Energy consumption and income:
An inverted-U at the household level?
Vivien Foster, Jean-Philippe Tre, and Quentin Wodon1
World Bank
September 2000
Abstract
Substantial empirical work has been done at the international level data in order to test for an inverted-U
relationship between income per capita and energy consumption and/or environmental pollution using multi-country
data. But there is a lack of similar work at the household level within a given country. In this note, we find an
inverted-U using data for Guatemala. The finding has implication for social and environmental policy.
1
The authors are with the Poverty group of the Latin America region at The World Bank. This paper was funded
jointly by the Office of the Chief Economist for Latin America (Guillermo Perry) and by the ESMAP program
(Dominique Lallement). The opinions expressed in this paper are those of the authors and do not necessarily
represent the views of the World Bank.
1.
Introduction
A stylized fact in the energy literature is the existence of a transition process whereby households
gradually ascend an energy ladder. The ladder begins with biomass fuels (firewood and charcoal), moves
to modern commercial fuels (kerosene and LPG), and culminates with electricity (e.g., Albouy and
Nadifi, 1999). The reality is of course more complex than suggested by this stylized energy ladder, and
the empirical work suggests that at any given point in time, households rely on a range of fuels that
encompasses at least two steps of the energy ladder (e.g., Barnes and Qian, 1992; Hosier and Kipondya,
1993; ESMAP, 1994; Eberhard and van Horen, 1995)2. Still, the ascent of the ladder is associated with
rising income, and the fuels which are higher up in the ladder tend to be more efficient (for lighting for
example, electricity is more than one hundred times more efficient than candles or kerosene lamps). As a
result, if we define net energy consumption as the product of gross energy consumption times an
efficiency factor taking into account the efficiency of the energy sources used by households, we may
observe an inverted-U relationship between gross energy consumption and income, even though net
energy consumption may be monotonically increasing in income3. This note finds evidence of such an
inverted-U using data for Guatemala. The finding has implication for social and environmental policy.
2
Methodology
To motivate the empirical work, we first present a model which, while extremely simple, does
suggest a rationale for a household-level inverted-U. The model will also help in defining the key
variables in the empirical work.
Consider a household’s whose utility depends on net energy
consumption NE, with NE=GE*EF, where GE is the household’s gross energy consumption and EF is the
efficiency factor which depends on the energy sources used by the household. The household’s utility
also depends on the efficiency factor, because more efficient energy sources such as electricity are easier
and cleaner to use (the efficiency factor is a proxy for the comfort level associated with the pattern of
energy use in the household). The utility function is W=W(NE, EF), with ∂W/∂NE>0, ∂W/∂EF>0,
∂2W/∂NE2<0 and ∂2W/∂EF2<0. The partial derivative of W with respect to gross energy consumption is:
∂W
∂W
∂W NE
=
EF −
∂GE ∂NE
∂EF GE 2
(1)
2
In Guatemala, according to the 1998/99 ENIGFAM (Encuesta Nacional de Ingresos y Gastos Familiares) survey
used in this note, each household uses on average 2.6 different types of fuels.
3
While substantial work has been devoted to testing for environmental inverted-U relationships at the international
level between income per capita and various types of environmental pollution (e.g., Selden and Song, 1994; HoltzEakin and Selden, 1995; List and Gallet, 1999; Heil and Selden, 2000; see also the special issue of Environment and
Development Economics of October 1997), there is no similar work at the household level to our knowledge.
At high levels of net energy consumption, increasing gross energy consumption may be
associated with a decrease in utility. In other words, households who can afford to do so will reduce their
gross consumption by switching to more efficient energy sources, and this may result in an inverted-U.
To test for the inverted-U relationship, we use the ENIGFAM (Encuesta Nacional de Ingresos y
Gastos Familiares) income and expenditure survey for Guatemala. The survey covers the period April
1998 to March 1999. The survey includes monthly household expenditures for various fuels (batteries,
candles, electricity, fuelwood, kerosene and propane gas). In the case of fuelwood, for the households
who gather their own wood, the survey provides an estimate provided by the household as to the cost of
purchasing an equivalent amount of fuelwood in the market place. In order to convert the expenditures
data into physical units of consumption, data on energy prices are required. Because the ENIGFAM did
not incorporate a price survey, regional unit prices were taken directly from the Guatemalan Consumer
Price Index. Dividing expenditures by unit prices yields estimates of the physical consumption for each
energy source. Next, since each fuel is measured in different units, it is necessary to convert them all into
a common unit of kilowatt hours for aggregation. This is done by applying standard conversion factors
(United Nations, 1987). The standardized measures of physical energy use are summed together to obtain
an estimate at the household level of total gross energy consumption GE in kilowatt-hours.
