Michael Alexander, Ph.D.

The Takeback (Rebound) Effect in Energy Conservation

I defended the dissertation on Monday 12/1/97, and the Committee accepted my results. The theoretical groundwork is sound in showing that there must be a takeback effect (that is, an n% technical improvement in energy conservation will result in a less than n% decrease in energy use), and the econometrics on heating and insulation in Manitoba strongly and conclusively supports that theory. More importantly, the model I present is capable of predicting the takeback effect, whereas the current models in the literature are only capable of analyzing the data after the fact (and given the paucity of data, they are not capable of doing that very well.) Further, although my data is limited to electrically heated homes in Manitoba, and to the effect of improved insulation, the work is easily generalizable to all energy consumers and all energy takeback effects. Further, it can be used on non-energy results as well. To coin a phrase, it can be generally applied to the concept of "technology elasticity" no matter what the technology is.

The theoretical work is derived using a Becker model of household production as its basis, and a model of individual utility originated by Hausman. Using data from Manitoba Hydro (who'se survey of its customers is excellent... vastly superior to the dataset available from the U.S. Department of Energy (DOE) I am able to fundamentally validate my results.

I would continue to appreciate it if anyone who feels they know of useful writings on these, or other potentially useful subjects would e-mail their suggestions to me.

Conclusion: Applications, Implications, and Extensions of Dissertation:

Based on the work presented in this dissertation, it is clear that there
is a measurable and predictable take-back effect of any residential
insulation project.  In this chapter I shall discuss the policy
implications of that take-back effect.  Using the theory developed in
Chapter 3, I shall first show a simple technique for developing similar
estimates of the takeback effect in other energy projects, and second show
how the work can be applied to any change in "production technologies"
including those which involve commercial and industrial end-uses of
commodities other than energy.  Finally, I will suggest future research to
further the understanding of the response of demand to changes in
technology beyond just the takeback effect.

I.	Application of the Results to Residential Heating Projects

The takeback effect will result in lower energy savings due to a home
insulation project (or an improved building insulation standard) than
would have been estimated using engineering estimates.  That difference
might (or might not) be enough to make a project which looked cost
effective (based on the engineering estimates) prove not to be cost
effective  The econometric results presented in Chapter 5 (as modified to
account for the effects of measurement error in the variable LOSS) permit
one to estimate the change in temperature settings of a typical household
which would result from changes in the level of heat loss due to changes
in the level of insulation.  The change in heat loss can be calculated
using equation (4.6).  An estimate of the takeback effect can be developed
with a little work, although the results will depend upon regional

Consider an energy conservation project which converts a home from poorly
insulated (having an r-value of 10) to the highest level of insulation (an
r-value of 40).  The heat loss would then be decreased from x to x/4.  For
poorly insulated homes, the median value of the variables which occur in
the key equations are:

DHOUR:  	30.9
EDUCATN2:	 4.0
PEOPLE: 	 3.0
HUMIDD: 	 0.0
RESET:  	 0.0

Therefore, by equation (4.3), prior to the change in insulation levels

(6.1)	LOSS = 34.5 *30.9/ 10 = 109.39

and after the change in insulation they become:

(6.2)	LOSS = 34.5 *30.9/ 40 = 27.35

Based on the regressions for temperature changes in Chapter 5:

· Night temperature would go from 19.92oC to 20.23oC (up 0.32oC),
· Daytime temperature would go from 20.46oC to 20.62oC (up 0.16oC),
· Evening Temperature would go from 20.27oC to 20.50oC (up 0.23oC), and 
· Average temperature would go from 20.19oC to 20.43oC (up 0.25oC)  

These numbers are consistent with the estimates reported in Schwarz and
Taylor (1995) and others which are discussed in Chapter 2.

Heat loss through the walls is, combining equations (4.5) and (4.6):


Therefore, if an energy project increases the r-value of the home by a
factor of four, then heat loss would be reduced to one-fourth of the
pre-project heat loss, if the temperature of the home is not increased
from the pre-project level.  Or, equivalently, the engineering estimate of
energy savings would be 3/4 of the energy used for heating prior to the
implementation of the project.  (Note that, at this point, we are only
discussing energy to replace heat lost through the walls, which is
actually about a third of the total energy used in heating, the other
two-thirds of the energy is used to replace heat lost through air
infiltration and through windows.)

