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LIBRARY
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This is to certify that the

dissertation entitled

ENERGY-SUBSTITUTION IN THE PAPER INDUSTRY IN BRAZIL: A
TRANSLOG FUNCTION APPROACH

presented by

 

Josmar Verillo

has been accepted towards fulfillment
of the requirements for

DOCTOR OF PHILOSOPHY degreein RESOURCE DEVELOPMENT

 

 

 

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ENERGY-SUBSTITUTION IN THE PAPER INDUSTRY IN BRAZIL: A
TRANSLOG FUNCTION APPROACH

By

Josmar Verillo

A DISSERTATION

Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

DOCTOR OF PHILOSOPHY

Department of Resource Development

1988

ABSTRACT

ENERGY-SUBSTITUTION IN THE PAPER INDUSTRY IN BRAZIL: A
TRANSLOG FUNCTION APPROACH

By

Josmar Verillo

This study' attempts to estimate energy substitution
possibilities in the manufacturing sector of the economy.
Unlike the majority of studies it focuses at the micro level
instead of the aggregate. The method employed involves the
use of econometric techniques to estimate translog cost and.
production functions, and the estimation of the Allen
Elasticities of Substitution (ABS) from the coefficients.
The data used in the study come from firms in the paper
industry of Brazil during the period of January, 1982 to
December, 1987.

When using aggregated data, findings concerning energy-
capital substitution are often controversial. Some authors
find substitutability while others find complementarity
between energy and capital. This study found that this
ambiguity also appears at the micro level. Even when the
firms belong to the same industry, two inputs can be
complements in one firm and substitutes in another.

The basic findings are: 1) Energy demand is found to be

responsive to price changes, 2) Fossil fuels and biomass are

substitutes, 3) Biomass and capital are substitutes, 4)
Fossil fuels and hydroelectricity are complements, 5)
Hydroelectricity and capital are complements, 6) Labor and
materials are substitutes, and 7) Capital and labor are
substitutes. The other elasticities are ambiguous, varying
from firm to firm, or not significant at the 5 per cent
level.

The method used did not capture the dynamics of the
data. Further research is needed in the improvement of the
method. The time span and the size of the sample should be
increased in future studies. For some industries five years
is too short a period to capture important structural
changes.

The ambiguity found in the' elasticity’ estimates is
enough to render assumptions behind some government policies
unwarranted. For the effect of macroeconomic policy it is
not correct to assume either energy-capital complementarity
or substitutabilityu Furthermore, some fuel groups are
shown to be complements rather than substitutes. In such
cases, government policies designed to encourage reduction
in the consumption of one type of fuel may increase
consumption of both fuels. Knowledge about those
elasticities of substitution may help planners to argue
against energy policies which have little chance of

succeeding.

Copyright by
JOSMAR VERILLO
1988

To Fernanda.

ACKNOWLEDGMENTS

This dissertation is the culmination of a long and
challenging endeavor. I obtained help from many people and
many sources and it will be impossible to thank everybody
here. I am particular grateful to Professor Thomas Edens
for his guidance, support, and friendship. My journey would
have been a lot more difficult without his help.

O My special thanks to Professor Paul Strassmann who
helped me with advice and guidance during difficult times of
my program and provided me with the opportunity of co-
authoring Th.e...-...,-Qlobal Construction Induetrz which was a
formidable experience.

My thanks to Dr. George Axinn who provided helpful
comments on my work, and who, as adviser of the Thoman
Fellowship program, provided me also with an insightful
experience in food security. My thanks go also to Dr.
Milton Steinmueller for his help and friendship.

I would also like to thank Eraldo S. B. Merlin for his
assistance in providing access to the firms of the Klabin
Group. Thanks to my friend Isidore Flores who helped me with
editing as well as in many other occasions during my stay at

Michigan State. My thanks also to Professor Peter Schmidt

V1

who helped me with clarifications of econometric concepts
and to Kwok Hung Cheung (Francis) for helping with economics
and statistics concepts.

Thanks is also due to The Conselho Nacional de
Desenvolvimento Cientifico e Tecnologico (CNPq) which funded
part of my program, and the Industrias Klabin de Papel e
Celulose s/a which provided funds for research expenses and
allowed me to conduct research in the firms of the Group. I
owe~ my thanks also to several employees of the Klabin
enterprises who helped in gathering the necessary data.

