Residential energy demand in the United States

Residential energy demand in the United States

Regional Science and Urban Economics 10 (19X0) 371 386. 0 North-Holland RESIDENTIAL ENERGY DEMAND IN THE UNITED STATES A Regional Econometric Analy...

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Regional Science and Urban

Economics

10 (19X0) 371 386. 0 North-Holland

RESIDENTIAL ENERGY DEMAND IN THE UNITED STATES A Regional Econometric Analysis T.R. LAKSHMANAN Bostmt Uniwr.sit_v,

and William

ANDERSON

Bosrcm, MA 0221.5, USA

Received March 1980 A static equilibrium and a dynamic partial adjustment model of residential demand for electricity and natural gas are presented and estimated for the United States over a recent period characterized by sharply increasing energy prices. The static model is estimated using Ordinary Least Squares while the instrumental variables method is used for the dynamic partial adjustment model. The estimates of long-run elasticities suggest the residential demand for electricity and natural gas are pric’e ar.d income elastic. Intercept and slope dummies used in the models identify significant regional differences in demand functions.

1. Introduction The formulation of energy policy and the assessment of alternative energy futures depend in large part on our shared understanding of diverse components and the major determinants of energy demand. Recent shortages and price increases of petroleum products underscore the importance of demand for other energy forms and the potential for interfuel substitution. For instance, the viability of conservation policies aimed at taxing energy forms such as gasoline or fuel oil depends to a great degree on the dynamic price elasticities of demand. The estimation of such demand elasticities for major energy forms --- oil. natural gas and electricity .- irr the residential sector is the focus of this paper. Three features characterize the model of residential energy demand presented here. First, we recognize that energy forms such as natural gas. electricity or heating oil do not yield utility in and of themselves, but are desired by the residential consumer as an inpllt to activities or processes that yield utility. Such activities use fuel burniq capital stock such as a water heater, air conditioner, stove or a lamp, which need energy as an input. The residential demand for energy is thus a derived demand for the services provided by that capital zquipment in conjunction with an energy source. If price of energy rises in this context, cutback in energy use can be anticipated. In the short run, since the capital stock and its technical characteristics are given.

the consumer can reduce the frequency and intensity nf use of the capital stock - e.g., turn the thermostat down, or drive less miles per week. Over time, however, if energy prices remain high, there will be a shift to a more energy-efficient capital stock, The more common static, equilibrium models focus upon only the demand for a fuel assuming instantaneous adjustment in the capital stock to changes in fuel demand [Honthakker (1951), Wilson (1971), Anderson (1972)]. Our model is a dynamic, partial adjustment model that makes more explicit the interactive r .ture of the demand for energy and its requisite fuel-using capital. Second, we depart from the frequent focus on one fuel’ and attempt to analyze the determinants of residential energy demand by different fuel types (natural gas, oil and electricity) recognizing to some degree the important substitution possibilities between fuels through the use of prices of alternative fuels. Third, the model provides a regionally disaggregated approach to demand analysis. Energy consumption and prices are more varied across regions than most consumption items and analysis based on nationwide data is inappropriate. Further, such an aggregate analysis is vitiated by regional differences in such factors as climate, population, migration and urbanization. Demand functions were, therefore, estimated using pooled time-series data for different states. The use of (intercept and slope) dummies for the census regions and the regions based on the level of urbanization highlights the regional aspects of residential energy demand. Finally, the model uses data on marginal prices for oil, natural gas and electricity that has become recently available from the Electric Power Research Institute. We begin section 2 with a brief discussion of our model and its alternative versions. Section 3 provides a brief survey of previous empirical work on residential energy demand. Section 4 presents the empirical results of the model. A brief set of concluding remarks appears in the final section. 2. The model Individuals combine fuels and fueLburning equipment in the home in various ways to produce different residential services (e.g., cooking, cleaning. cooling, heating, lighting, etc.). The demand for residential energy is a derived demand for the specific services provided by a fuel jointly with the capital stock utilized with that fuel. Any analysis of the residential demand for energy must consequently deel to some degree with the interactive demands for both energy using capital and the energy form used by that capital equipment.

