good, whereas a good with a positive income elasticity is referred L. r~ s i e-.- ,-,---.e-e.,< ~-,e

---

.~...--e-+,m_,.ww--,,,v.e-v w-i

-g ,,_, r ry,,+,. = v -evr-g w -v e -* w'r e* v*r wr+*-=

• • • 9 4

9-7--'

~ 13 to as a normal good. Inferior goods, while not common, do exist (at least for certai.' ranges). For example, as a person becomes wealthier, his consump-tion of hamburger is likely to decrease with increases in income since he is .r' i likely to substitute steak for the lower-grade hamburger. While the definitions of elasticity are fairly straightforward, the r-calculation of numerical values is not since there are two common mathemati-c., cal formulas used to estimate elasticity. The first defines what is called point elasticity and is represented as: 4"Y* Since this formula involves calculus, it implies only infinitesimal changes in price. On the other hand, another repres'entation, are elasticity, often is defined: f ) f aP h AQ "(Qi+Q2)/) 2 (Pi+P)/) 2 2 This means are elasticity is representative of an average elasticity between -i any two points, whereas point elasticity (as the name implies) represents the instantaneous elasticity at any one given point. Consider the following numerical example. Let the equation of a demand curve be defined as: Q = 14 - P t_ (~

t-L.

C. ~

6 14 Figure II-3 illustrates this demand curve, d Price 14 - 12 - r-10 - r' ^ P 8 1 l l AB 6-l B p 2 I 4-I g 1 1 2-3 I i i 1* 1 1 s e r-0 2 4 6 8 10 12 14 Q Q Quantity 1 2 Figure II-3. Calculation of elasticity. I Assume a price change from P to P has resulted in a quantity change from a i 2 Qi to Q2 The indicated arc elasticity is given by the formula: [ a0 AP

f

• " (Q1 + Q2)/2 (Pi + P )/2 2

l 3 -3 (6 + 9)/2 (8 + 5)/2

I.

't' 3 -3 W* 6.5 -0.867 = Thus, the elasticity over arc I is -0.867. (.. ,-,.-e-,------,-.n-- p-. .,,w-- - ~, -,.. -, y

a 15 l-Applying the point elasticity fonnula to points A and 8, we see that l-the instantaneous elasticities are, respectively, -1.333 and -0.556. J' =$*PA .PB_ "A dP Q '8 dP Q = A B = -1

• 8

-1

• 5

= I 9 4, = -1.333 = -0.556 It can be seen that the arc elasticity is a weighted average of the two point elasticities. Thus, if one is considering implications of a price change of the magnitude utilized above, the appropriate elasticity to employ is the arc elasticity rather than one of the point elasticities. 1 B. ESTIMATION F10CEDURE c-Econometric models of demand are usually estimated in linear or log-linear fonns. A linear model for the demand for electricity might be written as: Q= a + bP Application of ordinary 'least squares regression yields estimates for a and ,7-b. Recalling that point elasticity is defined as: / n = d_ Q, P, dP Q 1 we obtain as an elasticity estimate L. n=b

• P p

E o t 6 9 w , -- r --w. a ,-.p-. -r- --w, n,,, n ---~,-,e----- a r

16 Thus, the estimated elasticity is a function of price and quantity and can take on a range of values. As a matter of convention, the estimate is evaluated at the mean values for price and quantity. It thus becomes: n=b* The use of mean values is meant to make,it most representative of the entire demand curve, and is reminiscent of an are elasticity. The alternative functional form usually assumed is a log-linear speci-fication. Here, the model equation is of the form: I Q = AP" By taking logs of both sides, this model can be estimated by ordinary least i t, squares with the added advantage that the elasticity estimate is given directly by the estimate for a. Taking logs, we obtain In(Q) = In(A) + a*1n(P) Once again, elasticity is defined as: U=N*E dP Q h= CAP *~I=a ah = then

• a.

( =a T

i.

Thus, the estimated elasticity is given directly by the coefficient in the estimated equation. However, this convenience is gained at the cost of obtain- -i ing a fixed or constant elasticity estimate. This type of estimated elasticity

• U

,,-,y -m, .~-----.-,y-

• -,,------r

- we o -v,

17 does not vary with either price or quantity, and hence this type of demand model is referred to as a constant elasticity model. If the demand function happens to be linear, or of some other form where the elasticity varies, the constant elasticity model will provide only an approximation to the true value. However, for small changes in price and quantity, this approximation should be accurate to the same degree that linear approximations are used in calculus to represent nonlinear functional relationships. In other words, for small variations in price and quantity, the inaccuracy of this approxi-t mation should be negligible. C. POLICY IMPLICATIONS A study of the responsiveness of electrical energy consumption to price may be helpful in predicting the effects of proposed rate level changes, particularly as these are undertaken to remedy revenue insufficiencies. Thus, ~ if demand for electricity is determined to be price inelastic and a revenue shortfall exists, appropriate price ir, creases will increase revenues to their proper level. Conversely, with elastic demand and a revenue shortfall, an (,2 CL appropriate price decrease will increase revenues in the amount required. However, such cursory implications need to be examined in greater detail. It must be remembered that the elasticity estimates in this study were derived from energy, or kWh, data. Revenue shortfalls are most directly affected [ by capacity costs and changes in capacity needs may not be proportional to overall energy changes. Specifically, capacity needs are determined by peak i demand requirements. Thus, the question that needs to be answered, in addi-tion to determination of the energy elasticity, is what is the price e t y ,-__-__n..n-c__- w, s%y- ,-7y,

t t 18 elasticity of peak demand. A policy based solely on an energy elasticity

• may aggravate rather than alleviate a revenue problem.

The experience of some utilities with a decreasing Toad factor (and hence a degradation of the revenue status) associated with recent rate increases aptly illustrates this point. However, it should be mentioned, residential electricity rates have been of such a nature in the past so as to not permit any meaningful measurement of the price elasticity of peak residential demand. A small num-ber of experiments are presently attempting to gain information in this area. At this point it becomes appropriate to see what other investigators ~ have done in the area of elasticity estimation prior to this study. Moti-vation has been provided as to why elasticity estimates are of interest to utility decisionmakers, and sufficient technical information has been provided to define the issues in question. In the analysis section certain areas will be gone into in more depth to clearly resolve the questions this study finally ends up addressing. This discussion ignores the regulatory lag associated with a public monopoly. In general, there is a lag between the time a revenue shortfall is first experienced and the time when a rate increase can be approved through the proper regulatry agency. Fuel cost adjustment clausas have mitigated this effect to some degree; however, in periods of moderate to high rates of inflation, this lag induces more seve e effects that would otherwise exist. t g mW \\ b -.., + - ,-a, ,.,,,..+-.---.,,.w-. ,-.,n,- ---,-e gr,- ...-w, n-

19 III. LITERATURE REVIEW The previous section provided a background with which it is possible to understand what the concept " elasticity of demand" is and to enter into dis-cussions concerning it. The next step in becoming knowledgeable about the subject of the elasticity of demand for electricity is to discover what other investigators have written about it. At the beginning of this study an exten-sive review of the literature concerning the demand for electricity was under-1 taken. In this section the most important information gained from that review is summarized. The appendices to this report include a complete article by article review, and somewhat detailed analyses of the major studies of elec- [ tricity demand. This section is more directed toward information of direct value to this study of the lower peninsula of Michigan. The information gained was of several forms. By researching problems that developed during other in-vestigations, probable problem areas could be identified and special emphasis could be placed in these areas. By critically assessing what others had done, blind alleys could be avoided and avenues found fruitful for others could be utilized. In this way the literature review provided a large degree of direc-q- tion for this study. A. ELASTICITY ESTIMATES OBTAINED BY OTHER INVESTIGATORS As a starting point, it is useful to begin with a summary of the elasticity estimates obtained by other investigators. Table III-1 indicates 1 i-the diversity of results obtained in several studies. As can be seen, the

['

long-run price elasticity estimates range from -0.48 to -1.75 and long-run L. income elasticity estimates range from +0.18 to +1.64 (omitting the implausible negative result). These price elasticities overlap the regions that economists L.- g, t emur 7 ..w., y

(; 7 (- (. (.- 7-7-- Table !!!-1 i Semary of Selected Previous Elasticity Studies Published Studies Long-Run Short-Run Residential Residential Elasticities' Elastic 1 ties Author

Tyge, Data -

Price 'P7 fee Income 4 rice Income footnotes:

1. Mount et al.

Combined 1947-1970; State A -1.30 +0.30 -0.35 N.E. 8 8 a) derived from constant elasticity

2. Anderson (11 Cross-Section 1%0; State M

-0.91 +1.13 N.E. N.E. b

3. Anderson (2h Cross-Section 1960/1970; State A

-1.12 +0.80 N.E. N.E. b) cost of second 500 kWh mode) 4 C c

4. Halversen Combined 1

1961-19 A -1.15 +0.51 M.E. N.E. derived from FPC Tf8 1966(?)g9;Stcte

5. Wilson Cross-Section

City A

-1.33 -0.46 N.E. N.E. c) from 1970 regression with average

6. Fisher & Kayser Combined 1946-1949 and i

1961-1957; State A N.S. N.S. N.S. variable use per household as dependent

7. Houthakker. Verleger, d) Wilson does not specify year

& Sheehan Cumbined 1961-1971; State M' -1.02 + 1.67

8. Asbury (1)

(Simultaneous Supply e) difference in cost between 500 kWh and 100 kWh/ month FPC T f Demand Model) 1959/1%5/1970; State A -0.899 + 0.189 N.E. 'N.E. f) price determined by regression

9. Asbury (2)

Cross-Section 1959/1%5/1970; State A -1.039 +0.20 9 N.E. N.E. fit of supply model

10. Griffin Tlae-Series 1951-19711 Na tion A

-0.52 + 0.88 --0.06 +0.06 9)from1970results UnpublishedServiceAreaSlu[ffes ] h) assumed value-income excluded from analyses i

11. NERA Cross-Section

1) mean elasticity for period covered j) difference in cost between 750 b

al Net Use 1970; State M -0.48 +0.84 N.E. N.E. kWh and 500 kWh/ month FPC TES bj Appliance Oe-1970; Zip Code Areas b h k) termed" Intermediate" clsions Use (Missouri) M -1.75 0.00 N.E. N.E. elasticities by authors. i

1. C.K. 1.iew Time-Series 1 % 3-1970; Oklahoma Gas & Elec.

A -1.00 N.A. N.A. N.A.

2. Beauvais a) Cross-Section 1970; Va. E1. & Power Svc. Area N.A.

N.A. +0.16 N.E. N.E. b) Time-Series 1947-1970; Va. El. & Power Svc. Area A -0.80 N.A. N.E. N.E.

3. EA!

Combined 1965-1972; State I M --0.75 +0.64 -0.023 +0.020

4. Lacy & Street Time-Series 1967-1975; Alabama k

k Power Sve. Area A.H -0.53 +1.64 N.E. N.E.

5. Crist et al. -

Combined 1964-1974; So. Cal. Ed. Svc. Area A -1.26 N.R. N.E. N.E. M.E. = Not estimated. N.S. = Not significant. H.R. = Not reported. N.A. = Not applicable, i j TEB

• typical electric bill.

?

21 denote as elastic and inelastic. It is difficult to arrive at a concensus pertaining to the relative sensitivity of electricity consumption ta price or income variations, but the oublished studies do tend to congregate around a price elasticity estimate in the vicinity of unity. As explained elsewhere, this value of an elasticity estimate is counterintuitive because historically utilities have been successful in remedying revenue insufficiencies by raising the price of electricity. Further observation of Table III-1 indicates the predominant type of analysis has been of a cross sectional nature, although there have been some combined time-series / cross-section work and some pure time series work. A cross section analysis is one which utilizes data from various geographical observation points at one point in time. The primary times at which such analysis is done coticides with census years because a great deal of infor- -l mation is available only through the Census Bureau and only for census years. Time series analyses, where observations are taken at a certain geographical observation point over time, are often restricted to using much more limited data bases because detailed information is collected so infrequently.

However, if this limitation can be either minimized, or made small relative to limita-l tions on the cross section data, time series analyses can provide useful insight into the demand for electricity by residential customers.

Combined time-series / cross-sectional analysis, as the name indicates, combines time series and cross sectional data into a single data base. This greatly increases the data base, but restricts it to only those variables which can be collected on both time and cross sectional bases. Another problem exists in analysis of .i c u-1 l a M^

the meaning of the coefficients calculated in a combined analysis, their interpretation being more subtle than in a purely cross-sectional or time-series analysis. Another note should be mentioned concerning Table III-1. The maximum and minimum values given as estimates for long-run price elasticities both came from the same study. This occurrence is not surprising in view of the methodology employed in the study. The elasticity estimate of -0.48 is associated with what NERA refers to as " net usage". Essentially, net usage is defined as that use of electricity by consumers which has no alternative fuel. Therefore, within this category there is no possibility for adjusting the stock of appliances to another fuel source, and hence the estimated elas-ticity is expected to be relatively inelastic. Likewise, the appliance deci-sions use of electricity, for which there are direct substitute fuels available, i is expected to have elasticity estimates more elastic than net usage. Since the more usual econometric model uses total average use per customer, which consists of both net usage and appliance decisions use, it is to be expected that the price elasticity estimates obtained with the NERA model bracket the conventional average use model. elasticity estimates. It is theoretically i and intuitively pleasing that this expectation is realized. B.

