on the selection of an energy carrier for cooking or water heating. The model is then applied ... 3 Apart from purely economic factors, other social factors such as size of the family, occupation of the ..... f (Yi) =pVi [1 -pi] t]-Yi),. (9) where Pi = p(Xi).
~
Energy Vol. 20, No. 9, pp. ')29-936, 1995
Pergamon
0360-5442(95)00044-5
A MULTILOGIT
MODEL
Copyright © 1995 Elsevier Science Ltd Printed in Great Britain. All rights reserved 0360-5442195 $9.50 + 0.00
FOR FUEL SHIFTS IN THE DOMESTIC SECTOR
B.SUDHAKARA REDDY Indira Gandhi Institute of Development Research, Goregaon (E), Bombay-400 065, India
(Received 8 September 1994; received for publication 31 March 1995)
Abstract--The choice of energy carders by households depends mainly on their economic status. The role of the environment in which they operate is equally significant. The energy-ladder concept is used in this study to describe the way in which households climb the ladder with increase in economic status. A multilogit model has been developed to study the effects of different factors on the selection of an energy carrier for cooking or water heating. The model is then applied to explain energy-carder choices in Bangalore.
1.
INTRODUCTION
Urbanisation is a growing trend in India as it is in other developing countries. The percentage share of urban population in India increased from 17.3 to 35.4 between 1951 and 1991. ~ Urbanisation leads inter alia to shifts in the overall pattern of fuel/energy-carrier consumption. These carrier shifts are stimulated by an increase in the household income and also by the availability of convenient and sophisticated energy carriers such as kerosene, liquefied petroleum gas (LPG) and electricity. Furthermore, people in rural areas who used to depend on gathering firewood, cow-dung, and other agricultural wastes for cooking and water heating, switch to modern energy carriers on migration to urban areas. Other factors such as non-availability of agricultural wastes and cow-dung, lack of space for drying and storing these fuels, profitable utilisation of time, etc., induce households to change fuels. Therefore, the share of traditional fuels such as wood and charcoal has declined rapidly, from 67% in 1953-1954 to 32% during 1991-1992. 2 Rising urban energy demand has to be addressed as part of national development plans but this cannot be done without understanding fuel shifts that are taking place, particularly in the domestic sector.
2.
THE ENERGY-LADDER CONCEPT
The energy-ladder concept indicates that the pattern of energy use in different households varies with their economic status. Each step of the ladder corresponds to a different and more sophisticated energy carrier and the step to which the household climbs the ladder depends mainly on its income. While low-income group households use firewood, cow-dung, agricultural wastes, etc., middle-income groups use kerosene whereas high-income households utilise LPG and electricity. The height of the step is determined by economic factors like the capital cost of the fuel-utilising device, price of the energy carrier, and household energy consumption. Once the household decides to shift from one carrier to another, it has to decide on the quantity of usage because, with higher incomes, the number of dishes prepared increases, increasing the carrier consumption. 3 Apart from purely economic factors, other social factors such as size of the family, occupation of the head of household, family tradition, and availability of carrier also play a role in the choice of fuel. 4 3.
HOUSEHOLD-ENERGY CONSUMPTION IN BANGALORE
A preliminary survey of Bangalore's households indicated that the choice of energy carrier depends mainly on household income. As division of the city based on household incomes was not possible, geographical stratification was adopted under the assumption that households with similar incomes and E~Y 20-9-~
929
930
B. Sudhakara Reddy
Table I. Types of energy carriers used by households in different income groups. Figures in parentheses represent percentages.
No of Per capita monthlyincome households in the range group (Rs) Firewood Group Range 148 I 350 Total
112 121 120 138 193 1000
20(0.18) 15(0.12) 7(0.06) 3(0.02) I(0.01) 166(0.17)
Householdsusing different energy carriers (No) Charcoal
i Kerosene
LPG
12(0.08) 16(0.10) 12(0.11) 10(0.08) 9(0.08) 5(0.04) 2(0.01) 66(0.07)
29(0.20) 77(0.46) 75(0.67) 76(0.63) 56(0.47) 43(0.31) 17(0.09) 373(0.37)
0 0 3(0.03) 13(0.11) 21(0.18) 39(0.28) 86(0.45) 162(0.16)
Electricity Dung,waste, ete 0 0 1(0.01) 70.06) 27(0.23) 48(0.35) 87(0.45) 170(0.17)
37(0.25) 25(0.15) l(O.Ol) 0 0 0 0 63(0.06)
Total 148(1.00) 168(1.00) 112(1.00) 121(1.00) 120(1.00) 138(1.00) 193(1.00) 1000(1.00)
habits of consumption tend to aggregate in the same locality. The cost of the household is considered to be a proxy for income. A representative sample of 1000 households was chosen randomly from 4 clusters (250 in each) to obtain the characteristics of households. The designed sample was searched roughly for bias, inconsistency and variance in terms of household income, with encouraging results. Thus, each family in the city has the same probability of inclusion once the cluster is chosen. The household survey was based on personal interviews. The questionnaire consisted of the name of the head of household, family size, family income, type and quantity of energy carrier used, etc. During the survey, households were asked to enumerate the energy carriers used for cooking, water heating, lighting, etc. Households were divided into 7 per capita income groups: (i) < R s 100, (ii) Rs 100149, (iii) Rs 150-199, (iv) Rs 200-249, (v) Rs 250-299, (vi) Rs 300-349, and (vii) > R s 350. Energyconsumption patterns were studied as a function of income g r o u p : Households in different income groups use different types of carriers (Table 1). As shown in Fig. 1, the consumption of wood is high at the lowest levels of income. It declines with increase in income and is phased out at about Rs 500 per capita monthly income. The consumption of kerosene starts at a per capita monthly income of Rs 60, reaches the maximum at Rs 200 and then declines. The consumption of electricity starts at an income of Rs 140 and grows with increasing income.
