ALTERNATIVE METHODS OF ESTIMATION IN THE DEMAND FOR NATURAL GAS Thesis for the Degree of Ph. D. MICHIGAN STATE UNIVERSITY VENKATA' MADHAVA RAD TUMMALA 1963 ‘ .L tit-~31: ' -’W!".nye. run-J “""g ' '-1,V .fi‘.’ 4-41" ‘ MiChigan mate University w——- This is to certify that the thesis entitled ALTERNATIVE METHODS OF ESTIMATION IN THE DEMAND FOR NATURAL GAS presented by Venkata Madhava Rao Tummala has been accepted towards fulfillment of the requirements for M degree in Went JI. LI‘C/C/W4 (L)? (w 1. Major I professor Date Q/7 /é ,9 / / 0-169 ABSTRACT ALTERNATIVE METHODS OF ESTIMATION IN THE DEMAND FOR NATURAL GAS by Venkata Madhava Rao Tummala The basic purpose of this study is to develop some dynamic models to explain the demand for natural gas in residential, commercial and industrial sectors J and estimate them. It is a known fact, among econome= tricians and economists in general, that there exists competition among energy fuels and so the relevant econ0a mic variables are interdependent regarding the consump~ tion of natural gas. These variables belong to a system and hence if any aspect of any one of them is considered” it should be considered from the point of view of the system.as a whole. With this in View, a simultaneous equations system model is formulated which is capable of explaining the influence of the burner-tip price of natural gas (along with the consideration of the simulu taneous nature of economic relationships among the relem vant variables) on the consumption in each of the resiw dential, commercial and industrial sectorso It is also a known fact that the behavior of con~ sumption cannot be adapted immediately to changes in the Venkata Madhava Rao Tummala variables which condition it because of possible exis- tence of a "lag" in economic response. The economic re- actions, for a given change, are processes in time and these processes explain the nature of adaptive behavior of consumption. In relevance to natural gas demand, the economic response in the consumption of natural gas is subject to certain psychological, technological and institutional factors. In such a case a static demand model is inadequate to represent the decision making process in each of the residential, commercial and in- dustrial sectors. An attempt is made to formulate a distributed lag model to explain the reaction (or ad- justment) mechanism in the behavior of consumption of natural gas. This model is developed on the basis of an "expected-income" hypothesis which states that con- sumption during any period of time is determined by the consumer's expected income, not by his current income. The total consumption expenditures tend to be stable relative to current incomes and a change in current in- come tends to affect consumption only insofar as it affects consumers' notions of their "exPected" incomes. Several alternative econometric estimation pro- cedures are used to estimate the parameters of the two models described above: Ordinary Least Squares (OLS), Two-Stage Least Squares (ZSLS), Unbiased Nagar K-Class (UNK), Limited Information Single Equation (LISE), Venkata Madhava'Rao Tummala Three-Stage Least Squares (BSLS). These alternative sets of estimates are presented and compared. The equa- tions of the two models were fit using annual time series data for the State of Michigan for a sample period from 1947 to 1964. All data used were secondary, primarily from the records of federal government departments and other agencies; although some data series were trans- formed to meet the special needs of the study. Major findings of this study are as follows: from the results of the simultaneous equations system model, the burner-tip price elasticities of demand in the residential, commercial and industrial sectors are estimated as -0.4386, -0.6048, and -l.3344, respectively. The results also indicate that electricity is providing a keen competition to natural gas. From the results of the distributed lag model, the burner-tip price elasti- cities in the residential and commercial sectors are estimated as -1.6320 and -l.4378, respectively. Other interesting results such as estimates of income elasti- cities and cross-elasticities can be found in the text of the study. The coefficient estimate of speed of ad- justment is found to be 0.2 in the residential sector and 0.3 in the commercial sector. The corresponding re- sults in the industrial sector are rather not satis- factory. The two dynamic demand models formulated in Venkata Madhava Rao Tummala this study, thus presents some features that may have shed some new light and complemented the results db— tained in the earlier studies. Finally, it is hoped that these models may be applied successfully to the data of other states in this country. ALTERNATIVE METHODS OF ESTIMATION IN THE DEMAND FOR.NATURAL GAS BY Venkata Madhava Rao Tummala A THESIS submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Management Graduate School of Business Administration 1968 Dedicated to LORD VENKATESWARA ACKNOWLEDGEMENTS A study of this kind would be impossible with- out the understanding, cooperation and stimulating discussion of many people. I am deeply indebted to all of them. Particularly, I wish to express my sin- cere thanks to Professor Harold H. Wein who suggested this prdblem and has provided invaluable guidance and inspiration. Also I am indebted to Drs. Jan Kmenta and John F. Muth for their valuable help and guidance during the preparation of this study. This study would not have been started with- out the financial support of the Institute of Public Utilities, Michigan State University. I wish to ex- press my sincere gratitude to Dean Alfred L. Seelye of the Graduate School of Business Administration, Michigan State University, and Dr. Harry M. Trebing, Director, Institute of Public Utilities, Michigan State university, for making such financial support available to me throughout the entire period of the preparation of the study. I also want to express my sincere appreciation to the faculty of the Department of Management and Marketing, University of Detroit, ii for creating the necessary atmosphere while finishing the writing of this study. Sincere thanks go to Mrs. Nellie Hanks who patiently typed the first and final drafts. I want to take this opportunity to thank my father, mother, grandparents, and the gentlemen from Mantena, Sri A4 V. Subba Rao, A. V. Chalapathi Rao, A. Vankateswara Rao, A. Lakshmaiah, P. Venkateswara Rao, and V. RamamOhana Rao, who have inspired a great feeling in me toward higher education. Finally, I want to thank my wife, Parvati Vardhani, for her enduring patience, understanding and comfort during the years of my study. Venkata Madhava Rao Tummala East Lansing, Michigan August 1, 1968 iii TABLE OF CONTENTS ACMOWLEDGEDTE NTS O O O O O O O O O O O O O O 0 0 LIST OF TABLES O O O O O O O O C O O O O O O O 0 LIST OF ILLUSTRATIONS . . . . . . . . . . . . . Chapter I. II. III. INTRODIETION O O O O O O O O O O O O O O 1.1 The Characteristics of the Natural Gas Industry . . . . . . . 1.2 Scope and Nature of the Study . . 1.3 Methodology . . . . . . . . . . . . THE DEMAND FOR NATURAL GAS: REVIEW OF THE LITERATURE AND DATA.CONSIDERATIONS 2 1 Nature and Objectives of the Studies 2 2 Methodologies of the Four Studies. . 2 3 Need for Differentiation of Markets. 2.4 Prdblem of Homogeniety of Data . . . 2 5 Simultaneous Nature Among Natural Gas and its substitutes . . . . . 2 6 Expected Income Hypothesis . . . . . THE DEMAND~EOR.NATURAL GAS: THE STATIC APPmACH O O O O O O O O O O O O O O O 3.1 The Simple Static Demand Equation. . 3.2 Estimation of the Simple Static Demand Equations. . . . . . . . . 3.3 The Generalization of the Static Appr 03011 O O I O O O O O O O 0 O 3.4 Estimation of the Generalized Static Demand Equations.. . . . . THE DEMAND FOR.NATURAL GAS: A STRUCTURAL ECONOMETRIC MODEL . . . . . . s . . . 4.1 Introduction and Definitions . . . . 4.2 Specification of the Economic Model. 4.3 Statistical Specifications of the Economic MOdels o o s e o o o o 0 iv Page ii vi viii \O-hl-fl 16 16 21 34 41 46 54 60 60 63 68 78 91 91 96 109 Chapter V. VI. VII. APPENDI BIBLIOG Table of Contents (continued) THE STRUCTURAL ECONOMETRIC MODEL: EMPIRICAL RESULTS . . . . . . . . . 5.1 Some Theoretical Comparisons of the Estimators Used in the Stlldy O O O O O O O O 0 O O O O .2 Empirical Results . . . . . .3 Tests for Identifiability of a Structural Demand Equation. . . 4 Conclusions . . . . . . . . . . . THE DEMAND FOR NATURAL GAS: A DISTRI- BUTEDLAGMDDEL .......... Natural Gas Demand and the Rele- vance of Distributed Lag Models The Description of the Adjustment Process of an Economic Reaction The Development of the Distributed Lag Model . . . . . . . . . O‘Ch 0‘ 0‘ (h 01-5 (.1 N l'-‘ Results of the Model . . . . . . . SUMMARY AND CONCLUSIONS . . . . . . . . X A O O O O O O O O C O O O O O O O O 0 mm 0 O O O O O O O C C O O O C O O 0 Statistical Properties of the Model Page 113 113 118 118 125 134 134 140 143 159 164 179 185 199 LIST OF TABLES Consumption of Natural Gas in the United States According to Various USES, 1946-1964 c o o s o s s o o o 0 Percentage Increase in the Consump— tion of Natural Gas in Different End-Use categories 0 o o s o o o s 0 Simple Correlations Among Natural Gas and its Substitutes: Resi- dential Sector . . . . . . . . . Simple Correlations Among Natural Gas and its Substitutes: Commer- cial Sector . . . . . . . . . . . . . Simple Correlations Among Natural Gas and its Substitutes: Indus- trial Sector . . . . . . . . . . . . Number of Dwelling Units Having Cooking Appliances and the Corres- ponding Percentages for the Selected Types of Fuels: East North Central Regions . . . . . . . . . . . . . . . Number of Dwelling Units Having Heating Appliances and the Corres- ponding Percentages for the Selected Types of Fuels: East North Central Regions . . . . . . . . . . . . . . Schematic Summary of the Structural Econometric Model . . . . . . . . . . Structural Demand Equation, Resi- dential Sector: Coefficient Esti- mates and Related Statistics . . . . Structural Demand Equation, Commer- cial Sector: Coefficient Estimates and Related Statistics . . . . . . . Structural Demand Equation, Indus- trial Sector: Coefficient Estimates and Related Statistics . . . . . . Summary of a Test of the Identifi- ability of the Structural Demand Equations (Hood and Koopmans pro- cedure using LISE estimators) . . . . vi Page 47 48 49 51 52 112 119 120 121 122 List of Tables (continued) Table Page 5.3.2 Summary of a Test for Identifi- ability of the Structural Demand Equations (Basmann procedure using LISE eStimatorS) o s o s s o o o o o o 124 6.5.1 Coefficient Estimates and Related Statistics for Equation (6.3.15): Residential Sector . . . . . . . . . 168 6.5.2 Coefficient Estimates and Related Statistics for Equation (6.3.19): Commercial Sector . . . . . . . . . 169 6.5.3 Coefficient Estimates and Related Statistics for Equation (6.3.23): Industrial Sector . . . . . . . . . . 170 vii Figure 6.2.1 LIST OF ILLUSTRATIONS Economic Time Path of the Process of Adjustment when there is no "Antici- pation" in the Predetermined Variable Economic Time Path of the Process of Adjustment when there is "Anticipa- tion" in the Predetermined Variable Time Path of the Speed of Adjustment viii Page 141 142 161 CHAPTER I INTRODUCTION 1.1 The Characteristics of the Natural Gas Industgy The natural gas industry is one of the oldest public utility industries and plays a significant econo- mic role along with other public utilities such as elec- tric, telegraph and telephone industries. It supplies an indispensable service subject to government regulation at the federal and local levels. The origin of the rapid growth of the natural gas industry may be traced back to 1930. From this date on the growth in the gas consump- tion has been spectacular, particularly in the post-war years. The dramatic growth of usage of natural gas in the postdwar period may be attributed either to increased estimated reserves, or to the expansion of pipelines accompanied by vast technological innovations and develop- ments in gas pipe construction and operation. Also cer— tain characteristics of natural gas--economic and psycho- logica1--such as reasonable price, dependability of supply, cleanliness, controllability, high efficiency of utilization, encouraged the growth of consumption of natural gas. 2 The use of natural gas is ordinarily broken down into several end-use categories or classes of service: residential service, commercial service, industrial ser- vice, and other services. Residential service applies to customers supplied for residential purposes. The residential service includes use of natural gas mainly for cooking, water heating, kitchen heating, space hea- ting, air conditioning. Similarly, commercial service applies to customers primarily engaged in wholesale or retail trade, agriculture, forestry, fisheries, transpor- tation, communication, sanitary services, finance, in- surance, real estate (clubs, hotels, rooming houses, etc.), personal services. These customers use natural gas mainly for space heating, air conditioning and cooking. The industrial service applies to customers engaged in a process which creates or changes raw or unfinished ma- terials into another form or product. This service includes space heating and air conditioning also. Fi- nally, other services include services to municipalities or divisions (agencies) of state and federal governments. The consumption of gas under each of the end-uses is presented in Table 1.1.1. There is a gradual increase in usage in each of the end-use categories. But this gradual increase in usage is slowed down during the lSee Gas Facts, American Gas Association, Inc. Bureau of Statistics, New York, N.Y., 1966, PP. 242-243. HOAHmuoH one mo nooEpummoQ .m.D "nose: mo smmuom .maosm .HH .Ho> .xoonummw manhooflz domalmoma Hiaom< .oz poxooa .Umm .omm .oz pflnfinxm Hmoalowma "monoom eoa moo.m mmm.m mmm.m mem.a eme.m some use Hmo.m m¢H.m m¢¢.m mom.a mmm.m mama mma mom.a oom.a ~aa.m eoN.H one.m meme Hos Hmm.a mam.a mmm.¢ neo.a mem.m Home mad omn.a mme.a mmo.¢ omo.a moa.m coma mam emn.a emo.a mmm.¢ mam mam.~ mmma Ham eoo.a mnm.a emm.m New vae.m mmma «mm ome.H wmm.a mmm.m one oom.~ nmma mam Hma.a omm.a mmn.m has mam.m omma mam mom.a mma.a Hae.m mum «ma.m mmma Hmm eme.a moa.a Hmo.m mmm emm.H «mad Hom H5¢.H emo.a emm.m Hmm mmo.a mmma mom eme.a cam vae.m mam mmo.a ammo owe mee.H so» mmm.m woe mee.a Hmma Haw RmH.H mam mam.m mmm mmH.H omma was ooo.a omm on.H mam mam mama awe «mo.a was m¢e.a mam mom mama mmv 4mm mam nem.a omm mom head was mom Rom R~¢.H mam Hoe mama me me mmD COHDMHOCOO OmD OmD mmD “SNOW conumu camflm um3om oeuuooam aneupmsccH HmonoEEOU Hafiucmcwwmm Amos mo chAHHsz somalmema .momD unedum> on mowcuoood moumpm cones: may ca new Hohsumz mo GOAOQESmGOU H.H.a mamde 4 successive sub periods from 1940-1950 which can be evi- denced from Tables 1.1.1 and 1.1.2. The reason for this is either the saturation of new markets for gas in dif- ferent states or the competition from other fuels--coal, fuel oil, and electricity. The competitive aspects be- tween fuels and electricity is discussed in later chap- ters while formulating the necessary models to explain the demand for natural gas in each sector. TABLE 1.1.2 Percentage Increase in the Consumption of Natural Gas in Different End-Use Categories Residential Commercial Industrial Electric Power Period Use Use Use Generation Use 1946-50 81.2 60.3 55.1 104.9 1951-55 77.3 62.1 54.1 83.3 1955-60 46.1 62.2 37.3 49.6 1961-64 22.0 34.8 25.0 34.6 Source: Calculated from Table 1.1.1 1.2 Scope and Nature of the Study The basic purpose of this study is to develop dynamic models to explain the demand for natural gas in each of the sectors--residential, commercial, industrial, steam electric generating plants--and estimate them. By 5 doing this, one isxessentially estimating the relevant price and income elasticities in each of the above sec- tors.2 The problem of determining price elasticities in each sector is very important and plays a significant role because the natural gas industry is a regulated in- dustry, being regulated by the Federal Power Commission. The Federal Power Commission sets the wellhead ceiling price for initial contracts for natural gas which is supposed to perform an economic function. This function was clearly stated by Justice Jackson as: "Far sighted gas regulation ... will use price as a tool to bring goods to mar- ket ... to Obtain for the public service the needed amount of gas. Once a price is reached that will do that, there is no legal or economic reason to go higher; and any rate above one that will perform this function is unwarranted ... on the other hand if the ... price is not a sufficient incentive to bring forth the quantity 3 needed ... the price is unwisely low." Thus from the point of view of the Federal Power Commission, what price level should be adequate to per- form such an economic function is an important prdblem. In order to determine such a price, one must know the relationship between wellmouth price or wellhead ceiling 21f the demand models are assumed in double-log form, then the estimates of coefficients of corresponding price and income variables are the respective elasticities. Otherwise they are the corresponding "slopes." It is in this general sense the term "elasticities" is used. 3H. H. Wein, Natural Gas Supply and Demand, Docket No. AR 61-1, Federal Power Commission, Office of Economics, Washington, D.C., p. 7. 6 price and exploration, and also the relationship between wellmouth price and ultimate consumption. The wellmouth price afEects average wellhead field price which in turn affects the ultimate consumption through the burner-tip prices at the points of consumption of natural gas. The average wellhead field price is different from.the well- head ceiling price (for initial contracts) and is dis- cussed elaborately by Prof. Wein in his study.4 How well the average wellhead field price affects the burner- tip prices was studied extensively by Dr. Wein and estab- lished some sound statistical relationships between (i) the average wellhead field price and residential-commercial burner- tip price, (ii) the average wellhead field price and the burner-tip price of in- dustrial consumers.5 These relationships are useful for the Federal Power Commission to set up price because the Commission should be able to know the impact of wellhead ceiling price of initial contracts (through average wellhead field price) on the burner-tip prices paid by residential, com- mercial, and industrial users. Once the Commission knows 41bid., pp. 80-84. SIbido' Pp. 69-84 7 the above relationships, then it can evaluate the im- pact of wellhead ceiling price for initial contracts on the consumption of natural gas in various end-uses through the respective elasticities. Thus the price and income elasticities play a significant role in evaluating and regulating economic policies of the Federal Power Commission. It is in this context that some dynamic demand models to explain the behavior of consumption of natural gas are developed in this study. It is well accepted by various authors who stu- died the demand for natural gas in residential com- mercial and industrial markets that the demand depends jointly on the demand for other fuels, namely, fuel oil and coal, and on the demand for electricity.6 The nature of substitutability may vary according to the market, but the corresponding prices at the points of consumption would depend upon each other and hence in- fluence the rate of consumption of each other. For example, electricity has become popular for space and *water heating and so is providing a keen competition for natural gas. Similarly, coal is an important sub- stitute for natural gas in the case of steam electric generation. Therefore, while formulating the structural 6In Chapter 2, the studies of the respective authors are described and reviewed. No one has attemp- ted to formulate the models which take account of this kind of simultaneous nature among substitutes. 8 demand model for natural gas, one should consider this kind of simultaneous nature between natural gas and its substitutes. Such models are formulated, in this study, to estimate the concerned elasticities. These models are called, in econometric literature, the "simultaneous equation system" models. Also some alternative models are formulated to estimate the concerned elasticities in order to compare with "simultaneous equation system models." These alternative models are formulated on the basis of the lag in the response of the "effect" variable due to a change in the "cause" variables. The "effect” variable in the demand model is the quantity consumed of natural gas in each of the sectors and the "cause" vari- ables in the demand model are the respective price vari- ables, income variable and other exogeneous variables. The existence of lag in eXplaining the dynamic behavior of natural gas demand is explained in a later chapter. Some simple static demand models, along with some generalizations on static models formulated on the basis of economic theory, are formulated and estimated before the dynamic demand models are developed. These simple static demand models may not provide valid results but they may bring out in a specific way the deficiencies and limitations of static theory to eXplain the demand for natural gas. Or they may provide a way to formulate some dynamic models to explain the demand for natural gas in each sector. 