Substitution Elasticities in Swiss Manufacturing Sectors
between Energy, Capital and Labor
Lukas Mohler and Daniel Mueller
University of Basel
23rd Ph.D. Workshop on International Climate Policy
October 2011
Outline
Outline
1. Motivation
2. Literature Review and our Contributions
3. Empirical Strategy
4. Estimation Results
5. Concluding Remarks and Outlook
Motivation
Motivation
– Climate change mitigation will have a considerable effect on
production patterns, change energy prices and our welfare.
Motivation
Motivation
– Climate change mitigation will have a considerable effect on
production patterns, change energy prices and our welfare.
– Computational general equilibrium models (CGE) investigate climate
policy effects. These models have become more sophisticated in the
last two decades.
Motivation
Motivation
– Climate change mitigation will have a considerable effect on
production patterns, change energy prices and our welfare.
– Computational general equilibrium models (CGE) investigate climate
policy effects. These models have become more sophisticated in the
last two decades.
– The assumptions about the substitution elasticities are crucial for
the outcome in simulations of different scenarios.
Literature Review and our Contributions
I
Literature
Contributions to elasticities of substitution:
– Theoretical background for the estimation of elasticities: Berndt and
Christensen (1973), Jorgenson (1986) or Stern (2008).
– Capital-energy substitution debate: Berndt and Wood (1975),
Thompson (1995), Thompson and Taylor (2006) or Koetse et al.
(2007).
Literature Review and our Contributions
I
Literature
Contributions to elasticities of substitution:
– Theoretical background for the estimation of elasticities: Berndt and
Christensen (1973), Jorgenson (1986) or Stern (2008).
– Capital-energy substitution debate: Berndt and Wood (1975),
Thompson (1995), Thompson and Taylor (2006) or Koetse et al.
(2007).
Contributions to the climate policy analysis:
– Swiss perspective: Bernard and Vielle (2007), or Ecoplan (2007).
– International perspective: Boehringer et al. (2010).
Literature Review and our Contributions
II
Our contributions
– We estimate sector-specific substitution elasticities between energy,
capital, labor and material for Switzerland and 14 other countries.
– Comparison of the factor shares and the elasticities of substitution
between sectors, as well as between countries.
Literature Review and our Contributions
II
Our contributions
– We estimate sector-specific substitution elasticities between energy,
capital, labor and material for Switzerland and 14 other countries.
– Comparison of the factor shares and the elasticities of substitution
between sectors, as well as between countries.
– Moreover, we test whether capital and energy are substitutes or
complements. The use of sector-specific data for 15 countries gives
a detailed picture of the substitution patterns.
Empirical Strategy
Empirical Strategy
Empirical Strategy
I
The production model
– We assume a sector-specific production model with the input factors
capital (K), labor (L), energy (E), and material (M).
– Our specification of the production function is the translog
production function. For the estimation of the elasticities we use
cost functions instead of production functions.
Empirical Strategy
I
The production model
– We assume a sector-specific production model with the input factors
capital (K), labor (L), energy (E), and material (M).
– Our specification of the production function is the translog
production function. For the estimation of the elasticities we use
cost functions instead of production functions.
– We estimate cross-price elasticities (CPE), Morishima elasticities
(ME) and Allen partial elasticities of substitution (AES).
The CPE and the AES measure the quantity response of one input (∆si )
due to a price change.
The ME measures the response of a factor ratio (∆(si /sj )) due to a price
change.
Empirical Strategy
II
Estimation procedure
– The factor share equation is
X
sin,t = βin +
βij ln(pjn,t ) + βiny ln yn,t + βin,t t.
j
– The equation of the CPE and the AES elasticities are
CPEij =
β̂ij + si sj
β̂ij + si sj
, AESij =
.
si
si si
– The equation of the ME is
MEij = CPEij − CPEjj .
To estimate the model we apply a three stage least square estimator
(3SLS) and standard OLS.
Empirical Strategy
III
Covered countries and the aggregation of sectors
Covered countries:
Non-EU countries: Switzerland, Japan
EU countries: Belgium, Czech Rep., Denmark, Spain, Finland, France,
Germany, Hungary, Italy, Netherlands, Slovenia, Sweden, United Kingdom
Aggregates of Manufacturing Sectors:
Sectors
1
2
3
4
5
6
7
8
9
10
11
12
Description of the Manufacturing Sector
Food products and beverages
Textile products, leather and footwear
Products of wood and cork
Pulp, paper products, printing and publishing
Chemicals and chemical products
Rubber and plastic products
Other non-metallic mineral products
Basic metals and fabricated metal products
Machinery and equipment
Electrical and optical equipment
Transport equipment
Furniture, other manufacturing and recycling
Estimation Results
Estimation Results
Estimation Results
I
Empirical Strategy
Descriptive
Statistics:
Comparison
of Cost Shares
Empirical Strategy
III - Comparison
of Cost Shares
The cost shares of the input factors are defined as the costs of one input
– The cost shares of the input factors are defined as the costs of one input
factor factor
divided
by total costs. We start by looking at some descriptive
divided by total costs.We start by looking at some descriptive
statistics.
statistics.