In the short run, the consumer’s stock of residential appliances is fixed. The individual’s demand for energy (or the intensity of use of the fixed capital stock) is determined by the price of fuel used, the prices of competing fuels, income and other characteristics of the resident and climatic variables. If fuel prices rise, the consumer can alter in the short run only the intensity of use, e.g., turn the thermostat down or stop heating rooms normally unused, etc. If energy prices remain high, however, the consumer will in the long run acquire more energy efficient stock of appliances. An analysis of long-run energy demand should track such capital stock adjustments. A dynamic partial adjustment model is used here to describe the adjustment lag between desired demand for fuel and the demand for the requisite fuel using capital stock. We begin with the following static equilibrium model:

where i is the fuel type, i is lhe ,jth state. t is the rth year, Q& is the desired demand for energy form i. in statej in year t. y,, is the per capita income in statej in year t, P,j, is the marginal price of the fuel i in statej in year t, Prj, is the marginal price of competing fuels in state ,I in year t, W,, are the weather and climate conditions in statej in year t. This static equilibrium model assumes instantaneous adjustment in the capital stock to variations in fuel demand, so that short-run and long-run elasticities are equivalent. We replace this assumption with the notion inherent in partial adjustment models that short-run disequilibria in the relationship between energy and appliance demands arc possible. Lags involved in adding new capital stock or retiring undesired appliances lead to disequilibria and energy demand can ‘)nly partially adjust in the short-run until the capital stock adjusts. A fa niliar form of this dynamic partial adjustment model is2

Qi,jt - Qijr

1 =

j.(Q,'i, -Qijl

1

19

‘Thus dynamic flow adjustment model ih part of the Energy Demand block of ;1 Mu111 Regional Policy Model of the Economy. Environment and Energy Dcmand (MREEED). a multiregional. multi-industry. econometric model of the US [Lakshmanan ( 1979)]. MR EFED con&t\ of an intcrllmitcd set of modules anu determine region4 sector output. regional demand for various factor3 of productwn, repronal Income. consumption. and go\crnmcnt expenditures. regional energy demand and regional en\irvnrncntal residuals and IS current11 being estimated.

374

TR.

tc~kskmanc~t~ md

W Anderson.

Residential

etlergy

demand

in rhr US

QijI = (1 - ib)Qij,_ 1+ E.Q$,

where Qijl is the actual demand for fuel i in state j at time t, Qijt_, is the actual demand for fuel i in state j at time t, and i is the factor defining the speed with which actual demand adjusts to desired levels (0 < 2,< 1). In eq. (2) long-run responses involving full adjustment of capital stock to changed conditions are larger than short-run income and price demand responses. While this model differentiates between short-run and long-run demand, it does not analyze explicitly changes in the size and characteristics of energy using capital.

3. Prior empirical studies Several empirical analyses of residential energy (mostly for electricity) are available in the literature. The eight models summarized in table 1 provide examples of demand models of various vintages, and efficiencies developed over the last two decades. Some are static equilibrium models [Houthakker (1951). Anderson (1972), Wilson (19?1), Lyman (1973), Halvorsen (1975)J and others are dynamic adjustment models [Fisher-Kaysen (1962), Mount, Chapman and Tyrrell (1973), Houthakker, Verlager and Sheehan (1974)]. Some use appliance stock explicitly (Fisher-Kaysen). Others use a flow adjustment model (Houthakker, Verlager and Sheehan, and Mount, Chapman and Tyrrell). Some models specify marginal price (Houthakker, HVS), while most use only average price. There are variations in the geographic units (states, SMSAs, cities or utilities) and time periods (crosssections, pooled cross-sections, varying sets of years between 1937 and 1971) used in these models. The estimation procedures vary widely - linear, loglinear, Box-Cox functions, Ordinary Least Square, Two Stage Least Squares, Instrumental Variables, Error Components, etc. Given this diversity in variable specification, data sources, and estimation methods, the difficulty in comparing these studies is not surprising. While there ;Ire considerable differences, there are, however, large areas of agreem:nt. Except for Fisher-Kaysen, all studies identify a significant longrun elasticity of demand.” Estimates of income elasticity span, however, a fr-lr broader range (from 0 to 2.0). We postpone to the following sections any further appraisal of these specific empirical results. 31t has formulated appliance variables estimated

been noted that the Fisher-Kaysen results derive from the manner in which they their problem [Halvorsen (1975)-J. They regressed in effect the growth rate in stocks on the levels of economic variables and the rates of growth of non-economic (in first difference of logs). Such a formulation essentially precludes significant relationships between appliance stock and economic variables.