1,3 Methodology In literature, the estimation methods of struc- tural "simultaneous-equation system" are divided into two parts: (i) Structural Estimation: Single Equation Methods, (ii) Structural Estimation: System Methods.7 The basic difference between these two categories is that in single equation methods each structural equation of a complete system is estimated in turn as if the equation to be estimated is imbedded in the complete system. In estimating each structural equation, these methods con- sider only the predetermined variables that are excluded from the equation to be estimated, but not the excluded jointly dependent variables. No use is made of the estimates of the parameters of other structural equations. But in system methods, estimation of structural equations is carried simultaneously and they make use of restric- tions on the parameters of the complete system in esti- mating each structural equation.8 Since system methods use complete systems of structural equations, one may refer the second category as complete-system methods. 7A. S. Goldberger, Eggngmgggig_2h§2£y, New York: Jo n Wiley & Sons, Inc., Chapter 7. J. Johnson, Econo- metrig Methods, New York: McGraw-Hill Book Company, Chapter 9. 8Complete System is the one which has as many equations as there are jointly dependent variables. 10 Since the main objective in this study is to study the dynamic behavior of the demand for natural gas. no attempt is made to spedify a complete-system of equa- tions to include the supply-side of the natural gas in- dustry. And so the estimation of structural demand equa- tions of natural gas are carried out by single equation methods. The following are various methods that are approached: (1) Ordinary Least Squares (OLS)9 (2) Two-Stage Least Squares (ZSLS)lo (3) Limited Information Single Equation (LISE)ll (4) Unbiased Nagar KHClass (UNK)12 (5) Three-Stage Least Squares (3SLS)9 The OLS method is strictly a single equation tech- nique which does not account for a particular equation 9See J. Johnston, op. cit., Chapter 4, or A. S. Goldberger, op. cit., Chapter 4. 10H. Theil, Economic Forecasts and Policy, Amster dam: North-Holland Publishing Company, 1961, Chapter 6. J. JOhnston, op. cit.. PP. 258-260. 11T. W. Anderson and H. Rubin, "Estimation of the Parameters of a Single Equation in a Complete System of Stochastic Equations," Annals of Mathematical Statistics, Vol. 20, 1949. J. C. Koopmans and W. C. Hood, "The Esti- mation of Simultaneous Linear Economic Relationships," Chapter 7, Studies in Econometric Method, Cowles Commis- sion.Monograph, No. 14, W. C. Hood and T. C. Koopmans, editors, New York: thn Wiley and Sons, Inc., 1953. 12H. Theil, op. cit.. PP. 230-232. Chapter 6. A. L. Nagar, "The Bias and Moment Matrix of the General K-Class Estimators of the Parameters in Simultaneous Equations," Econometrica, Vol. 27, 1959. 11 being embedded in a complete system. There are usually two or more "jointly dependent" variables in each equa- tion and one may not know which "jointly dependent" variable to select as the dependent variable; and no matter which is chosen, the remaining variables will be correlated with the disturbance term in that equation because of the simultaneous nature of the relationships in the model. Thus the OLS estimates will be inconsis- tent. This fact may not rule out the OLS method because this method is computationally simple and asymptotic bias introduced by the OLS method of estimation may not be the most important property of an estimator but has to be 13 With these judged in conjunction with the variance. considerations in mind, the OLS method is tried in esti- mating the demand function of natural gas for each sector. Theil has described a general classification by which each of the above four methods become special cases under certain conditions.14 It is called a K—class esti- mation procedure. For K = 0, the K-class becomes OLS method and for K = 1, it will become ZSLS method. The K values for the LISE and UNK have to be determined for each of the single equations to be fitted. For the LISE method 13J. Johnston, op, cit., p. 253. 14H. Theil, op, cit., pp. 231-232. 12 the K values will always be greater than one for over- identified equations and equal to one for just-identi- fied equations. In one context, the K-value is derived in a manner such that it corresponds to a minimum ratio of residual variance—-i.e., the residual variance from regressing a linear combination of the "jointly dependent" variables on the predetermined variables in the equation, divided by the residual variance of the same linear com- bination of the "jointly dependent" variables regressed on all the predetermined variables in the complete sys- tem.15 In another context, the K-value corresponds to a minimum characteristic root of a determinant-equation.16 Similarly for UNK procedure, Nagar has proposed that the K-value should be calculated as 11-1 T K = 1 + where L is the number of predetermined variables in ex- cess of the number of coefficients to be estimated and where T is the number of observations.17 He has shown that this K—value can be expected to reduce a small sample bias of 2SLS (to the order of T-l) in most simultaneous equation studies.18 The last four procedures will give 15J. Johnston, op, cit., p. 256. lerid., p. 257. 17A. L. Nagar, 22, cit. 18Alternative K-values have been proposed by Nagar, but they have not been included in this study. 13 consistent estimates. The alternative models which explain certain "reaction or adjustment" mechanism are estimated by OLS method. The justification in using the "ordinary least squares" method of estimation is discussed in a later chapter where the formulation and the method of estima- tion of the corresponding models are developed. All these methods were programmed for use on the Michigan State university CDC 3600 Computer System and so the corresponding routines are used for estimating the res- pective demand functions of natural gas.19 Thus the main Objective of this study is to in- vestigate the endogenous mechanism to explain the con- sumption behavior of natural gas by formulating an economic model to represent the simultaneous nature among the concerned economic variables and then estima- ting the model using simultaneous equations estimation methods. Some alternative economic models to represent the "reaction" or'adjustment" mechanism may be formu- lated to explain the behavior of demand of natural gas. Ultimately, in a study of this kind, the investigator usually has the purposes of forecasting future values of economic variables and of predicting the consequences of various economic policies. So an attempt will be made to predict future values and the corresponding consequences. 19All these routines are part of the MSU-STAT system and are written with double precision arithmetic. 14 In order to achieve these purposes, the following se- quence of steps is followed in this study: 1. Formulation of economic models which are capable of establishing the "joint" relationships (the endogenous mechanism) among the concerned variables to ex- plain meaningfully the dynamic behavior of the demand for natural gas in each of the end-use categories, To estimate the structural parameters which will contribute to a better under- standing of the economic interrelation- ships of the economic models developed in (1). To employ the alternative simultaneous equations system estimation methods (noted as above), compare estimates from the alternative estimation proce- dures and ascertain the apparent advan- tages of any particular estimation method. To postulate alternative economic models estimate the parameters and compare these parameters with those Obtained with the simultaneous equations system approach, and finally 15 5. To utilize the information Obtained in (3) and (4) for predicting the changes in various economic variables. Taking this as a framework, we start the next chapter reviewing the literature previously investi- gated in the area of demand for natural gas. 15 5. To utilize the information obtained in (3) and (4) for predicting the changes in various economic variables. Taking this as a framework, we start the next chapter reviewing the literature previously investi- gated in the area of demand for natural gas. CHAPTER II THE DEMAND FOR.NATURAL GAS: REVIEW OF THE LITERATURE AND DATA CONSIDERATIONS 2,1 Nature and Objectives of the Studies In this chapter studies concerning the demand for natural gas in various end-use categories are reviewed. There are four studies that have dealt with the demand part of natural gas.1 Each is studied in a different context and with different objectives. In two studies the consideration of demand for natural gas is only a part of the complete study: while in the other two only the study of demand is considered. Dr. MacAvoy's study focuses mainly on the economic reasons for regulation in the natural gas industry. It was argued that there was 1P. W. MacAvoy, Price Formation in Natural Gas Fields, A Study of Competition, Monopsony, and Regulation, New Haven and London: Yale University, 1962. H. H. Wein, ngural Gas Supply apd nggpd. Docket No..AR 61-1, Federal Power Commission, Office of Economics, Washington, D.C., 1963 R. S. Villanueva, "An Econometric Estimation of User's Demand for Natural Gas," Ph.D. Thesis, University of Pittsburgh, 1964. P. Balestra, "The Demand for Natural Gas in the Residential and Commercial Markets: A Dynamic Approach," Ph.D. Thesis, Stanford University, 1965. 16 l7 monopoly control of in—ground gas and that the pipeline buyer paid higher—than-competitive prices for restricted amounts of gas and hence such kinds of monopolistic pricing in gas fields should be controlled as monopo- listic electric rates or rail freight rates were con- trolled. There were also statements that regulation 'was needed to prevent future price increases, since such increases would be derived at least in part from the use of monopoly power. These viewpoints prompted Dr. MacAvoy to study the characteristics of monopoly price formation, and of competitive and monopsony price formation in order to see which corresponds more closely to actual price formation in the 1950's.2 The pipeline companies "buy" volumes of natural gas under contracts in order to satisfy residential, com- mercial and industrial demands over extended periods. Of course, in practice as well as in economic theory of con- sumer demand, the end-use consumers will seek somewhat less natural gas over the lifetime of their burner equip- ment if the burner-tip price of natural gas is increased. Less demand for natural gas at the above markets implies lower aggregate demand by the pipeline companies in the producing regions. This is because the demand at the pro- ducing region by the pipeline companies is derived from the resale demand of residential, commercial and industrial 2P. W. MacAvoy,.pp, cit., p. vii. 18 users. It is (the demand for natural gas at the pro- ducing region) also affected by the maintenance costs of pipeline transmission companies and by requirements of interstate regulatory authorities. Therefore, in order to study the pipelines' demand for reserves of natural gas, one should study the demand for natural gas in residential, commercial and industrial markets. It is in this context that Dr. MacAvoy studied the demand for natural gas by home users and industrial users.3 Dr. Wein directed his study more toward the economic functions in setting the wellhead price by the Federal Power Commission rather than studying the price formation in natural gas fields. His study reveals "what the economic consequences of setting any wellhead price‘will be, how much exPloratory activity and what level of reserves can be expected at that price, what residential-commercial and industrial consumption will result from it, the reserve/production ratio that will ensue, and the effects of the wellhead price on burner tip prices."4 In order to study and provide answers for the above questions, one must know the relationship between wellhead price and exploration and also the rela- tionship between wellhead price and ultimate consumption 3Ibid.. pp. 33-37, 267-270. 4H. H. Wein, pp, cit., p. 8. 19 through burner-tip prices at the points of consumption in each end-use category. Dr. wein's study also pro- vides a means whereby the Federal Power Commission can keep in touch'with changes in the natural gas industry and adjust its regulatory policy from time to time. With these Objectives in mind and in order to study the effects of wellhead price on burner-tip prices, and consequently on the consumption of natural gas at the different endepoints of consumption, Dr. Wein pro- posed to study the demand aspects of natural gas in both the residential-commercial and industrial markets. Thus these two studies of Dr. MacAvoy and Dr. Wein are mainly policy oriented, useful in understanding and regulating the economic policies of the Federal Power Commission. The other two studies mainly revolve around the development of economic models and consequent estimation of the models by various econometric methods. So they are more academic in nature. For instance, Dr. Villanueva has stated that "the purpose of this study is to investi- gate the application of various econometric techniques to the measurement of demand in markets characterized by utility regulation of prices."5 His study, therefore, is concerned with the estimation of the parameters of the natural gas demand schedules of the major sectors of the consumer markets and the effect of the discriminatory gas 5R. S. Villanueva, pp, cit., p. l. 20 utility rate structure on the distribution of the fuel between the consumer groups. Besides this, he is also concerned with the economic rationale for the gas utility rate regulation. With these things as Objectives, Dr. Villanueva has studied the demand asPects of natural gas in residential-commercial, industrial and steam electric generating plant markets. It has long been recognized by economists and econometricians that a static demand equation, in general, is not adequate to represent the consumer behavior in the durable goods market. Rather some kind of dynamic mecha- nism should be built in to study the consumer behavior. For durable type goods, several studies are made which have incorporated some kind of "stock effect."6 Although natural gas cannot be properly called durable, its con— sumption, like that of electricity, fuel oil, is inti- mately related to the stock of gas appliances which are durable goods, and to a large extent it is governed by the existence of such stocks. Therefore, it is reasonable to incorporate a stock effect and some assumptions about the adjustment of their stocks over time in the demand function to explain the behavior of consumption of natural gas. Dr. Balestra's study is concerned with the development of such a model. He developed a dynamic demand model for natural 6See for example, F. M1 Fisher and C. Kaysen,,A Study in Econometrics: The Demand f9; Electricity in the united States, Amsterdam: North-Holland Publishing Co.: 1962. 21 gas whose consumption is technologically related to the stock of appliances.7 Thus, Balestra's study evolved mainly on theoretical development of model. The model is estimated by the econometric techniques more sophis- ticated than the econometric techniques used by the other three authors. Now each study is reviewed with respect to the analysis and methods used. Later in the chapter, the reasons why the Simultaneous Equation System model is formulated and why the State of Michigan is chosen for estimating the Simultaneous Equation System model will be discussed. 2.2 Methodologies of the Four Studies While studying the factors affecting the pipe- lines' demand for reserves of natural gas, Dr. MacAvoy has considered two forms of demand, namely, citydwide home demand and industrial demand.8 In forming the model for citydwide home demand he considered the price of gas for the marginal thousand cubic feet consumed per capita (p), price of fuel oil for the average consumption per capita (Po), temperature degree days (T), population in the city (N), and the median income per resident in the city (Y) as explanatory variables to explain the behavior 7P. Balestra and M. Nerlove, "Pooling Cross-Section and Time-Series Data in the Estimation of a Demand Model: The Demand for Natural Gas." Technical Report No, 8, Insti- tute for Mathematical Studies in the Social Sciences, Stan- ford, California: Stanford University, p. 1. 8P. w. MacAvoy, pp. cit. pp. 267-269. 22 of the consumption of natural gas. He has taken a cross- section sample of 52 united States cities for the year 1951 and used cross-section analysis to estimate the citydwide home demand function.9 In case of industrial demand, Dr. MacAvoy has studied the demand for natural gas in each industry. He considered average price of natural gas (Pgas), average price of fuel oil (P2), average price of coal (P3), average price of electricity (P4), average size of the firm (S), and the number of firms (F) as independent variables to explain the demand for natural gas in a particular industry. In this case also he used cross-section analysis.lo Assuming the linear form in both the cases, Dr. MacAvoy estimated the corresponding coefficients by ordinary least squares method of estimation. The con- clusions he has arrived at are as follows. In case of citydwide home demand, the demand elasticity varies over a range of relevant prices and "the extent of demand at each price varies from city to city as well, so that demand can be said to be less elastic at some locations than at others."11 Similarly, in case of industrial demand, he con— cluded that price elasticity varies greatly from industry 9Ibid” p. 267. 10Ibid., p. 269. 1111316. , p. 35 . 23 to industry. "The demand schedule in the meat processing or bakery product industries seems quite elastic at average price. The demand schedules in the structural Clay products industry and iron and steel industry are even less elastic at average prices. But the demand schedules in both motor vehicle and the beverage industries are highly elastic."12 He further commented that "the industrial demand equations and the home-con- sumption demand equation all exhibit some decrease in quantities purchased when the price increases. Demand is more elastic in certain industrial gas uses and least elastic at low prices for home use, and there is a great variation in elasticity, even given users that are the same in most respects."13 In an attempt to study the behavior of consumption of natural gas, Dr. Wein considered the aspects of con- sumption both in the residential-commercial market and in the industrial market. The forms of demand equations for each market are described below. Instead of studying the demand for natural gas by steam electric generating plants separately, he has included the consumption of natural gas by the steam electric generating plants in industrial con- sumption. Therefore, he has incorporated the "number of 12Ibid., p. 37. 13Ibid. p. 38 . 24 kilowatt-hours generated" by these steam electric genera- ting plants as a variable in the industrial demand model in order to measure the effect due to steam electric generating plants on the consumption of natural gas in the industrial market. After elaborate discussion, Dr. Wein formulated the models to explain the behavior of natural gas consumption in both the markets as follows: (1) Residential and commercial market a a 0. 1 2 3 A X91 X101 X111 X1 0. (2.2.1) ---— Y? 4 . ui 21 e 1:11210000044 where Y? = consumption of natural gas in the residential and commercial market in state i X9i = burner-tip price of natural gas in residential and commercial market in state i X . = price of fuel oil in residential 101 . . . and commerc1al market in state 1 X . = number of customers of natural gas 111 . . . . 1n re31dent1al and commerc1al mar- ket in state i X12i = degree days in state 1 (2) Industrial Market I _ Bl B2 B3 B4 BS (2°2'2) Yi ' B X131 X141 X151 Xl6i x171 [.3 . 5 v1 X121 9 i=1, 2,000.044 25 where Y: = consumption of natural gas in industrial market in state i Xl3i = burner-tip price of natural gas in industrial market in state i X14i = price of fuel oil in industrial market in state i X . = price of coal in industrial market 151 . . in state 1 X16i = industrial employment in state i Xl7i = number of kilowatt hours in state i _ . .14 X121 — degree days in state 1 Thus Dr. Wein formulated the demand functions in each of the markets, as functions of respective prices of natural gas, prices of closely related substitutes and the appropriate exogenous variables such as degree days and industrial employment. The data he used in order to esti- mate the corresponding coefficients in equations (2.2.1) and (2.2.2) are purely cross-section analysis. In order to analyze the stability of the regression coefficients a1, a2, a3, a4, in equation (2.2.1) and 51’ 82, B3, B4, BS, and 36 in equation (2.2.2) over time, he computed estimates of cross-section analyses for each year from 1955 through 1960.15 14H. H. Wein, 22, 912,. pp. 87-90. The notation was exactly followed as in Dr. Wein's study. Alaska, Hawaii, Maine and Vermont are not included in the analysis. Data for North and South Dakota are combined. Similarly data for Delaware, District of Columbia and Maryland are com- bined. 