To move from gross to net household energy consumption, we must take into account the
efficiency of various fuels. Cooking fuels vary in terms of the efficiency with which they generate heat
from one kilowatt-hour of fuel input. Similarly, lighting fuels vary in terms of their luminous efficacy,
which is the amount of light they provide from one kilowatt-hour of fuel input. Furthermore, any
particular fuel may exhibit a greater or lesser degree of efficiency (or luminous efficacy) depending on the
capital good with which it is used. For example, kerosene produces eight times more luminosity when
burnt in a hurricane lamp than in a primitive wick lamp (Van der Plas and De Graaff, 1988). In this note,
gross energy consumption figures were adjusted to reflect the efficiency of each fuel relative to the
efficiency of electricity in the same use using the parameters provided in table 1. The efficiency factors
show that for cooking, one kilowatt-hour of energy obtained by burning propane gas provides only 77
percent of the heat given by one kilowatt-hour of electricity, whereas wood is only 15 percent as efficient
as electricity. For lighting, the divergence is far greater. Kerosene wick lamps produce only 2 percent of
the luminosity of electricity per kilowatt-hour of energy used, whereas for candles the corresponding
value is a mere 1percent. Finally, batteries are believed to be about 90 percent as efficient as main power.
Multiplying gross energy consumption by the efficiency factors EF in table 1 yields an estimate of net
energy consumption in kilowatt-hours. Since the efficiency factors have been normalized against
electricity, the net energy amount NE can be interpreted as the total amount of electricity that the
household would have to consume to obtain its current level of energy consumption exclusively from
electricity. Net energy consumption is better than gross energy consumption to assess how households
meet their energy needs. Additionally, as mentioned earlier, households may place some value in the
efficiency factor itself, since it is associated with easier to use and cleaner (more healthy) energy sources.
In the empirical section, we provide measures of gross and net energy consumption by income
decile in Guatemala that suggest an inverted-U relationship. To test whether this relationship remains
when controls are included for factors other than income which may affect energy consumption, we also
use regression analysis. Let L represent a vector of geographic location dummies, H a vector of nonincome characteristics of the residents in the household (demographics, education and employment
essentially), E a vector of dummies indicating access to various energy sources including electricity, and
Y a vector of dummies for the position of the household in the distribution of per capita income by
quintile. We estimate:
log( NE i ) = β 0 + β 1 Li + β 2 H i + β 3 E i + β 4 Yi + ε i
log(GE i ) = λ 0 + λ1 Li + λ 2 H i + λ 3 E i + λ 4 Yi + υ i
(2)
log( EFi ) = γ 0 + γ 1 Li + γ 2 H i + γ 3 E i + γ 4 Yi + κ i
Given that NEi = GEi*EFi, we have for all parameter estimates βj = λjγj. The coefficient vector λ4
is the parameter of interest for the inverted-U hypothesis. Under the inverted-U hypothesis, we would
expect the parameters in λ4 to be lower for the lowest and highest income quintiles than for the middle
groups. By contrast, we would expect the parameters in the vectors β4 and γ4 to be increasing in income.
3.
Empirical results
Table 2 and Figure 1 give the mean energy expenditure, gross and net energy consumption, and
efficiency factors by income decile. On average, households in Guatemala spend US$247 for energy
goods per year, yielding gross and net consumption of respectively 13,090 and 3,236 kilowatt-hours. The
mean efficiency factor is 0.25. Household expenditures for energy rise steadily with income, with the
tenth decile spending 3.61 times as much as the first.
There is an inverted-U since gross energy
consumption peaks at around the fifth decile, and is lower in the tenth decile than in the first decile. By
contrast, net consumption is monotonically increasing in income, as is the efficiency factor (both are
normal goods). The top decile consumes more than three times as much net energy as the bottom decile,
and the efficiency factor rises from 0.16 in the first decile to 0.59 in the tenth decile as households switch
towards more efficient forms of energy such as propane gas and electricity.
These findings are confirmed in the regression analysis which is conducted with quintiles to
ensure enough observations in each income bracket. The results are provided in table 3. The coefficient
estimates in λ4 suggest again an inverted-U, with the largest coefficient estimate obtained for the third
quintile (the coefficient estimate for the fifth quintile is zero since this is the excluded dummy in the
regression). By contrast, the βs and γs are increasing in income. The same results (available upon
request) are obtained when the equations in (2) are estimated for urban and rural areas separately.
4.