SUMMARY

OF PROCEDURES EMPLOYED IN PAST STUDIES 1. Type of Estimation Procedure l As mentioned previously, the studies of electricity demand done prior ' L-to this one have primarily been of a cross sectional nature or a combined _ L_ nature. The primary impetus for using cross sectional analysis has been m e y_. ~ y_ ,_y

23 / a the availability of data, especially from the Census Bureau. The disadvantage is the temporal noncontinuity of the data. A major decision a researcher contemplating a cross section study must make is whether or not the data are sufficiently representative of " normal" conditions. For example, if a ~ census happened to be conducted during a period of wartime mobilization (with its associated rationing) or during other abnormal conditions (such as during the Great Depression or immediately after World War II), true relationships might be masked by rapid adjustments to non-marketplace imposed constraints. It is arguable that today's economic conditions, with large inflation rates and controlled and rationed energy, are not " normal". The requirement of " normal" conditions is restrictive and unfortunate because it is in abnormal times that accurate knowledge of true relationships is most valuable. A solution to the problem of representativeness is to pool or combine cross-sectional data across a period of time. By so doing, the time period spanned will contain enough observations as to be representative of normal conditions. However, as mentioned before, detailed data tend not to be collected on an annual basis. Therefore the combining of data often necessi-tates a less well-specified model using either less detailed or interpolated data. Even so, the combined approach does not guarantee the time period will be properly representative. For example, the period from 1930 to 1950 would not be considered representative of normal times. The long drawn out depres-sion, immediately followed by World War II and its full employment and ration- .ing is certainly not " normal". Estimates based on data from this period would be very suspect. W w w -.y,,- r-

24 M In addition to the problem of obtaining a representative data base, there exists the complicating possibility of changing relationships over time. Both Asbury's (1974) and Liew's (1972) studies present evidence of this phenomenon. Asbury performed the same regression analysis for three time periods and obtained the following price and income elasticity estimates: Year Price Elasticity Income Elasticity 1959 -0.87 0.40 1965 -0.92 0.38 1970 -1.03 0.20 Thus, Asbury's efforts point toward the demand for electricity becoming more sensitive to price changes and less reactive to income changes. On the other hand, Liew's study, based on time-series analysis, obtained the following elasticity estimates. Year Price Elasticity 1953 -1.13 1954 -1.03 1955 -1.08 1956 -1.17 1957 -1.29 1958 -1.30 1959 -1.24 1960 -1.11 1961 -1.04 1962 -1.00 1963 -0.86 1964 -0.82 1965 -0.85 1966 -0.89 i 1967 -0.98 1968 -0.86 1969 -0.76 1970 -0.64 Here the direction is toward the demand for electricity becoming less sensi-tive over time. This is the opposite of Asbury's results, but the studies c, p-

25-( are not strictly comparable. Asbury's study is intended to explain average total use per customer, whereas the University of Oklahoma study by Liew is concerned only with the gpw demand for electricity. The results in the Liew study are interpreted by its author as being reflective of the increased effectiveness of advertising and increased convenience of electrical appli-Taken in this light, the two results are not as contradictory as they ances. initially appear. It is entirely possible that non-price incentives are be-coming more important in determining new demand for electricity, but that the sensitivity of utilization of existing demand to price changes is increas-ing, as Asbury suggests. An alternative to either cross-sections or combined cross-sections / time-series analysis is a purely time series type of analysis. Few of the investi-gations listed in Table III-1 have utilized time series analysis. The pri-t mary reason has been the scarcity of reliable data. Another problem with time series relates to a multicollinearity problem. Many variables exhibit strong growth trends over time, a trait which causes them to be correlated with time, and hence with each other. This results in estimated coefficients not being statistically significant when in reality they are important to a model.. This can result in important variables being omitted, which then improperly biases the coefficient estimates for the remaining variables in r- ~ the model, f [ The problem of omitted variables is ever-present in any modeling effort because a model is a simplification of a real-world situation. bmittedvari-ables cause real problems only when they are correlated with included vari-ables. If not correlated with any included variables, an omitted variable ,,e n y _g -,.,--c p~ ,--,,e e

gg merely increases the standard error of an econometric model without biasing any of the coefficients. However, to the degree to which they are correlated with included variables, the omitted variables cause the estimated coefficients to pick up part of the effect cf the omitted variable, hence changing (bias-ing) the coefficient estimates. In a cross section study it is usually not true that included variables are highly correlated with omitted variables. But in time series work se many variables are correlated with time it does become a problem. One cure is to include a large number of variables, but this can result in statistically insignificant coefficient estimatos. It is a matter of economic logic and guesswork to determine if the statistical t results are then explained by inclusion of improper variables or by a multi-collinearity problem. The proper approach is to establish a theoretically rigorous model, and then include only the variables elicited by the model. t The advantages of a time series analysis, if data is available with which it can be done, needs to be weighed against the above disadvantages. One advantage, relating to the previous " normal times" factor, is that the coefficients are representative of an average over the time frame being in-vestigated. This averaging effect 'is one way of minimizing the effects of abnormal times, much like aggregation tends to average out and reduce random fluctuations. Another factor in favor of time series analysis, one of special relevance to.this study, is the possibility of separating long run and short run effects. The elasticity estimates arrived at through cross section analyses are usually interpreted as representing a long-run equilibrium. This is be-cause the price differences are not instantaneous type price changes and re-i i._ sponses to them, but more of an equilibrium price differential between regions

27 ~' that has probably existed for some time. On the other hand, procedures have been devised for time series analysis which at least purport to separate long-run and short-run effects. This separation, if successful, allows esti-mation of both long run response and momentary, and possibly not persistent, r' With so much electricity use being related to a stock of appliances response. which can be changed in the long, but not the short run, it is very possible

i that short run response can be very different from long run.

The basic point that can be made about the preceding discussion is that each type of analysis has its merits and its drawbacks. For this particular study time series analysis has important advantages that cross section does s Therefore it was decided to attempt to use all three types of analysis; not. cross section, time series, and combined; and then distill as much infonnation as.possible from each. t 2. Unit of Observation Independent of the type of econometric analyses performed, most econometric studies have tended to use the state as the unit of observation. The rationale for this choice is easy accessibility and consistency of reporting. Fkny government sources aggregate data to the state level. Many private and govern-mental units only collect state level data on an annual basis, greater geographi-cal conciseness being much more difficult to obtain, and more expens'ive. Therefore the greatest quantity of data, both for cross section and time series analysis, is available at the state level. i e L. ~

28 f Two major problems arise with the use of state data. On the theoretical sid(, the use of state data represents somewhat of a misspecification. Eco - nomic theory is oriented toward the concept of the marketplace. In this regard, the service area of a utility probably coincides more closely with this concept. Also, utilizing state data involves the analysis in the statistical prob-lem known as aggregation bias. This problem arises any time non-micro (i.e., individual) data are utilized., For example, consider the states of Washington and California. Washington has a smaller population than California, but a higher average use of electricity per customer. An aggregation of data by state in a regression designed to explain average consumption causes the Washington customers to be given the same relative importance as the California customers, when in fact they are of lesser importance because there are fewer ( of them. Any time data are aggregated, some kind of bias may enter and often the direction of the bias is not clear. This means the aggregation bias present in the price and income elasticity estimates cannot be determined without analysis of the micro-data, an insurmountable task when dealing with aggregated state data for the entire country. In general, the less aggregation possible the better since the amount of aggregation bias tends to be minimized. However, some researchers have argued that some aggregation is desirable. Their argument is based on the assumption - that aggregation will tend to " wash out" any transitory components of the in-dependent variables that may bias coefficient (and hence elasticity) estimates. _This argument has particular appeal in relation to income variables in light E e wear

==ww*. ww-eevaw w-~w s w,= -p:-+ --wew- -m-- e---*-- ,e-,-r ve

---

r scw--

w ---m --r--+- -c .pyi-w-y wr-w

~~ 29 of Friedman's " permanent income" hypothesis of consumption *. This argument, with its reference to transitory and permanent compor s of income in rela-tion to consumption patterns, is a relevant argument. Aggregation may solve this problem, but so might other procedures (such as a several year moving average of income) without introducing aggregation bias. r' In light of the arguments against aggregate data and those related to 5 the economic concept of the marketplace, it appears that the optimal approach to elasticity estimation lies with the use of micro-data from the service area of a utility. From this optimal approach, alternativec can be ranked in terms of their appeal. This means aggregation of company micro-data into divisions or regions is preferable to aggregation into company average data, which is in turn preferable to aggregation of company average data into state-wide average figures. ( The use of state data represents a tradeoff between aggregation bias and the convenience and detailed coverage associated with it. The convenience comes from the number of government journals reporting state-wide data, and the detailed coverage from the large number of federal and state agencies collecting data at the state level. The additional effort required to col-1ect data for comparing regions is justified if the regional electricity data is readily available from the company and the interest of the study is for a limited geographical area. Friedman (1957). M IM , ed m.

30 4 ( 3. Form of Estimating Equation In general, the estimation procedures employed by most investigations ~ have been fairly stra.ightforward. The form of the estimating equation may be linear (as is one presented by Wilson), but the dominant form is log linear. This dominance of the log-linear functional form is explained by the fact that the estimated coefficients can be in',erpreted as elasticity estimates. This requires the assumption that toe consumption of electricity follows a Cobb-Douglas production function, which is of the form: Q = AP"Y8 where Q is the quantity demanded, P is the price of electricity, Y is income, and A is a constant which acts as a scale factor. If logarithms are taken of both sides of the equation, the resulting equation can be fitted by ordi-nary least squares with the elasticities (see section II) represented by the estimated coefficients, ..e., i in (Q) = In (A) + a in (P) + 8 in (y) This particular functional form has no particular theoretical basis for pref-l erence over other forms, but the above computational advantage makes it popular. t C. SPECIFICATION OF VARIABLES The previous two sections have concerned themselves with the general subjects of elasticity estimates and general procedures. In this section the more specific area of exact specification of variables is addressed. ) All researchers seem to have reached a concensus as to what general variables should be included in a model of electricity consumption. The exact definition 4 f w

d 31 m he of how to measure these variables is not so generally agreed upon. Various definitions, especially for the price of electricity, have been used. In this section these definitions are discussed with special attention to strengths and weaknesses. The variables to be discussed include the dependent variable, the price of electricity, income, prices for alternative fuels, housing-type variables, weather variables, and appliance saturation variables. 1. Dependent Variables .; ~ Almost all the electricity demand studies of direct relevance to this study have used average consumption per customer as the dependent variable. However, some studies have attempted to estimate electricity demand by first I i - estimating saturation levels for various electricity using appliances. These ~~ ] studies have shown some diversity in their dependent variables -- early studies using percent change in the stock of major appliances and later studies using saturation levels for various appliances. Wilson demonstrated the correctness of saturation levels in his study " Residential Demand for Electricity". However, the use of saturation levels in linear or log-linear equations is j not without problems. It has been shown that the growth of saturation levels ~~ generally follows an "S-shaped" or logistic curve. The above estimation pro-cedures do not model the inflection point of an "S" shaped curve. The bias caused by this approximation procedure is unclear. Environmental Analysts, I Inc. (1974) developed a methodology for fitting logistic curves which mini-mizes this problem. This methodology had potential for this study when satur-ation levels were included as independent variables. L i~ v

5 32 2. Price of Electricity 1 Of particular importance in econometric modelling has been the choic'e i of the proper price variable. Economic theory is founded on marginal deci-sions and hence marginal price. Due to the existence cf-declining block structures (or so-called inverted rates for that matter), there is no unique marginal price. A customer in one block faces a aifferent marginal price than a customer in another block. In the face of this ambiguity, numerous investigators have utilized average price instead. The extent of this utilization can be determined by 't examining Table III-1. However, in spite of this pervasive use of average price, many writers have pointed out that this definition of a price variable is somewhat meaningless due to problems of simultaneity. In other words, l economic theory postulates that quantity demanded is a function of price; however, any two-part tariff

• or one-part multi-block tariff makes the aver-age price a function of the quantity demanded. Consider, for example, a two-p part tariff consisting of a $2.00 per month fixed charge (customer charge, I

minimum bill, etc.) and a single-block energy charge of 3.0c per kWh. If ~f customer A consumes 200 kWh per month nad customer B 300 kWh per month, then the average price per kWh is 4.0c for A and 3.674 for 8, even though the t_ marginal price faced by both is the same, i.e., 3.0c per kWh. This problem 't of simultaneity and the consequent use of average price biases price elasti-iL city estimates upward (i.e., toward more elastic estimates). I~ ' A two-part tariff consists of a fixed customer fee plus a variable L_ running or energy charge (which may be single or multi-block). ,F ! L_ r

33 Three primary methods have been suggested or utilized as means to avoid ~ this problem of simultaneity: (1) use of Federal Power Commission typical electric bills (TEB), (2) a simultaneous supply / demand model in conjunction r- [. with a two-stage least squares estimating procedure, and (3) a method suggested by Taylor to include both an average and a marginal price. Wilson simply utilized the TEB for 500/kWh month as his independent ~ price variable. Since 500 kWh per month is about the national average, this TEB is intended to yield a good measure of the interstate variation in the price of electricity. Asbury has pointed out, however, that the 500 kWh/ month TEB is particularly deficient in that it involves unrealistically high esti-mates of electricity consumption for water heating. To the extent that the actual use of electric water heaters across the county varies, the use of the TEB will bias elasticity estimates. Addressing this problem associated with the TEB, both Anderson (1972) and Houthakker et al. (1973) proposed " marginal" prices derived from the TEB. Anderson used the cost of the second 500 kWh per month and Houthakker et al. utilized the difference in cost between 500 kWh and 100 kWh per month. While these measures no doubt represent improvements, they are still subject f to aggregation bias. In this respect, it has been suggested that if aggregate consumption data are utilized, then some weighted-average, marginal-price variable is the appropriate variable. Harberger (1974) has suggested that the average price paid might be a closer estimate of the relevant average marginal rate than the construction of marginal rates from block differences in the TEB. Nonetheless, the general consensus leans toward the concept of a marginal price even if its adequate representation remains a difficult task. L. ~ 7 t~ t .-e - er y y w w e, e