26 After brief analysis, Dr. Wein concluded that the price elasticity of natural gas demand is inelastic (-.795) in residential and commercial market, and elas- tic (-2.55) in industrial market. The coefficient of burner-tip price variable is highly significant in both equations. These findings are for the year 1961. While examining the stability of the concerned estimated coef- ficients of equations (2.2.1) and (2.2.2), he found out that the price elasticity of natural gas demand is varied in both markets. For example, in the case of residential and commercial market, it is varied from -0.945 to -0.715 16 during 1955-1961. And in the case of industrial demand, it is varied from -2.872 to -2.546 during the period 1955-1961.17 After discussing the stability of the coefficients of each variable in each of the markets, he concluded that the estimated coefficients of the demand equations (for 1961) specified in equations (2.2.1) and (2.2.2), are sufficiently stable to describe the behavior of consump- tion of natural gas. Dr. Villanueva, while studying the user's demand for natural gas, has divided the gas demand into (1) resi- dential and commercial demand, (2) industrial demand, and *— 161bid., p. 95. 17Ibid., p. 94. 27 (3) the demand by thermal electric generating plants.18 He has also studied the total demand and total supply of natural gas from a system of "simultaneous equations model" point of view, but only to a limited extent. Dr. Villanueva has formulated several models in first dif- ferences of logarithms of the concerned variables for each of the above kinds of demand and estimated them by ordinary least squares method of estimation.19 For instance, while considering the demand for natural gas by residential and commercial consumers, he has con- sidered the price of natural gas, prices of competitive fuels, personal income, and temperature as explanatory variables and used the first differences of logarithms of these variables to eXplain the behavior of consumption of natural gas which is again expressed as a first dif- ference in logarithms.20 Similarly, he has formulated another model to explain the demand for gas service in order to separate that portion of the total demand response attributable to the response of gas service alone.21 To find out whether there is any "adjustment process" or "reaction mechanism" present in the natural gas consumption, he has also formulated Nerlove-type 18Villanueva,_qp. cit. lgIbido' p. 7: pp. 18-240 201bid., p. 18. 211mm, p. 36. 28 "lagged adjustment models."22 Similar models are formu- lated to explain the demand for natural gas by industrial consumers and by thermal electric generating plants.23 The estimating procedures of the concerned models are as follows: Both the time-series and cross-section analysis are used for each type of demand. The period under consideration for the time-series analysis is 1950- 1960 and the regression analysis is carried out for each census region. For cross-section analysis, each state is an Observation and thirty-five states are included in the analysis.24 Thus there are 35 Observations in cross- section analysis and the time periods considered are 1950 25 and 1959. In case of industrial demand, the demand models are formulated by individual industry categories 22Ibid., p. 23. Also see M. Nerlove, "Distributed Lags and Demand Analysis for Agricultural and other Commo- dities," U. S. Department of Agriculture, Agricultpral Hgndbook No. 141, June 1958. 23Ibid. Models of demand for natural gas in indus- trial consumers, pp. 72-75. Models of demand for natural gas by thermal electric generating plants, pp. 101-107. 24Ibid., p. 64. 25The number of states as Observations considered for 1959 cross-section analysis is 46. R. S. Villanueva, _p, pip,, p. 64. This is for residential and commercial market. For industrial market, the time periods considered for the cross-section analysis are 1951-52 and 1959-60. R. S. Villanueva, pp, 215,, p. 95. For thermal electric generating plants, the cross-section analysis is performed for the period 1960-61 only. R. S. Villanueva, pp, 215,. p. 116. 29 and then the above described time series and cross- section analyses are approached. The following are the conclusions from his analysis. He has found that there is a significant variation of price elasticites of gas demand among different regions in case of residential and commer- cial markets and industrial market.26 The same con- clusion is reached in the case of demand for natural gas by thermal electric generating plants. The cross- section analysis, in the case of residential and commer- cial demand, provides a "significant" evidence of the sensitivity of demand to variations in price and tem- perature.27 In the case of industrial demand and the demand for gas by steam electric generating plants, the cross-section analysis provided rather unsatisfactory results. The coefficient of determination, R2, is not 2 high compared to the R of Dr. Wein's cross-section 28 demand equations. All the adjustments models have exhibited little evidence of lagged adjustment of demand with respect to the corresponding explanatory variables. Dr. Villanueva also formulated a simple simul- taneous equation system" model consisting of total demand 26R. S. Villanueva, pp, pip, See the conclusions in the case of residential and commercial markets,pp.70-71: industrial market, pp. 99-100; thermal electric generating plants, p. 120. 271p1g,, p. 70—71. 28Ibid. ____ P- 95. 30 equation and total supply equation and estimated the model through the method of two-stage least squares.29 He has found a demand elasticity of price which varied between -.8 and -3.19 in three of the five regions and a demand elasticity of price of value -0.66 for the total United States.30 Dr. Balestra studied the dynamic behavior of natural gas in case of residential and commercial sec- tors. He did not study the dynamic behavior from.the standpoint of residential sector only, nor did he study it from the standpoint of commercial sector. He com- bined both, as similar to other studies in this area, and focused his attention on the dynamic consumption behavior of natural gas in the residential and commer- cial market. Balestra has based his demand analysis on two basic aspects, namely, 1. formulation of a demand function for commodities whose consumption is technologically related to the stock of appliances, and 2. estimation of parameters of the demand function when the demand function is cast in dynamic terms and when 2911616., pp. 137-152. 302228». P. 14. For comparison of these esti- mates with those of Residential-Commercial market, Indus- trial Market and Thermal Electric Generating Plants Mar- ket, see p. 149. 31 Observations are drawn from a time- series of cross-sections. Balestra has started with a simple static demand model to explain the consumption behavior in residential and commercial sectors and Observed that static demand analysis is inadequate to represent the behavior of the consumer in a market in which consumption is techno- logically related to the stock of appliances. This Ob- servation has led him to the incorporation of a stock effect in the demand function. The basic idea under- lying this approach is to consider the "new deman " for gas, i.e., that portion of demand that is free from past commitments. On the basis of this concept of "new demand," Balestra has formulated a dynamic model of demand in which the price variable has an effect primarily on the rate of growth of consumption rather than on its abso- lute levels. The other variables that appeared upon the starting assumptions in the model are lagged population, change in population (i.e., first-difference in popula- tion), lagged income, first-difference in income, lagged 31 consumption of natural gas. And the form of equation is specified as (20204) ---- G . = a. + a. P + a ti o 1 gti + a ANti 2Nt-l i 3 G + e + a Y t-li ti 4 t-li+ “SAYti + “6 31F. Balestra, pp, cit..P. 7 32 where . . 12 Gti = consumption of gas in BTU 10 in time period t of the 1th state Pgti = price of gas in time period t of the 1th state N _ . = population in time period (t-l) of t 13' the ith state Yt-li. = per capita income (in 1961 dollars) of time period (t-l) of the ith state Gt-l = consumption of gas in BTU 1012 in time period (t-l) of the 1th state Eti = stochastic disturbance £5 = first difference operator and cor- responds to the time period t of the ith state. In the case of a dynamic model as specified in equation (2.2.4), the application of ordinary least squares to the pooled sample of Observations (a time-series of cross section) produced inconsistent estimates of the coefficients of lagged endogenous variable.32 As far as equation (2.2.4) is concerned, there is only one such lagged endogenous variable. under certain restrictive 33 assumptions, the coefficient of this lagged endogenous variable is constrained at the value of one, in which case 32Inconsistent in the sense that the estimated coefficient of lagged endogenous variable is greated than one. J. JOhnston, Econometric Methods, New YOrk: MbGraw- Hill BoOk Company, pp. 211-221. 33F. Balestra, pp, cit., p. 10. 33 this variable can be shifted to the left hand side of equation (2.2.4) and estimation by ordinary least squares is then appropriate under fairly general con- ditions. For the more general case, i.e., for the case when the coefficient of lagged endogenous variable is not constrained at the value of one, Balestra has de- veloped two procedures to Obtain efficient and consis- tent estimates of the parameters of the dynamic model. The key assumption made by Dr. Balestra in this general case is the separation of the residuals into two com- ponents: a time-invariant regional effect and a re- mainder.34 The two estimating procedures he has de- veloped are as follows: 1. the maximum likelihood procedure-- which has turned out inapplicable in the case of the natural gas model,35 2. procedure to derive BAN (pest Asymp- totically Nprmal) estimates--which gave satisfactory results in the case of natural gas model. Dr. Balestra, after thorough and painful investigation, 34P. Balestra and M, Nerlove, "Pooling Cross- Section and Time Series data in the estimation of a dynamic model: The Demand for Natural Gas," Tppppical Rpport No. 8, Institute for Mathematical Studies in Social Services, Stanford, California: Stanford Uhi- versity Press, p. 14. 35Ipid., p. 27. 34 came to the following main conclusions: 1. "The over-all results seem to support the major hypothesis concerning price elas- ticity embodied in the dynamic model. It appears that for commodities such as gas, the total demand for the commodity is quite insensitive to price changes, however, the incremental demand for the commodity is more responsive for price changes. The estimated magnitude of the average price elasticity of the incre- mental demand for gas is less than unity, but it appears to be increasing over time (and is above unity in the last year con- sidered). The approach seems to suggest, in turn, that competition.from alternative sources of energy may become stronger in the years ahead. 2. The particular characteristics of the gas market necessitate the separation of the time period under investigation into two sub-periods corresponding to two techno- logically different stages of development: an innovating stage and a mature stage. The identification of different stages of development has important implications for the future. It seems that for future ex- pansion, gas must rely more heavily on the normal growth of population, household formation, and the like. Spectacular ad- vances in gas consumption are no longer as prObable as in the early 1950's except in those states in which gas is still a comparatively new commodity. 3. The application of the estimating proce- dures developed in this study to the pooled sample of cross-sections and time- series produces results that are plausible on the basis of p.priori theoretical reasoning and suggests that these methods may prove successful in similar studies of demand." 2.3 Npr for Differentiation of Markets Thus the four studies are different from each other with respect to the models the authors have considered and 36Ibid. p. 38. 35 ‘with respect to the starting assumptions they believed play a significant role in explaining the behavior of consumption of natural gas in the respective markets. Also the time factor regarding the availability and advancement in use of electronic computer techniques to estimate the appropriate demand models in a more complex setting may have forced the authors who studied the behavior of demand functions earlier than others to build simpler models. The one common viewpoint from these studies is that they agreed to study the demand of natural gas on the basis of major types of different use of natural gas, namely, residential-commercial, in- dustrial and steam electric generating plants. But there is one exception to this point: Dr. Villanueva formu- lated the demand equation in his system of simultaneous equation model on the basis of total demand consisting of the consumption by residential-commercial, industrial and steam electric generating plant markets. The structure of the different types of end-uses of natural gas suggests that it is necessary to distin- guish the basic types and classes of natural gas service. There are three types of service, namely (i) the "firm" service, (ii) the interruptible service, and (iii) the "off-peak" and "seasonal" service. The "firm" service is intended to have assured availability to the customer to meet his load requirements. 36 The load requirements come mainly from the type of weather (cold winters or hot summers) and the type of service the customers have. This service is ordinarily available to all classes of customers. Space heating, although required only in the winter season, is a firm service. The interruptible service, as the name sug- gests, is made available under agreements which permit the curtailment or cessation of deliveries. Interrup- tible customers are almost always the large-volume in- dustrial customers such as steam electric generating plants. The curtailment or cessation of deliveries ordinarily occurs when the gas is needed for "firm” service. Lastly, the "off-peak" and seasonal service is provided for intervals of time specified by the utility. This is a "firm" service. Added to these types of services, there are mainly four classes of natural gas service: (1) Residential Service, (ii) Commercial Service, (iii) Firm Industrial Service, and (iv) Interruptible Industrial Service. The differentiation between these classifications comes from the type of load factor they require. The resi- dential service requires a substantial regularity and a high load factor, ranging from 75 to 85 per cent in 37 37 The main uses in this service are most localities. domestic uses and space heating. The commercial ser- vice has the same specifications. The load factor in the firm industrial service varies from industry to industry and generally varies from 60 to 75 per cent. Generally the load factor in this class of service depends on the sensitivity of business conditions.38 The main uses in this category are, of course, the use of natural gas as inputs and for space heating. The interruptible service is generally considered to have no load factor since the sales in this class of service are made under the condition that service can be inter- rupted in any degree and at any time. Interruptible sales are depended upon by many gas distributors to fill in the off-peak summer "valley" (or low point) in demand and thereby to maintain the system annual load factor at a high level.39 These differences in the types and classes of service warrant a recognition in the study of demand of natural gas. A serious consideration should be given 379. J. Garfield and W. F. Lovejoy, Publip Utility Economicg, Englewood Cliffs: Prentice-Hall, Inc., 1964. p. 171 381bid., p. 171. 39Ibid., p. 171. 38 to these differences because they create the differen- tiation of prices and a variation in degree of compe- tition from other fuels in each of the four services in their corresponding markets. The gas distributing com- pany is compelled to charge differently to different types of service because of the inherent nature of the service. For instance, the rates for interruptible and off-peak gas ”should be something more than the out-of- pocket or incremented cost of providing the service and cannot exceed the prices of competitive fuels or the gas 'will not be 801d."40 The distributing company must con- sider the competition from other fuels while making sales to large industrial and steam electric power plants on the basis of interruptible service. Similarly by nature the "firm" service is a premium quality service and is therefore more valuable. In addition, the unit cost of serving numerous small customers may be higher compared to those of large industrial users and interruptible users. This causes the rates for residential use and commercial uses to be relatively higher compared to other uses. The degree of competition exists among energy fuels mainly because of the following reasons: One type or form of energy fuel is superior to all the others in a certain type of market. This is partially a function 401bid., p. 170. 39 of relative costs, but more important are the unique physical characteristics of the particular fuel. For example, in residential and commercial markets, natural gas has an advantage of physical characteristics such as clean burning, no odor, dependability of service compared to other competing fuels. Yet there is a keen competi- tion among fuels in these markets for heating, cooking, clothes drying, water heating, air conditioning, and refrigeration. CoOking is done primarily with gas and electricity, although coal and range oil are used in some rural and low income areas. The vigorous campaign staged by the electric appliance and electric utility distribution companies has resulted in substantial gains for electric coOking in many areas of the country. Such vigorous campaigns are initiated by gas distribution companies also. Similarly, gas and electricity compete for residential water-heating and clothes drying markets. As Dr. Balestra discussed, stocks of appliances through vigorous campaigns would accelerate the competition between natural gas and electricity. In residential heating market, oil and coal compete vigorously with natural gas through pricing and non price factors. Secondly, the substitution of one or more fuels for another may play an important role in changing the competitive structure. Physical characteristics are of minor importance here and the use of one fuel compared to another is primarily a function of relative costs of 40 the respective competing fuels. This is more prevalent in steam electric generating plants market where the gas service is based on interruptible basis. Almost all the plants in this market are equipped with machinery that can use competitive fuels like coal, fuel oil, so that they can take advantage of the lowest price among the alternative fuels. Thirdly, location of the pro- duction of the competitive fuels vary the degree of competition. For instance, for electricity generation in the Southwest region, natural gas is used as plant fuel almost exclusively. In west Virginia, coal is used, while in Maine and Florida, fuel oil is used. Thus, the above three things can influence the degree of competition in each market. Recognizing these facts, the four authors, while studying the behavior of consumption of natural gas, have divided the total market into three main submarkets, namely, residential and commercial, industrial, and steam 41 It would be still better electric generating plants. if the above division of markets were further divided as residential, commercial, industrial and steam electric generating plant markets. This would enable the research 'worker to understand better about the variations in prices and competitive aspects in each of the submarkets, rather 41Dr. MacAvoy studied the citydwide home demand and industrial demand for natural gas. He did not con- sider the commercial demand. 41 than understanding them in the above three/way submarket structure. Also there is a possibility of getting a more homogenous data for the concerned variables in a four/way submarket structure rather than in the three/way submarket structure. Therefore, in this study, the total market is divided into four submarkets and an attempt is made to study the behavior of consumption in each market by developing appropriate models. 