Policy implications
This paper has documented the existence of an inverted-U relationship at the household level
between energy consumption and per capita income in Guatemala. The finding provides a microfoundation for similar relationships observed at the international level using multi-country data. The
finding may also be used to suggest policy initiatives. Although this has not been discussed above, one of
the factors at the root of the inverted-U in Guatemala is the fact that butane gas is used for cooking only
by the highest income deciles, with the middle group still relying on wood. Part of the reason why butane
gas is not used more has to do with limited distribution networks, especially in rural areas. Butane is also
more expensive to use than wood when the cost of the equipment needed to use butane is taken into
account. More specifically, butane gas requires an investment of about US$ 200 in a butane stove,
whereas wood can be burned at zero capital cost using a primitive three stone stove. Furthermore, it may
be more difficult for poor households to budget for the purchase of butane cylinders. This is because
butane is sold in relatively large quantities  35lb cylinders costing around US$ 9  while wood can be
gathered in the amount required often without monetary outlay. Switching from wood to butane would
probably generate welfare gains for the poor. It would also probably generate health gains through
reduced indoor air pollution. Programs promoting the use of butane gas in countries such as Guatemala
could be financed using funds for carbon emissions reductions. While more work would be needed to
conduct a cost-benefit analysis of such an initiative, our results do suggest that it could be promising.
Table 1: Relative efficiency factors used to adjust from gross to net energy consumption
Cooking
Appliances
Relative
Fuel
Relative
luminous
efficiency
efficacy
Electricity
1.00
Electricity
1.00
Electricity
1.00
Propane
0.77
Kerosene
0.01
Batteries
0.90
Fuelwood
0.15
Candles
0.02
Car batteries
0.90
Sources: Leach and Gowen (1987); Van der Plas and De Graaff (1988). Electricity provides the baseline against
which the efficiency and luminous efficacy of other fuels are expressed. Hence, the factor for electricity is one.
Fuel
Lighting
Relative
efficiency
Fuel
Table 2: Comparison of energy expenditures with gross and net consumption across deciles
Energy
expenditures
(US$ per capita)
GE
Gross consumption
(kWh pa)
Per capita income decile
1
120
2
161
3
194
4
190
5
229
6
219
7
254
8
279
9
301
10
434
Overall mean
238
Ratio deciles 10: 1
3.61
Source: Authors’ estimation using ENIGFAM 1998/99
10,060
13,320
15,506
13,799
16,216
14,160
13,627
13,387
11,448
9,399
13,090
0.93
NE
Net consumption
(kWh pa)
EF
Efficiency factor
(Net/Gross kWh)
1,658
2,217
2,692
2,607
3,173
3,055
3,516
3,798
4,078
5,539
3,236
3.34
0.16
0.17
0.17
0.19
0.20
0.22
0.26
0.28
0.36
0.59
0.25
3.58
Table 3: Determinants of energy consumption and energy efficiency, Guatemala 1998/99
Log(GE)
St. Err. 95% Conf. Int.
Coef.
Coef.
Demographics
Babies
0.117 0.031 0.057 0.177 0.123
Children
0.170 0.025 0.121 0.219 0.179
Adults
0.320 0.030 0.262 0.378 0.359
Babies squared -0.006 0.009 -0.024 0.013 -0.008
Children squared -0.013 0.006 -0.025 -0.001 -0.018
Adults squared
-0.022 0.004 -0.029 -0.015 -0.027
Female head
0.257 0.050 0.159 0.356 0.285
Age of head
0.005 0.001 0.003 0.007 0.002
Education
Head 6-8 years -0.121 0.038 -0.195 -0.047 -0.014
Head > 9 years
-0.067 0.030 -0.126 -0.008 0.035
Spouse 0 years
0.354 0.057 0.243 0.465 0.327
Spouse 6-8 years 0.262 0.060 0.144 0.380 0.308
Spouse > 9 years 0.360 0.053 0.256 0.463 0.375
Employment
Head industry
0.102 0.030 0.043 0.160 0.057
Head family wk. 0.130 0.126 -0.118 0.377 0.109
Head public wk. -0.004 0.046 -0.094 0.085 -0.015
Head employed -0.064 0.044 -0.149 0.022 -0.094
Head searching -0.251 0.123 -0.492 -0.010 -0.230
Spouse industry 0.290 0.053 0.185 0.395 0.183
Sp. Family wk.
0.218 0.079 0.062 0.373 0.187
Sp. Public wk.