(19711

(197_:1

151 Lyman

and Kayscn

Wilson

(3)

Fisher

(1962)

(2)

electricity

of analysis

stock)

(apphance

demand

and

Cox

and long-run

electricity

demand

lop-linear

method

llow adju5tmcnt. Model. error comptlnents

RcGdential

1 stage c least squares

demand

nlodels

elasticity

Electricity

and variable

C‘onstant

Ielectricity).

demand

distribution

(appliance

price for 3 classes

or 4% s1:itcs

( 1960 7 I )

__~

___

diflerences

in

of electricity

pl-lcc

\I~z~llute

with

value of price

positively

income.

elasticity

correlated

Little own price elasticities

component results not different

Error

taries

from <)LS

method

the

price

with

Price

among

provided homogeneity

formulations

( -0.45 to - i.7) states.

to - 0.09)

to 0.54~ elastrcrty ( -0.03 and long-rule

Short-run

varies Ic\ cl of income

Cla
with

St/c of income linvcrsely)

( - I.0 to - 1.2) and Both static and dynamic (0.37

income

M:*:@nal

Substantial

( - 0.4 IO - 0.45) and long?-nm i,l.lktlcitjr ( -- 1.2J 0~ 11price elasticit!

ALU age price short-run

( -0.9)

Owtn price

or typical electricity bills. Time series and cross-sections

own price

and price

(0.20)

elasticity

Income

PC oled time series and cross69)

negative

( - 1.33) and negative income elasticity ( - 0.46)

Substantial elasticity

see: ion of 48 states (1961

70)

from 67 utilities

income

47 states [I946

data.

data,

1960)

stock.

Cm

X7 SMSAs

77 cities electricity (1966)

oil and electricity

price

foe coal,

Out insignificant

cross price elasticities

Nepatibv

elasticities.

Long-run own-electricity

50 states

1960

(- 1.12) and gas (-2.751

dati\

and cross price inelastic.

Il.1661

cross price (0.2 Ii and demand elasticities

study

_____-..

Appliance stock not related to elasticities for different regions appliance price. electricity (urbanization important) price, or current income

Own

income

( - 0.89).

Pioneering

own price

Marginal

__-Remarks __ .. short-run

models.

Elasticities

demand

70.

Short-run

Jcmand

data

energy

( 1946 57) average

Data

non-

of

static

38

I

towns annual

C‘cnsus of housing

price

Table residential

temporal data --___-_-

47 slates

1937

42 (U.K.)

Spatial

of se&ted

functions

demand

co..sumption,

box

Electricity

log-linear

linear

Lmear.

GLS

Ixmulation

OLS,

for 6 categories

appliances.

demand

Electricity

and dynamic

Log linear,

and gas demand. stock demand.

Electricity

in

Appliance

logarithms

demand. OLS on first differences

electricity

and long-run

_~--.-_~

Short-run

Log linear

consumption.

Annual

Houthakkcr

(1)

(1951)

Type

__~ --.-

Modeller(s)