The actual effect of an increase in household temperature on energy
consumption would depend on the numbers of hours that the house was then
being heated (if outside temperature exceeds the indoor temperature
setting, then no heating will take place). If we assume, as a crude
estimate, that a house in Manitoba will be heated roughly three quarters
of the time , then an average increase in temperature setting of 0.25 oC,
predicted by the model, would be an increase in degree hours (Fahrenheit )
of (0.75 *0.25*9/5 ) = 0.3375 degree hours, or (0.3375/30.9) = 1.0922
percent.  However, since the walls are now four times as energy efficient,
this would only decrease the energy savings by 1/4 * 1.09 percent from the
original engineering estimate of savings.

However, that is only the loss through the walls.  As I indicated in
Chapter 4, only one-third of the total heat loss for the house is through
the walls, the other two thirds are through air infiltration and loss
through windows.  (However, Generally speaking, improving the insulation
of a home will only decrease heat loss through the walls, so improving the
R-Value of the walls will not result in an energy saving for these other
two sources of heat loss.  Heat loss through these two sources would also
be proportional to the increase in degree hours of heating.  Therefore, if
heating increases by 1.09 percent, the additional heat loss through the
windows and through air infiltration would be two times the original heat
loss through the walls, times 1.09 percent.

Combining heat loss from the walls and increased heat loss through the
windows and air infiltration, the total increased heat loss would be ((2 +
1/4) * .010922) = 0.024575 (2.5 percent) times the initial (pre-project)
heat loss through the walls.  Since the engineering estimate of savings
was 3/4 of the pre-project heat loss through the walls, the takeback
effect is:

(6.4)	Takeback =
                              = 3 * 1.0922% = 3.2766%

Therefore, when a conservation project is evaluated based on an
engineering assessment of the energy savings, the benefits are
exaggerated, and projects which are not actually cost beneficial may
appear to be so when the takeback effect is ignored.  A 3.3 percent
takeback effect may or may not be sufficient to change the results of a
cost benefit analysis of a project from showing a cost beneficial result
to showing a non-cost beneficial result, depending upon the peculiarities
of the individual project.  However, it is clear that the 3.3 percent
takeback should be considered in evaluating the project.

A sample benefit/cost analysis (using the Minnesota Department of Public
Service’s Ben/Cost Model) for an insulation is presented in the appendix.
The first model run shows a benefit cost ratio (for the Societal Test,
which is the criterion that the Minnesota Department of Public Service
uses) of 1.02, based on an engineering estimate of savings, indicating
that the project is cost beneficial.  However, when the energy savings are
reduced from the engineering estimate of 18 percent to (.18*(1-.032766))
17.41 percent (see the second run), the benefit to cost ratio drops to
0.98, which indicates that the project is not cost beneficial.

II.	Generalizing Takeback Estimates for Other uses.

It would be comparatively straightforward to develop more accurate
estimates of the effectiveness of energy conservation measures before
undertaking an energy conservation program by generalizing the discussion
at the end of Chapter 3.  In the long run, it would not be necessary to
develop estimates of the level of energy services demanded for each
household for each end-use (heating, cooling, T.V.s, water heating etc.),
in order to apply the results of this study to other end-uses than
heating.  The work can be generalized from easily available data, as
discussed below.  There is a simple relationship between the price effect
on the demand for energy (which may be determined by more commonly
available data) and the price effect on the demand for energy services.  A
sketch of the relationship is presented below:

The relationship between the amount of energy services the consumer
receives (H)  and the energy used for providing the energy service (E)  is
defined by the transformation ratio (K)  between the two:

(6.4)	H = E * K

The price of obtaining a unit of energy service is:

(6.5) PH= (PE / K)

Since T/H =1, 

where	T is the total level of energy services ; and
	H is any increment to energy services. 

T/PH is (by substitution):

(6.6) (T/ PH) = [(E*K)] / [(Pe/K)] |K constant

Since K is a constant (this analysis assumes that the only changes in
demand are behavioral and not technological, i.e. that we are dealing with
a "short term" not a "long term" elasticity response), we can take it
outside of the derivatives, and simplify (6.6) to

(6.7)	(T/PT) = K2 * (E/Pe)

Therefore, given that we know (E/Pe), we can compute T/PT.  Since

(6.8)	PH = Pe/K

If, at T=T1, K changes from K1 to K2 then PT changes from Pe/K1 to Pe/K2,
and therefore T would change from T1 to

(6.9)	T2 = T1 + (T/PT) * (Pe/K2 - Pe/K1)

In terms of the original question, this means that E would change by (or
that the price induced takeback effect would be):

(6.10)	T1/K1 - T2/K2

Using that relationship, one could examine the short term price response
of demand for electricity for several end-uses, and the results could be
used for preliminary studies of the takeback effect in studies involving
other fuels, or, with minor modifications, in any study of the effect of
exogenously introduced technological change on the demand for a factor

III.	Expansion to Other Take-back Effects

Although the proceeding analysis was based on the takeback effect in
residential heating, the basic theory can be extended to cover the entire
gamut of takeback effects, including commercial and industrial processes,
although it may not be as easy to define the objective function being
maximized, and the equations to be solved in a corporate world may involve
complex simultaneous supply and demand modeling.