Finally, thanks to Lorival, Lizete, and Maria de
Lourdes; my brother, sister, and mother respectivelly, for
sharing the burden of taking care of our concerns in Brazil.
during the last eight years. My thanks go also to my wife
Fernanda who was a wonderful partner in this
entrepreneurship.

All mistakes are my responsibility.

V11

TABLE OF CONTENTS

LIST OF TABLES . . . . . . . . . .
LIST OF FIGURES O O O O O O O O O 0

LIST OF SYMBOLS AND ABBREVIATIONS.

CHAPTER 1. . . . . . . . . . . . .
Introduction. . . . . . . . .
Defining Energy. . . . .

The Role of Energy in Economic

Development. . . . .

Energy Price Differentials Among

Countries. . . . . . .

Price Differentials, Terms of Trade, and

Elasticities . . . . .
Addressing Priorities. .
Energy Substitution. . .

Organization of the Thesis

CHAPTER 2 0 O O O 0 O O O O O O O I

The Capital-Energy Complementary Debate . . .

CHAPTER 3 C C C O O O O O O O O O O

Econometric Models and Estimating

CHAPTER 4 O O O O O O O O O O O O 0
Data and Estimation . . . . .
Data 0 O I O O O O O I O

Elasticity Estimates . .

The Four Inputs Estimates.

Cost Function . . .
Production Function
The Six Input Estimates.
Cost Function . . .
Production Function

CHAPTER 5 O I I O O O O O O O O O 0
COMMENTS AND CONCLUSION . . .

viii

Problems. .

Page

xiv

xvii

NHH

13
14
17

18
18

34
34

53
53
54
62
65
65
66
67
67
7O

97
97

APPENDIX

APPENDIX A.
APPENDIX B.
APPENDIX C.

BIBLIOGRAPHY

ix

Page
125
127
139

176

Table

Table

Table

Table

Table

Table

Table

Table

Table

LIST OF TABLES

IKPC - Sure Parameter Estimates of E,
K, L, and M - Cost Function Jan/82
to Dec/87 . . . . . . . . . . . . . .

PCC - Sure Parameter Estimates of E,
K, L, and M - Cost Function Jan/82
to Dee/87 O O O O O O O O 0 O 0 O O 0

RIOCELL - Sure Parameter Estimates of
E, K, L, and M - Cost Function Jan/82
to Dee/87 O O O O O O O O O O O O O O

IKPC - Sure Paremeter Estimates of E,
K, L, and M - Production Function
Jan/82 to Dee/87. O O O O O O O O O 0

FCC - Sure Parameter Estimates of E,
K, L, and M - Production Function
Jan/82 to Dec/87. . . . . . . . . . .

RIOCELL - Sure Parameter Estimates
of E, K, L, and M - Production
Function Jan/82 to Dec/87 . . . . .

IKPC - Sure Parameter Estimates of
E1, E2, E3, K, L, and M - Cost
Function - Energy Disaggregated
Jan/82 to Dec/87. . . . . . . . . .

PCC - Sure Parameter Estimates of
E1, E2, E3, K, L, and M - Cost
Function - Energy Disaggregated
Jan/82 to Dec/87. . . . . . . . . .

RIOCELL - Sure Parameter Estimates of
E1, E2, K, L, and M - Cost

Function - Energy Disaggregated
Jan/82 to Dec/87. . . . . . . . . . .

Page

74

74

75

75

76

76

77

78

79

Table

Table

Table

Table

Table

Table

Table

Table

Table

Table

10

11

12

13

14

15

16

17

18

19

IKPC - Sure Parameter Estimates of
E1, E2, E3, K, L, and M — Production
Function - Energy Disaggregated

Jan/82 to Dec/87. . . . . . . . . . .

PCCI - Sure Parameter Estimates of

E1, E2, E3, K, L, and M - Production
Function - Energy Disaggregated

Jan/82 to Dec/87. . . . . . . . . . . . .

RIOCELL - Sure Parameter Estimates of

E1, E2, K, L, and M - Production
Function - Energy Disaggregated

Jan/82 to Dec/87. . . . . . . . . . . . .

IKPC - Sure Estimated Allen

Elasticities of Substitution, (AES)

Cost Function (E, K, L and M)

Jan/82 to Dec/87. . . . . . . . . . . . .