.___ .~___

Overview

4. Statistical results

The residential demand for electricity, gas and distillate oil is analyzed with the individual observation being the annual consumption of the fuel at the state level. Annual observations of energy consumption per capita by fuel type were obtained for the 48 contiguous states for the years 1972-1975. In economic theory, consumer decisions are based on marginal prices of consumer goods and we favor this approach. The exact specifications of other explanatory variables and the sources of data for all variables are presented in table 2. The static equilibrium demand model [eq. (l)] described in section 2 was estimated for the three fuels in log linear form using ordinary least squares (OLS). Since the dynamic flow adjustment model [eq. (3)] contains a lagged dependent variable, the residuals may exhibit interdependence through time such as first-order serial correlation. Under these circumstances, the OLS estimation of parameters is inconsistent due to bias. An instrumental variables method that can provide consistent estimates under these circumstances is used to estimate the flow adjustment model.4 The estimated static demand equations for the three fuels appear in table 3 (with the t values in parentheses). The electricity demand model performs well. The price of electricity, the price of gas and income are all statistically significant determinants of electricity consumption. The price of electricity has the expected sign, and plausible magnitude ( -0.642) and is the dominant determinant of consumption. Electricity demand is income responsive and the estimate is comparable to that of Halvorsen. Cross price (gas) elasticity while positive and statistically significant is only 0.06. The negative but statistically significant association between electricity consumption ar CJannC +ating degree days suggests warmer areas are cha .acterizPZ by higher en ‘rgy consumption. The reason for this perverse result lies in the frequent occurrence in the warmer regions where space heating (required periodically) can be provided by electric power at low capital costs. Such regional differences are not captured in a model estimated across 48 states. The residential demand for natural gas is strongly determined by the price of natural gas. income and heating degree days. The estimate of own price elasticity of natural gas at - 1.947 is below that of Anderson (1973). The high income elasticity (2.269) reflects the condition that the higher income ‘This methou provides consistent estimates by the use of an instrumental variable Zi such that (1) plim (~I;J:; ),‘I?=O, I;!) plim (x ::.x;);n is finite and non-zero. where zi = Z, -Z and xi = Xi -X. The first condition will be satisfied if Zi is uncorrelated with the error term 8i [Kmenta (1971)]. The second condition will be met if Z, and Xi are correlated with each other. An additional condition that helps to reduce the asymptotic variance, of the instrumental variables estimator is that plim (Z;;t-,).r~ is as large as possible ..- in other words, high correlation between the mstrumcntal variable % and independent variable X exists. The instrument used for of all other lagged independent \nriablcs. Y :,I 1 rn eq. (31 12a lmear combination

_.. .___^__

.----~_

---.--~

Varkhk

specikations _ ___.---

and data sources lbr the rcbidcntiul demand modul. ___. ____ _-_- -_ -.--__.__ .._.--__-._-_

Table 2 .__ _.__

Table 3 Logarithmic ___-

static equilibrium

Fuel type

Intercept

(1) Electricity

lO.OR2 (I 2.67)

(7) Gas (3) Oil

Gas price

mode1 of residential Electricity price

oi,

energy demand, ----

price

1972.-1975.

Income

Heating days

R2

0.06 (1.79)

- 0.642 (14.29)

0.491 (4.86)

-0.137 (6.02)

0.58

-7.519 (2.35)

- 1.947 (13.96)

- 0.052 (0.481

2.267 (5.55)

0.139 (1.61)

0.60

- 1.674 (0.45)

1.542 (10.24)

0.74 (3.88)

0.635 (1.61)

0.916 (6.12)

0.76

-0.01 (0.1)

states have a well deveioped system of gas pipelines, taking advantage of the economies of scale in delivery of gas by pipelines. There appears to be no explanation for the negative association between gas demand and electricity price unless regional effects are confounding a relationship estimated across all 48 states. The price of natural gas, the price of electricity, income and heating degree days are statistically significant determinants of the residential demand for oL5 However, there is a very weak and statistically not significant relationship between oil consumption and its own price. Part of the problem may lie with the data on the price of no. (2) fuel oil.” The results presented so far suggest thk existence of regional effects that may confound demand functions estimated across 48 states. Such regional differences in demand functions were analyzed through the use of dummy variables.’ First intercept dummies, which assume that different regions have the same slope coefficients but different intercept terms were developed. Slope dummy variables were also used to allow for differences in income and price elasticities among regions. Three types of regional divisions were identified --the census division. census regions and groups of states based on level of urbanization. In the third scheme the states were grouped in terms of quartiles of urbanization level distribution. The use of dummy variable method did not improve the performance of oil price variable in the oil demand model, suggesting more serious problems in oil price data than expected earlier. Further work was limited to the gas and electricity demand models. There appears to be strong regional differentiation in electricity and gas ‘The residential demand for oil has recciled littlc attention in the literature. One exception is its estimation as a share of total energy demand by Baughman and Joskow (1976). ‘Oil data are by far the most unreliable of the three energy price data sets used. Heating oil u5e data in the residential sector may include year to year industrial oil use as well. The data used here were obtained from Baughman and Joskow (1976) who attempted to some degree to iort out some of’ these data problems ‘SW !.laddala I 1973).