34 Taylor's method, which is detailed in the Bell Journal of Economics I-(Spring 1975), consists of including both an average and a marginal price. i Taylor's average price is the average price of electricity for consumption up to but not including the last block consumed in, with marginal price de-fined as the rate charged in the last block consumed in. Essentially, tne ~ methodology is designed to discriminate between the income and substitution effects resulting from a price change; the average price variable should pick up the income effect, and the marginal price variable, the substitution or pure price. effect. No known published studies have utilized Taylor's methodology. (Dise.ussion of our results with the Taylor methodology is found ~ in Appendix I.) 'j~ A third method utilized to avoid the problems of simultaneity has been estimation of a simultaneous supply / demand model. Asbury used this approach 'j( in his paper. The methodology of the simultaneous supply / demand approach

• consists of estimating a supply model with the price of electricity as the dependent variable. The fitted values for the price variable are then used in the demand model as the relevant independent price variable.

i In this manner, the simultaneous relationship between quantity and average price is eliminated, allowing consistent estimates to be obtained. Asbury also esti-mated his model using ordinary least squarer with average price as the inde-pendent variable. His apparent purpose is to estimate the distortion that results from ignoring the simultancity problem. Somewhat reassuring from a L,

practical modeling standpoint is that fact that the results obtained from this two-stage least squares analysis did not differ significantly from Asbury's Also referred to as two-stage least squares (2SLS). b .---~.--,-,,,----,,-.,,,-,-,,e~..,y v..------,-t- ""e-+-* w***=r** - - - ' * --"""w-'-w**

• t-'r s'a=e'

---"at-' =ve--w-e' v

35 ordinary least squares regression using average price. For example, the indicated own-price, cross-price, and income elasticities for each method were: Own price Cross price Income Ordinary least squares 1.03 0.31 0.19 Two-stage least squares 0.89 0.34 0.18 ? These results would seem to indicate that the use of average price, while extensively criticized on theoretical grounds, may not be quite as inappro-priate as generally claimed. It should be noted again that the use here of average price has resulted in upward biased own-price elast1 cities. The resolution of the proper price variable is still not 100 percent clear. Economic theory calls for the marginal price; however, as indicated there are problems associated with deriving an adequate empirical represen-tation of marginal price. Nonetheless, it has been effectively demonstrated that the use of average price results in upward biased own-price elasticities, which at best should be viewed as upper limits to the range of the true elas-ticity. 3. Income Although the specification of the price variable has represented the most difficult problem in econometric modeling of electricity deaand, the use of a proper income variable has also merited some discussion. Studies typically use-either median family income or per capita income. The alleged advantage of these variables, other than the obvious ease of collection, is the previously discussed relation of aggregation and elimination of transi-tory components of income. Friedman's " permanent income" hypothesis main- [_ tains that consumption is related, in a meaningful way, to the notion of v e-r ww T w t 9 r

36 " permanent" or normal income. Since measured income consists of a permanent and a transitory component, statistical techniques may not be able to detect the relationship between consumption and permanent income; hence, the argu-ment for aggregation of data, by which it is claimed the transitory effects a will be washed out, leaving one with a measure of permanent income. As noted earlier, aggregation bias may be serious enough to outweigh this alleged benefit. Aside from the above arguments, neither the use of per capita nor median family income accounts for the skewness that is known to exist in the distri-bution of income. Ideally, a model should be constructed to incorporate the skewness factor. However, this criticism may be of minor significance in light of a recent EAI study. One explicit exercise in this study consisted of considering the effects of skewness in the distribution of income upon the estimated income elasticity. It was found that the estimated income elasticity was not overly sensitive to assumptions about the distribution of income. 4. Competina Fuels Econometric models almost universally use the average price of natural gas as the price variable for alternative fuels. This price measure may result in biased estimates for cross-price. elasticities for several reasons. First, the same argument applicable to electricity prices (i.e., marginal versus average, and the associated bias problems) applies equally well to gas, since it is also sold under declining block tariffs. Furthermore, a proper specification might require the inclusion of both an average and a marginal price in order to isolate the pure price effect. t rW .n v.

37 Additionally, the relevant competing fuel may not even be natural gas. Asbury points out that, in New England, low sales of electricity coexist with high natural-gas prices, a condition contrary to expectations. However, he further notes that the explanation is due to the relatively low price of heating oil.* Thus, for New England and possibly other regions of the country, heating oil and not natural gas is the relevant alternative fuel. Consequently in estimating his model, Asbury constructs a price variable that is essentially a weighted average of natural gas and heating oil. As a test of the procedure, he repeats the analysis, changing only the price of the alternative fuel, restricting it to only natural gas. The results are presented below: Cross-Price Elasticity Obtained Type of Alternative Price Variable 1959 1965 1970 .i Natural gas only 0.19 0.14 0.17 Weighted average of gas.and oil 0.30 0.30 0.31 The results are somewhat striking though not unexpected. As can be seen, the use of natural gas alone results in downward biased cross-price elastici-ties and underestimates the role of competing fuels in detennining electricity demand. Another study that explicitly treats this problem of competing fuel price is that of Anderson (1973). Rather than constructing a composite price variable, Anderson elects to enter several competing fuel prices. In partic-ular, he considers gas, oil, bottled gas, and coal as alternative energy' ~~ Asbury's data predate the 1973 Arab-Israeli War and resultant quadrupling of oil prices. ,,s-s- .e e> g--- + yg-r w w ,wrg e-r--- -w w ow-et--.--

38 f sources. Anderson's direct estimates for the cross-price elasticities (with respect to electricity) for 1970 are: Fuel Type Cross-price Elasticity a Gas 0.30 a 011 0.27 a Bottled gas 0.00 Coal 0.12" a. Not significant at 0.05 level. Even though Anderson's results are not overly significant (a result partially induced by the large number of independent variables), it is important to note that the elasticities indicate that fuels other than gas compete with electricity. 5. Housino Characteristics Failure to adequately control for housing characteristics can result in implausible results. Wilson's negative income elasticity estimate is often cited as an example of this effect. Anderson further points cut that it is ~ important to select a housing characteristic variable that is not correlated with any of the other independent variables. In particular, he is critical of the use of average number of rooms per dwelling unit, asserting it is likely to be correlated with income and hence yield insignificant coefficients for both due to multicollinearity. Anderson prefers the use of average number of persons per households since he feels it is not likely to be highly correlated with income. However, the important feature is the necessity of controlling for housing characterstics. \\

== a W -+. g~

39 } A rather disaggregated study, such as one for an individual service area, may enploy something like an urban / rural ratio to account for different housing characteristics. However, it may also be necessary to control for such things I- - as percent of population living in apartments, or population density. ~ 6. Weather Variables Recent researchers have placed increasing emphasis on properly specify-ing climatic variables in their analysis. Somewhat surprisingly, a number of earlier studies only included an indicator of winter conditions, such as degree-days or mean December (or January) temperatures. Once again, Anderson seems to have pioneered with the inclusion of a summer temperature variable. i This extension is intended to capture the effects of the increasing air-conditioning load. F Some refinements of climatic-variable specifications have been suggested but apparently remain untried. Included in these are the use of a wind-chill index for the winter variable (since increased wind induces a greater heat loss from a structure, and hence a greater space-heating demand) and a temperature humidity index for the s'ummer variable (THI represents a better measure of discomfort than temperature or cooling degree-days and hence is more reflective of air-conditioning demand). A possibly optimal approach is to weight the winter and summer climatic variables by the saturation levels for electric space-heating and air conditioning, respectively. Anderson also presents an interesting argument that could have an impor- '~ tant bearing on properly representing the effects of winter climates on the demand for electricity. In discussing the lack of significance of Wilson's ' ( --m .-y v r

40 climatic variable (heating degree-days), he suggests this result may be due to opposing cold-related influences. Once electric heating has been installed, a colder climate induces more electricity use. But coldness of climate itself may be a deterrent to the purchase of electric heating equipment. Anderson ~ notes that, in a warmer climate, with relatively light heating needs, the differential operating cost of electric versus fossil-fuel heating will be low and other considerations (primarily installation costs) may dominate customer choice. In a colder climate, on the other hand, the differential operating costs may rise to the point where it deters the installation of electric heating equipment and thus reduces average household demand for electricity. 7. Appliance Saturation !.evels i~ il As mentioned in the dependent variable section, the proper appliance variable has been shown, in an evolutionary process, to be the saturation level. This saturation level can be used as independent variables as well as dependent, and it is as independent variables they become relevant to this study. Inclusion of appliance saturation variables makes the electricity price coefficient relate more to short term as opposed to long term price effects because the response is limited to changes in usage of the existing appliance stock. ~ D.

SUMMARY

Previous studies have not consistently shown either elastic or inelastic price response with response to electricity consumption, though experience i u \\ me g -,.4-w -4 y-w -e. ..w - - *, -,,.. - -, - - ~ m ---_,m.-. --em ,., - +

41 ) clearly indicates inelastic response. Previous investigations have used cross-section analysis, time-series analysis, and combined cross-section/ time-series analysis. None of the three procedures is clearly superior to the other two. Omitted variables, multicollinearity, and aggregation bias are frequently cited problems arising in econometric studies of electricity demand. Major data controversies exist over the proper price variable for electricity and how to quantify alternative fuel prices. Especially acute data collection problems should be expected for income data, housing characteristic data, alternative fuel price data, and weather data. Saturation level data is also often difficult to find, but its usefulness is more controversial than the previously mentioned variables. With this background a description of the collection of data for this study of the price elasticity of residential demand for electricity in the Lower Peninsula of Michigan can begin. ~ i e e o sN G , ~ ~, - -,,,

42 IV. DATA ..( A major portion of any research study is the data collection stage. It is somewhat of a misnomer to call it a stage, because after initial collec-tion some analysis is done and invariably more data collection is done. Before an investigator goes out to collect data it is necessary to obtain a solid background in the subject at hand (Section II provides the reader with an introduction to the theory behind elasticity), and at least prudent to thoroughly review any lit'.rature which exists relevant to the topi.c of re-search (the' literature.eview undertaken for this study is capsulized in Section III). Having prepared the reader of this report in both of the above areas, a detailed description of the data collected relevant to the study of residential electricity consumption in the lower peninsula of Michigan is p presented in this section. It begins with a brief description of the data-sought, followed by a short exposition on the data it was expected would be !i' available with which to do this study. However, as always, initial expecta-tions were not met. The remainder of this section describes (more or less in the chronological order it was obtained) the actual data that was collected, L, 4here it came from, and what transformations were required to put the data into a usable form. The basic data for the study begins with what econometricians call the dependent variable. In this case the dependent variable is effectively defined by the purpose of the study, it being the average use of electricity per resi-dential customer. s L. {' L g.. t _y y

43 '( A. DATA EXPECTATIONS Initially, it was envisioned that the major difficulty to be overcome wo>fid be the handling of large data bases. Both companies sponsoring this study maintain rather extensive master files on each of their customers. The major data not on the master file are income data and weather data. The weather data, it was thought, could be obtained rather simply. The income data posed the greatest obstacle, but it did not seem insurmountable. After all, with a data base of thousands (possibly hundreds of thousands) of individual customars, some method could be devised for assigning income values. The procedure that seemed the most practical was to obtain income values on l' a census tract basis, match the individual customer with his census tract, and then assign the average income for that tract to that individual. This individual customer analysis was to be the main thrust of the study. Cross-t sectional, time-series, and combined cross-section/ time-series analysis pro-cedures were to be applied to this data. As a verification check regional data, based on divisions for Consumers Power and counties for Detroit, were to be collected and analyzed on a~ time-series basis. In addition, the indi-vidual customer data was to be grouped in order to allow calculation of appli-ance saturation levels, and this data then analyzed on a time-series basis in order to separate long-run use tied to appliance purchases and short-run use associated with the utilization rate of presently owned appliances. However, as is often the case in research projects, expectations did I [; not become reality. The reality that changed the actual data base available was dollars. The utilities found it prohibitively expensive to supply the u. w e r y w. i,e, y. y-9, .w---

44 ~( individual customer data matched by census tract. Without a means of assign- 'ing income values to the individual customers the data would not be usable for the study. A major revision in the project was required. It became impossible to do any time series analysis of individual customers. Cross section analysis was possible by using appliance surveys the utilities had done or were about to do. At that point the basic plan was to rely on the regional data for overall elasticity estimates and use the individual customer data to effect the breakdowns by use and income blocks. Part of the motiva-tion for this decision was that the time series data was available long before a large portion of the individual customer dat,a (the Consumers Power individual customer data was not available until two months before the scheduled end of the study). B. REGIONAL DATA l. As mentioned before, the regional data was collected for use in a time series format.. Data was collected for the period 1950 to 1974 on an annual basis. Each service area was divided into geographical regions so as to use data at the lowest level of aggregation available. The geographical units 1 - are somewhat different for the two companies, but they are close enough to be considered as comparable as various states are in a national study. For Consumers Power, the 12 divisions were found to be the best regional unit. County data can be aggregated in a relatively straightforward manner to correspond to the division, and there is a wealth of information published. by various governmental units that uses the county as a basic subdivision of the state. Divisional data are maintained by the company and are readily accessible. ( s 'p~~v v r-n+ -g vs--

