K. Vaage r Energy Economics 22 2000 649]666 659
In addition, to justify the use of contemporaneous operating costs to explain the appliance choice we have to assume static expectations. As noted by Dubin and
Ž .
McFadden 1984 , whose sample is also a cross-section, this assumption is at best only approximately true, and ideally should be tested against a more complete
dynamic model, using panel data on consumer behaviour.
4. Results and discussion
The estimations are performed in two steps following a procedure suggested by Ž
. Heckman 1979 . In the first step the discrete choice is estimated by maximum
likelihood. The relationships between the observed choice i of the hth individualr household, d , and the explanatory variables are expressed with the following log
i h
likelihood function:
H N
Ž .
log L s d
log P 24
Ý Ý
i h i h
hs 1 is1
Ž .
After substituting Eq. 17 for P the log likelihood to be maximised becomes:
i h w
r m
H N
H N
N
i h
e
w r m
jh
Ž .
log L s d
log s
d w rm y
log e
25
Ý Ý Ý Ý
Ý
i h i h
i h
N
ž
hs 1 is1
hs 1 is1
js 1
w r m
jh
e
Ý
js 1
Ž .
In the second step the conditional demand Eq. 23 is estimated by OLS, with the parameter estimated on the first step used to calculate the variable represent-
Ž .
ing the interaction between discrete and continuous choices the selection term . 4.1. The discrete choice
In the model the households face four different heating systems: electricity only Ž .
Ž el
, electricity in combination with solid and liquid fuels, respectively el r wood .
Ž .
17
and el r oil , and a combination of all three el r wood r oil . The percentage
shares for the different alternatives are 5, 37, 23, and 35, respectively. The energy price in the case of mixed heating technology is calculated as the
average of the prices of the respective fuels. The prices of alternatives that are not chosen are calculated as the average price for consumers using appliance j in the
receptive county.
18
Household characteristics included in the discrete choice model are gross Ž
. Ž
. household income Income , number of rooms in the building Rooms , a dummy
17
Households with solid or liquid fuels as the only heating source were too few to be included as separate groups.
18
As noted previously, there is substantial regional variation in all energy prices in the survey at hand, which is fairly well reflected when the 19 county-averages are calculated.
K. Vaage r Energy Economics 22 2000 649]666 660
Table 1
a
Ž .
Estimated coefficients, the discrete appliance choice alternatives : el, el r wood, el r oil, el r wood r oil Variable
Choice Coefficient
S.E. t
-value log Price
] y
0.4315 0.2182
y 1.978
el r wood y
0.0091 0.0024
y 3.732
Income el r oil
y 0.0021
0.0024 y
0.882 el r wood r oil
y 0.0061
0.0024 y
2.544 el r wood
0.1977 0.1185
1.668 Rooms
el r oil 0.1301
0.1213 1.073
el r wood r oil 0.3218
0.1188 2.708
el r wood y
1.4649 0.3548
y 4.129
Buildum el r oil
y 1.9202
0.3877 y
4.953 el r wood r oil
y 2.7743
0.4311 y
6.436 el r wood
y 1.3930
0.3454 y
4.034 Agedum
el r oil y
1.6712 0.3688
y 4.531
el r wood r oil y
1.4912 0.3472
y 4.295
el r wood y
0.0420 0.3193
y 0.132
Climdum el r oil
y 0.5305
0.3374 y
1.572 el r wood r oil
y 0.79950
0.3337 y
2.396 el r wood
2.7128 0.4950
5.480 Appldum
el r oil 2.0288
0.5029 4.034
el r wood r oil 2.0730
0.4958 4.181
No. of observations 1307
Log-likelihood y
1520.019
b
LR -test
161.866
a
Ž .
The choice-specific coefficients are relative to the base category el electricity only .
b
Likelihood ratio-test of H : all coefficients but the constant terms equal zero.
Ž .
for building type Buildum , set to one for households living in blocks and zero for those living in detachedrundetached houses, a dummy for age of the building
Ž .
Agedum , set to one if built after 1975 and zero otherwise, and a dummy for warm
Ž .
climate Climdum , set to one for households in the five counties with highest average temperature and zero otherwise.
19
To be able to identify the choice specific parameters, one of the alternatives has to be used as the base category; we have chosen the el-parameters to equal zero.
Ž .
Results from the estimation of the model in Eq. 17 are reported in Table 1. From the negative estimate of the price coefficient it follows, as expected a
priori, that the model predicts lower probability for x as the price of this
i
alternative increases. Furthermore, the negative estimate implies that the disper- sion parameter m is positive, which is necessary for the model to make sense.
