Direct and Indirect Rebound Effects for U.S. Households with Input-Output Analysis
Brinda A. Thomas, Carnegie Mellon University, 240-672-1419, brindat@cmu.edu
Overview
Many policymakers support energy efficiency (EE) policies as a cost-effective method to reduce energy dependence,
criteria air pollutant emissions, and greenhouse gas (GHG) emissions, while providing economical energy services.
However, an investment in EE may not yield the energy savings expected from an engineering assessment due to the
rebound effect. Greening et al. (2000) and Sorrell (2007) classify the rebound effect in terms of direct, indirect, and
economy-wide effects. The direct rebound effect occurs when an EE investment decreases the operating cost of an
energy service, leading to more consumption. The indirect rebound effect occurs when the energy cost savings from
efficiency lead to a change in demand for other goods and services, which requires energy for their production
(known as embodied energy). Studies suggest that the indirect rebound effect varies by country between 10% to
more than 100%, in some cases (Brannlund et al., 2007; Nassen and Holmberg, 2009; Druckman et al., 2011; FreireGonzalez, 2011). The economy-wide rebound effect includes macroeconomic effects such the long-term structural
shift in the economy toward energy-intensive sectors due to the change in the relative price of energy services. A
simple definition of the rebound effect, equation 1, compares potential savings (in energy or emissions) (PES) from
an engineering assessment with actual savings (AES) accounting for consumer behavior and market effects.
R = 1-AES/PES
(1)
This study quantifies the indirect rebound effect and its relationship to the direct effect, using literature estimates of
the direct rebound effect, consumer demand theory, and an environmentally extended economic input-output
lifecycle assessment (EIO-LCA) model of the 2002 U.S. economy (Hendrickson et al., 2006; www.eiolca.net), using
2004 data from the Consumer Expenditure Survey in 2002$.
Methods
I model the indirect rebound effect using the Slutsky decomposition, which provides the theory of consumer demand
in response to price changes, to model the demand for other goods due to the substitution and income effects
occurring due to the lower price of energy services with an efficiency investment. Assuming a 10% direct rebound
for energy services using electricity, natural gas, or gasoline, which is consistent with U.S.-based econometric
studies of energy service price elasticities (Dubin et al., 1986; Greene, 2012), I construct the cross-price elasticity for
other goods and services using basic elasticity properties to obtain equation 2. This models the direct and indirect
rebound effect for a hypothetical efficiency investment in a service provided by a particular fuel by average U.S.
household from a static, constant-price, general equilibrium perspective, and does not consider the role of additional
capital costs for efficiency or increased household budgetary savings as a result of efficiency investments.
𝑅𝐷 + 𝑅𝐼 [%] = −𝜖𝑆,𝑃𝑆 + (𝜖𝑆,𝑃𝑆 + 𝑤𝑠 𝜖𝑆,𝐼 )
̅̅̅̅
𝐸𝑜
𝐸𝑆
+
𝜕(𝐸𝑜 𝑤𝑜 𝐼)⁄𝜕𝐼
𝐸𝑆
(2)
In (2), 𝜖𝑆,𝑃𝑆 is the uncompensated own-price elasticity for energy services, a measure of the direct rebound, and is
used to construct the uncompensated cross-price elasticity of demand for other goods with respect to the price of
energy services, 𝜖𝑂,𝑃𝑆 , together with a few other parameters. These include 𝜖𝑆,𝐼 , the income elasticity for energy
service s, and 𝜖𝑂,𝐼 , the income elasticity for good o from Taylor and Houthakker (2010), and 𝑤𝑜 and 𝑤𝑠 , the
household budget shares for good o and good i, respectively, from the 2004 Consumer Expenditure Survey in
2002$. In addition, I obtain the average primary energy or emissions intensity per average dollar of expenditure on
other goods, ̅̅̅
𝐸𝑜 = (∑𝑛𝑜=1;≠𝑠 𝐸𝑜 𝑤𝑜 )⁄(∑𝑜 𝑤𝑜 ), the primary energy or emissions intensity per marginal dollar of
𝜕(𝐸 𝑤 𝐼)
expenditure on other goods, 𝑜 𝑜 = ∑𝑛𝑜=1;≠𝑠 𝐸𝑜 𝑤𝑜 𝜖𝑂,𝐼 , and the average energy or emissions intensity per dollar of
𝜕𝐼
expenditure on an energy service, 𝐸𝑠 , from the 2002 EIO-LCA model (Hendrickson et al., 2006; www.eiolca.net).
Results
Figure 1 shows rebound effects in emissions units under four cases compared to the base case household carbon
footprint in 2004. The four cases include (1) reducing a ton of CO2e/yr which might be the perspective of a carbon
cap-and-trade regulation, (2) saving $107/yr on annual bills for a particular fuel, which might be the household’s
motivation, (3) saving 12 GJ per year in primary energy consumption, or (4) saving 10% of annual household
energy expenditures, either of which might be the goal of an efficiency standard. The four cases were chosen so that
the CO2e emissions reductions were the same across cases for electricity efficiency. Note that the level of efficiency
improvement, , varies by fuel type for the first three cases, but is held constant at 10% across the three fuels for the
1
43.5
No Rebound
Direct Rebound
Indirect Rebound
43.0
0.05
0.04
0.05
0.05
42.5
43.2
0.09
0.10
0.10
0.10
0.07
0.10
0.09
0.10
0.09
0.09
0.05
0.08
0.06
0.09
0.09
0.10
0.09
0.10
42.6
42.0
42.2
42.2
42.2
42.2
42.3
42.3
42.3
42.2
42.7
0.08
0.13
42.2
Base
Case
1 ton GHG savings
$107 Bill Savings
12 GJ Savings
Gasoline
Natural Gas
Electricity
Gasoline
Natural Gas
Electricity
Gasoline
Natural Gas
Electricity
Gasoline
Natural Gas
41.9
41.5
Electricity
2004 Avg. U.S. Household GHG Emissions
(ton CO2e/yr)
third case. Also note that the rebound effect in percentage can be directly derived from the 1 ton in GHG savings
case, i.e. the direct and indirect rebound in CO2e emissions from electricity efficiency is 0.10+0.09 = 19%. Rebound
effects in energy or emissions units are more relevant for the energy and climate system than percent rebound and
show how budget share, energy prices, and energy intensity per dollar on expenditure influence the relative CO2e
emissions reduction possible across fuels. In sensitivity analyses, I will show that as the U.S. electric grid becomes
less-carbon intensive, or the relative price of energy rises, the indirect RE will increase.
10% Reduc on in
Energy Bills
Consequence ofi Effic ency Investment
Figure 1: Rebound Effects in CO2e Emissions vary by fuel saved and policy goal
Conclusions
The results of this study show that residential EE investments do lead to a reduction in primary energy consumption
or, CO2e, NOx, or SO2 emissions. The direct and indirect rebound effects in primary energy or CO2e emissions are
between 15-25% for the average U.S. household, with variations depending on the type of fuel saved with efficiency
or household income. Indirect rebound effects of up to 40% in NO x or SO2 emissions are possible for efficiency
investments in natural gas energy services. This study ignores any incremental capital cost needed for an efficiency
investment, which may lower the indirect rebound effect further from these results. Detailed studies of the direct
and indirect rebound effect by fuel and energy service could lead to improved assessments of the cost-effectiveness
of EE and help the policymaker and utility manager to better understand economics of EE.
References
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