PCC — Sure Estimated Allen

Elasticities of Substitution, (AES)

Cost Function (E, K, L and M)

Jan/82 to Dec/87. . . . . . . . . . . . .

RIOCELL - Sure Estimated Allen
Elasticities of Substitution, (AES)
Cost Function (E, K, L and M)

Jan/82 to Dec/87. . . . . . . . . . . .

IKPC - Sure Estimated Allen

Elasticities of Substitution, (AES)
Production Function (E, K, L and M)
Jan/82 to Dec/87. . . . . . . . . . . . .

PCC - Sure Estimated Allen
Elasticities of Substitution, (AES)
Production Function (E, K, L and M)
Jan/82 to Dec/87. . . . . . . . . . . .

PCC — Sure Estimated Allen

Elasticities of Substitution, (AES)
Production Function (E, K, L and M)
Jan/82 to Dec/87. . . . . . . . . . . . .

IKPC - Sure Estimated Allen

Elasticities of Substitution, (AES)

Cost Function - Energy Disaggregated

(E1, E2, E3, K, L and M) Jan/82 to Dec/87

xi

Page

80

81

82

83

84

85

86

86

87

Table

Table

Table

Table

Table

Table

Table

Table

Table

Table

Table

Table

20

21

22

23

24

25

26

27

28

29

3O

31

PCC — Sure Estimated Allen

Elasticities of Substitution, (AES)

Cost Function - Energy Disaggregated

(E1, E2, E3, K, L and M) Jan/82 to Dec/87

RIOCELL — Sure Estimated Allen
Elasticities of Substitution, (AES)

Cost Function - Energy Disaggregated

(E1, E2, E3, K, L and M) Jan/82 to Dec/87

IKPC - Sure Estimated Allen

Elasticities of Substitution, (AES)
Production Function - Energy Disaggregated
(E1, E2, E3, K, L and M) Jan/82 to Dec/87

PCC - Sure Estimated Allen

Elasticities of Substitution, (AES)
Production Function - Energy Disaggregated
(E1, E2, E3, K, L and M) Jan/82 to Dec/87

RIOCELL - Sure Estimated Allen
Elasticities of Substitution, (AES)
Production Function - Energy Disaggregated
(E1, E2, K, L and M) Jan/82 to Dec/87. . .

Summary — Four Inputs (E, K, L and M)

Cost and Production Functions

IKPC, PCC, and RIOCELL . . . . . . . . . .
Summary - Six Inputs (E1, E2, E3, K, L, M)
Cost and Production Functions

IKPC, PCC, and RIOCELL . . . . . . . . .

Elasticities of Substitution
Reported in the Literature . . . . . . .

Input Productivity, Aggregated Data
IKPC, PCC, and RIOCELL (1982-1987) . . . .

Wage Rate - Average Cost Per Worker
Aggregated Data - Jan/82 Dollars . . . . .

Labor Productivity (Tons per Worker)
Disaggregated Data, IKPC, PCC, and RIOCELL
(1982-1987) a o o o o o o o o o o o o o o

Wage Rate - Average Cost Per Worker

Disaggregated Data, IKPC, PCC, and RIOCELL
Jan/82 DOllfiPS (1982-1987) 0 o o o o o o 0

xii

Page

89

9O

91

92

93

94

95

96

114

115

116

117

Table

Table

Table

Table

Table

Table

Table

Selected Studies on Factor Substitution

APPENDIX A

Findings and Methodology . .

Data

Data

Data

Data

Data

Data

APPENDIX B
IKPC - Four Inputs.
PCC - Four Inputs. .
RIOCELL - Four Inputs
IKPC - Six Inputs . .
PCC — Six Inputs. .

RIOCELL - Six Inputs.

xiii

Page

125

127
129
131
133
136

139

Figure

Figure
Figure
Figure

Figure

Figure

Figure

Figure

Figure

Figure

Figure

Figure

Figure

Figure

LIST OF FIGURES

Diagrams of Countries According to Energy
Status I I I I I I I I I I I I I I I I I

IKPC - Energy/Output Relationship. . . .
PCC - Energy/Output Relationship . . . .

