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