r~
I00125- - ~
h,
Firewood
Electricity
U
5O '8 ,.D I=
z
100
300
500
700
900
Per capita monthly income (Rs.)
Fig. I. Number of households using specified energy carriers vs per capita monthly income.
Multilogit model for fuel shifts
931
Table 2. Utilisation indices shoowing the dependence of income groups on energy carriers. Numbers in parentheses represent utilisation indices (UI 1).
Households using particularenergy carriers (No) No of Per capita monthly income households in the (Rs) Firewood Charcoal Kerosene Lt~ Electricity Dung, Group Range' range Waste, etc
3.1.
I
350 Total
148 168 112 121 120 138 193 1000
70(47.3) 50(29.8) 20(17.9) 15(12.4) 7(5.8) 3(2.2) 1(0.5) 166(16.6)
12(8.1) 16(9.5) 12(10.7) 10(8.3) 9(7.5) 5(3.6) 2(1.0) 66(6.6)
29(19.6) 77(45.8) 75(67.0) 76(62.8) 56(46.7) 43(31.2) 17(8.8) 373(37.3)
0 0 3(2.7) 13(10.7) 21(17.5) 39(28.3) 86(44.6) 162(16.2)
0 37(25.0) 0 25(14.9) 1(0.9) 1(0.9) 7(5.8) 0 27(22.5) 0 48(34.8) 0 87(45.1) 0 170(17.0) 63(6.3)
Carrier-utilisation indices
To interpret the pattern of consumption of these carriers, two utilisation indices were defined and calculated. The first utilisation index (UI~) refers to income group. It defines what fraction of households in a particular income group uses a particular energy carrier for a particular end use. We write UI i = XoJ ~ Xok = Xisk/xo •
(1)
k
The second utilisation index (UI2) refers to the energy carrier. It defines the fraction of households using a particular energy carrier and belonging to a particular income group, i.e. UI2 = XoJ ~ Xok = Xok/Xik • J
(2)
The carrier utilisation indices show that there is a variation in the contribution of different energy carriers to the energy mix of different income groups (Tables 2 and 3). The low-income groups (I and II) depend mainly on firewood and agricultural wastes. The middle-income groups (III-V) depend on kerosene and, to a certain extent, on charcoal as well as firewood. The high income groups (VI and VII) depend mainly on LPG and electricity. Thus, the choices in energy consumption reveal a pattern of substitution of one carrier for another. 6-s An attempt has been made to formulate a mathematical model that provides greater insight into the substitution process.
Table 3. Utilisation indices showing the distribution of energy carriers among income groups. Numbers in parentheses represent utilisation indices (UI 2). Energy carrier
Per capita monthly income (Rs) groups 350 1(0.01) 2(0.03) 17(0.05) 86(0.53) 87(0.51) 0 193(0.19)
Total 166(1.00) 66(1.00) 373(1.00) 162(1.00) 170(1.00) 63(1.00) 1000(I.00)
932
B. Sudhakam Reddy 4.
ENERGY-CARRIER
SUBSTITUTION
The fundamental assumption of the technological change is that there is an upper limit to the growth of a technology and the growth pattern follows a logistic path. Therefore, each technology undergoes different phases, viz., learning, growth, saturation, and decline. 9 It is assumed that (i) the new technology enters the market and grows or declines logistically and (ii) at any given time, only one technology will reach saturation. For the present study, firewood, charcoal, kerosene, LPG, and electricity are five different energy carriers competing through their appropriate devices (stoves) for adoption by households. The likelihood of choosing a particular carrier depends on the economic and social status of the household and the decision is discrete, i.e. selecting or not selecting. A multilogit model has been used to explain the probability of selection of the fuel for cooking and water heating by the household.