2,4 Prpblem pf Homogeniety pf Data Another important aspect that is commonly recog- nized by all four authors is the problem of "homogeneity of data." For example, the prices paid for the use of natural gas in the New England States are far different from the prices paid in the West South Central States, which are, in turn, different from those paid in the Pacific States. Thus they may not be representative in any of the markets. But they are at least homogeneous in each state. If cross-section analysis is used, this kind of "homogeneity prOblem" due to demographic factors may be reduced because cross-section analysis considers each state as an economic unit at a given time point. By this means, individual state differences can.be accounted significantly in estimating the demand functions. The cross-section estimation procedure necessarily assumes that it is possible to specify explicitly the differences among the economic units in such a way that once these characteristics are specified, the economic units will, 42 on the average, react in the same way to any particular 42 These reasons prObably may have led the 43 stimulus. above authors to use cross-section analysis. :Of course, there are certain draWbacks in using the cross- section estimation procedure that should not be over- loOked. Certain "nuisance" variables that may not influence significantly the behavior of consumption individually but may affect it collectively, may not be accounted in the statistical estimation of demand func- 44 If these variables are not taken into account, tions. one may question the underlying relationship. Some of the prOblems confronted by the "nuisance" variables may be removed by more elaborate cross-section classification with respect to the ”nuisance variables." But by making such elaborate classifications, at the same time, one may likely create more difficulties in getting the required data. Also "cross-section analysis, except under rather heroic assumptions, will not provide information on the influence of prices, which may be of importance in 45 long-term projections." However, these points should 42Y. Grunfeld, "The Interpretation of Cross—Section Estimates in a Dynamic Model," Econometrica, Vol. 29, 1961. 43There is an exception to this comment. Dr. Balestra used pooled time series of cross-section samples. 44L. R. Klein, 5p Introductipn tp Econpmptripg, Englewood Cliffs: Prentice-Hall, Inc., 1962, pp, 52-60. 45H. S. Houthakker and L. D. Taylor, Cppgumer Dempnd in the United Stateg, 1929-1970, Cambridge: Harvard University Press, 1960, p. 5. 43 not negate the use of cross-section analysis to esti- mate the demand functions becaust it may still provide an "insight into the mathematical shape of the impor- tant relationships and into the possible importance of a number of factors that cannot be readily isolated in time series’because of their trend like behavior.46 Another important aspect of "homogeneity prObé lem," particularly in the natural gas industry, which may destroy the homogeneous nature among Observations is the presence of the following set of factors: 1. the degree of urbanization, 2. the weather conditions, and 3. the availability of gas.47 These three factors are bound to cause the demand response in each market in a unique way from state to state or even from city to city. This is agreed by all the four authors. According to Dr. Balestra, the last factor, namely, the availability of gas, affects significantly the nature of the results and his analysis has suggested "the separation of the time period under investigation into two technoligically different periods. . . The behavior pattern in the gas market seems to be divided into periods corresponding to two stages of development, 46Ibid., p. 5. 47P. Balestra, pp, cit., p. 117. 44 48 an infant stage and a mature stage." This is justi- fied in his study because the transmission pipelines are not laid uniformly at the same time throughout the states so that all regions are supplied with natural gas. Some regions are provided with pipelines earlier than others. Consequently this caused the above stated differentiation of two stages in the natural gas market. PrOblems due to the weather conditions and urbanization would be reduced to a minimum if some kind of measure is taken by introducing these variables or their effects into the respective demand functions of natural gas. Drs. MacAvoy,‘Wein and Villanueva approached this point of view and used temperature as a variable in order to measure the effect due to weather conditions. And to take into account the effect due to urbanization, Dr. Villanueva used both time series and cross-section 50 Drs. MacAvoy and Wein used cross- Observations. section analysis to take into account the prOblem due to urbanization in analyzing the behavior of natural gas consumption. Thus, the above stated factors in- fluence the analysis significantly and should be given serious consideration in studying the behavior of con- sumption of natural gas. One other variation different 48Ibid., p. 119. 49R. S. Villanueva, op. cit., p. 4. SOIbid. . p. 100 45 from the above studies is attempted in this study. That is, only one state is selected and the entire demand analysis is investigated by building pertinent econo- metric models. By this approach, prOblems due to urbani- zation are bound to be reduced to a minimum. In order to reduce the prOblems due to weather conditions, appro- priate variable can be introduced in the demand model. The importance of availability of gas is already noted earlier. If one selects a state in which natural gas was introduced during the 1950's, then he may be left with a fewer number of Observations for the analysis and this may change the nature of analysis. Therefore, if one selects a state which has an ample number of Obser- vations over a relatively long maturity stage with res- pect to the availability of gas, the prOblem.posed by Dr. Balestra as well as the prOblem of a small number of Observations may be reduced to a minimum,so more weight must be given to this factor compared to the other two in selecting a state. There may be difficulty in using cross-section analysis because of the diffi- culty of securing data for the individual regions of a state. Also, one may be left with few Observations for the cross-section analysis. Therefore, the analysis of time-series is used in this study. By appropriate speci- fication of the demand model and by using advanced tech- niques of estimation, one may reduce the prOblems pointed out by the critics of time series analysis. For these 46 reasons the State of Michigan is selected for the analy- sis. In this state, natural gas was introduced much earlier and has a relative long period of maturity stage. 2,5 Simultaneous Nature Among Natural Gas and Itg Substitutes Another important point to be noted is that in all the four studies, electricity variable, which is an important substitute for natural gas than other fuels, is not included in either of the studies more explicitly. This can be seen through the simple correlations among natural gas and its substitutes that are presented in Tables 2.5.1, 2.5.2, and 2.5.3. "Competition between electricity and natural gas is one of the major prOblems to which managerial attention is devoted. Thirty years ago, gas had the coOking load in the home, electricity the lighting, and there was not much to scrap about in addition. But as each has sought to broaden its share of the energy market, this competition has led to continued improve- ments in the quality and performance of conventional gas and electric appliances, and to the development of new appliances. Now the crossover to those in the gas busi- ness is over. No service gas performs in the home can- not be performed by electricity also--not as well, of course, but at least adequately! Not only cooking, but ‘water heating, clothes drying, air conditioning, space 47 Table 2.5.1 Simple Correlations Among Natural Gas And Its Substitutes: Residential Sector Y1 Y2 Y7 Y8 Y1 .1.0000 Y2 0.7891 1.0000 Y7 -0.8438 -0.7636 1.0000 Y8 -0.0838 -0.0220 -0.0082 1.0000 Y1 = consumption of natural gas (millions of mcf) Y2 = index of burner-tip price of natural gas in residential sector (d/mcf) Y7 = index of price of electricity in residential sector (é/kwh) Y8 = index of price of fuel oil in residential sector (d/gal) Source: Computed from data in Appendix A.l 48 Table 2.5.2. Simple Correlations Among Natural Gas And Its substitutes: Commercial Sector Y Y Y Y 3 4 9 10 Y3 1.0000 Y4 0.5220 1.0000 Y9 -0.0340 -0.2971 1.0000 Ylo 0.2347 -0.2086 +0.8598 1.0000 Y3 = consumption of natural gas in commercial sector (millions of mcf) Y4 = index of burner-tip price of natural gas in commercial sector (é/mcf) Y9 = index of price of electricity in commercial sector (é/kwh) Y10 = index of price of fuel oil in commercial sector (e/gal) Source: Computed from data in Appendix A.l 49 Table 2.5.3 Simple Correlations Among Natural Gas And Its substitutes: Industrial Sector Y Y Y Y 5 6 ll l2 l3 Y5 1.0000 Y6 0.4040 1.0000 Y11 0.0920 0.4863 1.0000 le 0.2678 0.0507 0.2000 1.0000 Y13 -0.4556 -0.1088 0.6084 0.2356 1.0000 Y5 = consumption of natural gas in industrial sector (millions of mcf). Y6 = index of burner-tip price of natural gas in industrial sector (é/mcf) Y11 = index of price of electricity in industrial sector (é/kWh) Y = index of price of fuel oil in industrial 12 sector (é/gal) Y13 = index of price of coal in industrial sector (S/ton) Source: Computed from data in Appendix A.1 50 heating. and garbage disposal are all the daily battle- field."51 As more applications for natural gas and electrie energy are created, the arena in which compe- tition occurs continues to expand. The vigorous cam- paign staged by the electric appliances and electric- distribution industries may also have caused the in- creased use of electricity. The number of dwelling units having appliances equipped either for coOking or for heating to consume either natural gas, fuel oil, coal or electricity, and their percentage, are presented in the following tables for the East North Central Re- gion.52 From these tables one can see that in the case of coOking, the number of electric appliances increased from 21.5 per cent of the total in 1950 to 36.4 per cent of the total in 1960. For the same period, the number of natural gas equipment decreased from 65.6 per cent to 62.4 per cent of the total. This indicates the cor- responding usage of natural gas and electricity as energy fuels and shows the competition between them. But in 51Marvin Chandler, "The Utilities--An Increasingly Competitive Industry," Public Utilitieg Fortnightly, October 8, 1964, p. 57. 52East North Central Region consists of the follo- ‘wing states: Illinois, Indiana, Michigan, Ohio and Wis- consin. One can reasonably assume that the conclusions that can be derived from these tables can hold for the state of Michigan because of geographic proximity and other economic conditions that are similar among the states in the region. 51 Table 2.5.4 Number of Dwelling Units Having CoOking Appliances and the Corresponding Percentages for Selected Types of Fuels: East North Central Region Percentage Number of Number of ngr Type of Fupl Dwelling Units Dwelling Unitg 1950 Utility gasa 4,936 65.6 Liquid fuelb 326 4.3 CoalC 645 8.6 Electricity 1,617 21.5 Total 7,524 1960 Utility gasa 5,746 62.4 Liquid fuelb 48 0.5 Coalc 63 0.7 Electricity 3,344 36.4 Total 9,201 a. Utility gas is piped into the dwelling unit from a central system serving the community. Such gas is supplied by a public utility company, municipal government or similar organization. b. Liquid fuel includes fuel oil, kerosene, distillate oil, furnace oil, coal oil, stove oil, range oil, lamp oil, gasoline and alcOhol. c. Coal includes cOke also. Source: Col. 2: U.S. Census of Housing, 1950, 1960, U. S. Department of Commerce, Bureau of Census Col. 3: computed from Col. 2 52 Table 2.5.5 Number of Dwelling Units Having Heating Appliances and the Corresponding Percentages for Selected Types of Fuels: East North Central Region Percentage Number of Number of Year Type of Fuel Dwelling Units Dwelling Units 1950 Utility gasa 1,544 19.0 Liquid fuelb 1.692 20.8 Coalc 4,891 60.0 Electricity 18 0.2 Total 8,145 1960 Utility gasa 4,679 45.6 Liquid fuelb 3,358 32.8 Coalc 2,168 21.2 Electricity 39 0.4 Total 10,244 a. Utility gas is piped into the dwelling unit from a central system serving the community. Such gas is supplied by a public utility company, municipal government or similar organization. b. Liquid fuel includes fuel oil, kerosene, distillate oil, furnace oil, coal oil, stove oil, range oil, lamp oil, gasoline and alcohol. c. Coal includes cOke also Source: Col. 2: U.S. Census of Housing, 1950, 1960, U. S. Department of Commerce, Bureau of Census. Col. 3: Computed from Col. 2. 53 the case of heating, percentage equipment increased for both the fuels--both getting the market from coal. Thus electricity is an important variable to be considered while formulating the demand models for natural gas. Similarly, consideration of other competing fuels, namely fuel oil and coal, more explicitly is desirable. This makes the demand models more explicit and more accurate because most of the relevant variables are included in the models. By including explicitly all the relevant variables as much as possible, greater 53 Some kind of considera- homogeneity'would be attained . tion is given in all the four studies mentioned earlier, either by introducing directly the variables of substi- tute commodities or by introducing other variables capable of measuring the effects of the variables of substitute commodities. But no systematic account of the substitute variables is given in any study. A systematic account will be given in this study by de- veloping economic models based on simultaneous nature among the relevant substitute economic variables. To- gether with economic theory and statistical availability of data, a simultaneous equations system model‘will be developed and then by using advanced methods of statis- tical estimation the model will be estimated. In this ‘way one can recognize and discover the interdependent 53y. Gruenfeld, pp, cit., p. 399. 54 nature among the relevant substitute variables by giving an account for the joint or mutual determination of changes in economic variables. 2 E ected Nor 1 Inc me H othe i It is argued that "if a consumer unit knows that its receipts in any one year are unusually high and if it expects lower receipts subsequently, it will surely tend to adjust its consumption to its ‘normal’ receipts 54 In other words, rather than to its current receipts." the effects of changes in "expected normal income" are strong compared with changes in current income in under- standing the consumer behavior. They are even stronger compared with the effects of durations of "expected" 55 As future incomes about "expected normal incomes." said earlier in the first chapter, alternative economic models are developed on the basis of these ideas. The formulation of the corresponding model and estimation methods are discussed later in this study. Dr. Balestra formulated his dynamic model to exPlain the behavior of natural gas consumption by re- lating the consumption to the stock of appliances. He 54M. Friedman, A Theory of the Conspmption Fupc- tion, A Study by the National Bureau of Econppic Research, NeW’Yprk. Princeton: Princeton University Press, 1957, p. 10. 55Ms Nerlove,"Distributed Legs and Demand Analy- sis for Agricultural and Other Commodities;'Agricultural Marketing Service, U. S. Department of Agriculture, Washington, D.C., 1958, p. 29. 55 argued that the consumption of natural gas, at least at the household level, is closely related to the stock of appliances in existence and hence to a large extent it is governed by such stock. The concept he incorporated in formulating his dynamic model is appreciable because it can shed certain light to explain the consumption be- havior. But how significant the stock variable is in explaining the behavior of natural gas consumption is somewhat questionable. In the first place, the stocks are not made by consumers of natural gas, rather they are made by retail distributors of gas appliances. To that extent they are functions of cost of both gas- using and electricity-using appliances, campaign pro- grams engaged in by distributors, "expected normal in- comé'of consumers, prices of natural gas and its sub- stitutes, average consumption of the fuels by appli- ances, other things being held constant. With higher ”expected normal income" the consumer has means to replace a wearing oil furnace or stove with a gas fur- nace or stove. Or he may afford setting up air condi- tioning equipment in his house. This implies higher consumption of natural gas. Similarly, the lower the cost of appliances, the higher demand for appliances (consumption of the respective fuels), which is a dic- tated fact of economic theory of consumer choice. So it is conceivable to argue that the effects of the stock variable are included in the effects of the above 56 discussed variables. Also for relatively short periods of time horizon, prices of fuels may not have signifi- cant effects on the behavior of consumption, particularly in the case of natural gas. Thus either the cost of appliances or the "expected normal income" are relevant variables compared to the stock variables to explain the dynamic behavior of consumption of natural gas. In this study, some alternative economic models are developed only on the basis of "expected normal income" concept. The justification for using this concept is discussed above. Before we develop the simultaneous equations sys- tem model and alternative models based on the concept of "expected normal income," some static models will be de- veloped in the next chapter. These static models are helpful in choosing the variables that are to be incor- porated in the dynamic models. They may also serve as a standard of comparison for the dynamic models. But before we proceed to the next chapter, the notation followed on the variables both in the static and the dy- namic models is described: Y1 = average consumption of natural gas (millions of mcf) in the residential sector Y2 = index of burner-tip price of natural gas (é/mcf) in the residential sector Y3 = average consumption of natural gas (millions of mcf) in the commercial sector 57 index of burner-tip price of natural gas (é/mcf) in the commercial sector average consumption of natural gas (millions of mcf) in the industrial sector index of burner-tip price of natural gas (c/mcf) in the industrial sector index of price of electricity (é/kwh) in the residential sector index of price of fuel oil (d/gal) in the residential sector index of price of electricity (é/kwh) in the commercial sector index of price of fuel oil (e/gal) in the commercial sector index of price of electricity (d/kwh) in the industrial sector index of price of fuel oil (e/gal) in the industrial sector index of price of coal ($/ton) in the industrial sector constant term lagged (by one period) disposable per- sonal income in.Michigan lagged (by one period) number of degree days in Michigan lagged (by one period) consumption of natural gas in residential sector lagged (by one period) consumption of natural gas in commercial sector lagged (by one period) consumption of natural gas in industrial sector lagged (by one period) industrial em- ployment (in thousands) in Michigan 58 Z = lagged (by one period) index of price of electricity in residential sector Z = lagged (by one period) index of price 8 of electricity in commercial sector 29 = lagged (by one period) index of price of electricity in industrial sector Z10 = lagged (by one period) index of price of fuel oil in residential sector Z11 = lagged (by one period) index of price of fuel oil in commercial sector 212 = lagged (by one period) index of price of fuel oil in industrial sector 213 = lagged (by one period) index of price of coal in industrial sector 214 = disposable personal income in Michigan 215 = number of degree days in Michigan 216 = number of customers of natural gas in commercial sector . 217 = industrial employment in Michigan The data for all these variables are based on the State of Michigan. The compiled data in the form of tables can be seen in Appendix A.1. The demand models are not formulated for steam electric generating plant markets because in Michigan no use, or very little use, of natural gas is made by steam electric generating plants, so the analysis for this sector is not attempted and the consumption of natural gas in the industrial sector Obviously excludes the consumption of natural gas by steam electric generating plants, however small the 59 consumption is. Now we go to the next chapter where some static demand models are developed and analyzed. CHAPTER III THE DEMAND FOR NATURAL GAS: THE STATIC APPROACH 3.1 The Simple Static Demand Eguation The purpose of this chapter is to formulate some simple static models of demand for natural gas and esti- mate the parameters of the corresponding demand models. Static models can be helpful in choosing the variables which should be incorporated in a dynamic model. They also may serve as a standard of comparison for dynamic models. Also, the investigator may know: 1. the limitations and deficiencies of static theory to explain the demand for natural gas, 2. the relevant variables that most usually affect the demand for natural gas, and 3. the variables which are later to be incorporated in dynamic models. Because of these reasons, one may not neglect formu- lating (and estimating) some static models even if they give inconsistent results. Assuming that the consumer maximizes his utility function, the consumer's demand for natural gas may be 60 61 stated as a function of the burner-tip price and income. That is (3.1.1) ---- o = f (p n) where Q = quantity of natural gas consumed P = burner-tip price of natural gas at point of consumption M = money income Equation (3.1.1) may also be treated as a short-run demand model, because there is no "reaction mechanism” or "adjust- ment process" to explain the dynamic behavior of natural gas demand. For a relatively shorter period, the in- fluence of the prices of substitutes--coal, fuel oil, and electricity--is almost negligible, since the stocks of appliances owned by the community are assumed fixed in the short-run. So the price variables of substitutes are not included in equation (3.1.1). It simply explains the behavior of consumption for changes in burner-tip price (P) and money income (M). For these reasons, the static approach may be termed as the short-run approach. The demand model in equation (3.1.1) is simply stated in an abstract form. It is not useful for esti- mation purposes unless certain functional form is assumed. The following functionsl forms are assumed for equation (3.1.1): M Linear form (3.1.2) ---- 0t 8 a0 + a 2 t 1Pt+a 62 (3.1.3) ---- log Qt - Bo + Bt log Pt + 32 log M.t Double-logarithmic form Introducing a stochastic disturbance term, equations (3.1.2 and (3.1.3) may be written as:1 (3.1.4) ---- 0t = so + a1 Pt + a2 M.t + Vt and (3.1.5) ---- log Qt = so + pl log Pt + 82 log Mt + Ut One should note at the outset about the implicit assump- tions in equations (3.1.4) and (3.1.5). The implicit assumptions in the linear form, i.e., in equation (3.1.4), is that all positive elasticities will ulti- mately tend to one. But the double-logarithmic form implicitly assumes that the elasticity remains constant over the entire range of variables.2 Regarding the com- putational ease for Obtaining the elasticity coefficients between the two forms, double-logarithmic form is pre- ferred to the linear form for the coefficients of the variables in double-logarithmic form are the corres- ponding estimated elasticities. In addition to this, the double-logarithmic form leads to comparatively easy mathematical manipulations. 