== --m-gg,r---- vw

• er 4

.-w~ ,--e,

v. - - -~

--s---

---

,r,---.--m,

. ~ - e-n- ..m ,-,--,r ---,,-,r -gwe s v -o a-e w r -- - ro u-s

45 ( Detroit Edison maintains data on the county level, so that was chosen as the region unit for its service area. There are 13 counties in the company's service area. For the most part, these correspond to Detroit Edison's districts. Rather than use the district names, the county names are used because that avoids confusion in the instances where districts and counties do not corres-pond. The Ann Arbor division is the main area where districts and counties do not correspond. The small part of the Lenawee County served by Detroit Edison is part of the Ann Arbor district. The Howell , strict consists of those portions of Livingston and Ingham counties that are served by Detroit Edison. It might be confusing if these three instances arc referred to by county names while the rest are referred to by district names. Thus, county names are used throughout. A table of the district name corresponding to the county name (v'lere not identical) follows: ( District County Bad Axe Huron Caro Tuscola Sandusky Sanilac Ann Arbor Washtenau Ann Arbor Lenawee 'Howell Livingston Howell Ingham 1. Consumotion, Revenue, and Average Price for the Electricity Utilities lt. The first, and most complete, data obtained came directly from the two i [; utilities -- Consumers Power and Detroit Edison. For each of the regions c- -4 i ,,--g ~ r

46 ~ described'above ar.d for each year for the period 1950 to 1974 they provided total residential consumption for the year, total iesidential revenues for the year, and nuber of customers. For Consumers Power the number of customers was the average number of residential customers for the year, whereas Detroit 4 f Edison provided year-end (December 31) residential customers. The two companies do not have comparable data on number of customers recorded back to 1950, m ] but the difference between year-end and average should not make a difference in this study because year to year changes are more important to the esti-mation process. From this data it was a simple division to calculate average use per customer from total consumption and number or customers, and average price was calculated from total revenues and total consumption. Average ] price was calculated so comparison would be possible between the use of aver-3 age price and the correct (theoretically) msrginal price. d..( 2. Income The next type of data collected was per capita income data on a county level. It was available for the years 1950, 1959, 1962, and 1955-1974 inclu-sive. This was the most disaggregative data available over time with a siz-able number of observations. To be usable for the Consumers Power divisions this' data had to be further aggregated. The basis for the aggregation weights was the 1970 Census of Population. There population by township and by city 4 was available. From this data, using the procedure described in-Appendix B, the proportion of the county population actually served by a certain Consumers 'p l Power division was calculated for all counties. Since total' personal income and. total population were available by county for the abovementioned years L. !L ( w,- y, ---,r,,----.,,. ,,w,,- ,wr,- ,,n.- e -, e-m, e--,, ,.-,,,--a-.r.-

47 -f from the Bureau of Economic Analysis in Washington, D.C., these proportions ~ were used to calculate total personal income and total population for each division for each year for which data was available. These figures were then used to calculate per capita income for the divisions. Some interpolation was also required to provide data for the missing years. Statewide Michigan incomo data is available for every year since 1947 [' from the Survey of Current Business. A simple regression was run using this i statewide data as the independent variable and the available regional data as the dependent variable. The coefficients obtained in this manner were j. then used to obtain per capita income estimates for the years for which divi-b- sional data were not available. 3. Marginal Price of Electricity ( Several definitions for the marginal price of electricity were used in this study. Development of a marginal price was rather evolutionary -- starting with a definition used by others in a previous study and moving toward the price that was finally used which to our knowledge no one else has used before. In this section the three definitions used are given. In the analysis section a more thorough explanation of why certain definitions were considered deficient compared to others will be given. The first definition used for the marginal price of electricity was based on the annual 500 kWh Typical Electric Bill as report for the Federal Power i. Commission. The NERA studies and Anderson have used a similar price. The Typical Electric Bill data was supplied by the two companies. The Detroit m. Edison values are not those reported to the FPC, but are calculated in the 4.n M

48 i -( -same manner except for not including water heating allowances. Detroit Edison feels their electric water heating saturation level is so low that inclusion of it in their marginal price improperly biases the price paid by their custo-c- Note that this marginal price, as are all the marginal prices for elec-mers. tricity, is for the company as a whole and does not vary from region to region. This is because the set of rate schedules faced by the consumer is the same '[' throughout each company's service area, therefore the marginal price should be the same. To come up with a marginal price the 500 kWh TEB's were divided by 500 so the price would be a price per kilowatthour. These 500 kWh prices are still average in the sense that they include the fixed charges and higher charges for the first few kilowatthours which are effectively spread over the remaining kilowatthours and increase the measured marginal price. The other two prices remove this effect by eliminat-4 ing the effects of the lower part of the rate schedule. The second price, which occupies the center column.of Tables IV-1 and 1 IV-2, is based upon the difference between the 750-kWh and 500-kWh Typical Electric Bills. Houthakker and Environmental Analysts, Inc. have previously used this as a price of electricity. By using the price of consumption between 500 and 750 kWh, effects related to service charges and high initial rates are eliminated. The problem with this price, which the third price attempts to overccme, [ is that no account is made of the fact that average electricity consumption has grown over the last 25 years. 750 kWh per month was extremely high in 1950, but only a little above average in 1975. This means the 750-500 kWh price was representative of the habits of different consumers over time.

Ideally,

\\ r -m- ,.s,-,.,.,c.,..,...-.-.y,.-- man ~r ,..e,.

49 Table IV-1 [ Marcinal Prices for Electricity, Consumers Power Company Year 500 kWh TEB 750-500 kWh TEB 10 Percent 1950 1.598 1.34 2.00 1951 1.706 1.67 2.00 1952 1.706 1.67 2.00 t 1953 1.706 .1.67 2.00 1954 1.706 1.67 2.00 1955 1.706 1.67 2.00 1956 1.706 1.67 2.00 1957 1.706 1.67 2.00 1958 1.706 1.67 ?.00 1959" 1.706 1.67 2.00 1 1960 1.794 2.07 2.00 { 1961 1.794 2.07 2.00 1962 1.794 2.07 2.00 1963 1.794 2.07 2.00 1964 1.794 2.07 1.98 1965 1.794 1.94 1.88 1966 1.788 1.88 1.89 1967 1.788 1.88 1.83 1968 1.788 1.88 1.82 1969 1.788 1.88 1.90 1970 1.952 1.71 1.92 i 1971 1.952 1.71 1.98 l' 1972 2.114 1.58 2.25 l 1973 2.338 1.88 2.32 1974 2.554 2.10 2.73 - ' ' ' ~ ' ' ~ - - ' - - - - ' '~ """ "

50 Table IV-2 Marginal Prices for Electricity, Detroit Edison Company ~ Year 500 kWh TEB 750-500 kWh TEB 10 Percent 1950 2.638 2.18 2.75 ~ 1951 2.638 2.18 2.75 1952 2.638 2.18 2.75 . i' 1953 2.638 2.18 2.75 1954 2.638 2.18 2.75 1955 2.638 2.18 2.75 1956 2.638 2.18 2.75 1957 2.638 2.18 2.75 i 1958 2.638 2.18 2.75 r-1959 2.638 2.18 2.75 1960 2.638 2.18 2.75 (~ 1961 2.638 2.18 2.67 1962 2.638 2.18 2.56 1963 2.638 2.18 2.38 r 1964 2.638 2.18 2.25 l~ 1965 2.638 1.E5 2.25 1966 2.590 1.63 2.24 1967 2.59" 1.63 2.24 1968 2.590 1.55 2.24 1969 2.590 1.55 2,23 1970' 2.590 1.55 2.10 1971 2.634 1.84 2.09 1972 2.634 1.84 2.C3 1973 2.924 2.33 2.58 1974 2.876 2.60 2.81 ~

51 ( the marginal price should be the price for the same individual over the entire time period. One way to approximate this is to use a marginal price at the average level of consumption for the year, thereby tracking the " average" customer. Prices that attempt to do this are given in Table IV-1 and IV-2 and are labeled Bill 10 pr$ces. The 10 comes from an estimate

• that a custcmer can change his consumption by only about 10 percent on a short term basis.

The Bill 10 prices are calculated by referring to the rate schedules and calculating the cost of consumption at the average consumption per customer, the cost of consumption at a 10 percent lower level of consumption and taking. the difference between these two figures. A rate per kWh is found by dividing this number by 10 percent of the average consumption. As explained in the data appendix, these prices are weighted by the different rate schedules residential customers may face. These Bill 10 prices were the most appropriate prices devised in this study, and are the marginal prices of electricity except where otherwise noted. P 4. Alternative Fuel Prices i. Data on prices for a variety of alternative fuel sources were collected. Data for natural gas were by far the most extensive and reliable. Prices for No. 2 Fuel-Oil, Coal, and Propane were also collected, but these were of I mar,kedly inferior quality. Natural gas data were supplied by the four major gas utilities which serve the electricity customers of Consumers Power and Detroit Edison. The four utilities were Consumers Power Company, Michigan Consolidated Gas Company, I s. F. This estimate is attributed to Mr. Larry Lewis of the Consumers Power .1 Company Rate Department 'mu-o s --v..

52 Southeastern Michigan Natural Gas Company, and Michigan Gas Utilities Company. The data supplied included consumption, revenues, number of customers, and actual historical rate schedules. The rate schedules were used in the calcu-lation of marginal prices. The number of customers data did not arriva in time to calculate prices similar to Bill 10 prices for all the utilities. A different price was used, one which should not make too much difference be-cause natural gas consumption per customer has remained relatively flat over the last 30 years. The actual price used is most similar to a 500 kWh TEB. The cost of 10 Mcf of gas consumption per month was used as the marginal. price. As with electricity, these rates are companywide, with the exception of Michigan Consolidated Gas which has different prices for its Detroit division and .I for the rest of the company. In addition to these marginal gas prices, aver-age gas prices were calculated and used wherever an average electricity price 4 ( was used. ( Table IV-3 lists the sources for all gas data for the counties in the Detroit Edison service area. The bulk of the Consumer Power service area is served by Consumers Power, so no matching effort was required. The Grand Rapids, Northwest, and Muskegon divisions are primarily served by Michigan Consolidated Gas Company, and that data was used rather than Consumers Power data in these divisions. The other three alternative fuel prices collected were all found on something approaching a statewide basis rather than by individual prices. All were also more or less average prices. Average price paid per gallon by residential customers in Michigan for No. 2 Fuel 011 was found in the American t Petroleum Institute's publication Facts and Figures. This price is not a c_ m

53 f-r3 Tabl e. IV-3 ra. Sources for Natural Gas Data Within Detroit Edison Service Area County Gas Utility Huron Consumers Power (Saginaw Division) Lapeer Consumers Power (Pontiac Division) Macomb Consumers Power (Macomb Division) Monroe Michigan Gas Utilities fi ' Lenawee Consumers Power (Jackson Division) Oakland Consumers Power (South Oakland Division) Sanilac Southeastern Michigan Natural Gas St. Clair Southeastern Michigan Natural Gas ( Tuscola Consumers Power (Saginaw Division) Washtenaw Michigan Consolidated Gas Livingston Consumers Power (Lansing Division) L-Ingham Consumers Power (Lansing Division) Wayne Michigan Consolidated Gas (Detroit Division) ' L. b. c (b k V s. -me -__,______,-,,,-y, _-,_.-,,___._y-- --.,y y-----.,.,.-y-c -, _y- ,. ~,.,,-- ,r.---- ~w, ,g-,

v 54 P very good measure because it is highly aggregated, and fuel-oil prices can i vary greatly within the state of Michigan. More detailed data has been col-r- lected only since 1973, so this was the best that could be found for use in .(. 1 the regional time series work. A measure of coal prices was obtained from the Bureau of Mines' " Mineral i t Industry Survey". The data consisted of the annual average wholesale cost r-in dollars per ton, F08 Detroit. Again, this data is highly aggregated, and it is wholesale rather than retail. ,f. The Propane data was even less useful. It was obtained from various

u issues of " Gas Facts", a publication of the American Gas Association.

This 7 price series is even less properly specified for our purposes than the previous two. It is statewide and propane prices vary widely from town to town. It ~

I

is wholesale rather than retail. And it is an index of prices rather than ![ actual prices. The method of calculating the index is unclear, so interpre- .,y tation of this series is extremely haphazard.

)

5. Weather Data

?

i The primary weather variable col,lected for this study was heating degree days.

Most of that data was supplied by Consumers Power. Consumers Power provided anraal heating degree days for each of their divisions except the Muskegon division (heating degree day data are collected by the gas portion of Consumers Power; since there is no gas service provided by Consumers Power i in the Muskegon Division, they do not collect weather data there). For.the .-l{ purpose of this study tne heating degree day data for tnc Grand Rapids divi-sion was used in the Muskegon division. ik l j .( L' y-e'

---

e*

- - - - - + - -

• e-w

=-<--

---

e

+- -wav-= -em-= ,=- ---

---

ww-v

---=5 a = mir T --Yp-

55 t Detroit Edison provided heating degree day data on a less extensive {~ basis. The only two weather data collecting stations for the Detroit Edison company are at the Detroit Metropolitan Airport and the Detroit City Airport. Information from several Consumers Power Company division was used to supple-(- ment the Detroit Edison data in coming up with a heating-degree day time series for each of the Detroit Edison regions. Table IV-4 details the data {' used for each Detroit Edison county. Any reference to named divisions indi-cates utilization of Consumers Power data. Average, in the table, means the arithmetic mean of the two values. Some efforts were made to collect other weather data, but only heating i degree days were easily accessible for the Consumers Power Company divisions. Analysis done with the Detroit Metro Airport data indicate this might not be much of a problem because winter and summer weather conditions are cor-L related. It was possible ta collect cooling degree day and THI data for Detroit Metro Airport. As will be expounded upon in the analysis section, 4 I the additional variables did not appear to add much information. This eased the data collection effort. The cooling degree data is available, but it would have been a major effort for the Consumers Power staff to obtain it for every year since 1950 for each division. [ 6. Housing Characteristics i Obtaining reasonable data for housing chcracteristics proved to be an extremely difficult and unrewarding task. We were unable tc find any measure L. of housing characteristics in Michigan collected on an annual basis. The ( best information availab'e was county level information from the 1950, 1960, (. f t.. 4 em

56 p*r 'f c' i Table IV-4 Sources for Heating Degree-Day Data Within Detroit Edison Service Area County Data Utilized -i e HURON Northeast Division LAPEER Flint Division i MACOMB Average of Detroit City Airport and Pontiac Division MONR0E Detroit Metropolitan Airport LENAWEE Jackson Division OAKLAND Pontiac Division SANILAC Average of Northeast Division and Saginaw Division i 3 ST. CLAIR Average of Detroit City Airport and Pontiac Division TUSCOLA Northeast Division f WASHTENAW Detroit Metropolitan Airport LIVINGSTON Average of Lansing Division and Pontiac Division v INGHAM Average of Jackson Division and Landing Division WAYNE Average of Detroit City Airport and Detroit Metropolitan Airport 5 l' ' k.