consumption. All but one census division, and one urbanized region t-law statistically significant intercept dummies as evident in table 4. The inter{ :pts arc higher as one proceeds south and uest from New England and the North East. Further, it appears that the more rural a state is the higher its per capita electricity consumption becomes. What is noteworthy is that o\,erall explanatory power of the model improves in this version and cross !gas) price elasticity is more pronounced and statistically significant. Regional analysis improves the performance of the natural ga.- demand as well (table 5). All the census divisions and census regions have significantly different intercepts. Per capita gas consumption increases generally i,, a south and westerly direction from New England. Urbanization does not appear to be a useful variable to differentiate states in terms of gas consumption. The own price elasticity becomes - 1.087, which is close to most estimates. Estimation with census division dummies improves the performance of the electricity price variable --. theoretically appropriate sign and higher magnitude. The wea.ther variable becomes statistically significant in the natural gas model. The results presented so far suggest that the regions exhibit differences in levels of per capita residential energy consumption. The degree to which there are regional differences in responses to price and income signals is analy;led next in table 6. In the natural gas demand model. 6 of the 9 census dikions hu\c Ggllificantly di%xent OL\II and cross price elasticities. All but one of the census divisions eshibit varying income el,tsticities. At the level of the larger census regions. the evidence in favor of different regional income elasticities is stronger but mixed in the case of price elasticities. Own price elasticity appears to be an inverse function of IeveIs of IJrbanization. Since in general, the per capita incomes directly lary with urbanization le\,els. gas price elasticity appears to be an inverse function of the level of income. The high but statistically significant cross price and income elasticities in Neln! England warrant a comment. This region contains three urban, industrial high income states with well developed gas network and three less urban. lower income states with limited access to natural gas delivery system.* In the case of electricity demand. a few cencus divisions and census region exhibit differences in own price elasticities. However, regionalization based on census regions do not bring out such differences. Price elasticity of electricity appears to be related to the letci of urbanization. Our results suggest that price elasticity increases a.; the states become less urbanized (lower incomes) except in the most rural states which have lower price elasticities. They do not corroborate the work of Lyman (l’J73) who found price elasticity to be a positive function of income. The dynamic partial adjustment models for residential electricity and gas “Further, the price of electricity is about ct~mparcd with the lower incnmc states.

50”,,

higher

(1974) in the high income

stoic;.

a:,

7IR. Lakshmanan

380

and W? Andersan.

Residential

energy

demand

in the US

Table 4 Logarithmic

sratic model of residential -

Intercept

electricity demand 1972-1975.”

(regional

intercept

dummies)

---

Own price

Cas price

income

Heating degree days

- 0,430 (7.45)

0.305 (5.46)

0.572 (5.25)

-- 0.127 (4.44)

0.69

- 0.462 (8.64)

0.177 (4.15)

0.40 (3.973

-0.126 (4.36)

0.644

- 0.554 (11.65)

0.076 (2.29)

0.835 (6.33)

-0.184 (7.04)

0.623

RZ

Census dirisiOt1 New England

8.708 (9.49)

Middle Atlantic

8.728 (0.2)

Eastnorth central

8.868 (2.37)

Westnorth central

9.0 (4.24)

South Atlantic

8.898 (3.04)

Eastsouth central’

9.066 (4.21)

Westsouth central

9.066 (4.13)

Mountain

9.159 (5.97)

Pacific

9.029 (3.79)

Census region

Northeast

10.284 (11.77)

North central

10.417 (2.78)

South

10.434 (4.19)

West

10.579 (5.31)

Lrbanized

region

Top quartileb

7.311 (7.16)

Second quartile

7.48 (4.10)

Third quartile

7.65 (4.19)

Bottom quartile

7.76 (4.01)

“The t values are in parentheses. The 48 states were arranged with quartiles qaartlle refers to the most urhanked stales.

based on the level of urbanization.

The top

TR. Lukshmunun

Logarithmic I_

static

model

and W Antifrson,

of residential

_- -_I_-_---~

Residentiul energy demand in the L’S

Table 5 natural gas demand 1972 1975.”