1The justification for including the stochastic disturbance term is explained by J. JOhnston in his book Economic Methods, New Ybrk: McGraw-Hill BoOk Company, pp. 4-7- 2P. Balestra. "The Demand for Natural Gas in the Residential and Commercial Market: A Dynamic Approach." Ph.D. thesis, Stanford University, 1965. 63 Evan though the choice between the two forms in- volves a compromise among several criteria including eco- nomic theory, goodness of fit, and simplicity, it is not intended to select one functional form compared to the other.3 Rather it is in the general interest of showing the results of short-run static models to explain the demand for natural gas. The results of both the func- tional forms are presented and evaluated in this chapter. 3.2 Estimation of the Simple Static Deppnd Egpapions The method used for estimating the corresponding demand functions of natural gas for residential, com- mercial and industrial sectors is ordinary least squares based upon time-series data. The time-period considered is 1947-1964 and so there are 18 Observations on each variable of the corresponding models. Disposable per- sonal income is used instead of personal income in the residential and commercial demand equations. The 3The goodness of fig can be judged by the coef- ficient of determination, R . One should note two points in comparing the two functional forms: (1) it is the pp;- rected coefficient of determination R2 which is defined as: -2=2 K 2 R R - T_K_1 (l-R ) not R2 to be used in comparison. (T corresponds to the number of Observations and K corresponds to the number of exogenous variables). (2) The corrected coefficients of determination should be calculated, in the case of double- logarithmic functional form, on the basis of antilog of the dependent variable and should then be compared with the corrected coefficient of determination based on linear functional form. See page 217, A. S. Goldberger, Econo- metric Theory, New York: John Wiley & Sons, Inc. 64 following are the estimated demand functions in both the linear and double-logarithmic functional forms:4 1. Residential Sector Linear form: + 0.0180 Z Y = -142.3611 + 0.4223 Y 1t 2t 1t (1.3143) (0.0022) (0.75) (0.00) R2 = 0.9300 d = 0.9748 Double-Logarithmic form: log YltL= -4.633l - 1.2485 log Y2t:+ 2.2492 log th. (0.9438) (0.1998) (0.20) (0.00) R2 = 0.9516 d = 1.0726 2. Commercial Sector Linear form: Y5t= -12.8523 - 0.3675 Y6t+ 0.0060 z1t (0.9438) (0.1998) (0.20) (0.00) R2 = 0.8358 d = 0.5575 4For the explanation of the variables, see Chap. II, p. 56. The number in the brackets under the estimated coefficients are the standard errors of the estimated co- efficients and the numbers below the standard errors are the corresponding significant prObabilities. For example 1.3143 is the standard error of the estimated coefficient 0.4223 and 0.75 is the significant prObability at Which 0.4223 is diffgrent from zero. 0.00 means some value less than 0.005. R is the coefficient of determination and d is the Durbin-Watson-d statistic for testing the auto- correlation in residuals. 65 Double Logarithmic form: log Y I -7.6172 - 1.5830 log Y + 2.9565 log 2 5t 6t 1t (1.1919) (0.2878) (0.20) (0.00) 32 . 0.9178 d = 0.7286 3. Industrial Sector Linear form: Ygt- 138.5042 + 1.7127 Ymt- 0.1961 261: (1.0093) (0.0896) (0.11) (0.05) R2 = 0.3659 d = 0.5853 Double-Logarithmic form: log Y9t= 3.6279 + 3.2189 log Ylot- 2.7028 log z6t (1.3684) (1.5357) (0.03) (0.11) R2 = 0.3900 d = 0.7097 From these estimated equations the following interpreta- tions may be made: 1. The signs of all the coefficients except for the price coefficient of the linear form in the residential sector, and the price and industrial employment coefficients of both the forms in the industrial sector, are correct according to economic theory. But the coefficients of the price variable in all forms except double-log form in the 66 industrial sector are not statistically significant.5 For the coefficient which turned out to be statistically signifi- cant, the sign of the coefficient is wrong. For some forms the standard errors of the coefficients of the price variable are larger than the coefficients themselves. In all forms the standard errors of the co- efficients of the price variables are con- siderably larger. 2. The coefficients of the income variable turned out to be statistically significant in both the residential and commercial sectors.6 For the industrial sector they are not highly significant and have the wrong signs. For the residential and com- mercial sector they indicate that the natural gas is a "luxury" commodity because the income elasticities in each of the sec- tors are greater than unity. This result os rather suspicious. Why should natural gas 5That is, the null hypothesis that the coefficient of the price variable is not different from zero is accep- ted. 6That is, the null hypothesis that the coefficient of the income variable is not different from zero is not accepted. 67 be such a "luxury" commodity (or service) when it is well known that natural gas is used to satisfy basic needs such as coOking, space heating and water heating. Thus they are misleading. One plausible explanation for higher values for income elasticities is that they may have included other effects in addition to income effect and consequently the values of income elasticities are larger than unity. One other plausible explanation may be that as income increases, people may install a new air conditioning equipment or buy a new gas range or dryer to replace an old one. This would increase gas consumption. According to economic theory, the variable 261! industrial employment, should have a positive sign. It is used in these equations to explain the influence of industrial acti- vity on the consumption of natural gas. So naturally the higher the industrial activity, the higher the consumption of natural gas. That means the coefficient of ZGtzshould be accompanied by a positive sign. Similarly, the price variable should be accompanied by a negative sign. But the signs of the esti- mated coefficients are in the reverse order for both the variables. This may imply 68 that these two simple static demand models are inadequate to represent the demand for natural gas in the industrial sector. 4. The coefficient of determination, R2, is high in each equation except for the in- dustrial sector. This high R2 may be mis- leading since the high R2 may have occurred because of the presence of endogenous vari- able on the right hand side of each equation. Actually the price variables in each sector are not exogenous, they are endogenous vari- ables in reality as already explained in Chapter II. These endogenous variables are involved in explaining the variation in an- other endogenous variable, namely, the quan- tity of natural gas consumed. This causes high R2.7 From these conclusions, one may gather that these two Simple static models provide an insufficient explanation Of demand for natural gas in each sector. £2.»3 The Generalization of the Static Approach The results of the preceding section indicate 'tllat the simple static demand models fail to provide a -.__ P. Balestra, pp, cit., p. 46. 69 satisfactory explanation of natural gas demand. This may be due to inadequate specification of the models themselves, apart from.the static nature of the models themselves. Therefore, in this section some sort of generalized static approach will be approached to ex- plain the natural gas demand. This approach may serve as a bridge between the static approach and the dynamic approach.which will be developed later. This approach is developed on the basis of the approach followed by Professor Fisher and Professor Kaysen.8 Their model states that "the demand for electricity, for household use, is derived from the demand by the community of households for the services of its various stocks of white goods."9 Hence they formulated the demand function for electricity as: ' n (3.3.1) ---- D = 2 K. W. t j_=1 1t 1t t=lpzpsooooT ‘where Dt = total metered use of electricity in kilowatt hours by all households in the community during the period t Wit = 1th white good possessed by the com- munity during the period t 8F. M4 Fisher and C. Kaysen, A Study in Econo- metpics: The Demand for Electricity in the United Statpg. Amsterdam: North-Holland Publishing Company. 1962. 9Ipid., p. 10. 70 Kit = parameters representing the intensity of use of the Wit10 For a relatively short period of time, they have assumed W. to remain the same and Ki as a function of the 1t t following form:11 a. I3 _ 1 1 Kit ' Ai Pt Yt where Pt = average price of electricity per kilowatt hour to households Y t per capita personal income Ai, ai and Bi are constant parameters In this section an attempt is made to formulate somewhat more generalized demand models than the demand models of the previous section, to explain the natural gas demand in each sector. The corresponding results and conclusions are presented in the next section. Let St be the stock of gas appliances in period t and At be the rate of utilization of this stock of appliances of gas in period t. We may write: t = 1' 2' O O O O O T For a short period, one may assume that St to be constant or the periOd of consideration is such that St may be treated as given. But )(t can be varied according lOIbido I P. 11. 11Ibid., p. 13. 71 to the price of the gas or temperatore, or income. Therefore, it can be assumed without loss of generality, that (3.3.4) ---- 7\ where th = Z14t= ZlSt= a Z B Z 1 =AY 14t lSt t 2t index of burner-tip price of natural gas in the residential sector in period t disposable personal income in period t degree days in period t The prices of closely related substitutes may influence )t but they do so only in a longer time period. Since the time period is so short in this analysis, one may neglect putting price variables of substitutes in equa- tion (3.3.4) substituting equation (3.3.4) in (3.3.3) and adding a stochastic tern“ V (3.3.5) ---- Y ‘where Ylt = Y2t = Z141;= Z151;= 1t t i V _ a B — A thl Z Z S consumption of natural gas in residential sector (millions of mcf) in time period t index of burner-tip price of natural gas in residential sector (c/mcf) in time period t disposable personal income in time period t degree days in time period t It is almost impossible to secure data on St for each t (t = l, . T), and “estimation of 2' s o O O 72 similar quantities ... is simply impossible on any rea- 12 sonable standard of accuracy." The possible way out in such cases is to eliminate St by some way and this can be done if one assumes an exponential growth in St' although certain price must be paid by making such an assumption. But the estimation procedure turns out very simple by making such an assumption. Moreover, it is not that bad an assumption because the exponen- tial growth in population (demonstration effect) would tend to make the growth in stock of appliances in an exponential fashion.13 Thus st is assumed as (3.3.6)---- st = (1 + K) st_1 where K = rate of growth in the stock of appliances during the period t Since the growth in St is rather smooth, K cannot be expected to change violently and it is not unreasonable to assume K as a constant real number. Taking the logarithms to both sides of the equa- ‘tion (3.3.5) 12Ibid., p. 27. 13Ibid., p. 28. The chief trend in st probably cIomes from the introduction and increasing use of new Eijppliances. To some extent the buying of new appliances dispends on the community in the sense of if his neigh- Itmor bought an electric or gas appliance, he may tend to Dy the same because of the influence of his neighbor. C>rif many appliances in that community are gas appli- ainces, he may tend to buy a gas appliance. Such effects Eire called demonstration effects. In these situations, t:he number of the appliances sold is proportional to the r1umber already in use. 73 (3.3.7) ---- log Y1t= 109 A + a 109 Y2t+ ‘3 1°9 2141: + log 215 t+ log St +Vt Lagging (3.3.7) by one period and subtracting it from (3.3.7), one may Obtain (3.3.8) ---- log Y - log Y a(1og Y - log Y 1t lt-l= 2t 2t-1) + 8(log Zl4t- log 214t_1) (log Z 15 t " le t-l) ) + (log St - log St-l + Vt - Vt-l Similarly, taking logarithms to both sides of equation (3.3.6) log St = log (1 + K) + log St-l or log St - log St-l = log (1 + K) Substituting this in (3.3.8) (3.3.9) ---- log Y1t - log Y1 t-l= a(log Y2t- log Y2 t-l) + (3(log Zl4t‘ log Zl4t-l) + (log ZlSt - log 215 t-l) + log (1+K) + Vt- vt_l Thus a first-difference equation is obtained to eXplain the demand for natural gas in the residential sector. By letting Y1 t = log Y1 t ' log Y1 t-l * = — Y2 t 109 Y2 t log Y2 t-l 74 * — — 214+. " 1°9 Z141: 1°g Zl4t-1 * = - Z15 t 1°9 Z15 t 1°9 215 t-l * = ... Vt Vt Vt-l K* = log (1 + K) and substituting in (3.3.9) one may Obtain + 32* + V* * ____ a a * * (3.3.10) Y K + aY 14t ZlSt‘l' t 1t 2t: One can see that the first differencing method results in making the trend in the growth of stock appliances a constant term. And the variable St is elimi- nated in equation (3.3.10). This equation is used for estimating the demand function of natural gas in the residential sector. This is essentially a static model because of the following reasons: 1. No specific attempt is made to estimate substitution effects since no substitu- tion variables are present. 2. No dynamic element that changes through time is involved in equation (3.3.10). 3. It tells the intensity of gas use relative to the price changes in natural gas, in- come changes, and temperature changes and changes in St' 4. It does not involve in "expected or perma- nent income" hypothesis which is important in considering the growth factors of stock of gas appliances or any other new 75 installations of gas-using equipment as argued in Chapter II. 5. Stock effect, a related prOblem to (4), is not explicitly specified in equation (3.3.10). The related constant (K in k* = log (1 + K)) is included in constant term K* which does not explain the be- havior of the consumption of natural gas except adding something to "sacle" effect (i.e., K the constant term.) Equations similar to (3.3.10) corresponding to commercial and industrial sectors can be formulated res- pectively as: (3.3.11) ---- Y3t= K* + alY4t+ a2Z14t+ a3235t+ U“; where Ygt - log Y3t- log Y3t-1 th = log Y4t- log Y4 t-l Z’141: = 109 2141: ' 1°9 Z14 t-l 2151-. = 1‘39 let" 109 Zl5 t-l U1 = Ut ' Ut-l K* = log (1 + K) and Y"r51: - K1! +BlYIOt+ 32Z15t+53217t+ut 76 where Y5 t = 109 Y5 t " l°g Y5 t-l * — _ Y6 t - log Y6 t log Y6 t-l * - - Z15 t ’ 1°9 ZlSt 1°9 Z15 t-l * — _ 215+. ‘ 1°9 Z17 t 109 z17 t-l U: = Ut ' Ut-l K* = log (1 + K) where Y3": = consumption of natural gas in commercial sector (millions of mcf) in time period t Y4t = index of burner-tip price of natural gas in commercial sector (é/mcf) in time period t Y5t = consumption of natural gas in industrial sector (millions of mcf) in time period t Y6t; = index of burner-tip price of natural gas in industrial sector (2 mcf) in time period t Zl4t; = disposable personal income in time period t ZlSt; = degree days in time period t Z17t; = industrial employment in Michigan in time period t Yi t-l= lagged (by one period) variable of Y. (i = 3: 4' 5! 6) :L t zit-1 = lagged (by one period) variable of Zi t (i = 14, 15, 17) Balestra loOked at the demand for natural gas in residential and commercial market from another angle. He has postulated that the "gas consumption is also a function of the availability of gas (or pipeline 77 4 Thus he has formulated a demand function capacity)."1 of the form (3.3.13) ---- log Gt = A + a log Pt + 6 log Y£ + I log Wt1+ U t where . . 12 Gt = consumption of gas in BTU 10 in period t Pt = price of gas in period t Yt = per capita income in period t Wt = average stock of appliances in period t Ut = random disturbance In the short run W cannot be expected to change violently t and so he assumed an exponential growth in'Wt, i.e., (3.3.14) ---- w, . (1 + K)‘Wt_1 where K is the given rate of growth in W£I5 The variable Wi can be eliminated from equation (3.3.13) as St is eliminated from equation (3.3.5) and the resulting equa- tion can be Obtained as ..--.. *= * * *- (3.3.15) Gt A + aPt + pvt + u* t where * = - Gt log Gt log Gt-l * = — Pt log Pt log Pt-l 14 P. Balestra, pp, cit. 15Ibid. 78 Y: - log Yt - log Yt-l U; = Ut ' Ut-l A* = log (1 + K) Following Balestra and adding a new variable, namely 215‘: the number of degree days, one may Obtain an equation of the form (3.3.10) 11* a w * WWW” 151:+ t * 2t:‘+ pz + i Z Yit 14+. for the residential sector. But this equation is formu- lated on the basis of "availability of gas" hypothesis or what Balestra calls "capacity effect" hypothesis. Thus both the hypotheses, namely the demand for natural gas as a function of stock of appliances and also as a function of availability of gas, lead to the same form of demand equation. In the following section the results of the estimated demand functions, one for each sector, are presented. 3,4 Estimation of the Generalized Static Demand Eguations In the preceding section certain first-difference equations are Obtained to represent the demand functions of natural gas. Before presenting the estimated results. the importance and the use of first-difference models in time-series analysis is discussed. It is well known that economic time-series tend to be serially correlated. First-differencing may serve roughly to remove such serial correlation. Also, as already seen in equations (3.3.5)- (31319), first-differencing the logarithms of variables 79 having exponential trend, the trend part may be removed and treated as a constant term. The method of first-differencing tends to re- move serial correlation only when the errors in the original time-series are perfectly positively corre- lated. Consider, for example, the following scheme in a simple two variable relation: (3.4.1) -—-- (Yi (Vt + a + B Zt V t evt_1 + Ut Wk 1 where Ut satisfying the assumptions (3.4.2) ---- E(Ut)= 0 t t+s 2 (3.4.3) ---- E(U U )= :0 ’ ~ 8 # 0,:v-t ‘6 , ' 8 = 0. Vft It can be easily verified that V <3 I t '- téo e Ut-t Thus, from (3.4.2) and (3.4.3) V = E ( t) 0 2 2 2 2 E (Vt) = E (Ut) + P E (Ut_l) + 94's (U:_2) + . . . = o2 (1 + 92 + 94 + . . . .) 2 1 =o'-————- (1- 92) Also 2 _ 2 av — szfvt - E( Vt);7 2 = E(Vt) 80 Thus 2 2 1 (3.4.4) ---- c a e V (1-92) Similarly, it can be shown that _ s 2 2 ==Qs-£L3- ($950) (1- e ) Suppose we take the first-differences for the original relation Yt = a + 5 2t + vt and let the residuals in the first-differences of'Vt by et, i.e., at = Vt ' Vt-l I 2 0 0 Its variance, 06,13 defined as a: = EA-et ' Eat-72 Since E et = EVt - E Vt-l — 0 2 2 Ce E et _ 2 sf'wt - vt_l)_7 = Ezgvz - 2 v ‘v + ‘V2 .57 t t t 1 t 1 _ 2 - 209 (1- P) But (3.4.6) ---- 3 - 62 1 (1-9?)2 a: ..-.-. 2 o 62 . (1" e) (l-Q) - 2 62 ( 1 ) 81 Thus 2 2 . ce = c if f = 1 a: = 202 if Q = Consider (3'4'7) ”'7' E(et et-s) = E [(vt -Vt-1)(Vt-s ' vt-s-1)-7. = EA-VtVt-S-Vtvt-S-1-vt-1vt-s + Vt-l Vt-s-lt7 =98 o3.- ems?- eerwesai =2863I1-e--];-+1) ges-l.62(ze_ e2 62 =_(8-1—_(1_e)2 1'€2 _ s-1 2 (1-2) "'9 6 (1+0 The two expressions in equations (3.4.5) and (3.4.7), namely 2 E omcHEnmumooum moanmflum> acmocmmma Naucfioo mcoflumoom ocmEmQ HonouUSHum AMQOE UHmBmZOZOUM A¢MDBUDmBm HEB m0 >m¢ZZDm UHFdmeUm H.m.v wHQmE CHAPTER V THE STRUCTURAL ECONOMETRIC MODEL: EMPIRICAL RESULTS 5,1 Some Theoretical Comparisons of the Estimators Used in the Study In the previous chapter, we have discussed the development of the structural econometric model, suitable for the statistical methods of estimation. More specifi- cally, we have specified the demand function for the i-th SECtOI as: “11Y1t+ ai2Y2t+ “13Y3t+ ° ° ' ' ai6Y6t + Bi0Z0t+ 511Z1t+ ' ' ' ° 9113 Z131: +Uit=0 i 1,2,3; t = 1,2, . . . . 