RIOCELL - Energy/Output Relationship

Fuel Oil Use and Prices - IKPC, PCC,

and RIOCELLI I I I I I I I I I I I I I I
IKPC - Elasticity of Substitution -
Energy/Capital . . . . . . . . . . . . .
PCC - Elasticity of Substitution -
EnerEY/Capital I I I I I I I I I I I I I
RIOCELL - Elasticity of Substitution -
Energy/Capital . . . . . . . . . . . . .
APPENDIX C

IKPC - Energy - Fitted Equation - Cost
FunCtion " 4 Inputs. 0 o o o o o o s o o

IKPC - Energy - Fitted Equation -
Production Function - 4 Inputs . . . . .

IKPC - Capital Fitted Equation - Cost
Function - 4 Inputs. . . . . . . . . . .

IKPC - Capital - Fitted Equation -
Production Function - 4 Inputs . . . . .

I
O
O
(.0
fl

PCC - Energy - Fitted Equation
Function " 4 Inputs. 0 o o o o o o o o

PCC - Energy - Fitted Equation -
Production Function - 4 Inputs . . . . .

xiv

Page

104
105

106

110

121

122

123

142

143

144

145

Figure

Figure

Figure

Figure

Figure

Figure

Figure

Figure

Figure

Figure

Figure

Figure

Figure

Figure

Figure

Figure

Figure

Figure

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

PCC - Capital - Fitted Equation - Cost
Function - 4 Inputs. . . . . . . . . . .

PCC - Capital - Fitted Equation -

Production Function - 4 Inputs . . . . . .
RIOCELL - Energy - Fitted Equation — Cost
Function - 4 Inputs. . . . . . . . . . . .
RIOCELL - Energy - Fitted Equation -

Production Function - 4 Inputs . . . . . .

RIOCELL - Capital - Fitted Equation - Cost
Function - 4 Inputs. 0 o o o o o o o o o o

RIOCELL - Capital - Fitted Equation -

Production Function - 4 Inputs . . . . . .
IKPC - Biomass - Fitted Equation - Cost
FunCtion - 6 Inputs. 0 o o o o o o o o o o
IKPC - Biomass - Fitted Equation -
Production Function - 6 Inputs . . . . . .

IKPC - Fossil Fuels - Fitted Equation -
Cost Function - 6 Inputs . . . . . . . . .

IKPC - Fossil Fuels - Fitted Equation —
Production Function - 6 Inputs . . . . . .

IKPC - Hydroelectricity - Fitted Equation

Cost Function - 6 Inputs . . . . . . . . .
IKPC - Hydroelectricity - Fitted Equation
Cost Function ~ 6 Inputs . . . . . . . .
IKPC - Capital - Fitted Equation —

Cost Function - 6 Inputs . . . . . . . . .
IKPC - Capital - Fitted Equation -
Production Function - 6 Inputs . . . . . .
PCC - Biomass - Fitted Equation -

Cost Function - 6 Inputs . . . . . . . .

PCC - Biomass - Fitted Equation -
Production Function - 6 Inputs

PCC - Fossil Fuels - Fitted Equation -
Cost Function - 6 Inputs . . . . . . . .

PCC - Fossil Fuels - Fitted Equation -
Production Function - 6 Inputs . . . . . .

XV

Page

148

149

150

151

152

153

154

155

156

157

158

159

160

161

162

163

164

165

Figure

Figure

Figure

Figure

Figure

Figure

Figure

Figure

Figure

Figure

25

26

27

28

29

30

31

32

33

34

PCC - Hydroelectricity — Fitted Equation
Cost Function - 6 Inputs . . . . . . . .

PCC - Hydroelectricity - Fitted Equation
Production Function — 6 Inputs . . . . .

PCC - Capital - Fitted Equation -
Cost Function - 6 Inputs . . . . . . . .

PCC - Biomass - Fitted Equation —
Production Function - 6 Inputs . . .

RIOCELL - Biomass - Fitted Equation —
Cost Function - 5.Inputs . . . . . . . .

RIOCELL - Biomass - Fitted Equation -
Production Function - 5 Inputs . . . . .

RIOCELL - Fossil Fuels - Fitted Equation
Cost Function - 5 Inputs . . . . . . . .

RIOCELL - Fossil Fuels — Fitted Equation
Production Function - 5 Inputs . . . . .

RIOCELL - Capital - Fitted Equation -
Cost Function - 5 Inputs . . . . . . .