Table: Comparison of the cost shares: Switzerland vs. median of all countries
Labor
Sector
1
2
3
4
5
6
7
8
9
10
11
12
CHE
0.177
0.303
0.336
0.344
0.167
0.284
0.297
0.343
0.287
0.262
0.284
0.297
Med
0.165
0.247
0.260
0.240
0.159
0.242
0.252
0.228
0.252
0.230
0.161
0.279
Material
CHE
0.624
0.491
0.445
0.375
0.461
0.487
0.406
0.410
0.510
0.471
0.534
0.466
Med
0.590
0.497
0.501
0.406
0.428
0.458
0.378
0.484
0.483
0.488
0.616
0.464
Energy
CHE
0.016
0.020
0.017
0.035
0.015
0.030
0.045
0.024
0.006
0.005
0.018
0.014
Med
0.020
0.020
0.026
0.029
0.058
0.028
0.067
0.039
0.013
0.011
0.011
0.017
Capital
CHE
0.184
0.186
0.201
0.247
0.357
0.199
0.252
0.223
0.197
0.261
0.164
0.223
Med
0.232
0.203
0.214
0.291
0.334
0.255
0.298
0.227
0.228
0.247
0.189
0.220
Estimation Results
I
Descriptive Statistics: Comparison of Cost Shares
The cost shares of the input factors are defined as the costs of one input
factor divided by total costs. We start by looking at some descriptive
statistics.
Estimation Results
II
Elasticities between labor and capital (CPELC )
Labor price on capital input
4
4
3
3
2
2
1
1
0
0
-1
-1
-2
-2
-3
-3
-4
-4
1
2
CHE
3
BEL
4
CZE
DNK
5
ESP
6
FIN
FRA
7
GER
8
HUN
ITA
9
JPN
10
NLD
SVN
11
SWE
12
UK
Estimation Results
III
Elasticities between energy and capital (CPEEC )
Energy price on capital input
20
20
15
15
10
10
5
5
0
0
-5
-5
-10
-10
-15
-15
-20
-20
1
2
CHE
3
BEL
4
CZE
DNK
5
ESP
6
FIN
FRA
7
GER
8
HUN
ITA
9
JPN
10
NLD
SVN
11
SWE
12
UK
Estimation Results
IV
Capital-Energy Substitution Debate
We then calculate Morishima elasticities between capital and energy.
Displayed are the percentages of positive sector-estimates:
Table: Country comparison of the substitution patterns
Country
Energy-Capital
Energy-Labor
Capital-Labor
CHE
BEL
CZE
DNK
ESP
FIN
FRA
GER
HUN
ITA
JPN
NLD
SVN
SWE
UK
65%
85%
77%
65%
58%
88%
62%
81%
77%
69%
77%
81%
77%
69%
77%
50%
77%
85%
85%
81%
73%
81%
92%
88%
77%
85%
92%
88%
77%
85%
81%
77%
77%
77%
81%
58%
88%
81%
73%
77%
69%
81%
73%
77%
69%
Concluding Remarks and Outlook
Concluding Remarks
Concluding Remarks and Outlook
I
Concluding Remarks
– There are considerable differences between the elasticities both
across sectors and across countries.
Concluding Remarks and Outlook
I
Concluding Remarks
– There are considerable differences between the elasticities both
across sectors and across countries.
– Therefore, using sector-specific estimates in CGE models will
improve the reliability of forecasts and simulations of different
mitigation policies.
Concluding Remarks and Outlook
I
Concluding Remarks
– There are considerable differences between the elasticities both
across sectors and across countries.
– Therefore, using sector-specific estimates in CGE models will
improve the reliability of forecasts and simulations of different
mitigation policies.
– Whether energy and capital are substitutes or complements depends
on the sector of interest. Moreover, the country also matters.
– There are major differences between countries when comparing the
rate of sectors where energy and capital are substitutes.
Concluding Remarks and Outlook
II
Outlook
Yet to be done:
– Estimate the elasticities with other production function
specifications.
– Test whether more restrictive assumptions change our results.
– Analyze the differences between short-run and long-run elasticities.
Thank you for your attention!