0.093 0.075 -0.055 0.240 0.085
Sp. Employed
-0.241 0.050 -0.339 -0.143 -0.167
Sp. Searching
-0.025 0.205 -0.427 0.378 0.085
Location
Norte
-0.032 0.076 -0.181 0.117 -0.076
Nor-oriente
-0.060 0.074 -0.204 0.084 -0.033
Sur-oriente
-0.049 0.057 -0.160 0.062 -0.121
Central
-0.053 0.062 -0.174 0.069 0.000
Sur-occidente
-0.225 0.070 -0.363 -0.087 -0.221
Nor-occidente
0.432 0.110 0.216 0.648 0.054
Peten
0.388 0.112 0.168 0.608 0.068
Income p.c.
1st quintile
-0.177 0.061 -0.297 -0.058 -0.923
2nd quintile
0.120 0.051 0.021 0.219 -0.593
3rd quintile
0.205 0.041 0.125 0.286 -0.416
th
4 quintile
0.127 0.034 0.060 0.194 -0.302
Access
Public electricity 0.019 0.102 -0.182 0.219 0.662
Private elect.
-0.092 0.040 -0.170 -0.014 0.553
Butane
-0.121 0.054 -0.226 -0.016 -0.185
Urban household -0.379 0.035 -0.448 -0.311 -0.032
Constant
7.803 0.102 7.603 8.004 6.575
Source: Authors’ estimation using ENIGFAM 1998/99.
Log(NE)
St. Err. 95% Conf. Int.
Coef.
Log(1/EF)
St. Err. 95% Conf. Int.
0.025
0.020
0.024
0.008
0.005
0.003
0.040
0.001
0.075
0.140
0.313
-0.022
-0.027
-0.032
0.206
0.000
0.171
0.218
0.406
0.007
-0.008
-0.021
0.364
0.003
-0.006
-0.009
-0.040
0.002
0.004
0.005
-0.027
0.004
0.016
0.013
0.016
0.005
0.003
0.002
0.027
0.001
-0.038
-0.035
-0.070
-0.008
-0.002
0.001
-0.080
0.003
0.026
0.017
-0.009
0.011
0.011
0.008
0.025
0.005
0.030
0.024
0.045
0.048
0.042
-0.073
-0.013
0.238
0.213
0.292
0.045
0.082
0.416
0.402
0.458
-0.107
-0.101
0.027
-0.046
-0.016
0.020
0.016
0.030
0.032
0.028
-0.146
-0.133
-0.032
-0.108
-0.070
-0.068
-0.070
0.085
0.017
0.039
0.024
0.101
0.037
0.035
0.098
0.043
0.063
0.060
0.040
0.164
0.010 0.104 0.045
-0.089 0.307 0.020
-0.087 0.056 0.011
-0.162 -0.026 0.030
-0.422 -0.037 -0.021
0.099 0.267 0.107
0.063 0.312 0.031
-0.033 0.203 0.008
-0.245 -0.088 -0.074
-0.238 0.407 -0.109
0.016
0.067
0.024
0.023
0.065
0.028
0.042
0.040
0.026
0.108
0.014 0.076
-0.110 0.151
-0.036 0.058
-0.015 0.076
-0.148 0.106
0.051 0.162
-0.052 0.113
-0.070 0.086
-0.126 -0.023
-0.322 0.103
0.061
0.059
0.045
0.050
0.056
0.088
0.090
-0.195
-0.149
-0.210
-0.097
-0.332
-0.119
-0.109
0.044
0.082
-0.032
0.097
-0.111
0.227
0.244
0.043
-0.027
0.072
-0.053
-0.004
0.379
0.321
0.040
0.039
0.030
0.033
0.037
0.058
0.059
-0.035
-0.103
0.013
-0.117
-0.077
0.264
0.204
0.122
0.049
0.131
0.011
0.069
0.493
0.437
0.049
0.040
0.033
0.027
-1.019
-0.673
-0.481
-0.356
-0.827
-0.514
-0.352
-0.248
0.745
0.714
0.622
0.429
0.032
0.027
0.022
0.018
0.682
0.661
0.579
0.393
0.809
0.766
0.664
0.464
0.082
0.032
0.043
0.028
0.082
0.501
0.491
-0.269
-0.087
6.414
0.823
0.615
-0.100
0.023
6.735
-0.643
-0.645
0.064
-0.347
1.229
0.054
0.021
0.028
0.018
0.054
-0.749
-0.686
0.008
-0.383
1.123
-0.537
-0.604
0.119
-0.311
1.334
Figure 1: Gross and net energy consumption and efficiency factor
by per capita income decile
4.00
Efficiency factor
3.50
3.00
2.50
Net energy consumption
2.00
1.50
1.00
Gross energy consumption
0.50
0.00
1
2
3
4
5
6
7
8
9
Decile
Source: Authors’ estimation using ENIGFAM 1998/99
10