RIOCELL - Capital - Fitted Equation -
Production Function — 5 Inputs . . . . .

xvi

Page

166

167

170

171

172

173

174

175

AES

A13

C

CL
Cruzado
Cruzeiro
E‘

E1

Fiscal OTN

G13
IBSLS
ICs

IKPC

KLME

LIST OF SYMBOLS AND ABBREVIATIONS

Allen Elasticity of Substitution
Elasticity of substitution from production
function

Cost

Coal

Brazilian currency since February, 1986
Brazilian currency until January, 1986.
Energy

Biomass

Fossil Fuels

Hydroelectricity

Elasticity of demand

OTN used for taxation purposes, daily
readjusted

Elasticity of substitution in general
Iteractive Three Stage Least Squares
Industrialized Countries

Indnstrias Klabin de Papel e Celulose S/A
Capital

Refers to the 4 input model Of estimating
cost and production functions.

Labor

xvii

LICs

ln

OECD

OECs

OEICs

OELICS

OICs

OIICs

OILICS

OLS

ORTN

OTN

PCC

Pi

RIOCELL

SHARE

SHAREI

SHAREZ

SHARE3

SHARK

SHARL

SHARM

Si

Less Industrialized Countries

Natural logarithm

Materials

Natural gas

Hicks Elasticity of Complementarity
Organization for Energy Conservation and
Development

Oil Exporting Countries

Oil Exporting Industrialized Countries

Oil Exporting Less Industrialized Countries
Oil Importing Countries

Oil Importing Industrialized Countries

Oil Importing Less Industrialized Countries
Ordinary Least Squares

Indexed National Treasury Bonds

Indexed National Bonds, monthly readjusted.
Papel e Celulose Catarinense S/A

Price of input 1

Riocell S/A

Share of energy in the total cost

Share of biomass in the total cost

Share of fossil fuels in the total cost
Share of hydroelectricity in the total cost
Share of capital in the total cost

Share of labor in the total cost

Share of materials in the total cost

Share of output i in the total cost

xviii

SIC

SURE

TOE
Translog
UPC

URP

VAR

Standard

Industrial Classification

Seemingly Unrelated Regression Equations

Tons of oil equivalent

Transcendental logarithmic function

Standard
Standard
readjust
Variance
Quantity

Output

Unity of Capital
readjustment unity - used to

wage rates.

of input i

Elasticity of substitution from cost function

Partial derivative

xix

CHAPTER 1

INTRODUCTION

This dissertation investigates the general area of
energy substitution, with special focus on the paper
industry in Brazil. The study of input substitution using
translog functions at the macro level was argued against
recently by John Solow on the basis that the methodology is
not appropriate for macro-level studies. This work will
focus at the micro level, the firm. The objective is to
learn something not only about the process of energy-capital
substitution but also about the appropriateness of the
methodology, which consists basically of a technique for
estimating demand functions derived from translog cost and
production functions, and subsequent calculation of the
elasticities based on the estimated parameters.1

Fist, however, the study must be put in the context of
a broader picture, including the dilemma facing Less
Industrialized Countries (LICs), and the importance of
government policy concerning energy use, conservation and

substitution.

 

1. Blitzer, C. R. "Energy-Economy Interactions in Developing
Countries" Ihe Eneggx Jguggal Vol. 7, No. 1, 1986.

1

Defining Energy

Energy may be looked at from several perspectives. In
areas where more elaborate energy sources are not present,
the main source of energy is human energy. In order to
avoid any misinterpretation of what is meant by energy in
the context of this thesis, a definition should be in place.
Depending on the discipline analyzing energy, the
distinction between human and other sources of energy
becomes blurred, so a cuttoff point will be provided in
order that this study be confined to those limits. Energy
in this study is constrained to include certain types of
fuel including oil, coal, biomass, and hydroelectricity.’

It must also be clarified that in thermodynamics energy
does not disappear, it is simply converted to a different
form. From an economists’ perspective, when energy is used
in the production process, for all intents and purposes, it
disappears. 'This study' will not be concerned. with the
energy contained in the paper produced by the firms; it will
be concerned only with the energy used to manufacture the

product.

The Role of Energy in Economic Development
Energy plays a major role in the achievement of a

higher standard of living among industrialized nations. It

.. mun..." u."

 

2. Hydroelectricity is electriCity generated by dams, water
falls, etc... Water at a certain height contains an
energy potential. When this potential is released and
converted into electricity, it is referred to as
hydroelectriCity.