As for the estimated income coefficients, high household income appears to increase the probability of choosing electricity as the only heating device. Combi-
19
Continuous data on age of building and average outdoor temperature are not available in the Energy Sur
¨
ey .
K. Vaage r Energy Economics 22 2000 649]666 661
Ž .
nations with solid fuels wood are particularly unpopular among high-income households.
Both the type and the age of the building have significant impacts on the appliance choice. The estimates imply that households living in blocks choose
electric heating more often than other households do; especially the combination el r wood r oil
is relatively infrequent in block apartments. Furthermore, heating technology based only on electricity appears to be more frequent in new buildings.
Note that ‘new’ is defined as built in 1975 or later, which is the year after the first oil crisis. Not surprisingly, the appliance combination that includes oil has a
particularly low probability of being chosen.
The number of rooms in the building and our measure of climate conditions do not influence the appliance choice in a significant way, except for the probability of
choosing the el r wood r oil alternative. This alternative’s choice probability in- creases with the number of rooms, and decreases if the household is located in a
relatively warm region.
Included in the discrete choice equation are also dummy variables for each of Ž
. the respective alternatives named Appldum in Table 1 . The dummies should be
interpreted as measuring unexplained attributes, i.e. attributes that influence the choice in question, but which are not accounted for by the explanatory variables. In
Hanemann’s model these attributes are related to quality aspects, but also other properties may be accounted for by the dummy variables. It turns out that their
coefficients are highly significantly different from zero. Nevertheless, the hypothe- sis that the constant terms represent all the explanatory power in the estimating
equation is strongly rejected by the Likelihood Ratio test reported at the bottom of Table 1.
4.2. The continuous choice Explanatory variables
20
in the conditional energy demand equation are the Ž
. Ž
. Ž
. selection term
Select , energy price log Price , income log Income , and the
household characteristics from the discrete choice equation: number of rooms Ž
. Ž
. Ž
. log Rooms , type of building Buildum , age of building
Agedum , and climate
Ž .
Climdum . Hence, the energy price and the listed household characteristics are
allowed to influence the energy demand directly, measured by their respective parameter estimates, and indirectly through their effect on the selection term.
Ž .
Finally, the potential direct impact from some additional household characteris- Ž
. tics is tested for. These are the inside net floor area log Floor , the number of
Ž .
persons in the household log Person , a dummy for whether there are small Ž
. children in the household Childum , set to one if children and zero otherwise, and
Ž .
an ownership dummy Owndum , set to one if the apartment is rented and zero otherwise. Table 2 reports the estimated coefficients from two versions of the
20
Ž .
The variables, except the selection term and the dummies, are transformed to logs; see Eq. 23 .
K. Vaage r Energy Economics 22 2000 649]666 662
Table 2 Estimated coefficients, the conditional energy demand
Variable Full model
Reduced model Coefficient
S.E. t
-value Coefficient
S.E. t
-value Constant
8.7751 0.4946
17.743 9.0800
0.2952 30.757
log Price y
1.2903 0.0732
y 17.631
y 1.2426
0.0651 y
19.078 log Income
y 0.0688
0.0332 y
2.075 ]
] ]
log Room 0.5258
0.0745 7.060
0.6295 0.0542
11.622 log Floor
0.2544 0.0600
4.242 ]
] ]
log Person 0.1001
0.0458 2.186
0.1082 0.0332
3.260 Childum
0.0321 0.0439
0.730 ]
] ]
Buildum y
0.7445 0.1058
y 7.035
y 0.6667
0.0909 y
7.332 Agedum
y 0.4798
0.0921 y
5.210 y
0.3834 0.0775
y 4.947
Climdum y
0.2946 0.0461
y 6.398
y 0.2780
0.0421 y
6.603 Owndum
y 0.2033
0.0401 y
5.063 y
0.2249 0.0399
y 5.640
Select y
0.7994 0.1285
y 6.219
y 0.6650
0.0981 y
6.777 No. of observations
1306 1306
2
Adjusted R 0.435
0.427 S.E. of residuals
0.533 0.537
RSS 367.441
373.593 Ž
. F
overall 92.395
122.713
conditional demand model. The first one includes all variables listed above; the Ž .
second is a reduced version, where variables are omitted i if their coefficients are Ž .
estimated to be insignificantly different from zero, andror ii if they are highly Ž .