18. It is a usual procedure in all the estimation methods used in this study to use only one appropriate jointly dependent variable which is used in the left hand side of the equation. For example, if one considers the struc- tural demand equation for the residential sector, all = -1. Similarly, if one considers the structural equation for the commercial sector, a23 = -l, and so on. And the re- sulting structural demand equation for the residential 113 114 sector can be rewritten as:1 (5‘1'1) ""’ Ylt= “12 th+ 310 Z01-.+ B11 Z11:+ ‘312 Z2t + B13 2312+ 517 271: + [3110 Z101;+ ”it t = 1,2. . . . . 18. The same procedure is applied for the other two equations. With this specification and with the assumptions made in Section 4.3,2 one can note some of the theoretical dif- ferences among the alternative estimators used in this study. Since each structural demand equation contains two jointly independent variables, and if one selects one of these two variables as the dependent variable, the other one will be correlated with the stochastic distur- bance term in that equation because of the simultaneous nature of the relations in the structural model. This makes the estimates of the structural parameters obtained by the method of ordinary least squares (OLS) inconsis— tent. The basic idea in the two-stage least squares method of estimation (ZSLS) is to replace the right-hand side jointly dependent variable, namely Y21f'with appro- priate estimates based on the least squares regression lNotice that a -= o for j = 3.4.5.6 and (fit: 0 for i = 4,5,6,8,9,ll,l2£13 because of the specification of the structural demand equation for the residential sector. 2See pp. 109-111, Chapter IV of this study. 115 of Y and the predetermined variables in(5.l.D,_ The 2t. estimates of the structural parameters obtained by this procedure are consistent.3 Theil has shown a general procedure called (K)-class estimation which provides a whole family of estimators of the structural equation (5.1.1), of which two-stage least squares procedure is a special case.4 The unbiased Nagar K-class (UNK) is one other special case of the above mentioned (K)-c1ass family of estimators. This method was proposed by Nagar and the K-value of the unbiased Nagar K-class estimator has plim (k-l) = 0, and this property establishes, in general, the asymptotic property of consistence for that (K)-c1ass estimator.5 The limited information single equation (LISE) was developed prior to the two-stage least squares and 3See H. Theil, Economic Forecasts and Policy, Amsterdam: North-Holland Publishing Company, 1961, pp. 231-237; and R. L. Basmann, "A Generalized Classi- cal Method of Linear Estimation of Coefficients in a Structural Equation," Econometrica, Vol. 25 (January, 1957 . 4H. Theil,.gp,cit.,.pp. 231-237. 5A. L. Nagar, "The Bias and Moment Matrix of the General K-Class Estimators of the Parameters in Sinultaneous Equations," Econometrica, Vol. 27 (October, 1959). 116 (K)-c1ass procedures by Anderson and Rubin.6 Their approach is an application of the maximum likelihood principle under the specification that the structural stochastic disturbances are normally distributed and utilizing only restrictions on the structural equation being estimated. Under the normality assumption, esti- mates are consistent and are also asymptotically normal and efficient.7 However, Theil has shown that limited information single equation estimators are members of the (K)-c1ass family, and hence, consistent with or without the normality assumption.8 The essential idea in three-stage least squares estimation procedure is to express each equation in such a way that all predetermined variables are involved and then to apply generalized least squares to the whole set of relations to estimate all structural parameters 6T. w. Anderson and H. Rubin, Estimation of the Parameters of a Single Equation in a Complete System of Stochastic Equations," Annals of Mathematical Statistics, Vol. 20,(October, 1949). See also T. W. Anderson and H. Rubin, "The Asymptotic Properties of the Estimates of the Parameters of a Single Equation in a Complete System of Stochastic Equations," Annals,ogyMathematicaliStatistics, Vol. 21 (December. 1950). Also see H. Chernoff and H. Rubin, "Asymptotic Properties of Limited Information Estimates Under Generalized Conditions," Studies in Econometric Method, W, C. Hood and T. C. Koopmans (eds.), _O_Eo Sit-OI Pp. 200—212. 7T. W. Anderson and H. Rubin, QR. cit. pp. 570-582. 8H. Theil, 92, cit., pp. 231-237. 117 simultaneously.9 The three-stage least squares esti- mates are consistent and, in general, they are more asymtotically efficient than the two-stage least squares estimators.10 This very brief summary of the properties of the estimators provided by the alternative methods is per- haps sufficient to indicate that the principal theo- retical differences are based on large sample proper- ties. We know only a limited amount of information about small sample properties of the alternative esti- mates as indicated primarily from Monte Carlo studies.11 Among the methods employed in this study, the three-stage least squares procedure is presumably the most suitable estimation method from the standpoint of asymptotic 9See, for example, J. Johnston, Econometric Methods, op. cit., PP. 266-268. 10A. Zellner and H. Theil, "Three Stage Least Squares: Simultaneous Estimation of Simultaneous Equa- tions," Econometrica, Vol. 30 (January, 1962). ' llProminent among them are the following: (1) R. Summers, "A Capital-Intensive Approach to the Small Sample Properties of Various Simultaneous Equation Estimations)’Econometrigg, Vol. 33, 1965. (2) A- L. Nagar, "A Monte-Carlo Study of Alternative Simultaneous Equation Estimators," Econometrica, Vol. 28, 1960. H. wagner, "A Monte—Carlo Study of Estimates of Simultaneous Linear Structural Equations," Econometrica, Vol. 26, 1958. For a brief description of these studies, and some other studies, see J. Johnston, Econometric Methods, 92, gig., Chapter 10, pp. 275-295. 118 efficiency.12 .5,2 Empirical Results We now present the empirical results for the respective structural demand equations Obtained by em- ploying the alternative methods of estimation described in the previous section. The variables appear in each equation without any transformations on them. In pre- senting the results, a standard table format is used throughout; namely, the estimated structural coeffi- cients are listed first, their estimated standard errors are directly beneath, and then the corresponding "t—values beneath the estimated standard errors. ”The corresponding results, one for each structural equation, are presented in Tables 5.2.1, 5.2.2 and 5.2.3. 5.3 Tests of Identifiability of a Structural Demand Eggation As we have pointed out in Chapter IV, the iden- tifiability of the coefficients in a particular equation depends first of all upon the number of jointly depen- dent and predetermined variablex excluded from that 13 equation. The validity of the g_priori exclusion of 12J. C. Cragg, "On the Relative Small-Sample Properties of Several Structural Equation Estimators," Econometrica, Vol. 35 (January, 1967) In this paper, Cragg arrived at the conclusion that three stage least squares and full information maximum likelihood estima- tors were better than two stage least squares, Nagar unbiased K-class and limited information single equation estimators. 13See page 95, Chapter IV of this study. 00H.m can» umummum mum mmsHm>uu mchcommmuuoo or» MH Hm>wH Home Mom H as unsoHMHsmHm Oman mum mosh .Ho~.~ cane “museum 119 one mmsHm>Iu one NH Hm>wH ucmu Mom m an uCMUMMflsmHm waamowumfiumum who mmumfiwumm ucoflowwmmoo snag omem.H- mon.~ «Hem.H ammo.~ ~mm~.¢ ammo.ou man.o moms.o noeH.o mmmm.o ¢m~¢.o eomm.o oHH~.ou ooMH.~ mmo~.o oboe.o mmHm.H Hemm.HHu some.ou H mama Hmv moHe.ou mmwm.ou seem.o mm¢~.ou otov.H moma.mu mmm¢.o om>¢.~ momm.o mm-.H mono.H mono.~ mHmm.on m~om.ou mh¢~.o mmm~.ou NHo¢.~ mmoe.o mnem.mu H mmHH Awe mo~m.Hu mmem.H Nosm.o mHmm.H smoo.m a¢v¢.Hu Hm-.o oHeH.H «mom.o mwom.o Heme.o momm.o nHom.ou mHHm.H mHHH.o ommh.o mHHm.~ ~mmm.oH- memm.Hu H x2: Ame mhmn.Hu Hvom.H momm.o eme¢.H HmHH.m HomH.Hu on-.o mmHH.H oma~.o cumm.o ohms.o mmHm.o ~mm~.on oomo.~ omoH.o non.o Noon.~ Hsom.HHu mmao.Hu H mama Ame muco.o omms.n memH.H Hoem.ou memm.o Hm~o.on mmmm.H mmH~.o ommm.o ~m~m.o maos.o umhe.o vmmo.o con.o ammo.o oeHH.ou momv.o mmm~.~n omm¢.ou H moo HHV smUHBmHadam nflaflflmm 924 mmB¢ZH9mfl BZNHUHhhflOU umOEUmm A0 meuom mammfluomhn 0:0 00 00:9 .0000 mum? coflumoom umnp Eoum mucmflowmmooo mHQmwum> pmcfleumpmoonm pmosHoxm 030 0030 0000300Q>£ 0:» m0 om0m00cm©0 nm>o 00 sowpmsom 0003003000 HmHsoflpumm men 00:0 mumoHosH on 00600 :0 mmposo cw tom: 00 omHmHusmpw p003 m£B« z Hmoa.o 00mH.H m©m0.H m©m0.N 00 .00 m : 0000.0 mNmm.N NONm.0 Nomm.m A0 .00 N «:pmHMOucmp0: N000.m momm.o Nvmv.H Nwov.N Av .hv H moq H H coflmsaocoo usmo Moo m moflpmfiuMpm HI Hue a m p .m.Q.m 00 030> 0000 0:0 < < < HMOHuHHU mo wsHm> AmqumEHumm mmHH mcflms muspoooum unnammmv mZOHBNDOm QZdZmQ AfimDBUDmBm mmB m0 NBHAHdemHBZmQH mOm BmMB d m0 Nmfizzbm N.m.m OHQMB 125 As expected, each of the structural demand equations is "identified." 5.4 Conclusions As expected, the three stage least squares (BSLS) procedure provided estimates that seem consis- tent with the day to day experience and theoretical reasoning. Day to day experience may force us to think that the price elasticity of demand may be inelastic since an increase in the burner-tip price of natural gas may not force the consumers of natural gas to switch to alternative fuel energies because, in general, the costs associated with replacing natural gas are higher. Similarly, theoretical reasoning reflects the "cross- elasticities" of demand, namely, price elasticities of electricity and fuel oil, with respect to natural gas 18 demand, are expected to have positive signs. The coefficients of Z and 2213 being the lagged (by one lt period) disposable personal income and the number of degree days, are expected to have positive signs. With minor exceptions (in the sense that the coefficients of the variables are not statistically significant at 5 per cent level for those whose signs of the coefficients are not in the right direction), we base our analysis with respect to the 3SLS method of estimation. 18Actually these are not cross-elasticities by definition because the variables involved are lagged variables. 126 Residential Sector: The signs of the coefficients except for the lagged index of price of fuel oil (Z1019 are in the right direction. Since we have assumed the linear logarithmic structural demand functions, the coef- ficient of Yth the index of burner-tip price of natural gas, is the price elasticity with respect to the demand of natural gas. As shown in Table 5.2.1, it is estimated as -0.4386. This indicates that a one per cent increase in the burner-tip price of natural gas ia associated with a 0.4386 per cent de- crease in the consumption of natural gas, all other things remain constant. The coefficient estimates of th! lagged consumption of natural gas, and Z7t! lagged index of price of electricity, as expected are positive. The economic implications of these variables are as follows: A one per cent increase in the average con- sumption of natural gas in the previous period is associated with a 0.2693 per cent increase in the suc- ceeding year. This increase may have come either from the lag in the behavior of natural gas consumption or from the "new" uses of gas (as explained in Chapter IV)19 made during that period. Similarly, a one per cent in- crease in the price of electricity causes 2.1306 per cent of increase in the natural gas consumption. The 19See page 100, Chapter IV of this study. 127 coefficient is also statistically significant at 5 per cent level. This probably is a significant result db— tained from the structural demand relation of the resi- dential sector which signifies the competition between electricity and natural gas. This substantiates the facts that are already noted in Chapter II.20 Contrary to the theoretical reasoning, the sign of the coeffi- cient of Z the lagged index of price of fuel oil, lot? is negative but is not significant statistically. This probably is because the price of fuel oil is consis- tently decreasing (except for the year 1954) over the period of consideration of this study and the burner- tip prices of natural gas are either increasing or re- maining relatively the same. Yet the consumption of natural gas increased over the same period. This indi- cates that fuel oil is losing its market in the resi- dential sector for reasons other than price differentials which have prevailed, and consequently the price variable of fuel oil may not enter into the decision making pro— cess of consumers concerning the choice of fuel energy. Both the coefficient estimates of lagged dis- posable income, thf and lagged number of degree days, ZZt! are positive. The estimate of Z is statistically 1t. significant both at 5 per cent and one per cent levels. The coefficient reflects the fact that the consumption 20See pages Chapter II of this study. 128 of natural gas would be increased by 1.8156 per cent for one per cent increase in the previOus period’s income. This, by definition, is not an "income elastiCity" because the "independent" variable is not the current disposable income but the disposable income in the pre- vious period. For our analysis purpose, we refer to it as "indirect elasticity." The high value of the coef- ficient of Z namely 1.8156, may be due to the inclu- 1t? sion of the effects of both the lagged disposable income and population in Z In particular, the effect of the lt' number of customers of natural gas in the residential sector, whose disposable income is included inlet! might have been included in the coefficient of th. Apart from this, the coefficient estimate reflects the impact of higher disposable income in the previous period that may cause people to have additional com- forts or to satisfy their desires (for example, by buying a new gas-using appliance). As one can expect, the colder the weather, the higher the consumption of natural gas and this fact is substianted by the sign and magnitude of the coefficient estimate of Z2t7 One can see from Table 5.2.1 that 3 SLS esti- mators differ considerably from the other four procedures. In particular, the LISE estimates differed considerably from BSLS procedures as well as from the other procedures. The sign of the coefficient estimate of Z7t:is negative and even the magnitudes of each coefficient differed 129 considerably. This possibly is because of high Kevalue where K = 2.4642, which is substantially larger than its asymptotic limit of 1. This high value of K or equiva- lently a higher least variance ratio in LISE proce- dure, may indicate, in general, the existence of high correlations between the jointly dependent variables that are included and the predetermined variables that are excluded from the structural demand equation. The relatively high value of K in LISE estimation procedure may be due to either (1) mis-specification (of) the . model, or (2) a larger loss in degrees of freedom rela- tive to the size of the sample, when "fitting the de- nominator" of the "least variance ratio," as compared to fitting the numerator.21 That is, linear combina- tions of the specified jointly dependent variables, in the structural demand equation, are regressed on not only those predetermined variables specified in that equation in the "numerator" but on all predetermined variables in the system in the "denominator." The ratio of these two then defines the least variance ratio. This suggests that the residual variance in the denomi— nator may be substantially smaller than in the numerator 21See for example S. G. Unger, "Simultaneous Equations System Estimation: An Application in the Cattle- Beef Sector," Ph.D. Thesis, Michigan State University, 1966. He also Obtained poor coefficient estimates for LISE compared to other procedures, pp. 90-119. Also see J. Johnston, 92, 923,, Chapter IV, pp. 288-290. 130 simply because the number of predetermined variables in the system is larger relative to the sample size. We cannot, however, say, a_priori whether a high K-value will result in a substantial influence on the estima- tors (relative to the K-class estimates) in a particular structural equation. In the case of the commercial and the industrial sectors also, LISE procedure provides estimates which are considerably different from the estimates of the coefficients obtained from 3SLS and other procedures. And the same arguments made above hold in these situations also. Commercial Sector: The coefficient estimates of each variable in the structural demand equation for natural gas in the commercial sector has its eXpected sign (using BSLS procedures). The estimated coefficient of Y4t! the in— dex of burner-tip price of natural gas, is -0.6049, which itself is the price elasticity of natural gas demand since the structural demand function is assumed to have a double logarithmic form. This indicates that there ‘will be a 0.6048 per cent increase in the natural gas consumption for one per cent decrease in its burner-tip price. The price elasticity of demand in the commercial sector is slightly elastic compared with that of the residential sector, which is reasonable to expect. The coefficient estimate of Z41! the lagged consumption of natural gas in the commercial sector, is 0.8542 and is 131 22 This is the only variable whose highly significant. coefficient estimate is statistically significant and consequently is important in explaining the consumption of natural gas in the commercial sector. The magnitude of the estimate of the coefficient indicates that one per cent increase in the consumption of natural gas in the previous period would increase the consumption in the succeeding period by 0.8542 per cent. As we have argued in the case of residential demand, this increase may have come from "new" uses that have taken place during the period. The magnitude of "indirect" cross-elasticities of demand with respect to the prices of electricity and fuel oil are 0.0655 and 0.0363, respectively. The "in- direct" income elasticity in this case is estimated as 0.5078 and the coefficient estimate of the lagged number of degree days is 0.3026. Industrial Sector: The estimated coefficients of all variables and Z have expected signs. The magnitude 2t. l3t. of the estimated coefficient of Y except Z 61! the burner-tip price of natural gas in the industrial sector is -l.3344. This also is the price elasticity of natural gas demand in the industrial sector. As the size of the estimator indicates, 22That is,the coefficient estimate is statis- tically significant at both one per cent and 5 per cent levels. 