However, there is no fundamental difference between producers and
consumers.  (Indeed, this is the insight which leads to the Becker style
household production function.)  For consumers, the utility to be
maximized is an elusive theoretical construct based on several arguments.
For a producer, the utility is more concrete and based on a single
argument - profits.   For both, energy is an input to the production
function, not an argument to the utility function itself.  For both, an
increase in the efficiency of use of an input to the production function
results in a decrease in the total cost of production.

Similarly, once the form of the production function and the consumer's
reaction to a change in price have been determined, it is not necessary to
know the actual form of the utility function.  Rather one can go directly
from the price sensitivity of the demand function for energy for a given
end-use to the sensitivity to improvements in technology, as described
above.  The only practical problem which must be solved, is determining
the price sensitivity of demand for a given end-use.  I offer some simple
suggestions in the following section.

IV.	Suggestions for Future Research

The work done here is directly applicable in a wide variety of areas of
technology assessment.  Two suggestions for further development come
immediately to mind.  The first of these is developing estimates of the
takeback effect in various end uses with other derived demands.  The
second area is a straightforward extension of the concept of the take-back
effect to look at the related "income" or cross-elasticity effects, which
would further diminish the energy (or other) savings from an improvement
in production technology.  This second area can be expanded into the realm
of "cross-technological elasticity." by looking at the effect that a
change in the efficiency of use of one input has on the demand for other
inputs into the production function.

	A.	Estimating Other Takeback effects

As shown above, the take-back effect is relatively simple to compute given
an estimate of the price elasticity of demand for a given energy service,
or indeed of any primary demand.  If the underlying production technology
does not change, however, then the short term price response in the
consumption of energy (or any other derived demand) for a particular
end-use will be the same as the short term price response for the energy
(or other) service.

For instance, the Parti and Parti approach estimated the change in
electricity consumed for various end-uses based on changes in price and
income.  In the short run that is also the change in the demand for energy
services based on changes in price or income, since, by definition of
“short run,” consumers have not changed the technology they use to produce
those services with.  Using the transformation methods outlined above, one
could therefore estimate technological elasticity from such a study
without any other econometric gyrations.

	B. Inputs Used in Other Aspects of Production

Electricity is a good example of an input which is used in more than one
aspect of production.  In a household, it is used independently in the
production of heat, of air conditioning, of refrigeration, of hot water,
of cooking, etc.  A cost savings in one end-use (say heating), may well
lead to an increase in its use in another end-use due to cross price

A similar result could occur in an industrial process, where electricity
might be used at a number of steps along an assembly line.  Increasing the
energy-efficiency of one use of electricity along the line might lead to
lower prices for the product, and hence through the takeback effect,
increased uses at other points in the line.  Or it might increase the
demand for complimentary goods, which are also produced using electricity.

In such a case, the difference between engineering estimates of energy
savings and actual savings will be greater than the take-back effect, in
and of itself, would explain.  An extension of this work to look at
cross-price elasticities for services would be a logical step, which could
be approached using the framework presented here.

V.	Conclusions

The essential insight of this work is that changes to responses in
technology are simply responses to changes in price.  Once that is
established, and the production function is adequately defined,
traditional tools are fully capable of estimating changes in demand due to
technological changes.  This is true whether we are talking about "own"
technological elasticity which was examined in this work, or "cross"
technological elasticity, which is a comparatively simple extension of the
work done here.

The techniques presented in this work have the second advantage of
permitting a better estimate of energy savings before a project is put
into place, rather than afterwards.  In addition, these techniques permit
the effect of a project to be estimated using the entire population of a
service area (or beyond) rather than based on a very limited sample size.
This will permit more accurate estimates of the effects of energy
conservation projects.

The size of the take-back effect will vary depending upon the price
elasticity of demand for the primary argument in the utility function.  In
the case of heat, the price elasticity is not very large, but might be
large enough to affect the results of a cost/benefit analysis of an energy
conservation program.


If you have any questions, suggestions, or comments, please e-mail me at urban@leprechaun.com.

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