3

is an important and pervasive input. It has been associated

with increased use of capital and labor productivity

enhancement. Labor productivity in 103 has increased
considerably due to the use of energy. Evidence indicates
that as a country goes through the stages of

industrialization, output becomes more energy intensive.3
This fact raises questions about the capability of Less
Industrialized Countries (LICs) to increase their standards

of living in a world of steadily dwindling energy resources.

Energy Price Differentials Among Countries

Energy prices differ among countries. An appropriate
way of establishing the true cost of energy is to measure,
at the local level, the basket of goods traded for the
equivalent of a barrel of oil, or any other energy
equivalent. Such an analysis shows that imported energy is
often considerably more expensive in countries which depend
on primary goods or low specialization manufacturing exports
to earn foreign exchange needed to purchase oil.‘ To
illustrate the point, terms of trade for Brazil deteriorated

from an index of 100 in 1977 to 55 in 1985. That translates

 

3. Energy in Transition:l985-2010, Final Report of the
Committee on Nuclear and Alternative Energy Systems,
National Research Council, flatiggal Agaggmy 9f
Sciences, Washington, 0.0., 1979. page 109; Cleveland
at al. (1984).

4. "The Effects of National and International Policies on
Renewable Resource Use," in {Lansfigrming flatugal

Efiémework for Development Policy, Keneth Ruddle, and
Dennis A. Rondinelli, The United Nations University,
1983.

4

to a loss of roughly 45 per cent in purchasing power.5
Exports are valued significantly less than imports. In
order to better understand the effects of the energy crisis
in different groups of countries, they may be classified in
two» major categories: industrialized. countries (ICs) and
less industrialized countries (LICs). The 103 can be oil
importing industrialized countries (OIICs) or oil exporting
industrialized countries (OEICs). The LICs can also be
subdivided into oil importing less industrialized countries
(OILICs) and. oil exporting less industrialized. countries
(OELICs). This classification is shown in Figure 1.

The lower prices of commodities, and higher prices of
industrialized goods make the energy crisis a thing of the
past for the 103, at least for the time being. This
explains the decrease of research activity in alternative
energy sources, conservation, and energy substitution among
these countries. The wealth transferred in the 1970s from
the 0103 to the OECs has been reclaimed, in part, by the
01103. The OILICs, however, lost purchasing power when oil
prices were increased and they had to pay more for it; they
lost again when 108 increased the prices of their goods to
compensate for the higher oil prices. This may be one
explanation for the relatively increasing impoverishment of

OILICs. Their share of the global pie declined considerably

 

S. Baer, Werner; "The Resurgence of Inflation in Brazil,
1974-86, Wordmgeyelgpment, Vol. 15, N.8, 1987, p. 1013.

 

5

as their products faced lower demand and increased

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

competition.
Figure 1
I All Countries I
Less Industrialized Industrialized
Countries Countries
LICs ICs
r“|——I , r-“|"“n
Oil Oil Oil Oil
Exporters Importers Importers Exporters
OELICs OILICs OIICs OEICs
Oil Importing Countries I
0108
. -- _- -- -- -- -- -- -- -_ -- -- J
Oil Exporting Countries
OECs J

 

 

The OILICs face the paradoxical situation that to
increase exports, they may have to become more energy
intensive. ICs demand energy-intensive products. The
products are more elaborate, which causes them to have a
larger energy content than the products demanded in less

industrialized societies. lJCs trying to increase exports

6
to that market must necessarily turn their production
process into a more energy-intensive one, unless they are
able ix) produce technological innovations capable of
generating elaborated products with low energy content, or
if they are able to tap other sources of energy (like sun
light, for example) at lower cost. This is not likely to
happen in the near future because LICs are known to import
technology from the ICs.‘ Energy intensity can only
increase if significant technological advances are not made

in the LICs.

Price Differentials, Terms of Trade, and Elasticities
Industrialized products do not suffer supply and demand

shocks which cause export earnings and the entire economy to

be essentially unstable.7 Production of video cassette

players, cameras, autos, or capital goods takes some time to

increase since plants need to be built. Production is
affected only years ahead. In the case of crops, there are
sharp fluctuations from one year to another. It is common

to see large number of farmers planting corn because in the
previous year prices of corn were good. When a farmer loses
money on a crop, he normally tries something else. If

everybody follows the same logic, following a year of low

 

o‘em-e o-I- ”cu-us... . . u

6. 8051n, Kim; and Fairchild, Loretta; "Capital Intensity
and Export Propensity in Some Latin American
CountrieS." Oxford Bulletin QIMEQQDQMIgfiméng
Statistics. N- 49. 1987 (2).