57 and 1970 Censuses. Two variables were calculated from the census data, the percentage of population considered urban, and the percentage of residential living units in multiunit dwellings. The county data was aggregated in divis-ional data for Consumers power divisions using the same weighting factors as for the income data. A simple linear interpolation was made between census years in order to supply missing data. The line between 1960 and 1970 was extrapolated through 1974 to provide data for the years 1971 through 1974. This interpolation, forced by the paucity of data, is so coarse as to seriously question the value of using it. The percent urbanization is almost reduced to being a simple time trend. This is the major area where more precise data would be useful. 7. Appliance Saturation Levels J Both Consumers Power and Detroit Edison supplied either appliance satura-tion data directly or information from which saturation levels could be derived for electric space heating, electric water heating, and air conditioning. Consumers Power provided saturation levels for the three appliances at the divisional levels from their Appliance Saturation Surveys of 1955, 1959, 1964, .g 1970, and 1975. Census data for 1950 was used to augment this data. Linear - 1 interpolation was used to estimate data for missing years, except for the water heating data, which could not be taken back any further than 1955. The information from Detroit Edison came in a different format. Air m conditioning saturation levels were obtained by interpolating census data , i,,e ll at the county level. For space and water heating, the data consisted of [' the numbers of residential customers being billed under the special water and 4; ri \\ L il d

58 t y space heating rates, this data being available on an annual basis for the 4 counties comprising the Detroit Edison service area. For water heating the data was available from 1950 through 1975; however, similar data for space heating customers were only availab?e back to 1964. Census data from 1950

and 1960 were used to extend this variable back to 1950.

8. Cost of Living Deflaters Much of economic theory is predicated upon real and not nominal money variables. Comparison of nominal variables results in distortion properly l attributed to inflation. The conventional thing to do is to deflate nominal money variables by a price index, usually the U.S. Consumer Price Index. That is the procedure used in this study to convert to real terms. It would have been desirable to have a more local cost of living indication, but one r-for the area outside the Detroit SMSA could not be found. Inside the Detroit l SMSA, comprising Wayne, Oakland, and Macomb counties, the Detroit SMSA consumer price index was available and was used. The difference between the two is very slight. Use of the Detroit index reflects an t.ttempt to measure the cost of living within Michigan as accurately as possiizle. 4 C. COMPANY LEVEL DATA Company level data were assembled from the ~ regional data for use in time-series analysis. In most cases this amounted to simple aggregation of the regional data into company data. The marginal prices for electricity required no aggregation because they are company level anyway. The consumption, revenue, income, urbanization, and multi-unit housing regional raw data were simply f 4 M ..,. - _ _ = _,., - .. -, _ - ~ - . _... ~,... . m

6 59 n ( added together, and then the proper divisions were performed. After the company data was so formed the same ir.terpolation procedures were used as for the regional data. These procedures were regression for income and linear interpolation for urbanization and multiunit housing. No appliance saturation levels were calculated at the company level, though they could have been. Weather was not aggregated. Rather, Lansing heating degree days were used for Consumers Power and the average of Detroit City Airport and Detroit t Metro Airport were used for Detroit Edison. Formation of a marginal natural gas price on a company level was more involved. Weights, shown in Table IV-5, were arrived at based on numbers of customers served electricity. This basis was necessary because consumption data on a regional basis was not available in areas served by other than l~ Consumers Power. '( { D. INDIVIDUAL CUSTOMER DATA ( Some individual customer data was collected and used in cross section analysis. A 1973 appliance survey for Detroit Edison and a 1976 appliance 'f survey for Consumers Power were used, both because they were the only surveys with any income data. Very little was required in the way of data transfor-mation in order to make the numbers usable. The most significant change was converting the appliance variables to binary variables. A binary variable is ' ~ one which can take only two values. In this case, one level indicates a cus- .F 'i tomer does not have any electrically powered appliance of the type in question and the other indicates ownership. By making the ownership value the larger of the two numbers the coefficient in the estimated equations can be thought of as representing average annual electricity consumption attributed to that ~ j appliance. Therefore, the values were ordered in that manner. c' I e r-

n ' 60 -1 1 - ^

r,

cq -

e,? r ; *-

• i.. ;J C ;a ?: g i ! c4 ca c4 -

. i, yo0 o c ; e. o o O C r; r, y c c o o ' s .I ._ ;2. ..', o, .t+.....J,c e u.,1 u,. 4 L.:.;.,c1.,,i a,sJ c.s e x; o-

..:. t.ss 11.n O O O - u c

') <;oopo .( . p - rot, 0 039,2 O rc O c '3 00**O i . 7.. rm... N. OC" s v s o e.,

• C

.2 o ..m-p -1 j.,. ;i.; ; -i? e.- -),, ; ;y * ;, c, y cy a e, -0 J.;.4 %. J"; ' u';)'.'.i.) 9 *J 9 -) p.- - -+..... ~ ,,.4,.,,.4-,'.4-.4. . m .4 o -4 o.,.o e. i f.J A. a., ph.$ L.t '..eq ,p Ci # .m t ..e. f.; t, t 1 s* J fh,4.** * ,A J .*+A s c.- O o.s v o o ",,2 OI*1 p o o G o a c o O o - o. + ? ;; U t . 3 i, 1 - i i i i -e i-~*-t-I '.-6 = . J La L.! W J L LI L.2 LJ U.J 'o.-J ' ! w J W il W LJ U LJ

m. a.s;

• c) ;- ooornooom o;oOCOOOO G t

, *i Q O T k O C C C G Q P ~~3 *f)OQDQQO Oc F. < r, -.' O, r. C O J (

• O C o t. OCv 00COCUC

- L) e4 O.*?-iN OO s)NO?s:.4L7C.T O r) h3 - .[- . t,,:J to r ! c ; e, - u 0. C O. h O G C3 P. r. !. 0 - r 2 33 Q f 4 C) C C ' s 2 .. +..s e s .-. s. +.. v d'"- s** p) p hj.. e f:*e (- ; h, M (+y p y)-- p;p) q p)p.3i.)gg. N N C2 i Ci ti :k ';s ti :1 C: ?t M N Ct h N C :3 C1 c CJ t: N ' o s C. '.Of o c o C O 0 0 0 C 0 6 0 0 0 0 0 0 0.0 ! I i ~ i : I '-I f I I t ! I't ( J i.:1 W f.4. f L2 G 'd.:J 14 J L-i w U W U l.:1 W '. J LJ ' J U W U a' W. f socG

- O J ouoaOcoO000 O t; occoo

• c < *.7

- - C .y V O F: O o O O O O O o o *J O o o C O ' ,g OOG u O O O C O O O C O O C O ".ro O O O O O O' g _ cy ; :.

is; --

s~,at .e e4 4 n n,. t, L 3 v o n a c c, - W N. c f G

M M e t 1 ' 4., O CO C.

. C4 N 'A. sc. C; O o C J N. e + b b

• .!Fn'"8 '

'" U") f53 M :.+ M 77 M 7* - f*1 f * %

• T V C/

vt ff f," M L*j M O C D C D D D O (4 bDDDD@D~Y ODDODODD G - a n e a s n -4 a, n a 4 u > e a c-a os a-nae J 7' O O */ ?. O O e4 N :, O t 9 w 93 O 7 ) O N C*, O N M N 4 O O . g 3 q q.; q m so. q q sej q q 9. o la D It) p':. n ti) 1;) n in n. n

37020,

..? ~ t-M CJ N -4 H C v C* 03 h 2 i2 D v M CJ e4 e4 m, ~

m.....

Q e-. W U .k-m. .O g 80 o h 6 0,.:*. C C - CCOO

• 6.CCCOCOOCCCCOOC

^ : D 0,

.. e4 i t 1 O 42 P 03 D O N O H O M M "? 03 4 h C-

.{ o M. ? ).' o ;- 23 h H 4 <4 4 *4 9 M O' N v ei 02 N 0- O f.* e4 O

• '2 C I M M ~ 'O r m G. G ; O C e4 e4 M M e'
• D lD N3 N O y

ic ey cc e-g c:. 4 - ; -ir; pi y ;.; q ;) ej;q p3 n n p) n u -e

• * * * +. +

4 ( 4 OI E ar= M t;.

• .<1 OOO

.C

• • 'C-O O C O O r.) O O O O O

. f.E4 C J.4 0. v - < i c v n -) ;- r-9 v N N s M e v G

• • b.

Q 3 C3 > ; 3 ^ !. C 02 T - M Q A Q ;3 D B V D ~ e< 3 . - O ; - S C o c C'. c..? O r* c,re, c c c. c 0- o c. c, c. c. .. N r 1.-; i t f *s bl M. N. CJ N.'.l N 010 M N (1 M M. U N. N M. ^.! cl p O C.O O O O,0.C C O O v Q Q O C' Q O'O O O O O Q O C C t ~f,J.4 M ;O M M 03 Os e O ? O C 0 0 v -4 e4 er 4 e: QJ 0 C ; q Q 0- 0;.*

• .G C2 C+ v4 N M M ** C i *+ 4 N M N M M M *r T eS v (1o4c3%0-00C-COOOOOC^COOOO00OvO

'.N C'O Q 4 4 A.l' N fsf N NT Nf< h h. b. N N N N N N.

r3.. ?

1 5

!,.. : d N ^3 C5 O * + N M d'. ) I C7 0- O - ' f 4 M ** h e;

}, f; ;- %.7.') !.1 O d W 9 41 a3 T.

10 ; 4 4 'C N N 3 I-a %e -I h_ m 6

61 ( For the Detroit Edison data this was the only transformation necessary. But for Consumers Power a little more was required. In a number of their survey questions the breakdown was more detailed than just ownership. As an example, refrigerator type was asked -- frostfree or not. Frostfree re-frigerators use more electricity than do manual defrost, so the refrigerator m variable should have three levels. The lowest is for non-ownership, the middle for manual defrost and the highest for frostfree. A number of such multilevel variables were formed. A complete listing is given in Appendix D. The other data that were generated for individual customers were average prices. No marginal price could be developed because all the customers of each company face the same rate schedules, and the two surveys could not be combined because they were taken at different times. For Detroit Edison the average price was calculated by dividing total consumption by total revenue ( for that customer. Data for Consumers Power did not include total revenue. The basic rate structure at the time of the survey was a flat schedule. Therefore a total figure was calculated by multiplying total consumption by this flat rate and then adding twelve times the monthly service charge. This sum was then civided by total consumption to give what is called in our re-gression results the average price. Actually, no charges resulting from the fuel clause adjustments are included in the " total" revenue figure, thereby giving a downward bias to the average price. Some comment needs to be made concernirg the income variables derived from the individual customer data. The income variables represent various income ranges. As such they are rather imprecise measures of income. This has ramifications in the interpretation of results, as will be made clear. 1 h m.. m w

4 62 q - E. SPECIAL' PROBLEM AREAS AND ALTERNATIVE DATA SOURCES During 'de course of the study, various data ana'alies and/or service i < area irreguiarities required that special assumptions be made in order to expedite the investigation. One such assumption concerned Consumers Power's Pontiac division. This division, consisting of the old city limits of Pontiac, is owned and operated by Consumers Power, yet Detroit Edison gener-ates the power for the region, and consumers within it face Detroit Edison tariffs. ~ For this latter reason, it was logical to treat the Pontiac division as if it were in fact part of Detroit Edison's Oakland district, and this was done. Within the Detroit Edison service area, there are six counties that are not completely serviced by Detroit Edison. These counties are Oakland, ( Livingston, Monroe, Washtenaw, Ingham, and Lenawee. Socioeconomic data are-disi ggregated only to the county level (apart from census tract data, which art available only within standard metropolitan statistical areas). In view of the lack of a method of allocating urban / rural, housing, or income charac-teristics within these counties to establish the distribution of the particu-lar characteristic across the given county, these districts were treated as if they encompassed the entire county. Given the extent of physical con-formance between actual county and the service area county or district, this problem is probably negligible for Oakland County, marginally important for 1 -. Livingston, Monroe, and Washtenaw Counties, and potentially important for , t 'l, Ingham and Lenawee Counties. 1 W v -.,e -,..,-e,.,~ ,,,,,-,-.y--, c,, e, .,r--,-,--,,. e--.. .,--,,,,---,,----am,--.,,,,,,,,-,w.,,-,.,.v., ,w-.<.m--,.e.-,--. .,a,

t 63 W i Sources other than those previously described were investigated in order to obtain additional data for other socioeconomic variables. The Michigan State Statistical Abstract and County Business Patterns were both checked for information concerning income and unemployment. County Business Patterns performs a data breakdown on the basis of industry groupings (SIC codes) at the county level. The time costs involved in aggregating these data are prohibitive. It would have been necessary to combine figures for all in-dustry groupings into one figure for each county, for each of 83 counties and each of 25 years. The Michigan State Historical Abstract does have some in-formation on income and unemployment. However, the Bureau of Economic Analysis has the same income data source and is more current, not having the publica-tion lag time of the Michigan State Historical Abstract. The unemployment data are only published for the years 1969 to 1972 in county fonm. This is ( too small a number to be used to extrapolate unemployment figures for the entire 25-year time period being analyzed. \\

64 V. ESTIMATION OF DEMAND f The previous sections have described the various steps in this study that precede the actual attempt to estimate the residential demand for elec-tricity in the lower peninsula of Michigan. The estimation process is the final mechanical step before the real crux of this study, which is the analy-sis of the estimated coefficients and of the demand for electricity. The estimation effort involved trying a large number of different equa-tion specifications,for the various types of data available. The effort was more or less concurrent with the data collection effort in that early runs were made with a relatively small data base, and as new data became available it was incorporated into the estimating equations. To describe the various estimation equations it is convenient to divide the effort into l_ three components which focus on the nature of the data base. The data bases became available in sequence, so this division also orders the estimation i process. The first stage involved time series analysis with the regional data base. Next is the combined cross section/ time series analysis using the complete regional data base. Third is cross section analysis using the individual customer data base, the last data collected. A. TIME SERIES ESTIMATION OF DEMAND 1. Regional-level Estimation of Demand a. Initial Estimation Efforts The first demand equations were estimated when only the most basic data was available. These data included consumption, average price of elec- ~ tricity, income, average price for natural gas, and marginal prices based W- ,,y , _ +, g.

