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Modelling the energy demand of households
Kurt Kratena, Ina Meyer, Michael Wueger
WIFO (Austrian Institute of Economic Research)
Demand system with stocks and‚service prices‘
Expenditure function for non-durables with utility (u) and prices (pi) +
Expenditure for durables I with price (pI)
Main features:- Appliance stocks energy efficiency- Dealing with “service prices” and demand (‘rebound’
effect !)- Combining time series & cross section estimation
IppuCG Ii ),(
dtKKppuCe Iittr )(),(min )(
Demand system with stocks and‚service prices‘
Converting energy flow (E) into service (S):
Impact of the efficiency parameter (ES) on the ‘real price of service’
Budget shares = service shares
ES
SE
ES
ES
pp
C
Sp
C
EpSE
Demand system with stocks and‚service prices‘
Optimality conditions for cost minimizing:
Shephard’s Lemma envelope condition
Impact of capital stock on expenditure given by efficiency improvement-effect:
: technical progress & consumers’ choice
ii
i xp
puC
),(
Ii pr
K
puC)(
),(
KC
Sp
K
puC
K
puCESSES
ES
ii
log
log
log
log
log
),(log
log
),(log
KES
log
log
Impact of stock (changes) on efficiency
: technical progress & consumers’ choice
ADL-model with long run elasticity of efficiency wrt. to
energy prices (consumers choice) and capital stock
(autonomous/embodied technical progress)
Elasticities:
KES
log
log
m
tE
n
tEtES
l
ESpK
1,
0,,
10
loglogloglog
1
1
Almost Ideal Demand System (AIDS) or Quadratic AIDS for C(u, pi)
Budget share of AIDS
Budget share of QUAIDS
Restrictions
jijijii P
Cpw loglog
2
)(log
)()(loglog
pa
C
pbpa
Cpw i
jijijii
0 ; 0 ; 1111
n
ii
n
iij
n
ii 0
1
n
jij jiij
ii
.0
AIDS model for C(u, pi)
Elasticities
1. Income elasticities (direct derivation)
2. Price elasticities
General: ij,COMP = ij,UNCOMP + iwj (Slutsky equation)
ij,COMP …compensated price elasticity
ij,UNCOMP …uncompensated price elasticity.
i
ii
i
wC
x
1log
log i
i
C
w
log
AIDS model for C(u, pi)
Elasticities
2a. Uncompensated price elasticity
where ij is the Kronecker delta and ij = 1 for i = j and
ij = 0 for i ≠ j.
2b. Compensated price elasticity
ijj
i
ijC
ijw
w
ij
i
jiij
j
iUij w
w
p
x
log
log
Quadratic AIDS model for C(u, pi)
Elasticities
1. Differentiate wi wrt. to C and pj :
P
C
pbC
wi
i
i
ilog
)(
2
log
2
log)(
loglog
P
C
pbp
p
w ji
kkjkjiij
j
i
ij
The Quadratic AIDS model
Elasticities 2. Derive elasticities from ’s :
Income elasticity
Uncompensated price elasticity
where ij is the Kronecker delta and ij = 1 for i = j and ij = 0 for i ≠ j.
General: ij,COMP = ij,UNCOMP + i wj (Slutsky equation)
1i
i
i w
ij
i
ij
ij w
Dynamics of energy demand (Ei)
Totally differentiating E wrt. time (t)
Direct effect & indirect effect via service demand.
Total impact:
Direct (price induced-price) rebound effect
Indirect (price induced-income) rebound effect
dt
dS
S
E
dt
dE
dt
dEij
j
ii
ij
j
i
d
Ed
1
log
log
ii
C
ii
U
iiw
C
ii
Empirical application
Austria (1990 – 2006)
USA (1972 – 2005)
Austria (1990 – 2006) & Household Budget Survey 2004/05
- National Accounts (private consumption, COICOP)- Efficiency of household appliances: Refrigerators,
freezers, washing machines, dish washers, TVs, dryers, heating, water heating and cooking (National Lawrence Berkeley Laboratory, ODYSSEE database)
- Efficiency of private car fleet
Efficiency, AustriaSpecific Consumption Index: Electricity by Electrical Appliances
60.00
80.00
100.00
120.00
140.00
160.00
180.00
200.00
220.00
1970
1972
1974
1976
1978
1980
1982
1984
1986
1988
1990
1992
1994
1996
1998
2000
2002
2004
2006
Index
Refrigerators
Freezers
Washing Machines
Dish Washers
TV
Dryers
Index Weighted Average Applicances
Efficiency, Austriatechnical ODEX (specific consumption)
80.0
85.0
90.0
95.0
100.0
105.0
110.0
115.0
120.0
125.0
130.0
1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006
heating (technical) index
water heating (technical) index
cooking (technical) index
Efficiency, Austria
4
5
6
7
8
9
10
1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007
l / 1
00 k
m
gasolinedieseldiesel-eq.