132 natural gas demand in industrial demand is elastic, thus indicating a 1.3344 per cent decrease in its consumption for every one per cent increase in the burner-tip price. As in the residential and commercial sectors, the esti- mated coefficient of the lagged consumption of natural gas is 0.9070 and is highly significant. And conse- quently this variable has considerable significance in explaining the consumption of natural gas in the indus- trial sector. The higher consumption in the succeeding period, as indicated by the magnitude of the estimate, may be eXplained by the intensity of use of natural gas in the industrial sector. This is already argued in Chapter IV, or it may be explained by the release of more gas from the residential and commercial sectors (where the gas service is a "firm” service) to the in- dustrial sector (where the service is based on "inter- ruptible" service). The coefficient estimate of the lagged index of price of electricity, Z is 4.2673 and is statistically 9 t' significant at 5 per cent level. The coefficient esti- mates of Z and Z the indexes of price of fuel oil 12t. 13tf and coal, are not statistically significant. The esti- mates of the coefficient of Zl3tldoes not have an ex- pected sign. So is the case for Z2tf And the coeffi- cient estimate of lagged industrial employment, Z6t! is 0.3919. The negative sign to the coefficient estimate of Z is rather unexpected. The data on the prices of 13t. 133 coal used in this study is taken from that of steam electric power plants data. And the steam electric power plants in Michigan do not use (or consume very little, at least prior to 1964) natural gas as an input to generate electricity. Because there is no other source of data on coal prices, the above source was used. Consequently, the index of the price of coal may not pro- vide a good measure of the effect of coal as a substi- tute for natural gas in the industrial sector. One would expect that the price of fuel oil in the industrial sec- tOr would have more effect than an elasticity of .4. This result, together with the wrong sign of the coal price elasticity, is rather discouraging. In the next chapter, an alternative demand model is developed and the corresponding results will be presented later in the chapter. The basis for de- veloping such a model is already discussed in Chapter I. CHAPTER VI THE DEMAND FOR NATURAL GAS: A DISTRIBUTED LAG MODEL 6.1 Natural Gas Demand and the Relevance of Distributed Laq Models The dynamic model developed in this chapter is based on the generally accepted idea that current deci— sions are influenced by past behavior. An economic re- action, say the reaction of the quantity of a certain commodity demanded brought about by a change in its price, is a process in time. This is because the behavior of the consumption cannot be adapted immediately to changes in the variables which condition it. This is well known in economic theory which often distinguishes between short run and long run reactions. Part of the reaction may take place after the lapse of one period, another part of the reaction taking place during the second period, and so on until after a certain number of periods the total reaction is completely realized. Then one may say that the quantity demanded is fully adjusted to the new price. Similarly, reactions to an increase in disposable income, on the consumption of a certain commodity, take their full effect only after some time has passed. In 134 135 such cases the economic reactions are spread over time and we have a distributed lag where the term "lag" is defined as the lapse of time between a cause and its effect. But in some cases, the lag may be a specific time, say three hours, or three days or three months. In such a situation we have simple lag. Thus the economic reactions described by behavioral relation- ships between the jointly-dependent or endogenous variables and the predetermined variables may be termed as processes in time. These processes eXplain the nature of adaptive behavior of endogenous vari- ab1e(s) to a given change in predetermined variables and can be described by a graph of economic time path. But before that, the nature and dependent relation- ships between the endogenous and predetermined vari- ables in economic models that cause the distributed lag response or adjustment mechanism will be explained. Of course, particular relevance is given to the beha- vior of demand for natural gas in each of the residen- tial, commercial and industrial sectors. There are several factors that reflect the distributed lag response in the consumption of natural gas either for a given rise in the burner-tip price or for an increase in consumer's income, but the following are the main factors: 1. psychological, 2. technological, 136 3. institutional.1 We can reasonably assume that people are slow to change their pattern of consumption or their level of living radically in response to changes in prices or income. This is mainly because of two reasons: (1) presence of psychological inertia in human beings, and (2) imperfect knowledge of the market. Psychological inertia prevents instantaneous readjustment of the behavior of the consumer to a changed situation. Once a housewife made it a habit to use a gas stove or gas furnace for space heating, it may be hard to convince her to buy an electric range when the gas stove is worn out unless there is a substantial advantage in buying an electric range. Habit is a powerful force and may persist although the reason for it has disappeared. Similarly, the imperfect knowledge of the market may lead to a lagged reaction. A.change in the burner-tip price of natural gas may not be known to every potential consumer. In that case, the total effect of the change in burner-tip price will only be realized when every potential consumer is fully aware 1L. M. Koyck, Distributed Legs and Investment Analysis, Amsterdam: North-Holland Publishing Company, 1954, pp. 5-9. M. Nerlove, "Distributed Lags and Demand Analysis for Agricultural and Other Commodities, Agri- cultural Handbodk No. 141, United States Department of Agriculture, Washington, D.C., June, 1958. PP. 1-4. 137 of the price change. Another set of factors that leads to a lag in the reactions of the consumer is the set of technological factors. The economic theory of the consumer choice is based on the fact that a consumer maximizes or satis- fices a certain level of satisfaction, subject to res- traints. We need not argue here the validity of the maximizing or satisficing assumption underlying consumer choice. The existence of either assumption is valid in this case because we are interested in showing the exis- tence of lagged reactions rather than arguing the pros and cons about these assumptions. Just as a firm pro- duces a product with fixed as‘well as variable factors, so a consumer produces a satisfaction with stocks of durable as well as semi-durable goods. The level of satisfaction he attains is mainly a function of prices of the durable or semi-durable goods, costs of main- tenance, apart from other things. For example, in case of natural gas, the level of satisfaction attained is in part a function of the prices of gas ranges, electric ranges, oil furnaces, gas furnaces, electric furnaces, and the prices of these fuel energies apart from the maintenance and other costs. Also the lifetime of each of the above equipments may play a part in accounting for the consumer's level of satisfaction. An increase in the burner-tip price of natural gas may provide an incentive to consumers to substitute other services for 138 it; but they may not do so immediately because it may be too costly to replace the gas-using equipment with others. Even if the consumer wants to replace his equipment, he may require time to buy an appropriate appliance. Apart from this, he may face the restric- tions from the distributors of these appliances because the stocks of appliances are maintained by them. The distributors are also susceptible to changes in the prices of the energy fuels. Technological factors making substitutes available also affect the consump~ tion of natural gas. That is, there should be a gas pipeline or appropriate appliance for a consumer to be able to substitute for a given change in the price of, say, electricity. There was an increase of 77 per cent, 62 per cent and 54 per cent in the consumption of natural gas in residential, commercial, and industrial sectors, respectively, during the period 1950-1955.2 This is mainly due to the vast expansion in transmission and dis~ tribution network through technological innovations and developments. The technological innovations made possible pressure welding for joint lengths of pipeline, develop= ment of thindwalled pipe which can withstand extremely high pressures, manufacture of larger diameter pipes, dew velopment of large capacity high speed compressors for booster stations. And these, in turn, made possible the 2Table 1.1.2, p.‘4, Chapter I of this study. 139 spread of the transmission and distribution network which made larger amounts of natural gas available. Because of the presence of these points, a complete and immediate adaption to a changed situation is not possible, thus causing a lag in the reaction of consumers of natural gas. The technological reasons play an important role compared to psychological reasons mainly because the consumption of natural gas is related to the stock of appliances rather than the variation in burner-tip prices of natural gas. It is also conceivable to think that disposable income may play a significant role compared to burner-tip prices because the effects in stocks of appliances can better be explained by changes in dis~ posable income rather than the changes in burnerwtip prices. Institutional factors may also produce a certain regidity which leads to a lagged reaction in the consue mers of natural gas. These factors influence the reacW tions through (1) the regulation, and (2) habit. For example, a given increase in the price of electricity or a given increase in disposable income may not bring an increase in the consumption of natural gas unless there is a pipeline connecting to the home. But pipeline cone struction can only be done through a regulatory process which may be of several years' duration. Similarly, burner-tip prices of natural gas are susceptible to changes in the prices of its substitutes. But gas and 140 electricity prices are regulated, oil and coal are not, so that it may be some time before all fuel prices ad= just to their proper competitive relationship, if they do so at all. The lag introduced by habit needs no eXw planation. Thus the regulatory aspects, together with habit induce lagged reactions, which would show up in the behavior of consumption through the movement along or the shift in the demand curve of natural gas. The next section is devoted to the description of how or in what form the adjustment mechanism may take place in the consumption for a given change in either the burner—tip prices or the disposable income. 6.2 The Description of the Adjustment Process of an Economic Reaction For simplicity, let us assume that the demand functions are functions of only one “predetermined” variw able, i.e., either burner-tip price or disposable income.3 Also the economic reaction may not be the same for each individual consumer of natural gas. That is, some indie vidual consumers may react immediately or after a short lag, some may be very slow for one reason or another and will react after a long period, and others may be grouped 3Burner-tip price is strictly not a “predeter= mined" variable as it is pointed out in Chapter 4. But for our simple explanation of the adjustment process, we assume temporarily that it is a predetermined variable. 141 between these extremes. So, generally, the lag in the reactions of a number of gas consumers will be distrie buted over a period of time and we describe the process of reactions in the adjustment process by a continuous curve. One may think that the value of an endogenous variable at time, say, t1, is the average value of a;l gas consumers. This value is, of course, subject to the lagged response. Let Yt be the quantity of natural gas consumed and let Xt be the disposable income that the community has at time t. Suppose at t = 0, say, an increase in Xt was introduced causing a change in Yt° The figure 6.2.1 would explain the possible description of adjuste ment process in the quantity consumed. For a given rise in income and hoping the continuation of the new level, 78‘3" Figure 6.2.1 Vt 9% [ ’,'\§‘ ___._,_.__‘,/I ‘~‘__‘_‘____0\\’t/d'xt f L LT_‘ ; L L 4 4 a L L ( L j t 142 the consumer may either replace an electric appliance with a gas using appliance or may have a new gas using air conditioner. This would increase his consumption of natural gas. Thus demand would increase at the begine ning periods and then decrease slightly as described by dY dt time-path of the adjustment process. If the consumers, the graph of dYt/dt. So ' essentially describes the on the other hand, anticipate an increase in their diam posable income, an increase in consumption may start earlier than the time t = 0, in which case the following figure will describe the timewpath. Similar arguments can be made with respect to the price variable, i.e. the effects of burner-tip prices on the consumption of natural gas. It should also be pointed out that the time-path or adjustment process of a reaction depends Xe *9“ Figure 6.2.2 0 . 7t h /r O Xt \ -....-I’” ‘~-\-,._ --....OWC/dxt o‘ t J L AA A I Lit 143 on the unit period. That is, the time path of Yt if Yt is measured in mcf (millions of cubic feet) per month, is different from the time path of Yt if Yt is measured in mcf per year. These explanations are simple and yet are capable of throwing some insights into the mechanism behind the adjustment process of our economic reactions. More complex situations can be thought of and described analagously. One can fit an appropriate mathematical model to describe the situations handled in the figures 6.2.1 and 6.2.2. Based on the economic theory of cone sumer choice and other g_priori assumptions that seem realistic for the study under consideration, one can construct a mathematical model capable of describing the behavior of the consumption of natural gas. This is what is discussed in the next section. 6.3 _The Development of_the Distributed Laq Model ‘ It was argued in Chapter II that the changes in total expenditures for consumption in response to changes in income may be considered from a different approach.5 It is reasonable to assume that consumers wish to even out their consumption to a certain extent over their "lifetimes" or at least over the foreseeable future. In suCh a case, an individual consumer tends to save when his income is temporarily high and to dissave when his income is temporarily low. The total consumption during 5Chapter II, p. 54 of this study. 144 any period of time is thus determined by the consumer's expected long-range income, not by his current income. Consequently, the total consumption expenditures tend to be stable relative to current incomes and a change in current income tends to affect consumption only ine sofar as it affects consumers' notions of their, "expected" incomes.6 With these ideas and with the basis of economic theory of consumer choice, the quan= tity of natural gas demanded can be assumed as a function of the burner-tip price of natural gas, price of eleCe tricity, price of fuel oil, "expected“ income, and nume ber of degree days. One should note that in this study, the words "expected normal income09 and “expected” income are invariably used to represent the same meaning. For simplicity, the word "expected” income will be used in this chapter. If we consider the residential sector, then the data for the above variables can be taken from the residential sector. The prices of electricity and fuel oil enter into the equation as substitutes for natural gas and the number of degree days and expected income variables enter into the equation as exogenous variables. That is, the demand equation can be expressed as: 6M. Nerlove, pp, git.. PP. 417° Also see pp. 20m 37, M. Friedman, A Theory_of Consumption Function, Princee ton: Princeton University Press, 1957. 145 = ,* . “'3'“ "" Ylt F(Y2t' Y7 t! Yet” 2"14):" 215 t) where the variables Yltf Yth Y7t, Y8tf and ZlSt are de- fined as in Chapter II.7 and ZI4t is expected disposable income in period t. Assuming linear form and adding a disturbance term, (6.3.1) can be written as: _ - , 15' (6.3.2) Ylt;— a0 + alYZt;+ a2Y7tg+ a3y8t,+ a4zl4t" + “5215 t + 8t where St = random disturbance or assuming double logarithmic form and adding an appr0e priate disturbance term, (6.3.1) becomes (6.3.3) ~--- log Ylt:= BO + Bl log Y2t;+ 32 log Y7t > p t + B3 log Y8t;+ a4 log zl4t. + as log Z15 t+ U: where Ut = random disturbance Now we have to define ZI4t? This is so defined that when substituted either in (6.3.2) or in (6.3.3) it should be able to provide us a distributed lag model which is capable of explaining the progressive nature of adaptations in the behavior of consumption of natural gas to a changed situation. In the literature of distributed lag models, the form of distribution of lag is appl’O'cEtCi-In-EC'1 in mainly three forms: 7Chapter II,pp.56“58 of this study. 146 1. Make no assumptions as to the form of the distribution of lag. 2. Assume a general form for the distribution of the lag and estimate the corresponding form. 3. Develop a specific model based on g Epigpi, considerations which yield a specific dis~ tribution of lag only incidentally. In developing the distributed lag model for our purpose, the third approach is used. So the expected disposable income is defined as: cum—.... * = “'3'“ 214+. ”:0 C1: Z14 tart: where Z14“;T = disposable income in period t e T T=Oglyzgo s o o of t=1029 o o o o o 18 8The first approach was used by F.F. Alt and J. Tinbergen. The second approach was used by:[ Fisher and L. M. Koyck, and the third was used by M. Nerlove, M. Friedman, P. Cagan, and J. F. Muth. All three ape proaches were discussed in Nerlove's study but the indie vidual studies can be seen as follows: F.F. Alt, u“Diem tributed Lags," Egonometrica, Vol. 10, 1942. P. Cagan, "The Monetary Dynamics of Hyperminflations,“ in M. Friedman (ed.), Studies in the Quantity Thegpy of Money, Chicago: University of Chicago Press, 1957. I. Fisher, "Note on Short—cut Method for Calculating Distributed Lags," International Statistical Bulletin, Vol. 29, 1937. M. Friedman, A Theory_of Consumption Function, National Bureau of Economic Research, Princeton: Princeton Uniw versity Press, 1957. L. M. Koyck, $93. pip. J. E. Muth, "Optimal Properties of Exponentially Weighted Forecasts,“ Journal of the American Statistical Association} Vol. 55, No. 290. 1960. M. Nerlove, lgg, gig. 147 Now one has to know the form of the coefficient CT in equation (6.3.4). As discussed already, it may be ex~ pected that the psychological, technical and institu- tional factors prevent an immediate adaptation to a changed situation but may cause an increase in the conw sumption in the earlier periods and tapering off in successive periods after reaching a maXimum. lncoru porating this idea, one can assume that the sequence C C C2, . . . . may be increasing in its first 0' 1' terms but must be continuously decreasing once the maxim mum has been reached. In many cases the coefficient C0 is the biggest of all and it is valid to assume that CT < CT-l for all T 3;l. This is precisely the kind of argument that is made in Section 2 of this chapter in explaining the timeapath of adjustment process, so it is reasonable to assume a geometric decrease in CT, i.e. (6.3.5) mm CT= KT; Ogl < 1; T = 0,1,2, . . . . Similar to this form is also the assumption of Koyck inlflfi ingenious development of distributed lag model.9 There is another advantage to using (6.3.5). It simplifies greatly the difficulties that arise in statistical estiw mation of the demand function and certain other 9L. M. Koyck, loc. cit.. pp. l9~22. Also a brief discussion on the various forms of CT based on assumptions made by several research workers in econometrics is given in E. Malinvaud, Statistical Methods of Economics, Chicago; Rand-McNally & Company, 1966, pp. 479m481. 148 characteristics which we discuss below. substituting (6.3.5) in equation (6.3.4): (6.3.6) 214:. E 7. 214%“: T-O = z + lZ + izz 4— 141: 14 tel l4t2~2 ° ‘ ' T . J')‘ Zgl4t.«=t+ ° ° ° t = 1,2, . . . . 20: O gul < l The final form of the demand function of natural gas in the residential sector can be obtained by the substituw tion of (6.3.6) in (6.3.2). By doing so, we have: (6.3.7) ~-~- Ylt= a0 + alY2t+ a2Y7t+ a3 8t f’og 'r ‘ + a4 2 A Z T=O 14 ten: + “5215 t + 8t This equation can be estimated, but unfortunately it is too difficult for estimation purposes because it inn volves an infinite number of parameters, namely, a0, a1, 2 +. a2. a3, a4, a5, la4, l a4 . . . ., to es-imate and also because of possible multicollinearity due to the pree sence of the variables Z 0,1, . . . .). Fore l4t=¢ (T = tunately, we can avoid all of these difficulties by differencing the equation (6.3.7). This can be done as follows: Lagging the equation (6.3.7) by one period and multiplying the resulting equation by A, one obtains: 149 1t-1 ' Mo + M1Y2t-1 + ML4 [214 t-l+ ”1413-2 2 + iet_ (6.3.8) ---- H + lo. + M 2Y7 t-l 3Y8 tel + M‘szls t-l l Subtracting (6.3.8) from (6.3.7) and rearranging the terms (6.3.9) —--«_- Ylt - ml t_1= non-M + a1(Y2 t- KY2 tm1) + “2(Y7 t " W7 t-l) + “3(Y8 t " 7W8 t-l) + “4 z14 t + “5(315 t ”15 tel) + (at - let-l) This equation is suitable for estimation purposes in the sense that it is much simpler compared to (6.3.7). .This is because, in the first place, it involves only the param meters a0, a1, a3, a and l, subject to certain res~ 4' “5 trictions on the coefficients of the variables ngbml In the second place, the lSthf multicollinearity prOblem due to Z (i = 2, 7, 8) and Z l4t-’t (T = 0.1, I 0 O ) is completely eliminated in equation (6.3.9). But the parameter 1 is now overidentified in the sense that the estimates of it are provided by the ratios of the coef- fiCients of either Y2t-1’ Y" or Y7t-1' Y or Y 2 t 7 t 8 t-l’ Yator le t-l' 215 t‘ 80 in order to estimate the cor- responding coefficients we assume various values for'l in the admissible interval [70 1) and the equation with 150 respect to a value of A is selected for which SSE, the sum of squares of residuals, is minimum. The method of estimation is described in Section 6.5. Equation (6.3.9) can be more conveniently are ranged by defining the following: (6.3.10) —--- Yit = Ylt- ”it-1 Yiét = th ' “(2 t-l Y; t = Y7 t " W7t-1 Y5. = Yet ' W8t-1 235 t = Z15 t " 7‘215 t-l as = (10(1 - 7x) 8: = 8t - let_1 When these new variables are substituted, (6.3.9) can be expressed as: (6.3.11) Y1 a0 + “1351-." a2Y7t+ a3Y8t+ (14214,: * * + a5215t+ 8t a. .