65 on 500 kWh TEBs and on 10 mcf per month. The gas data was initially avail-able for only the Consumers Power divisions, but in relatively short order data from the other gas companies was received. Initial equations were esti-mated in both linear and log-liner forms, for both average and marginal prices, and in both nominal and real terms. Attention quickly focused on the log-linear specification for two reasons. The time series data tended to grow over time, and the logarithmic transformation tends to make the data more homoskedastic. Also, the equation statistics appeared markedly better for 2 this specification, these statistics including the R, the standard error as a percent of the dependent variable mean, and an F-test for the equation. It was also noted that inclusion of a lagged dependent variable (for purposes of separating long run and short run effects) had a great effect on the equa-tion, the coefficient for it being uncomfortably close to one. I b. Addition of Housing Characteristics ~ The data concerning percent urbanization and percent multiunit hous-ing were then added. Both were very significant, in a statistical sense, ex-cept when the lagged dependent variable was included. This was especially true for the percent urbanization. Again, equations were estimated for both aver. age and marginal prices, and in nominal and real terms. A problem of autocorrelati:n in the residuals (when there was no lagged dependent variable) was noted i.: many equations. Other statistical tests indicated improvement ~ in explanatory ability of the model when housing characteristics were in-cluded. c. Inclusion of Additional Alternative Fuel Price Data At this point more information on alternative fuels became available. k The price data for fuel oil, coal, and propane were included as independent variables in addition to the previous variables. e -r-- e

66 The coal and propane series often ended up with negative coefficients in the r L equations, an unexpected result. This was attributed to the wholesale and r aggregate nature of these series, and to the other uses to which they serve as fuels. Only the number 2 fuel oil series seemed to give plausible results, i~ Future specifications included only combinations of natural gas and fuel oil as alternative fuel prices. d. Inclusion of Appliance Saturation Levels Two attempts were made at incorporating the appliance saturations levels into the regional time series analysis. One was simple inclusion of the levels as independent variables. Whan this was done the signs of many of the appliance variables, and the other independent variables, became highly variable from region to region. This was taken as an indication of model ( inadequacy because there are expectations about what the proper signs are for the in::ome variable, alternative fuel variables, and the price of elec-tricity variables. The second thing was to do a two stage estimation where the first stage entailed estimation of appliance variables and the second stage was to include these estimated appliance saturation levels in an electricity demand estimating equation as independent variables. The second stage was never carried out, though, because so little promise was shown by the first. Appliance saturation levels were, in the end, not considered useful in the regional time series work, and therefore not included in any further estima-tion work. L e . -, ~, -.. - - ... -,. ~,... -.

67 ( e. Lagged Independent Variables The initial efforts used a lagged dependent variable to separate long and short run effects. This forces the effect over time to be the same for all variables. To allow each variable to establish its own pattern vari-ous lags for income and fuel prices (electricity, gas, fuel oil) were added as independent variables in specification not including a lagged dependent variable. No pattern was discerned in these efforts, so it was discarded and the lagged dependent variable approach utilized. f. Weather Variables On a regional basis heating degree days were included as an indepen; der.t variable. For most regions the coefficients for heating degree days were statistically insignificant, but for a few they were significant and of g the proper s.icn. For these regions the heating degree day variable was in-cluded as an independent variable in the optimal regional model. The lack of significance for most regions may be the lack of real variability in the heat-ing degree day data, as will be expounded upon in the next section. g. Electricity Price - Marginai As expounded in Section II, the marginal price is called for in economic theory. Up until this point the marginal price utilized had been l the one based on 500 kWh Typical Electric Bills. By this time conclusions had been reached as to which of the independent variables properly represented u. that which they were intended. The appliance saturation level and coal and i propane prices were judged inadequate, the percent urbanization and percent "~

('

multiunit were considered weak as data sets. The different marginal prices ~ l ( r,m c w .e y ..--e ---,,=y, ,-..m wv--

68 for electricity described in Section IV were derived at about this time, and all were tried in estimating equations using only those additional inde-pendent variables thought to plausibly represent what they were intended. The electricity prices based on the difference between the TEBs for 750 and 500 kWh performed the least satisfactorily. The so-called Bill 10 prices gave results in accordance with expectations. Since this price has the best theoretical basis it was the one chosen as the marginal price for elec-tricity. Table V-1 reports the basic statistics and coefficient esti=ates for each of the 24 regions making up the service areas of Consumers Power and Detroit Edison. The electricity prices and natural gas prices are margi-nal prices. All dollar values are expressed in real terms. The basis for choosing which alternative fuels -- gas or fuel oil -- would 5e included was based upon which gave the most reasonable (positive) sign and which was f most statistically significant. A more complete analysis of these results and what they actually mean to this study is given in Section VI. 2. Comoany Level Denand Estimation After completing the regional time series analysis that data was aggre-gated into company level data, as explained in Section IV. This ccmpany-level data was used to run regressions using the " good" variables from the regional analysis. These regressior.s are reported on in Appendix F. Suffice it to say, the regional analysis was considered more relevant, and Section VI pro-vides the best company-level analysis. One worthwhile aspect of the company level analysis concerns the weather variables. Data was available for the Detroit Edison service area to test pm +- 9 t y,- e

.. J 1. 7- ). N ote V-1 Regional Time-S: ries Modal 1 Demand = AElectricity'* Income" Gas 6 *0il' *HDD** Demand (-1)P Coefficient Estimated Long-Run Elasticity 2 Region R F-ratio Electricity Income Gas Oil HDD Electricity Income Gas Oil Central .9975 1880 . 213 *. .052 .088** -1.67 .41 .69 Battle Creek .9984 2936 .252* .024 .068** -1.85 .18 .51 Northeast .9977 2075 .128** .084** .113** -1.22 .80 1.08 Flint .9983 2134 .165** .176* .229* .166** -1.16 1.24 1.61 Grand Rapids .9975 1925 .243* .081 .183** -2.14 .71 1.61 Jackson .9984 2270 .198** .043 .029 .038 -1.47 .32 .22 .28 Kalamazoo .9974 1816 .231* .0001 .093** -1.61 .00 .65 Lansing .9981 1930 .255* .057 .077 .051 -1.61 .36 .49 .32 Muskegon .9969 1520 .062 .093 .093 -0.85 1.27 1.27 Saginaw .9985 2316 .250* .090** .159** .183** -1.62 .58 1.03 Northwest .9964 1005 .168 .124** .119 .174** - 2.98 2.20 2.11 3.09 Huron .9959 1158 .086 .008 .041 -0.61 Lapeer .9990 3496 .098** .067 .033 .160* -0.80 .55 .27 Sanilac .9967 1417 .099 .060 .015 -1.12 .17. St. Clair .9976 2000 .145** .026 .005 -0.79 .14 .03 Tuscola .9982 2637 .093** .050 .009 -1.25 .12 Oakland .9965 1336 .070 .073 .071 -0.57 .59 .58 Macomb .9970 1569 .128** .043 .176** -0.73 Washtenaw .9963 1278 .146* .089 .220* -1.10 .67 1.66 Lenawee .9959 1148 .109** .046 .088 -0.54 .23 Livingston .9981 1904 .064 .055 .070 .058 -0.49 .42 Ingham .9957 1422 .046 .033 .148** -0.31 .22 Monroe .9982 2566 .149** .011 .120** -0.81 .06 Wayne .9969 1503 .229* .107 .102 -1.13 .53 .50 (Reference Tables E-1 through E-24 of Appendix E)

• Significant at 1 percent level m
  • Significant at 10 percent level

70 l 1 l the effects of weather data 'for heating degree days, cooling degree days, and maximum THI (temperature-humidity index). Table V-2 gives these re-sults. It indicates heating degree days is as good a weather variable as f any, and including both a winter and a summer variable does not increase the significance of weather factors over just the winter variable. This is be-Gl cause the winter and summer degree day data are highly correlated, as can be seen graphically in Figure V-1. It appears this effect is caused by the large lakes surrounding Michigan. This tends to contribute to a mild summer after a cold winter because the lakes, especially Lake Michigan, tend to exert a greater cooling effect for a longer period. B. COMBINED CROSS-SECTION/ TIME SERIES ESTIMATION OF DEMAND The analysis reported thus far in the report has been of a time-I series nature (data from a single place varying over time). Another type of analysis combines time-series and cross-sectional analysis into one set of results, and is called combined time-series / cross-sectional analysis. The data made available in the course of this study allow a combined time-series / cross-sectional analysis to be performed only on a regional basis. The data base used was the regional data for each company. By separating 1 the two companies effects due to slightly different aggregation procedures were eliminated as a source of mixing error. The procedure used js called t " Seemingly Unrelated Regressions". This procedure was chosen over other (, possible procedures, such as the Balestra-Nerlove technique, because it requires less stringent assumptions concerning the form of the residuals t without sacrificing any generality. The major disadvantage of using this s _. f

7_ f-Table V-2 Comparison of Weather Related Variables for Detroit Edison HDD THI CDD HDD + THI HDD + CDD Coeffi-t Coeffi-t Coeffi-t Coeffi-t Coeffi-t Variable cient statistic cient statistic cient statistic cient statistic cient statistic Electrical 4 Price (500 kWh) -6508 -5.8 -6096 -6.5 -6192 -6.8 -6941 -5.4 -6199 -5.3 Gas Price (10mcf) 617 3.6 562 3.4 588 3.8 619 3.5 589 3.3 Income .909 8.2 .939 7.6 .910 8.5 .946 7.6 .909 8.1 Weather Variable .1574 -0.669 -6.194 -0.194 .4399 1.214 .2789 -0.951 .0026 -0.009 -28.00 -0.711 .438 0.979 i Constant 12458 3.8 11377 3.1 10583 5.1 16415 2.5 10611 2.81 2 Adjusted R .9684 .9678 .9699 .9676 .9683 Auto- . AUTO (2)= AUTO (2)= AUTO (2)= correlation +0.45 +0.45 +0.52 AUTO (2)=+0.51 U

7__ .q 6700 1200 6600 lleating Degree Days s 6500 \\ 1100 s \\ \\ 6400 \\ \\ i 6300 l 1000 n 6200 I 4 E E g 6100 900 E o o E E g 6000 2 8

c o

l 5900 800 5800 5700 / 700 / / / 5600 Cooling Degree Days 5500 p = -0.564 600 i i 50 55 60 65 70 75 0 Figure V-1. Degree Day Correlation, Detroit City Airport

73 r procedure was a limitation on the size of the data base which precluded ,~ combining the data for both companies into one set of equations. The major benefit to be gained from such a procedure is that a relationship that exists between regions but not axplicitly accuunted for by the independent '[~ variables when used in separate regressions will be incorporated into the final coefficients of the " Seemingly Unrelated Regressions" procedure. f* Not unexpectedly, the tests we ran using this procedure did not produce any enlightening results. The coefficients were little changed from the more conventional time-series crialysis. This was not unexpected because the time-series work " explained" so much of the variation in demand that there 4 was very little combining the residuals could add to the analysis. There is f. 'l somewhat of a tendency for the coefficients to be less varied from region to region, but the degree of shift from previous work can be explained by purely ( random correlation effects. Because the single equation analysis is much cheaper and this more expensive procadure does not yield important results, very little additional work was done using this procedure after initial test-i ing. The detailed results from the " Seemingly Unrelated Regressions" are given in Appendix H. C. CROSS SECTION ESTIMATION OF DEMAND i 1. Regional Cross Section Work I t The same data as used for the time series work was used in cross sectional analysis by making each region an observation and running a regression fcr each year. It was in this type of analysis that the percent urbanization and { L e mi -4 r-

t 74 ~ 1 percent multiunit housing data held the most promise because the data reflects. f 5 geographical changes much more accurately than changes over time.