correlated with some other explanatory variable s . Ž
. As explained in Section 2, the chosen parameterisation implies a direct price
elasticity of y1. Our estimated elasticities are even higher: y1.29 and y1.24 in the full and the reduced models, respectively. Compared to several other studies,
these elasticities are relatively high, which calls for some elaboration. In a broad international survey from a period that approximately covers the one
Ž .
under study in the present paper, Bohi 1981 summarises that the own price elasticity of energy typically is found to be inelastic in the short-run. An elasticity
of approximately y0.2 is suggested as an average. The long run elasticity is, Ž
. however, considerably higher in absolute value , typically ranging from y0.7 to
Ž .
y 1.3. Vaage 1998 surveys several Norwegian studies, mostly based on aggregated
time-series data. He reports short-term price elasticities from y0.14 to y0.25, and long-term elasticities from y0.29 to y0.67. Several questions now arise. Firstly,
are the elasticities in the present paper most naturally interpreted as short- or Ž
. long-term estimates? Secondly, are there other properties with the chosen model
that might explain the comparatively strong price response? The standard argument in analyses based on time series data is that the response
to a price change is smaller in the short-run, when the demand is limited by the given stock of installations, than in the long-run, when the appliance has been
K. Vaage r Energy Economics 22 2000 649]666 663
optimally adapted to new conditions. With cross-section data the distinction short-termrlong-term generally is somewhat more involved. In the present model,
however, we explicitly model the joint optimisation of appliance and appliance use, which implies that the derived estimates must be interpreted as long-term effects.
As earlier mentioned, this calls for some extra assumptions compared to standard, one-step models. The reported elasticities are, of course, no final argument for the
correctness of the behavioural assumptions, but it is noteworthy that they do not reject the hypothesis of long-term optimisation.
Furthermore, the degree of mixed heating technology is high in Norway, with as much as 80 of the households in the survey combining two or more fuels.
Without any changes in the appliance stock these households are able to switch between different fuels, which, ceteris paribus, implies a high response to price
changes.
Finally, our model includes a selection term to take account of the possible influence from the appliance choice on the energy demand. We have earlier argued
that if the assumption of joint optimisation is correct, the omission of this variable in standard models implies a mis-specification bias. In our case it is possible to
21
Ž indicate the direction of the bias.
Firstly, since r - 1 by assumption see Section .
Ž .
2 , the coefficient of the excluded variable, r y 1 in Eq. 23 is negative. Secondly, the selection term is derived from the estimation of the appliance choice probabil-
ity. As reported in Table 1, the discrete choice model predicts lower probability for a given choice as the price of this alternative increases. This would imply a negative
Ž regression coefficient from a regression of the choice probability and thereby the
.
22
selection term on the corresponding energy price. Hence, the mis-specification
bias is positive, since its two components both can be shown to be negative. Even if the magnitude remains unknown, the direction of the bias implies that we expect
Ž .
higher absolute price elasticities in the present model compared to alternatives where the interdependency between the choices are not accounted for.
Moving on to the income elasticity, it is not significantly different from zero in Ž
. the reduced model and even slightly negative y0.07 in the full version. A minor
fraction of the energy consumption may be expected to have a rather high income Ž
. elasticity electricity for stereo racks, dishwashers, etc. . However, as 70]80 of
the energy consumption represents heating, the low elasticity comes as no surprise. The estimates are quite in line with other reported studies where discretercontinu-
ous models have been applied,
23
but contrary to analysis based on time-series data, where the long-term income elasticity typically exceeds unity. High income elastici-
ties from time-series data probably reflect the following: as the households } over
21
The bias implied by the omission of a relevant variable is the product of the coefficient of the excluded variable times the regression coefficient in a regression of the excluded variable on the
included variable.
22
Ž .
No simultaneity is involved, since we refer to the hypothetical regression of an estimated probability on the price variable.
23
Ž .
Ž .
Both Dubin and McFadden 1984 , Nesbakken and Strøm 1993 report positive income elasticity, Ž
. but also in their analysis the elasticity is very small in magnitude approx. 0.1 .
K. Vaage r Energy Economics 22 2000 649]666 664
time and on average } have become richer, they have increased their stock of energy appliance, which in turn has generated an increase in the energy consump-
tion. The effect of income variation across the population, at a given point of time, appears, on the other hand, to be negligible.
The results in Table 2 clearly illustrate the direct influence on the conditional energy demand from a wide range of household characteristics. This includes
size,
24
type and age of building, number of persons in the household, climate, and ownership; variables which all enter the model in a significant way and with
plausible parameter signs and sizes. Finally, the selection term turns out to be highly significant, and its coefficient
has the expected negative sign.
5. Concluding remarks