- 6 6 This form is used for estimating purposes. The method by which this equation is estimated is discussed in Section 6.5. Again considering the equation (6.3.3) as the demand function, the corresponding expected disposable income is defined as: (6.3.12) ---- log 2* = S, dT log Z 14 t T=0 14 t-q: 151 where the coefficients dT decrease geometrically (T = O, l, . . . .) as discussed earlier. Then we define (if: = 6”” T=O,l,2..... and after substituting this in (6.3.12), we have: a 109 21,” = 2: 6" log 2 T=O L4t-T This is substituted in equation (6.3.3) and the resul- ting equation can be expressed as: (6.3.13) ---- log Ylta (30 + [31109 Y2t+ (32109 Y7t + (33109 Y8t+ (14 E109 Zl4t +5logZ l4 t-l + 5210 Z 9 14 t-l ' ' ' ' + 0.5109 ZlSt+ Ut Lagging this equation by one period, multiplying the resulting equation by 5 and subtracting it from (6.3.13), one Obtains: (6.3.14) ---- log Ylt- 5 log Y1t_1= (30(1 - 5) + [31 [log Y2t- 5 log Y2 t-l] + [32 [log Y7t - 5 log Y.7 t-l] + ‘33 [“9 Yet" 5 1°9 Y8 t-l] + (34 log 2141-. + (35 [log Y15 t- 5 log Z15 t-l] + Ut - 5Ut_1 152 Again defining the following terms as before, log Y‘it = log Ylt - 510g Yl t—l log Y; t = log Y2 t - 5log Y2 t-l log Y; t = log Y7 t - 5log Y7 t-l log Y’B‘ t = log Y8 t - 5log Y8 t-l 109 zit: = 1°9 z15 t " 5109 Z15 t-l and ($5 = 30(1 - 5) U: = Ut - Gut-l and substituting in the equation (6.3.14), we Obtain the form suitable for estimation purposes: -u—- = * (6.3.15) Y‘it [30 + (31 log Y§t+ [32 log Y7t + B3 log Y*t+ (34 logY 8 14t: * * 151;+ U1: + B5 log Z By giving various values to 5 in the admissible interval [TD 1) and by using the method of estimation described in Section 6.5, equation (6.3.15) is estimated. The rem sults are tabulated in Table 6.5.1. Similar to equations (6.3.11) and (6.3.15), the demand functions of natural gas for commercial and induSm trial sectors can be developed. Assuming that the form of the demand function in the case of the commercial sec— tor is linear, the demand function of natural gas is defined as: 153 (6.3.16) ---- Y3t= Y1 + Y2 Y4t+ Y3 Y9t+ Y4 Yiot * + Y5 Z1.61;+ Y6 Z151;+ Vt where the variables, Y3t' Y4 t’ Y9 t’ Ylot and 215 t are defined as before10 and Z16t: = expected number of natural gas customers in the commercial sector in time period t Vt = random disturbance The variables Y4t' Y9 t’ and YlOtare included in the demand function because they are the price variables of the natural gas and its substitutes, electricity and fuel oil. The variable Z is included because of the 15t: reasons argued as in the case of the residential sector. As before, in order to explain the adjustment mechanism is so defined that it should be capable of ' * 1“ Y3t’ Zl6t providing a distributed lag model. t! the expected 216 number of natural gas customers in the commercial sec- tor, is used to reflect the influence of the number of customers of natural gas on the consumption. For example, if two different places, maYbe cities or states, were to be compared, in which all factors other than the number of customers of natural gas were the same, it is Obvious that the place which had more natural gas customers tends to consume.more than the place with fewer natural gas cuStomers. And without loss of generality, we might argue that the total consumption expenditures tend to 10Chapter II ,pp .56-58 of this study. 154 be stable relative to the number of natural gas customers in the current period, and a change in the consumption of natural gas is significantly explained by the "expected number of natural gas customers" in the commercial sector. This is because the "expected number of natural gas cus- tomers" in the commercial sector reflects the consump- tion of natural gas by the new customers, apart from the customers already using natural gas. The new customers, in a given locality, may be brought into use either by replacing old, non-gas using appliances with new gas- using appliances or by laying a new natural gas pipeline to the given locality. After appropriately defining Zietzand substituting it in the equation (6.3.16) we can Obtain: (6.3.17) ---- Ygt = Y1 + YZYZt” Y3Y3t+ Y4Y'iot + Yszl6t+ Y6215 t+ V: where Y3}. = Yst' GY3t-1 3’21; = Y4t" 9Y4t-1 Y3». = Y9t' BY9t-l Y1501: = Y101-.” 9Y10t-1 z15t = 2151:" ezis t-l Y1 = Y1(1 - 6) * - Vt I Vt th-l 155 Again assuming double-logarithmic form in the demand function, that is, assuming the demand function as: (6.3.18) ---- log Y3t = 711 + 7'12 log Y4t+ n31og Y9t + T74109 Y10t+ ”5109 Z151; * + T16105" Zl6t+ et an equation similar to (6.3.17) can also be Obtained in this case as: (6.3.19) ---- log Y'gt = n: + 712109 Y*t+ 713109 Y* 4 9t: + 1r14.1091 Y1Ot+ T151“? 215 t + 1r16mg z161:+ 6: where log Y3 t = log Y3 t - wlog Y3 t-l log th = log Y4t - (clog Y4t-1 log Y9t = log Y9 t - wlog Y9 t-l 109 Y10t ' 109 Y10t ‘ “109 Y10 t-l Log Z15 t = log 215 t - wlog 215 t-l n1 = n1 (1 - w) e;. = et - wet_l Equations (6.3.17) and (6.3.19) are used for estimating the respective coefficients and results are tabulated in Table 6.5.2. As in the commercial sector, the demand function for natural gas in the industrial sector is assumed as: 156 (6°3'20) "" Y51-.= ”1 + V2 Y6t+ V3 Y111:+ V4 Yth + v5 Y131:+ v6 2151: * + ”7 2171:" Vt where Y5:! Y6 t' Yllt' Y12t’ Y13 t’ ZlStand Z171:are 69'" fined as before11 and 217t: = expected industrial employment in industrial sector in time period t Vt = random disturbance. Being the burner-tip price of natural gas and the prices of electricity, fuel oil and coal as substitutes for natural gas, the variables Y6 t’ Yll t' Y12 t' and Y are is 13t. included in the equation (6.3.20). The variable 2 lSt: included to measure the effect on the consumption of natural gas in the industrial sector due to changes in temperature. The reason for including the industrial employment variable in the demand function of natural gas for the industrial sector as already mentioned in Chapter IV is mainly to show the effect of industrial output on the consumption of natural gas. Just as argued in including "expected income" in the demand function of natural gas for the residential sector, we argue here that the consumption of natural gas in the industrial sector depends on "expected industrial llSee 3356-3. Chapter II of this study. 157 output" in the sense that the industrial consumers expand their production activities on the basis of what they feel about the future and consequently the total of consumption of natural gas tends to be stable relative to current industrial output and a change in the current industrial output tends to affect consump- tion only insofar as it affects consumers' notions about the "expected industrial output." Since we are using industrial employment series to measure the in- dustrial output series, we include "expected industrial employment" to explain the consumption of natural gas. Defining the "expected industrial employment" as --sm-I * = (6.3.21) Zl7t: E T-O T w Z17 t-T t = 1,210 o o and substituting in (6.3.20) one Obtains the following function: ....-- = * * * , * (6.3.22) Ygt V1+V2Y6t+ v3 Y11t+ x4 Y12t * * + v5 Y13t+ V6 Z15:;+ V7 Z171: * + vt where * = _ Y5t YSt W5t-1 y* = Y - WY 6t 6t 6t-1 * = - Yllt Yllt W11 t-l * — _ Y121-. Y121: W12t-1 y* - Y l3t ‘ 13t‘wY13t-1 158 * — .— Z15 t ‘ Z15 t W215 t=1 * - - v1 - Vl(l W) * — - Vt ‘ Vt th-l By using the estimation method described in Section 6.5, the coefficients vi, v2, v3, v4, v5, v6, and v7 can be estimated. Assuming the demand function in log-linear form, the appropriate demand function can be derived as: (6.3.23) ---r 109 Ygt; = H1 + H2 109 Y21;+ p’3 log Yllt; + (L4 109 Y12t+ “'5 109 Y”in + ”6 109 Zist+ ”7 109 2’171: + s: where log Y; t = log Y5 t "' (9109 Y5 t-l log Ygt = log Y6. - (>109 Y6t-1 109 Y1lt; = log Y11t:" wlog‘ylltrl 109 Yiz t = log Y12 t ' (p109 Y12 t-1 109 Y13 t = l°g Y13 t ‘ @109 Y13 tel log 215 t = 109 Z151: " $9109 Z15 t-l ”1 = u1(l - ¢) 5: = St ' wst-l Equation (6.3.23) is used to estimate the respective coef- ficients and the corresponding results are tabulated in Table 6.5.3 (see Section 6.5). 159 6.4 Statistical Properties of the Model In this section some of the important charac- teristics of the model are discussed. It is already noted that the distributed lags arise in theory when any economic cause realizes its effect only after some lag in time, so that the effect is not felt immediately at a single point of time but rather is distributed over a period of time. This is what makes an economic reaction a process which describes the progressive nature of adaptations in behavior of endogenous variables. There» fore, any formulations of economic relationships that may give rise to distributed lag models is related to the following two prOblems: l. estimation of the speed of adjustment, i.e., the estimation of a parameter that indicates the time period that has to elapse for the long—term re- action to take place, and 2. estimation of demand elasticities of price and income.12 Now by considering any one of the demand functions de— veloped in the previous section, it will be shown that certain coefficients of the demand function reasonably indicate the measure of the speed of adjustment and the price and income elasticities of the demand for natural 160 gas. Consider the equation (6.3.14) in a slightly difw ferent form (6.4.1) ---- AY = 60(1 - 5) + Bl log Y 1t 2t - 515 log'YZtQl + [32 log Y7t- 5(32 log Y7 tel + [33 log YBt- 5B3 log Y8 tel + $4 log 214t;+ B5 log zlSt. 535 log Z - (l e 5) log Y 15t-1 lt-l + Ut - 5Ut_l where AYt = log Ylt- log Yl t-l when an equilibrium is attained, AYltL= O and calling the newequilibriumT-o-gm'YI-IL it follows from the above equation that13 (6.4.2) —-~- 139—f; = fi+§7 Eu - 5) + (31 log Y2t - 615 log Y2 t-1+ (32 log Y7t " 5B2 109 Y7 t-1+ ‘33 log Y8 t - 5B3 log Y8t—l+ (34 log 214+. + ‘55 109 Z15 t ‘ 5B5 109 Z15 t»: + Ut - GUFSE] substituting log Y (1 - 5) for the corresponding 1t terms in (6.4.1) it follows that 13L. M. Koyck, oc. cit., p. 23. 161 (6.4.3) ---- AY = (1 - 5) ° log Y 1t. 1t. - (1 - 5) log Y i.e., log Ylt- log Y1t-1= (l - 5)E.og Ylt- log Ylt-fl This can be interpreted that the actual change in the con- sumption of natural gas in period t is the proportion of the change that would be necessary to attain equilibrium in that period. This would indicate reasonably about the progressive nature of the adaptive behavior in the consumption of natural gas. And so this coefficient can be taken to indicate the speed of adjustment. 'The maximum value that the speed of adjustment can take is 1 since 0 5_5 < l. The higher the value of (1 - 5), the higher the speed of adjustment, and conversely. At one extreme (l — 5) can be equal to 1 in which case = log Y log Y 1t 1t that is, the speed of adjustment is so great that the consumption reaches its equilibrium in the unit period of time for a given change in the predetermined variables. \Ofij‘r Figure 6.4.1 A\ ‘ -— ' (\-6) : \‘0 MY“; 5 a 70. \ r ‘I 8) ‘ O. l tel 162 At the other extreme, (l - 5) can equal zero in which case log Y is reached to a changed situation only lt after a long period of time. This period can be the longest of the periods of adjustment. The corresponding graphs are described in Figure 6.4.1. Similar arguu ments can be made for the rest of the demand models developed in the previous section. Again, if we consider the double-logarithmic demand function specified as in equation (6.3.14), the coefficient estimates of log Y and log Z are res- 2t. l4t: pectively the price and income elasticity estimates of natural gas demand. Thus with the models developed in Section 6.3, we may estimate the coefficient of the speed of adjustment and the price and income elastici- ties of natural gas demand. Another main characteristic of the models de— veloped in the previous section is that the method of estimation described in Section 6.5 provides us the consistent estimates for the coefficients of the respective variables. One possible difficulty of esti- mating the demand models is already noted in Section 6.3. This difficulty is avoided by assuming the values to the coefficient of the lagged variable of the consumption in [T6, 1). It was argued by Professor Koyck that if the random disturbances, say Ut in (6.3.14) are all cor- related as: 163 then it is possible to Obtain consistent estimates of the coefficients provided p is equal to the coefficient of the lagged variable of the consumption, i.e., pro- vided that p = 5.14 He further argued that "there is empirical evidence that (6.4.4) is not contradictory 15 Thus if to quite a large body of economic data." we assume that the random disturbance terms follow a first-order Markov scheme, then following Professors Koyck and Hildreth, it is possible to Obtain consis- tent estimates.16 Thus, these models are capable of explaining the adjustment mechanism in the behavior of consumption by providing us the consistent esti- mates of the speed of adjustment and the burner-tip price and income elasticities. And at the same time, these models should provide an alternative means of looking at the demand situation other than the demand from the simultaneous equations system model. In the following section, the results of the models are pre- sented. 14L. M. Koyck, loc. cit., pp. 32-37. lsIbid., p. 34. 16C. Hildreth and J. Y. Lu, "Demand Relations with Autocorrelated Disturbances," Technical Bulletin 276, Agricultural Experiment Station, Michigan State University, November 1960, p. 14. 164 645 Results of the Model In this section, the results of the demand models developed in Section 6.3 are presented. Only the log—linear demand models are estimated. In that section, we have noted the possible difficulties in estimating the parameters of the respective models. These difficulties can be seen as follows: Consider the demand model ____ * = * * (6.5.1) Ylt a0+a1Y§t+ azY;t+a3 Y8t + a Z + a Z* * 5 14t 6 lSti-et t = 1'2, 0 e o e where the variables are defined as in Section 6.3. equation can be expressed in matrix notation as (6.5.2) ---- y* = 3* a + 8* where Yfiul “o * Y*= Y12 : (1: (11 * Y1,18 “6 _ * * * 1 7‘ Y21 Y71 Y81 Z141 * = _ * z 1 X Y32 Y72 Ysz Z142 — * * 1 x Y3,18 Y7,18 Y8,18 Z14,18 18 This * Z15 1 * Z15 2 * Z15,1 165 and 'k 8123 let us assume that a: are normally and independently distributed with zero mean and same variance 62.17 Then the likelihood function of 6* can be expressed as (6.5.3) -'--- F(e*; x, a, 0'2) = (___1_2_)18/2 2nd Exp 2 g 8*. 8* g 20 But from (6.5.2) 8* = Y* - 2* a (6.5.4) ---—- F(Y*; i, a, .52) = (__1__2_)18/2 2nd 1 * EXP ( 2 (Y ”2* “Viv-2* a) ) 20 As denoted, this likelihood function depends on the para- meters 1, a and oz. The dependence of F(‘) on 1 can be seen through the definitions of Y* and Z. More specifi- cally, it can be seen as follows: 17The results are presented for double—logarith~ mic demand functions because they came out better statis- tically compared to linear demand functions. But the method of estimation is described for linear form because of the Obvious simplicity in the notation. The analysis is exactly the same for the double-logarithmic demand functions. * — Y1,1 Y1,1 M"1,0 Y1,1 Y1,o * -— ... = ... Y " Y1,2 Y1,2 ”1,1 Y1,2 " Y1,1 ( * _ Y1,18 Y1,18 ”1,17' Y1,18 Y1,17 = Y - 13? Similarly, Z* can be expressed l-Y21"’215l lYZO"°'O’ZlSO *.._ .. .. ”’1 Y22"‘2152 " lY21°°"°'2151 1 -- Y ° ' Z15 18 1 Y o 2 2,18 ' 2,17 ‘ ' ' ' 15,1 = z - )[z- and Y*—z*a=(Y—iY)-(z-)Cz')a substituting this in (6.5.4) F(Y: 7x. a. <52) = (_l_§)18/2 EXP E - ‘Lz' [EY-AY') 2nd 26 - U -(z-).z) a] [(Y-x'f) - (Z—lZ) a ( Now the parameters 1, a, 62 are estimated by maximizing this likelihood function. To do that, we take the loga- rithm to the above equation and the relevant part of the logarithm of the likelihood function is given by (6.5.5) --=-- L(Y; A, a, 52) = _ Jig log 0'2 _ 4.2. 26 BY—KY) - (Z-XZ) a]. [(Y-x'Y') - (z-iE) a] g 167 Following Dr. Hildreth, we consider the sum of squares of residuals, s(Y:).,a)= [(Y-iY') -(z-iE)a]'EY-fii) -(z—).E) a] and the values of l and a that minimize S are those which a?)18 So to find estimates of the maximize L(Y; l, a, parameters A and a, we minimize S. But direct methods of finding minimum appear quite cumbersome and hence certain 19 I The iteraw interative procedures are to be adopted. tive procedure to minimize S followed in this study is quite similar to that followed by Dr. Hildreth. Various values for 1, equally spaced at intervals of length 0.1 in the admissible interval of 1, (TD, 1) are given and then S is minimized with respect to a. The corresponding results for the demand equations (6.3.15), (6.3.19), and (6.3.23) are now presented in Tables 6.5.1, 6.5.2, and 6.5.3. 18C. Hildreth and J. Y. 1411, ICC. 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(2)and (3) Minerals Yeafbodk, Bureau of Mines, U. S. Department of Interior, Washington, D.C., editions for 1948-1964. Col. (4) compiled from.Tables A.1.2 and A.1.3 (See Source of Table A.1.3). Col. (5) Refinery and terminal prices for No. 2 fuel oil, Detroit Area, Platt'g Oil Price ngdbook and Almangg, editions for 1955-1963; 1964, Petroleum Facts and Figgges, 1965 edition. 192 TABLE A.1.5 NATURAL GAS CONSUMPTION AND DEMAND FACTORS, COMMERCIAL SECTOR, MICHIGAN, 1946-1964 (I) (2) (3)7 T4) (5) Cons. of Burner-tip ' Price of Price of Year Natural Gas price electricity fuel oil (mcf) _(é/mcf) (élkwh) (gZQal) 1946 6.16 74.3 2.70 5.23 1947 7.04 72.0 2.58 7.76 1948 6.88 72.5 2.62 10.27 1949 7.32 83.4 2.84 6.98 1950 10.75 77.2 2.86 7.74 1951 13.27 75.9 2.83 8.65 1952 13.87 77.5 2.80 7.99 1953 14.01 86.7 2.76 7.73 1954 15.34 80.2 2.74 7.84 1955 16.52 80.5 2.67 8.81 1956 20.31 86.1 2.67 9.60 1957 26.62 79.5 2.64 10.02 1958 32.02 79.6 2.55 8.86 1959 38.46 80.4 2.53 9.07 1960 43.00 79.8 2.53 9.10 1961 42.84 89.8 2.51 9.10 1962 64.50 88.1 2.48 8.95 1963 68.68 86.4 2.45 8.60 1964 74.37 2.42 8.60 86.0 Source: Cols.(2) and (3), see Source of Table A.1.4. Col. (4) see Source of Table A.1.4. Col. (5), Refinery and Terminal Prices, No. 5 Fuel Oil, Detroit Area: Platt's Oil Price Handbodk and Almanac. See Source of Table A.1.4. 193 TABLE A.1.6 NATURAL GAS,CONSUMPTION AND DEMAND FACTORS, INDUSTRIAL SECTOR? MICHIGAN, 1946-1964 (1) (2) (3) (4) 75) (6) Cons. of Burner-tip Price of Price of Price of Year Natural Gas price electricity fuel oil coal (mcf) (gzmcf) (pikwh) (eggal) 4(S/ton) 1946 23.11 43.9 1.20 4.76 5.99 1947 27.62 38.5 1.19 7.84 7.80 1948 23.26 48.8 1.26 9.47 7.96 1949 27.47 55.0 1.26 6.74 7.61 1950 39.20 50.3 1.23 7.49 7.83 1951 39.96 53.2 1.25 8.40 7.71 1952 45.51 51.0 1.27 7.74 7.77 1953 59.04 54.1 1.24 7.11 7.82 1954 53.23 54.8 1.25 7.09 7.43 1955 60.30 53.3 1.17 8.06 7.17 1956 65.80 54.8 1.23 8.61 7.63 1957 73.55 53.6 1.26 9.02 7.94 1958 90.25 54.9 1.35 8.19 7.98 1959 100.17 61.3 1.30 8.57 7.88 1960 122.02 55.2 1.28 8.60 7.71 1961 144.21 55.4 1.30 8.60 7.65 1962 141.32 53.1 1.24 8.45 7.36 1963 149.91 53.5 1.22 8.10 7.33 1964 168.21 53.1 1.20 8.10 7.28 *This sector excludes the consumption of natural gas by steam electric plants. ‘ Source: Cols. (2) and (3), see Source of Table A.1.4. Col. (5), Refinery and Terminal Prices, No. 6 Fuel Oil, Detroit Area: Platt's Oil Price Handbook and Alm nac. See Source of Table A.1.4. Col. (6),"Steam-Electric Plant Factors, An Annual Study by the Department of Economics and Trans- portation," National Coal Association, Washington, D.C. W111...» TABLE A.1.7 194 NATURAL GAS DEMAND FACTORS, RESIDENTIAL SECTOR, MICHIGAN, 1947-1964 (1) (2) (3) 1(4)?» (5) (6) (7) Year Y1 Y2 Y7 Y8 Zia Z15. 1947 44.07 96.76 98.53 85.23 7,873 6,864 1948 43.81 98.23 97.80 111.60 8.584 6,120 1949 47.58 105.01 103.30 103.07 8,663 6,635 1950 75.71 96.53 105.13 101.49 9.776 6,684 1951 99.31 94.72 103.66 105.55 10,595 6,643 1952 103.04 96.08 101.83 105.15 11,074 6,187 1953 103.88 109.75 99.63 104.76 12,540 6,132 1954 118.48 107.61 97.80 117.15 12,639 5,998 1955 128.17 105.23 96.34 112.19 13,873 6,749 1956 155.14 106.36 94.87 115.16 14,843 6,197 1957 170.00 104.89 93.41 119.72 14,781 6,399 1958 173.21 106.70 92.67 111.00 14,648 6,905 1959 192.96 107.49 92.67 107.23 15,383 6,787 1960 201.98 107.83 93.41 102.48 15,852 6,688 1961 218.08 112.34 92.67 99.21 15,873 6,637 1962 234.48 112.47 92.31 99.90 16,741 7,179 1963 242.89 112.35 91.94 100.20 17,939 6,047 1964 251.97 112.24 91.21 91.58 21,557 6,804 Source: Cols. (2)-(5), (7), derived from Tables A.1.4 and A.1.l. The base period 1947-1949 is taken for computing the index. Col. (6), Michigan Statistical Abstracts, Sixth Edition, 1966 195 TABLE A.1.8 NATURAL GAS DEMAND FACTORS, RESIDENTIAL SECTOR, MICHIGAN, 1947-1964 (1) (2) (3) (4) (5) (6) (7T 1: at E; 22 Z; Z7 zleO 2” 1947 6,938 6.696 37.74 99.63 60.06 101.16 1948 7,873 6,864 44.07 98.53 82.23 96.76 1949 8,584 6,120 43.81 97.80 111.60 98.23 1950 8.663 6.635 47.58 103.30 103.07 105.01 1951 9,776 6.684 75.71 105.13 101.49 96.53 1952 10,595 6,643 99.31 103.66 105.55 94.72 1953 11,074 6,187 103.02 101.83 105.15 96.08 1954 12,540 6,132 103.88 99.63 104.76 109.75 1955 12,639 5,998 118.48 97.80 117.15 107.61 1956 13,873 6,749 128.17 96.34 112.19 105.23 1957 14,843 6,197 155.14 94.87 115.16 106.36 1958 14,781 6,399 170.00 93.41 119.72 104.89 1959 14,648 6,905 173.21 92.67 111.00 106.70 1960 15,383 6,787 192.96 92.67 107.23 107.49 1961 15.852 6,688 201.98 93.41 102.48 107.83 1962 15,873 6,637 218.08 92.67 99.21 112.83 1963 16,741 7,179 234.48 92.31 99.90 112.47 1964 17,939 6,047 242.89 91.94 100.20 112.35 Source: Derived from Tables A.1.7 and A.1.4. 196 .¢.a.¢ manmfi m0 mousom mom .hmv .aOU .h.a.< manna m0 mousom mom .m.a.< magma Eoum ©m>auma .Aoav .AvaAmv .maOU “mousom mm.maa omN.a Na.moa N¢.am m®.m0 Na.moa Om.om ON.maa hm.¢h voma hm.maa ONN.a am.boa vm.Nm Om.¢® Na.moa N¢.am mh.maa m©.m® mwma om.maa mma.a aa.moa ®©.mm wm.mv am.hoa vm.Nm hm.maa Om.¢® Noma V0.moa mha.a aa.moa Ov.¢m oo.m¢ aa.moa ®©.mm ON.maa wm.N¢ aoma mm.moa mma.a mh.moa O¢.¢m ©¢.mm aa.moa O¢.vm vo.moa OO.m¢ coma mh.¢oa moo.a v~.moa ma.mm NO.Nm mh.moa O¢.vm mm.moa wv.mm mmma m©.voa moO.a wa.oma am.mm N@.©N vm.woa ma.mm mh.voa NO.Nm mmma mm.maa 0mm aa.maa m®.mm am.ON Va.oma am.mm m©.¢oa N®.®N hmma ow.maa 0mm ¢®.moa m®.mm mm.®a aa.maa m®.mm mm.maa am.ON omma h¢.maa 0am OO.¢m fiN.NOa vm.ma ¢©.moa m®.mm mm.maa mm.©a mmma Na.vaa mvo m®.Nm mm.NOa ao.¢a oo.¢m ¢N.Noa h¢.maa Vm.ma mmma aO.NOa hmo ow.mm mv.¢oa hm.ma m®.Nm mm.NOa Na.¢aa aO.Va mmma am.mm VNQ Nh.moa O©.moa hN.ma om.mm m¢.voa aO.NOa hm.ma Nmma No.aoa aoo am.Nm Nb.®oa mh.oa Nh.moa O©.moa am.mm hm.ma amma mb.moa wow m®.mm hm.moa mm.h am.Nm Nh.@oa N©.aoa mb.oa omma m¢.mm hhv wa.mma ©5.hm mm.® m®.mm hm.moa wh.moa mm.h mvma bb.¢m mvw mo.mm hN.®m mo.h ¢a.mma ©h.hm m¢.mm mm.® mfima om.hm mm¢ ah.N© mh.OOa ©a.© mo.mm hm.©m hh.vm mo.h hwma maN @aN aaN mN wN 0a? 0% UN m? 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