Efficiency, U.S.Calcuted efficiency for fuels
60,00
70,00
80,00
90,00
100,00
110,00
1972 1975 1978 1981 1984 1987 1990 1993 1996 1999 2002 2005
spe
cifi
c e
ne
rgy
use
fuel oil
gas
electricity
gasoline
Efficiency, U.S.: energy & service price
Gasoline and oil
20,00
40,00
60,00
80,00
100,00
120,00
140,00
160,00
1972
1974
1976
1978
1980
1982
1984
1986
1988
1990
1992
1994
1996
1998
2000
2002
2004
energy price
service price
Efficiency, U.S.: energy & service priceGas
10,00
30,00
50,00
70,00
90,00
110,00
130,00
150,00
170,00
1972
1974
1976
1978
1980
1982
1984
1986
1988
1990
1992
1994
1996
1998
2000
2002
2004
energy price
service price
Efficiency, U.S.: energy & service price
Electricity
20,00
30,00
40,00
50,00
60,00
70,00
80,00
90,00
100,00
110,00
120,00
1972
1974
1976
1978
1980
1982
1984
1986
1988
1990
1992
1994
1996
1998
2000
2002
2004
energy price
service price
Estimation results: price elasticities, Austria
Uncompensated price elasticitiesFood Clothing Gasoline /Diesel Heating Electricity
Food -0.1152 -0.0117 0.1444 0.0902 -0.4074Clothing -0.0398 -1.5864 -0.3328 0.3653 0.0563Gasoline 0.8612 -0.7920 -0.4789 0.2070 -0.4818Heating 0.1766 1.0283 0.1646 -0.2742 0.7325
Electricity 0.5912 0.1740 -0.8385 0.9552 -0.1278Compensated price elasticities
Food Clothing Gasoline /Diesel Heating Electricity Food -0.0958 -0.0021 0.1481 0.0930 -0.4051
Clothing -0.0054 -1.5683 -0.3261 0.3704 0.0603Gasoline 0.7621 -0.8423 -0.4979 0.1923 -0.4936Heating 0.6282 1.2573 0.2524 -0.2075 0.7860
Electricity 0.7525 0.2558 -0.8071 0.9791 -0.1087
Empirical results: Austria
Rebound effects:
Gasoline: 50%, heating fuels: 20%, electricity: 10%, range in the literature: 10% - 30%.
Pure income rebound effects:
Gasoline: -1.9%, heating fuels: 6.6%, electricity: 2%.
Decomposing energy demand:
Further decomposition of dS/S into:
price rebound, income rebound, other factors
S
dSd
E
dE
Decomposition: Austria
overall growth in % Gasoline/Diesel Heating Electricityenergy demand 9.97 12.16 26.81
efficiency 28.24 27.19 15.62service demand 38.20 39.36 42.43
of whichprice rebound 14.06 5.64 1.70
income rebound -0.54 1.81 0.30other effects 24.68 31.90 40.43
Estimation results: price elasticities, U.S.
Uncompensated price elasticitiesFood Clothing Gasoline Heating Electricity
Food -0.4766 0.0986 0.1135 -0.0291 -0.0820Clothing 0.3437 -0.8239 -0.0296 -0.0143 0.0591Gasoline 0.7265 -0.1153 -0.1347 0.1370 -0.4701Heating -0.5894 0.0105 0.3224 -0.1916 -0.4589
Electricity 0.0222 -0.6243 -0.0241 0.1031 -0.1786Compensated price elasticities
Food Clothing Gasoline Heating Electricity Food -0.3430 0.0563 0.0893 -0.0391 -0.0965
Clothing -0.0938 -0.6865 -0.1100 -0.0474 0.0108Gasoline 0.8760 -0.0674 -0.1587 0.1483 -0.4536Heating -0.1799 0.1418 0.3977 -0.2175 -0.4137
Electricity -0.8527 -0.9048 -0.1849 0.0369 -0.0842
Empirical results: U.S.
Rebound effects:
Gasoline: 16%, heating fuels: 21%, electricity: 8%, range in the literature: 10% - 30%.
Pure income rebound effects: electricity 9.4 %.
Long-run elasticity of efficiency
Gasoline Heating Electricity long run elasticity
energy price 0.069 0.064 0.046capital stock 0.171 0.427 0.081
Simulation results: U.S. (long run change
in energy prices and capital stocks)
price elasticity short run imlicit (long run)Gasoline -0.1587 -0.563Heating -0.2175 -0.467
Electricity -0.0842 -0.153capital stock elasticity long run imlicit (long run)
Gasoline -0.171 -0.167Heating -0.427 -0.175
Electricity -0.081 -0.091
Conclusions
Rebound effects: main link between top down andbottom up modelling
Efficiency has only a limited impact on energy demand during low energy price-periods service demand is the driver of energy demand
Long run impact of prices exceeds short run impact by far