Electronic Supplementary Material (S4) – Details of Methodology
We start by defining the rebound effect according Druckman et al. (2014) as the percentage of
offsetting actions
in relation to expected savings
.
(1.1)
For the estimation of potential rebound effects in terms of resource use, we are in particular
interested in offsetting action
effects
and income effects
. Simplifying, this could be expressed as the sum of the time
. This means, more specifically, the total effect in terms of
resource use results from a new mix of activities and consumption patterns due to a changing
disposability of time and income.
(1.2)
The income effect is defined as the product of marginal propensities to consume
terms of €) and resource intensity
of consumption category
(in
(in terms of kg/€).
(2.1)
While the time effect results from the multiplication of the marginal propensities to time use
(in terms of h) with the resource intensity of time use category
(in terms of kg/h).
(2.2)
In microeconomic terms, we derive Engel curves (see chapter 5.3) showing the relationship
between a consumer´s income and the goods bought. The slope of the Engel curve at any
point is known as the marginal propensity to consume and measures for a marginal change in
income the resulting change in the consumption of good
. The ratio of the marginal
propensity to consume the good to the average propensity to consume is defined as the
income elasticity of demand of good
consumption of good
and measures the proportional change in the
as ratio to the proportional change in income that causes the change.
(3.1)
The same propensities are defined for time use
along harmonized time use categories
depending on a marginal change of working hours .
(3.2)
The resource intensities of consumption are defined as the ratio of total material requirement
(
) per total expenditure
along COICOP in Germany. The total material
requirement induced by the German household consumption was calculated using a model
that allows the estimation of the global resource effects of German consumption. The applied
model is based on the so-called Environmentally Extended Input Output Analysis (EE-IOA).
The EE-IOA is a tool, which reflects the (global) environmental direct and indirect effects
resulting from production and consumption within one economy. It is based on information
on the production and trade structure of an economy as well as on the environmental pressures
associated with them. The most prominent results from the EE-IOA are the estimations of the
domestic and global environmental pressures from the consumption perspective. In the case of
material use the results of the calculation are commonly called “material use footprints" and
represent the total direct and indirect material used along the whole production chain of each
domestically produced or imported consumed product. In the case of Germany the calculated
TMR values represent the resource use footprint (i.e. direct and indirect TMR) of the
corresponding product group consumed by the households in Germany. The data on
expenditure of the German households were extracted from the Eurostat database. For a
detailed rationale of calculations of the total material requirement, please refer to Watson et
al. (2013, annex A) and Moll and Acosta (2006).
(4.1)
More sophisticated is the definition of total material requirement per time use categories. The
total time use
in category
is the average load of time use in Germany according the
National Survey on Time Use in Germany.
The total material requirement of time use is a re-allocation of the total material requirement
of consumption along those harmonized time use categories.
(4.2)
The marginal propensity to consume in equation (3.1) is estimated using multivariate OLS
regressions of expenditures
budget)
per category
and a vector of covariates
on disposable income (as total expenditure
and an error term
.
(5.1)
The marginal propensity to consume in equation (3.2) is estimated using a panel regression
according Hausman- Taylor (1981) of time use
in category
vector of endogenous time-varying covariates
, a vector of exogenous time-unvarying
covariates
on vector of time use
,a
, and a vector of endogenous, time-unvarying variables
(5.2)
We follow Hausman and Taylors (1981) research rationale for defining the four subgroups of
variables.
exogenous, time-varying variables and potentially uncorrelated with
such as time use
for job, education, sleep etc.
endogenous, time-varying variables und potentially uncorrelated with
such as socio-
economic characteristics like schooling years etc.
exogenous, time-unvarying variables and potentially uncorrelated with
such as gender
and birth cohorts
endogenous time-unvarying variables und potentially uncorrelated with
are not
identified.
Isolating the effect of working hours in time use in category j, the result is an HT-Estimation
of marginal propensities to time as a function of working hours , exogenous time use
endogenous, time-varying socio-economics
demographics
,
and time-unvarying, exogenous socio-
.
(5.3)
The unknown parameters
MPT in (2.1) and (2.2) with
and
and
and
are estimates of MPC and MPT. By substituting MPC and
in equation (5.1) and (5.3), as well as substituting
from equation (4.1) and (4.2) in equation (2.1) and (2.2), we derive:
(6.1)
And for
(6.2)
With average budget shares defined as the ratio of expenditures
and time use
in time use category
in consumption category
with respect to total expenditures
and total time
, respectively.
Replacing
and
in equation (1.2) with equation (6.1) and (6.2) the offsetting action is
(7.1)
And the rebound effect in equation (1.1) by substituting the expected savings
income effect
and offsetting action
with
with equation (7.1) is thus
(7.2)