4.1. Formulation of the model Regression analysis is a method of studying the relationship between dependent and independent variables which take values in some subset of real numbers. But this method is not suitable for discrete choice problems where the dependent variable takes binary values, such as yes-no and present-absent. Such problems are better analysed within the framework of quantitative and limited dependent variable analysis. '° Assuming a logistic distribution of the underlying error term, a logit model is therefore used to analyse the probability of selecting a particular energy carrier against a specified alternative. Here we use a series of simple logits to determine the choice between each pair of energy carriers. In this study, the dependent variable Y denotes the level of preference of a particular fuel with respect to another fuel (for example, wood against LPG) and is thus a logical variable. The values, one and zero can be assigned to Y, depending on whether the fuel is preferred over the alternative fuel or not. The independent variable is the vector X denoting the characteristics of the household, i.e. size and income of the family, price of fuel, etc. The basic assumption is that the log-odds ratio (defined as the ratio of the probability of preference of the fuel to non-preference) is linearly regressive over the independent variables. The regression coefficients are determined using maximum likelihood estimation (MLE) over the sample households consisting of a set of n points in the form (X,Y). Let p(X) denote the probability that Y equals one when independent variables assume the value of X. Then
p(X) = p ( Y = 1)
(3)
[1 - p(X)] = p ( Y = 0).
(4)
p(X)/[ 1 - p(X)]
(5)
R = In {p(X)/[1 -p(X)]}.
(6)
and
The odds ratio is defined as
and the log-odds ratio as
The logistic model assumes that log-odds can be expressed as a linear combination of values of independent variables x = ( X , , x 2 , ... x , ) ,
i.e. k
R =
x,/3, = x / 3 , I
(7)
Multilogit model for fuel shifts
933
where k is the number of independent variables and /3 the regression coefficients. The problem of interest is estimation of parameters which denote the contribution of the ith household character to the log-odds ratio. The model may be interpreted as follows. Suppose the problem of interest is determination of the probability of any household preferring the energy carrier under study. Let A = (at, a2 . . . . a~,) be the vector corresponding to the household (here, it is implicit that A need not belong to the sample studied, but its value must belong to the range of variable X). Substituting X = A in Eq. (7),
p(A) = exp (A)/[1 + exp (A)].
(8)
Thus, the analysis is used to study preferential fuel characteristics of households (Table 4).
4.2.
Estimation of fl
Let the number of households in the sample be N and let N, be the number of households using the pair of energy carriers under consideration [as an example, in the case of shifting of households from firewood to charcoal (FW:CH), Nt is the number of households using either wood or charcoal] where Nt < N. Corresponding to each household, we have the vector Xi (i = 1, 2 . . . . N]). The binary responses are Yi which have the independent Bernoulli distributions. Ys denote the presence or absence of a particular fuel and the Xs household characteristics. The distribution is then
f (Yi) =pVi [1 -pi] t]-Yi),
(9)
where Pi = p(Xi). Assuming that fuel selection by household is independent, the joint distribution is the product of n such terms, i.e. NI
N]
f = "n'f = -tr [p~]~ [1(1 _p~)]~-r~. I
i= I
The log likelihood is the sum of individual likelihoods, viz., Table 4. Variables included in the model. Sl.no
Symbol
Variable Response variables
PI I'2 I'3
Firewood Charcoal
I>4
LI~ Elecuicity
P5
Kerosene
Independent variables
FS FII FI2 FI3 FI4 PR
Size of the family Per capita income, dummy for Rs < 150) Per capita income, dummy for Rs 150-299
Per capita income, dummy for Rs 300-500 Per capita income, dummy for > Rs 500 Relative price of carder (per energy unit) dummy if < 0.5 of other
AV OCP TR
Availability dummy (1 if the energy carrier is available to the household 0 otherwise) Occupation dummy (1 if the head of the household is employed 0 otherwise) Tradition dummy (1 if the household uses the energy carrier as a tradition 0 otherwise)
(lO)
934
B. Sudhakara Reddy NI
log/= L = ~
[Y/lnpi
+ (1
- Yi)ln(l
-Pi)] •
(ll)
i= I
Since the probabilities are modeled in terms of the log-odds ratio, the value of p(Xi) from Eq. (5) may be substituted into Eq. ( 1 1 ) with the result NI
L=Y
Yi) In(1
[Y~ lnexp(Xfl)/l + exp(X/3) + (1 -
- [exp(X/3)/1 + exp(X/3)]
i=1 NI
=Z [Yi ln(Xi~i) - Xi e x p ( - X~)/1 + e x p ( - X/3)
(12)
/=1 NI
--Z Yi ~
X°[3J- ~i ln[l + exp ( ~ X°[3)j]
i=1
The necessary condition for the function to be a maximum is obtained from 0L
NI
n
"=
j= 1
----Z, 0/3./ [YYu exp( X Xu/3/1 + exp
/ 1 + exp -j=_]
X0
.