(regional

intercept

381

dummies)

Intercept

Own price

Electricity prier:

Income

Heating degree days

- 9.609 (2.40)

- 1.087 (4.46)

0.48 (I .97)

2.121 (4.46)

0.287 (2.38)

0.60

- 1.654 (9.041

0.180 (0.79)

7.182 (5.03)

0.198 ( I ho)

0.56

- 1.955 ( 13.66)

-0.IS9

1.x09 (3.27)

0.226 (2.04)

0.55

R2

Census division New England Middle Atlantic

IO.422 (3.02)

Eastnorth central

IO.959 (4.62)

Westnarth central

10.825 (4.05)

South Atlantic

10.579 (3.54)

Eastsouth central

I I .209 (4.3 I )

Westsouth central

11.136 (3.85)

Mountain

IO.927 (4.0)

Pacific

10.75 (3.18)

C‘l’IlSIISrrgion Northeast

-8.166 (2.18)

North central

-7.619 (2.67)

South

- 7.664 (2.15)

West

- 7.723 (1.93)

i~rhtrni~~~~lrcgiftrt Top quarttleh

- 4.065 (I .95)

Second t]Uilllile

- 4.320 (1.50)

Third quarttle

-4.199 (0.72)

Rottom quarttlc

-- 4.345 (1.62)

“The t values are in parentheses. hThe 48 states were arranged with quartiles quartile refers to the most urbanized states.

(0.95)

----based on the level of urbaruzation.

The top

Table 6 Regional

price and income elasticities of residential demand (slope dummies) 1972--1975. Natural

gas

for naturzl

gas and electricity

Electricity

-

Own price

Own price

Electricity price

- 1.947 (13.96)

- 0.082 (0.48)

2.267 (5.55)

-0.642 (14.29)

New England

- I .398 (2.60)

3.720 (5.72)

6.384 (5.?3)

- 0.388 (2.70)

Middle Atlantic

-0.13 (0.87)

- 0.322 (2.95)

1.171 (2.64)

- 0.204 (1.59)

Eastnorth central

- 1.322 (1.48)

0.401 (3.01

1.185 (2.31)

- 0.082 (1.23)

Westnorth central

- 0.622 (1.98)

0.224 (3.85)

0.767 (3.48)

- 0.348 (0.20)

South Atlantic

-2.661 (3.55)

-1.123 (5.89)

2.787 (2.21)

0.064 (2.46)

Eastsouth central

-1.44 (1.59)

- 0.038 (3.72)

0.859 (1.77)

2.73 (2.90)

Westsouth central

0.322 (0.90)

0.355 (2.80)

-0.513 (3.33)

-0.101 (1.05)

Type of region

United States (48 states)

Income

Cerlslls dit:ision

Mountain

-0.564 (3.0)

0.562 (3.75)

0.314 (4.22)

- 0.668 ( I .49)

Pacific

- 0.885 (1.01)

0.348 (2.33)

I .561) (0.74)

- 0.558 (0.51)

Northeast

- 0.695 (1.94)

1.35 (2.35)

7.291 (6.21)

- 0.304 (2.12)

North central

-0.54 (0.20)

0.34 (1.28)

1.004 (4.12)

- 0.257 (6.23)

South

- 1.737 (2.14) - 0.6:55 (0.6 i

- 0.05 (2.78) 1.779 (0.76)

0.792 (4.46) 0.794 (4.62)

- 0.207 (0.58) - 0.507 ( 1.07)

Top quartile

- 0.9 17 (2.79)

Second quartlle

- 1.336 (0.65)

- 0.698 (1.51) il

1.02 (0.72) ‘I

Third quartile

- 1.745 (1.59)

d

Bottom quartlle

- 2.068 (2.83)

a

CunsLrs region

West

L’rbtrilixrl

repic~r~

“Slope dummies not reported estimates of elasticities.

____~-

0.62 (3.84)

-0.251 (2.23) - 0.677 (3.10) -0.719 (2.61) - 0.592 (2.51)

:ince the base region did not have statistically JR3

0.67 1

significant

TR. Lukshmanun

Dynamic

und W A~~dersor?.Reside~rttnl energy demund in thr C’S

partial adjustment

electricity

demand,

197 !-1975.