However, the estimation results were unacceptable because the electricity price co-

[ efficient came up with a positive sign, an unacceptable result from a theoreti-cal standpoint. This. reflects a limitation of the estic.ating procedure. ^ The problem arises because of the lack of substantial electricity price vari-ation (there being only two prices, one for each company) and the makeup IJ of'the Detroit Edison service area. The Detroit Edison customer faces higher prices for electricity than the Consumers Power customer. But most of the Detroit Edison regions (these outside of Detroit) have higher average consump-tion than the Consumers Power regions. Rather than being a price phenomenon, j this is caused by the low degree of urbanization in the Detroit Edison non-Detroit regions. The percent urban variable was intended to control for i; this. But, by weighing each division equally, a severe distortion was intro-duced. The Wayne county consumption is almost half of. the company's resi-dential load, yet it counted only as one of thirteen divisions. The other twelve divisions, ten of which are sparsely populated, counted equally. In i effect this meant there were ten Detroit Edison divisions with high consump-tion and high prices,' eleven Consumers Power divisions with. low consumption and low prices, two Detroit Edison divisions with low consumption and low i prices, two Detroit Edison divisions with high prices and medium consumption, { and one Detroit Edison division with high prices and low consumption. The logical thing to do would appear to be to weight the division dif-ferently so as to eliminate this problem, but the dependent variable is so "( closely related to the basis on which rational weights should us based that a high degree of bias might be introduced and the results could not be trusted. . g... b c n -.r, - -,~ ~ r 4 -,,e-- -~,~,,,,m -,e--n- -,mm, - 4 --..p. ,ea -->m-. y-- ,m.a, ..r.,-+- w,,-m v

75 2. Individual Customer Cross Section Estimation of Demand Cross sectional analyses were also performed using the individual customer data for each company. This was the only data available which allowed estimation for different income groups and different usage groups. There is a problem in using the price of electricity in these equations, as will be explained in Section VI. For this reason regressions were run that included a price variable, and that did not include a price variable. Also, a number of appliance ownership indi.cators were used to separate long run and short run response, the equation including the appliance variables measuring short term response, those without the long term. Tables V-3, 4, 5, and 6 summarize some of the equation statistics and coefficients. i. Details of each regression are provided in the appendices as indicated. The tables indicate the sample size for each regression and the mean annual consumption of electricity for that sample. The percent Standard Error is r the standard error of the regression divided by the dependent variable mean. The coefficient for the income variable is included when it was a major determinant. The "Others" column lists.the other variables found to be major determinants through a stepwise regression procedure. When included in the specification the average price variable coefficients are also included. There is very little information relevar.t to price elasticity in these tables. There is some information concerning characteristics of various groups, such as the increase in average usage as income increases. Also, the relative consistency of what the major determinants were gives valuable infor-i mation about electricity consumption. The similarity in this re' gard between Detroit Edison and Consumers Power customers is worth noting. However, the r-standard error in all cases is high enough that these results should not be m considered definitive. s. g r-9

76 Table V-3 l Individual Customer Results Which Do Not Include Appliance Variables or a Price Variable

• CONSUMERS POWER l

Sample

1. obs Dep. Mean

% Std. Err. Income Others Total Sample 1533 6914.7 87.0 356.7

Rooms, (3.82)

Family Use Blocks 0-500 kWh/mo 783 3370.9 46.1 Rooms, Family 500-1,000 kWh/mo 581 8401.3 19.7 Family l over 1,000 kWh/mo Income Blocks 1 0-$4,000 4,000-10,000 451 6190.1 120.0 Rooms, Family 10,000-15,000 387 7189.1 76.9 Rooms, Family 15,000-25,000 387 7772.8 64.0 Rooms, Family over 25,000 138 9133.5 79.3 Rooms DETROIT EDISON Total Sample 711 7044.0 60.9 654.7 Rooms, Family, (6.9) Age Head i Use Blocks 500 kWh/mo 342 3780.0 29.7 202.7

Rooms, (6.4)

Family .500-1000 kWh/mo 294 8110.8 18.8 217.3 Rooms (3.5) l over 1000 kWh/mo Income Blocks 0-$5,000 122 3745.8 60.7 Family 5,000-10,000 141 5360.4 51.5 Rooms, Family 10,000-15,000 216 7684.7 67.0 Rooms, Family l[ 15,000-25,000 170 8622.1 52.8 Family over 25,000 62 10804.0 52.5 Rooms, Family Reference Tables 1-9 and 19-27 of Appendix I 1 No independent variable statistically significant at 95 percent level ' Me e gww-w a -rw,,,e-,,- --v---w t y-r et -v~+- e --e --v-- t' +T ye-ev-* - - = * - - -

i 77 Table V-4 Individual Customer Results Including Aop11ance Variables But Not a Price Variable

• CONSUMERS POWER Dep.

% Std. Sample

1. obs Mean Err.

Income Others Total Sample 1310 7142.3 78.8 227.3 Rooms, Family, Freezer, Dryer, (2.32) Stove, AC, Water ~ i Use Blocks 0-500 kWh/mo 648 3456.3 42.4 Rooms, Family, Fre9zer, Dryer, Water 500-1,000 kWh/mo 509 8370.3 17.7 Rooms, Family, Freezer, Dryer, l over 1,000 kWh/mo Income Blocks 0-$4,000 125 4520.6 49.2 Freezer, Dryer, Water 4,000.10,000 382 6400.0 112.5 Family, Freezer, Dryer, AC, Water 10,000-15,000 338 7339.0 68.9 Family, Freezer, Dryer, Stove, Water 15,000-25,000 343 7846.7 54.8 Rooms, Family, Freezer, Dryer, Water over 25,000 122 9627.5 68.8 Family, Freezer, Dryer, AC DETROIT EDISON Total Sample 711 7044.0 53.2 309.1 Rooms, Family, Freezer, AC, Dryer, " (3.8) Stove Use Blocks 0-500 kWh/mo 342 3780.0 28.1 170.4 Room.e, Family, AC, Freezer, Dryer, (5.5) Stove 500-1,000 kWh/mo 294 8110.8 17.3 142.8 Family, AC, Freezer, Dryer, (2.5) Stove over 1,000 kWh/mo l Income Blocks 0-$5,000 122 3745.8 50.6 Family, Freezer, Dryer, Stove 5,000-10,000 141 5360.4 41.5 Family, Rooms, AC, Freezer, Dryer, Stove 10,000-15,000 216 7684.7 56.4 Family, Rooms, Freezer, Dryer, Stove 15,000-25,000 170 8622.1 47.0 Family, Freezer, Dryer, Stove over 25,000 62 10804.0 47.9 Family, Rooms, AC I t; Reference Tables 10-18 and 28-36 of Appendix I 1 No independent variable statistically significant at 95 percent level %e -a, s-w e y-m y --e-

78 Tab 1'e V-5 Individual Customer Results';ncluding an Average Price Variable and No Specific Appliance Variable

• CONSUMERS POWER i -

Sample hbs Dep. Mean % Std. Err. Income Price Others ' Total Sample 1533 6914.7 86.9 357.8 2.45 Family, Rooms (3.8) (1.1) Use Blocks 0-500 kWh/mo 783 3370.9 45.9 -1.36 Family, Rooms (2.4) 500-1,000 kWh/mo 581 8401.3 19.6 -1087.5 Family (2.3) over 1,000 kWh/mo 169 18223.0 42.9 -773.5 .2E+06 (2.1) (15.3) Income Blocks 0-$4,000* 170 4457.7 57.5 -55.5 (3.6) 4,000-10,000 451 6190.1 120.1 -1.44 Family, Rooms (.5)- 10,000-15,000 387 7189.1 74.8 -375.7 Family, Rooms (4.9) 15,000-25,000 387 7772.8 63.0 -63.6 Family, Rooms (3.7) 4 over 25,000 138 9133.5 78.8 -168.2 Rooms (1.7) 4 DETROIT EDISON ' Total Sample 711 7044.0 53.5 265.5 -5095 Rooms, Family (3.0) (14.5) Age Head-Use Blocks 0-500 kWh/mo 342 3780.0 16.6 92.5 -2276 Family, Age Head (4.8) (27.8) 500-1,000 kWh/mo 294 8110.8 17.5 222.7 -2220 Rooms (3.9) (6.7) over 1,000 kWh/mo 75 17747.0 40.5 -10947 (3.1). Income Blocks 0-$5,000 122 3745.8 42.6 3031 Family (11.1) 5,000-10,000 141 5360.4 37.1 3885 Family (11.8) 10,000-15,000 216 7684.7 56.2 9231 - Rooms !~ 15,000-25,000 170 8622.1 43.5 (9.8) 8062 Family (8.9) over 25,000 62 10804.0 48.0 12541 Rooms (4.7)

• - Reference Tables 37-45 and 55-63 of Appendix I~

y' mi-"g-,ww9 w-ew-9--.g-y --vww+*w-w g---swp+--y g -it

• p

,w-----g --*gJcwm wyt ---m--we-T y +.wp g,-3 -'g g yyy-w y, i mer wWWw.fw,-rgr1 y

79 Table V-6 Individual Customer Results Including An Average Price Variable and Appliance Variables

• CONSUMERS POWER Sample fobs Dep. Mean

% Std. Err. Income Price Total Sample 1000 7395.5 78.0 -105.0 (5.5) Use Blocks 0-500 kWh/mo 474 3485.0 37.5 -39.0 (8.7) 500-1,000 kWh/mo 400 8382.5 17.5 +1633.6 (2.5) over 1,000 kWh/mo 126 18974.0 45.9 .24E+06 Income Blocks (13.0) 0-$4,000 89 4208.9 39.3 -164.1 (5.5) 4,000-10,000 266 6739.7 120.3 -91.2 (.8) 10,000-15,000 263 7623.7 61.8 -1170.7 (4.6) 15,000-25,000 285 7988.8 45.1 -96.2 (/.2) over 25,000 97 9755.9 61.2 -106.2 (1.2) DETROIT EDISON Total Sample 711 7044.0 40.6 279.3 -1243 (4.2) (3.8) Use Blocks 0-500 kWh/mo 342 3780.0 15.6 81.7 -2506 (4.5) (28.1) 500-1,000 kWh/mo 294 8110.8 16.4 158.7 -1827 (2.9) (5.7) over 1,000 kWh/mo 75 17747.0 30.8 1529.9 (2.7) Income Blocks 0-$5,000 122 3745.8 31.3 -1909 - (8.3) 5,000-10,000 141 5360.4 26.~6 -2792 (10.7) L_ 10,000-15,000 216 7684.7 37.4 -2847 (3.7) 15,000-25,000 170 8622.1 29.7 -1840 (2.2) ~ over 25,000 62 10804.0 42.7 -6973 (2.5) ~ Reference Tables 46-54 and 64-72 of Appendix I .-_.y, + -r.

80 VI. ANALYSIS After running a number of regressions which are supposed to produce estimated coefficients for equations which represent electricity consumption, it becomes necessary to analyze exactly what the statistical results are saying. The conclusion we have come to is that econometric procedures do i_ not yield valid estimates for price elasticities for a single utility service area

• which are to be used in any policy formulation.

Note we are not saying we could not do it (for data limitation reasons), but that the procedures are inappropriate given the historical data that do exist. We are also not saying that all other econometric studies are incorrect. Most previous studies were national in scope, and on a national level there are things that can be done to overcome problems which are insurmountable for a single service area. Also, if detailed individual data, including income is collected now and for some time then it may become possible to do a more definitive econometric analysis. In order to make clear how we arrived at this conclusion it is necessary to go into a little more detail concerning the implicit assumptions made in an econometric demand analysis. One of the major difficulties in an econometric investigation of demand functions is what is referred to as the " identification" problem. The situ-ation arises because consumption data represent market clearing quantities, or the intersections of various demand curves with various supply curves. This issue derives its name from the problem of determining which curve is ~ shifting and what the proper variables to control for this shifting are. Once properly specified or controlled, such an estimated function is said '~ Unless the utility has different rates for different residential customers that depend on where they live. m 46 4$ am g W$@

81 to be " identified". In general, a scatter diagram of the interse?tions be-tween the various supply and demand will take on one of three general foms. These three basic patterns are illustrated in Figure VI-1. Figure VI-la illustrates the pattern one would expect to find with a relatively stable demand function and a shifting supply curve. On the other hand, Figure VI-lb represents the expected pattern given a relatively stable supply curve and a st.ifting demand curve. Lastly, Figure VI-Ic illustrates the situation that obtains when both supply and demand curves are shifting. P P P Q Q Q a b c Figure VI-1. Typical patterns of observed market quantities and prices. i-t = eem g s-

82 ~ If-a demand relationship is properly specified or identified, then one expects to find a situation as illustrated in Figure VI-la. Such a scatter results from a relatively stable demand curve being intersected by a shift-ing supply curve. Figure VI-2 details this condition mere clearly (assuming deter =inistic rather than statistical relations). P S 2 31S 3 4 B A C D Q Figure VI-2. Elasticity estimation with properly identified demand curve. Here, the shifting supply curve traces out the demand curve through the inter-section points A, B, C, D. From these intersection pointt, an elasticity of e demand can be estimated. N8

83 A point of confusion, as it relates to estimating elasticities of demand ~ for the electric utility industry, is that the supply curve for electricity is also downward sloping like a demand curve. This means that, if a demand model is not properly specified or identified, a 3catter diagram as illustrated in Figure VI-la may still be observed by the intersection of a shifting demand curve with a relatively stable supply curve. Such a situation is illustrated in Figure VI-3 (assuming a stable supply curve for illustrative simplicity). P I A' C' S U 0 D 2 7 3 Q Figure VI-3. Elasticity estimation with improperly identified dimand curve. In this case, the improperly controlled demand curve shifts and traces out the supply curve through the intersection points A', B' and C'. If the investigator assumes that these intersections trace the demand curve and uti-lizes them to calculate an elasticity, the result will be an overstated esti-mate of the true elasticity of demand (in fact, what would have been estimated from the situation illustrated in Figure VI-3 is the supply elasticity). s L% ..,,,,,,.s..m. -..-w

84 This discussion provides the background to explain why, for each of the. j two forms we estimated electricity consumption (cross section and time series), . l the price coefficients should not be construed as allowing calculation of price elasticities. A. CROSS SECTION ANALYSIS A general argument in favor of cross-sectional studies has tu do with the relative homogeneity of residential customers. This homogeneity across regions implies a relatively stable demand curve across regions when the demand func-tion is properly specified. Since generating costs across regions (especially at the national level) will be different due to such factors as generating mix (i.e., proportions of nuclear, coal, and hydroelectric capacity), public versus private ownership, government subsidization (such as the TVA), etc., a situation representative of a shifting supply curve exists. Hence, it may be possible to trace out the demand curve and thus estimate the elasticity of demand. However, it should be pointed out that the above argument does not hold for an individual utility service area when considering a cross-sectional investigation. In this case, it is impossible to get any price variation (except for artificially induced variations produced through the use of aver-age price) other than the different prices represented in the multiblock i tariff, since all consumers face the same rates. In such a case, a perfectly v st6ble supply curve exists in the form of a' declining step function (assuming a declining block tariff). Since, in any model, it is impossible to perfectly i I.. e e e w -,--e