(13)
-j=j
This is a system of n non-linear equations where j is the number of explanatory variables. These equations were solved using the statistical subroutine package CO5NBF. The log-odds ratios of different fuel combinations are given in Table 5. The parameter estimates presented in the tables indicate the effects of changes in the independent variables on the log-odds ratios but not on the probabilities themselves. A non-zero estimate means that the percentage changes in Pl and p~ are not the same. For any p,., however, a zero estimate does not mean that the probabilities do not change. In particular, the effect on a particular pi depends on the magnitude and sign effects on all other log-odds ratios. From the results presented in Table 5, we observe that the majority of the parameters are significant. If wood is considered as the base, then the choice between firewood and kerosene is influenced mainly by the size of the family and occupation of the head of the household. The preference for LPG and electricity is mainly associated with income. In the case of kerosene, its choice over firewood is influenced by the income of the household and price of the fuel. The choice between kerosene and LPG is insensitive to family size; price,t income, and availability of LPG seem to be the most important factors. Table 6 summarises the main results of the logistic estimation in terms of the effects of each parameter on the log-odds ratios involved. The sign of the effect (positive, negative, or zero) shows only factors that are statistically significant. As anticipated, the effects of income have the same signs. On the basis of the energy-ladder hypothesis, each move from a lower to higher income category leads to a greater probability of selecting kerosene over firewood and charcoal ( K W : F W and KW:CH have positive signs for income variables F2, F3 and F4), and a move into the highest income category increases the probability of choosing LPG or electricity over firewood, charcoal and kerosene (EL:FW, LPG:FW, KR:LPG, CH:LPG have positive signs for F2, F3 and F4). As seen from Table 6, at the lower levels of income, there is a negative tendency for households to use LPG or electricity. Also, family size and occupation of the head of the family play a role in fuel selection. With increase in household size, there is a greater probability of firewood being preferred to kerosene in low and middle income groups.
*Given variations in fuel prices, many situations may arise. For example, if the LPG price increases and the kerosene price remains constant, then the fuel shift may be from LPG to kerosene. If households choose LPG over kerosene even if there is an increase in the price of LPG, it means that households are prepared to pay higher costs for greater convenience. Thus, cost minimisation does not automaticallyensure conveniencemaximisation. Trade-offcosts for convenienceare unavoidable.
Multilogit model for fuel shifts
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936
B. Sudhakara Reddy 5. CONCLUSIONS
The results of the fuel shifts in the residential sector of Bangalore confirm the hypothesis that the step to which the household climbs the energy ladder depends mainly on income. It is from this perspective that policy makers should think in terms of encouraging fuel substitution. However, as times change, societies become more egalitarian and this energy-ladder concept based on income may disappear. For this to happen, policy intervention must be directed towards altering the economic factors. In urban areas, this can be done by (i) reducing prices and increasing availability of LPG and electricity and by (ii) subsidising the initial cost of LPG and electric stoves for poorer sections of the society. In rural areas, afforestation programmes and energy-conservation measures through efficient wood stoves will decrease the stress on resources. Thus, the energy-ladder concept serves as a useful guide to policy formulation and intervention.
Acknowledgements--The author is grateful to A. K. N. Reddy (President, International Energy Initiative, Bangalore) for providing insights into energy-carder substitution process. Despite constraints on his time, he meticulously read this paper and offered valuable comments and suggestions. Acknowledgementsare also due to J. K. Parikh, P. V. Srinivasan, R. Ramanathan, and S. Sarkar (IGIDR, Bombay) for their valuable suggestions. REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10.
Anon, Census of lndia, 1991, Part X-A, Bangalore (1991). A. K. N. Reddy and B. S. Reddy, Energy--The International Journal 19, 561 (1993). R. H. Hosier and J. Dowd, Resources Energy 9, 347 (1987). M. Alam, J. Dunkerley, and A. K. N. Reddy, "Natural Resources Forum", United Nations, New York, NY (1985). B. S. Reddy, "The Energy Sector of the Metropolis of Bangalore", Ph.D. Thesis, Indian Institute of Science, Bangalore (1990). E. Mansfield, Econometrica 29, 741 (1961). J. C. Fisher and R. H. Pry, TechnoL Forecasting Soc. Change 3, 75 (1971 ). A. W. Blackman, Technol. Forecasting Soc. Change 3, 441 (1972). C. Marcetti, Technol. Forecasting Soc. Change 4, 77 (1972). G. S. Maddala, Limited Dependent and Quantitative Variables in Econometrics, Cambridge Univ. Press, Cambridge, U.K. (1989).