Lagged dependent variable

Own price

Gas price

Income

Heating degree days

3.653 (2.16)

0.585 (4.44)

- 0.298 (3.38)

0.04 ( 1.06)

0.298 (2&i

- 0.08 (2.66)

0.64

2.383 (1.39)

0.544 (4.31)

-0.19i (2.24)

0.23 1 (3.62)

0.469 (3.53)

- 0.083 (2.43)

0.72

0.501 (3.90)

- 0.208 (2.32)

0.126 (2.56)

0.261 (2.06)

- 0.071 (2.03)

0.67 1

0.666 (5.15)

-0.162 ( 1.X2)

0.047

0.662 (4.59)

-- 0.125 (3.97)

0.682

(I.30

Jnterceyt United States

Table 7 model of residential

383

R2

Crnsus dirision NW

Enpland

Middle Atlantic

2.346 (0.53)

Eastnorth central

2.449 (0.86)

Westnorth central

2.591 (2.63)

South Atlantic

2.499 (1.63)

Eastsouth central

2.525 (2.41)

Westsouth central

2.399 (0.27)

Mountain

2.445 (1.07)

Pacific

2.183 (3.05)

4.614 (2.72) 4.707 (1.67) 4.749 (2.19) 4.838 (3.45) Urgtrrliml

Top quarlile Second quartile Third quartile Bottom quartile

rcgicw

- 0.373” (--0.19) il a

I_

___-I_

aNone of the intercepts

in this formulation

is statistically

______

significant.

_

TR. Lokshmanan

384

and W. Anderson, Residential

energy demand in the US

Table 8 Dynamic

partial adjustment

model of residential

natural

gas demand.

Heating degree days

R”

2.003 (2.98 I

- 0.01

0.55

0.526 (1.68)

1.69’ (2.24)

0.177 (1.09)

0.604

0 .__ ‘37 (0.80)

I .76S (2.50)

0.08

0.57

(0.51)

Intercept

Lagged dependent variable

Own price

Electricity price

Income

- 8.506 (2.0)

0.379 (1.65)

- 1.378 (3.20)

-0.115 (0.53)

New England

- 9.438 (1.78)

0.329 (1.59)

- 0.487 (1.02)

Middle Atlantic

- 8.583 (2.50)

Eastnorth central

- 7.969 (3.92)

Westnorth central

- 8.085 (3.51)

South Atlantic

- 8.37 (3.12)

Eastsouth central

-7.713 (3.78)

Westsouth central

- 7.837 (3.24)

Mountain

- 7.99 (3.46)

Pacific

-8.167 (2.74)

0.369 (1.76)

- 0.99 1 (2.18)

0.338

- 1.4 (3.25)

United States

1972. 1975.

(0.1)

Ctxsu.s division

Ce)rsrrs region Northeast

-- 8.544 [ I .74)

North central

- 7.895 (2.46)

South

- 7.943 (2.08)

West

-8.179 (1.88)

L’rhtmi:rd

Top quartile Second quartile

rrgirjn - 5.262” (0.96) a

(1.69)

-0.213

(0.87)

Third quartile Bottom quartile

a

aNonc of the intercepts

in this formulation

is statistically

significant.

demand are presented in tables 7 and 8. Both rlodels show lower estimates of the coefficient associated with the lagged dependent variable than is common in the literature. It must be noted that the period here (1972 1975) is one of rising prices of gas and electricity as compared with the 10 or 15 year period before the early ‘seventies used by most modellers. For the United States, the short-run price elasticity of electricity is -0.298 (long-run -0.718) and the income elasticity 0.298 (long-run 0.718). At the aggregate level of the 4 census regions, the regional intercepts are significantly different. The use of the dynamic flow adjustment model with intercept dummies makes gas price elasticity statistically significant. The short-run gas price elasticity of residential natural gas demand is - 1.378. yielding a long-run price elasticity of - 2.118. As in tlz static model, census divisions and regions evidence different intercepts. 5. Concluding comments

A static equilibrium and a dynamic partial adjustment model of residential electricity and natural gas demand have been estimated over a recent period with an experience of increasing energy prices for the United States. Residential demand for electricity and natural gas are price responsive. The longrun elasticities of electricity demand are -0.718 for marginal price of electricity and 0.72 for income and about 0.5 for gas price.9 The corresponding estimates for natural gas demand are respectively - 2.118, 2.003 and 0.78 for price of electricity. The price elasticity of electricity demand varies with the Ievil of urbaniration. The price elasticity of natural gas demand appears to be an inverse function of the level of income. A general finding of the analysis reported here is that significant regional differences in demand functions exist. Various subnational regions appear to respond to price and income differently. The challenge for the future is to account for these neglected regional diffcrenccs in a more general model.

References

386

TR. Lakshmanan

and B? Anderson, Residential

energy demand in the US

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