Estimating the Direct Rebound Effect in the Residential Energy Sector: An Application in Spain - Green Energy and Efficiency: An Economic Perspective - page 167

where, P E is the price of energy. From ( 4 ) it can be seen that an increase in the
energy ef xed, reduces the cost of useful work

and should therefore increase demand for the services produced. This shows that
ʷ ε ( S ) will always be positive. If 0 <

ciency of the system, with P E being

ʷ ε ( S ) < 1, the increase in energy ef ciency

produces energy savings. When, ʷε ( S ) > 1, a situation known as “ back re ” occurs,

i.e. an increase in results in an increase in energy consumption E .

From ( 4 ) it can be observed that an increase in

ε

has the same effect on the cost
of useful work as a decrease in P E , ceteris paribus . This condition, known as
symmetry, taken together with the assumption that P E is exogenous (the assumption
under which the price of energy is not related to changes in energy ef

ε

ciency) turns

Eq. ( 3 ) into:

g e ðÞ ¼ g P S ðÞ 1 ð 5 Þ

:

ned as the price elasticity of
the useful work of the demand for energy services, is useful when there is not
enough variation in energy ef

This new way of calculating the rebound effect, de

ciency in the data. However, this de nition could

give rise to problems due to the dif culty in obtaining an objective measurement of

S. One way of overcoming this problem is to assume not just symmetry and
exogeneity but also that energy ef

ciency is constant. This turns expression ( 5 ) into

the following:

g e ðÞ ¼ g P E ðÞ 1 ð 6 Þ

The rebound effect is now measured in terms of the price elasticity of energy
demand. This expression requires that the demand for fuel, for which the price
elasticity is obtained, be closely linked to the service whose energy ef

ciency is

improved.

2.2 The Models

If the assumptions of symmetry, exogeneity and constant energy ef ciency are met

and the demand for residential fuel is linked to heating and domestic hot water
services, the direct rebound effect for those services is obtained by estimating the
residential demand for electricity and natural gas.
Given that electricity consumption is observed at all the households in the
sample, demand for electricity is analysed via a classical regression model. Simi-
larly, given that natural gas is only consumed at 38.9 % of the households in the
sample, demand for gas is estimated using the model proposed by Heckman [ 9 ].