---

,,,,w

85 control or identify the demand function, it will be subject to some varia-tion. Therefore, the situation illustrated in Figure VI-4 will exist. T-P o. A i 1 (B c S D1 02 D3 .~

(

Q I-Figur-e VI-4. Estimating block structure " elasticity." Here, the shifts in the demand curve have merely traced out the blocks'in s the tariff with the resulting " elasticity" estimate being merely representa-tive of the degree to which the block structure is declining. The foregoing argument is not intended to disparage cross-section studies as a valid method-ology in elasticity studies, but merely to indicate the method's lack of applicability to a study dealing with a single service area. It might be noted that this argument would not be valid if customers in a single serv-ice area and within the same use-block faced different prices. Such is the { case in France, where El$ctricite' de France differentiates electricity prices by distance from the generation source. 'I t, The previous paragraph referred to artificially induced variations being produced when average price is used as the price variable. For most ( 3 h

86 7 normal goods, this problem does not arise because average price and margi-nal price are identical. Consumers can buy as many units of a certain good as they want at the market price. This is the type of good that general eco-nomic textbooks deal with. However, the electricity rate structure has gener-(' ally been made up of declining blocks until recently. Thus, the more electricity a customer uses, the lower the price block he consumes in and the less his f, next kilowatthour costs him. The economic theory described earlier is based on marginal utility. This, in turn, implies that the price the electricity consumer is reacting to is the price for one additional unit of electricity; hence, the name marginal price. With a declining block structure, the aver-age price is higher than this marginal price. Furthermore, artificial vari-(l, ations are produced because the average price is different for every customer, as it is determined by consumption. In an estimation procedure, this vari-t ation is interpreted as consumption changing in response to price variation, t a reversal of cause-ar.d-effect. Every customer face:; just one set of rate ~ i schedules, so there is no price variation. The differences in price associ-( ated with average price are not orice responses but merely a manifestation u of rate structure. The individual cross section work for this study provides some empiri-cal verification that the use of average price measures more about the supply curve than the demand curve. The Detroit Edison data was collected in 1973 i { when Detroit Edison customers faced a declining block structure. The Consumers Power data came from 1976 when their customers had been facing a flat rate structure for a few years. Regressions were run (re. ported in Appendix I) { where an average price representation was included as an independent variable. L + l, .u-

87 I The Detroit Edison results indicated mostly elastic and statistically signifi-g cant price response, while the Consumers Power results indicated a very (statistically) insignificant price coefficient varying around zero. 1 The point of this is that the individual customer cross section analysis is not useful in determining an elasticity of demand for electricity, and therefore also not helpful in determining quantitative elasticity estimates i for other factors. However, information of a qualitative nature can be drawn from the analysis, the most relevant relating to income effects. The first point that can be made concerns the relationship between income [ and consumption. Table VI-1 indicates extreme, mean values, and standard deviations for the various income groups analyzed in this study. It clearly indicates that higher income customers tend to have higher usage. This is not the same thing as saying a high income customer is a high usage customer; it is a statement concerning aggregated averages. A utility must base its pol'cy 1 j on what "most" customers will do since any policy must inevitably affect dif- ^ ferent customers in different ways. If the above relationship concerning income and consumption is accepted, then Table VI-2 can be used to make i qualitative assessment of the elasticity of demand. Table VI-2 summarizes results for regressions using the individual l j customer data which include an average price variable and appliance variables. Of special interest are the. Detroit Edison results partitioned by income. It is at the lower consumption levels that the biasing effects of using the average price should be the e.rongest. The decrease in elasticity estimate 1 L as income goes up, and also in the previous group as consumption goes up, l;.. ~. .( ,,,a

88 i g Table VI-1 F Consumption Analysis b3 Income Group Standard Grouping Mean Mirdmum Maximum Deviation Obs CONSUMERS POWER \\ 0-$4,000 4457.7 20 12458 2652.1 170 4,000-10,000 6190.1 1 135742 7577.9 451 I 10,000-15,000 7189.1 69 68512 5733.5 387 15,000-25,000 7772.8 11 35323 5276.8 387 over 25,000 9133.5 49 45651 7797.4 138 DETROIT EDISON f 0-$5,000 3749.8 717 16101 2628.5 124 5,000-10,000 5360.4 688 21671 2930.0 141 ( 10,000-15,000 7684.7 1583 42746 5489.5 216 15,000-25,000 8625.4 1214 34001 4710.7 172 over 25,000 11047.0 1502 46515 6846.3 64 i ~ 4 ( c. l. k 1. 's

89 i Table VI-2 f -- Calculated " Elasticity" ' Estimates From the Individual Customer Datal - ( ( Sample . I CONSUMERS POWER DETROIT EDISON Total .061 .550 i significance of a group of regression coefficients taken together. i 10. INCOME ELASTICITY - An indicator of the responsiveness of changes in the quantity demanded of a good to changes in income. Mathematically defined as: I dQx y n, dY { See also: " Normal Good" and " Inferior Good" 11. INFERIOR GOOD - By definition, a good whose consumption decreases in association with increases in income. The inccme elasticity for such a good is negative. 12. INVERTED RATES - A pricing scheme for electricity that results in one or more of the " tail" blocks of a tariff being priced l higher than the preceding blocks. 13. LIFELINE RATES - A scheme of pricing electricity that results in low a rates for a so-called minimum subsistence level of kWh per month and much higher rates for any consumption above and beyond the minimum level. 1 2. L -- ---*~ -

98 7 GLOSSARY (Cont.) 14. MULTI-COLLINEARITY - A statistical term used to describe a condition of high statistical correlation between two or more variables. 15. NORMAL GOOD - Sy definition, a good whose consumption increases in ~ association with increases in income. The income elasticity for such a good is positive. 16. 0WN PRICE ELASTICITY - An indicator of the responsiveness of changes in the quantity demanded of a good to changes.in the price of that good. Mathematically defined as: dQ P n=gx* x If n <-1 demani referred to as elastic If -1<n<0 demand referred to as inelastic R I If n = -1 demand referred to as being of unitary elasticity. 17. R-SQUARED - Also called the " Coefficient of Determination." A statistic indicating the proportion of variation in the dependent variable that is explained by the regression. 2 (written R ) is a sample size corrected E Adjusted R 2 version of the R statistic. 18. SIMULTANEITY - A problem in a codel when not only is the dependent variable a function of a particular independent variable, but also that independent variable is a function of the y dependent variable. i 19. SUBSTITUTE GOOD - A comodity that is consumed as an alternative or substitute for another commodity. Two commodities are defined as substitutes if the cross price elasticity between them is positive. 20. T-STATISTIC - A test statistic utilized to assess the significance of single regression coefficient. As a rule of thumb, a t-statistic of greater than 2 (in absolute value) indicates L, a given coefficient is significantly different from zero. i m ---n,

99 r REFERENCES Anderson, K., Residential Demand for Electricity : Econometric Estimates for California and the U.S. Santa Monica: The Rand Corporation, R-905-NSF, January 1972. t , Residential Energy Use : An Econometric Analysis, The Rand Corporation, R-1297-NSF, October 1973 i " California's Electricity Quandry : III Slowing the Growth Rate," prepared for California State Assembly with support of National Science Foundation, September 1972. Asbury, J. G., The Econometric Approach to Electricity Supply and Demand Review and Analysis, Working Paper, Argonne National Laboratory, May 1974. Battelle Memorial Institute, "A Review and Comparison of Selected United States Energy Foregasts," Richland, Washington, December 1969. Beaudoin, B., G. Browne, and F. Lin, " Price-Demand Elasticity," New England Power Service Company, Westboro, Massachusetts, March 1973. Beauvais, E. C., "Econometric Estimates, Residential Section, Demand Elasticities," Virginia Electric Power Company,1973. Boley, T. A. and D. L. Walker, "The Effect of Prices and Economic Growth on Consumer's Energy Requirements," Paper 1.3-S, 9th World Energy Conference, Detroit, Michigan, September 1974. Bonneville Power Administration, Imoact Study, Bonneville Power Ad-ministration, Portla7d, Oregon,1973. Cargill, T. F. and R. A. Meyer, " Estimating the Demand for Electricity by Time of Day," Applied Economics, Vol. 3, pp. 233-246,1971. Chapnan, L. D., T. J. Tyrell, and T. D. Mount, " Electricity Demand Growth and the Energy Crisis," Science, November 1972. " Predicting the Past and Future in Electricity Demand," Cornell Agricultural Economics Staff Paper,1972. Coyle, E. P., "A Note on the Price Elasticity of Electricity," Public Utilities Fortnightly, November 18, 1976, pp. 38-39. l Crist, M. S. et al., " Estimation and Application of Price Elasticity," Southern California Edison Company,1974. f Cudahy, R. D., "Some Thoughts on Rate Base and Rate Design," Public L Utilities Fortnightly,, November 20, 1975. L. lL

100 Doctor, R. D. et al., California's Electricity Quandry: III Slowing the Growth Rate, The Rand Corporation: R-1116-NSF/ C5A, 1972. '~ Environmental Analysts, Inc., Electricity Demand and Load Forecasting with Application to the Wisconsin Utilities Service Area, Garden City. New York, 1974. i [ Felton, J. R., " Competition in the Electric Energy Market Between Gas and Electricity " Nebraska Journal of Economics and Business. Fall 1965. Fisher, M. and C. Xaysen A Study in Econometrics: The Demand for Electricity. in the United States, Amsterdam: North-Holland Publishing Company, 1962. Friedman, M., A Theory of Consumption Functions, Princeton University Press, Princeton, New Jersey,1957. Griffin, J. M., "The Effects of Higher Prices on Electricity Consumption," Bell Journal of Economics, Autumn 1974, pp. 515-539.

Gujarati, D., " Demand for Electricity and Natural Gas," Public Utilities Fortnightly, January 30, 1959.

Guth, L. A., "How to Evaluate Elasticity Studies," Electrical World, January 15, 1974. Halvorsen, R., " Residential Electricity: Demand and Supply," Discussion Paper No. 71-7, Environmental Systems Program, Harvard University, [ February 1972. "Long-Run Residential Demand for Electricity," Discussion Paper No. 73-6, "Short-Run Determinants of Residential Electricity Demand," Discussion Paper No. 73-10, Institute for Economic Research, University of Washington, 1973. Heineman, G., D. A. Nordman, and E. C. Plant, "The Relatior. ship Between s Summer Weather and Sumer Loads-A Regression Analysis," IEEE Trans-actions on Power Apoaratus and Systems, Vol. 85, pp.1144-1151,1966. Houthakker, H. S., P. K. Verleger, Jr., and D. P. Sheehan, " Dynamic Demand Analyses for Gasoline and Residential Electricity," Presented at the Economic Society Meetings, New York, December 1973. 'i Lacy, A. W. and D. R. Street, An Econometric Analysis of Residential Elec-tricity Demand for Alabama Power Company, Alabama Power Company,1975. t Landon, J. H. and J. W. Wilson, "An Economic Analysis of Combination i Utilities," Working Paper 19, Case Western University, Research Program

[

in Industrial Economics, Cleveland, Ohio,1970. Liew, C. K., "The Price Structure and Market Share in the Case of Energy Industries," Oklahoma Gas and Electric Company,1972. ,y .-.y w -

J 101 F

Lyman, R., " Demand Conditions in the Electrical Power Industry: An Econometric Study," Unpublished Ph.D Dissertation, Northwestern University, f,

Evanston, Illinois, 1972. <\\ Moore, T. G., "The Effectiveness of Regulation of Electric Utility Prices," Southern Economic Journal, 1970. Mount T. D., L. D. Chapman, and T. J. Tyrell, Electricity Demand in the United States: An Econometric Analysis, Oak Ridge: Oak Ridge National Laboratory, ORNL-NSF-EP-49, June 1973. Pace, J. D., "The Poor, the Elderly, and the Rising Cost of Energy," Public i Utilities Fortnightly, pp. 26-34, June 5,1975. I Powell, K. B., " Price Elasticity Can Be Misleading," Electrical World,

l December 15, 1973.

Renshaw, E. F., "The Pricing of Electricity," Public Utilities Fortnightly, January 1, 1976. Roth, W. E., " Micro-data Measurement of Residential Rate Restructuring," Public Utilities Fortnightly, January 15, 1976. Tansil, J., " Residential Consumption of Energy 1950-1970," ORNL-NSF-EP-51 Environmental Program, July 1973. s Taylor, L. D., "The Demand for Electricity: A Survey," The Bell Journal of Economics, Spring 1975, pp. 74-110. Treadway, H., " Electric Rates and Energy Shortage," Public Utilities l Fortnightly, December 5, 1974. Wald, H. P., "Recent Proposals for Redesigning Utility Rates," Public Utilities Fortnightly, September 13, 1973. Wilder, R. P. and Willenborg, J. F.; " Residential Demand for Electricity: A Consumer Panel Approach," Southern Economic Journal, Vol. 42, No. 2, October 1975. Wilson, J. W., Residental and Industrial Demand for Electricity: An b. {moirical Analysis, University Microfilms, 1970. Wilson, J. W., " Residential Demand for Electricity," Quarterly Review of Economics and Business, Vol. II, No.1, Spring 1971, pp. 7-22. fm t .l' ~ -.. .e ,}}