7. Murray, David; "Export Earnings Instability: Price,
Quantity, Supply, Demand?“ Economic Development and
Cultural Change, October, 1978.

7

prices, a great number farmers would raise an alternative
crop. If the majority chooses to grow the same crop, the
same thing would happen again. The difficulty in planning
what to grow is that nobody knows with certainty what the
demand for the commodity is going to be at the time of
harvest. Besides the uncertainty in the demand side there
is the uncertainty in the supply side because there is no

way to know how much of each crop is being cultivated.°

Even within the same country, it is very difficult to
plan how much of each crop to sow. ID) many countries the
government intervenes to try to avoid the problem of over
'cultivation. Yet, significant mismatches between supply and
demand happen. When it comes to the international market,
the farmers in South America do not know what the North
Americans are planting. It might be the case that most
farmers will go to the same crop which means that an excess
supply of that commodity will emerge in the international
market. A familiar situation arises. Sellers lower prices
as an incentive to buyers causing revenues to fall sharply.
Countries depending for revenues to import oil on crops
subject to overcultivation will be in a position where they

have to borrow for energy imports, or to cut consumption.

 

8. New techniques like remote-sensing techniques may help
USDA and FAQ to know how much of each crop is planted.
But this is known only after the fields are sown, and
this information may never get to the farmers. The
knowledge about the amount of each crop planted all
over the world may in fact harm the farmers instead of
helping them.

8

The competitive market for crops exists, in part,
because entry is easier than in other very specialized
activities. Knowledge to practice agriculture is public
information at the reach of any interested customer. It is
a popular belief that hunger is associated with lack of
production. Commonly advocated solutions to the problem of
hunger call for increases in agricultural production. Some
programs succeed in increasing agricultural production only
to find out that there are no buyers. Hunger exists because
the entitlements to buy the products are not available, not
because there is lack of production or knowledge to go into
the business of agriculture.’ Knowledge to grow crops is
not lacking; it is made available anywhere in the globe.
Knowledge is not a constraint in the same way as it would be
in building a microchip. The latter kind of knowledge is
kept in private hands as much as possible so that rent for
the exploitation of that knowledge can be maximized.

The point to be made is that the market for primary
products is inherently unstable because entry is easy,
making competition intense. Demand fluctuates severely from
year to year; it is difficult to plan in advance what to
sow. Once the crops are sown, there is no reversal. Many
products are perishable, while others have close substitutes

which creates pressure to sell fast. These characteristics

 

9. Sen, Amartya; Poverty and Famings; Agmgssay on

Entitlement_anglnescixation. Clarendon PreSS. Oxford.
1981.

9

in agricultural products are not shared by many of the IC’s
products.

One can argue that technological knowledge is a matter
of degree. Some technologies are public knowledge, others
are not. 'The LICs are active in the areas where the
technology of production is public knowledge; ICs are active
in the areas where technology is private knowledge. To be
successful in the markets where technology is public
knowledge, the producer' must have lower cost or higher
quality. There are near public knowledge technologies which
are still not within the reach of lJCs because of lack of
capital and organizational constraints.lo The LICs are
active in markets where the ICs can enter and compete
freelyu The LICs, however, do not have the option of
choosing to compete in the high technology markets.H The
U.S., for example, is active in markets for both
agricultural and high technology products.

In the case of high tech products like audio
recorder/players, trucks, computers, optical devices,
advanced medicines, machine tools, robots, and chemicals;
knowledge is a constraint, if not at the level of physical

production, at the level of organization and marketing, or

 

- - -.. .flqnamsuu

10. An example is the automobile. Production is capital
intensive, and competitive prices may be achieved only
with the type of organization the Japanese and the
Americans have. The specialized knowledge in this case
is in the organizational aspect of production, not in
the assembly line itself.

11. There are exceptions, but they cannot be explained
solely on the grounds of economic policy.

10
capital availability. It. is difficult for the LICs to

compete in this market. Production of such goods is
restricted to firms in the ICs, while demand for the
products exists all over the world, including the LICs.

It is very difficult for LIC governments to convince
their urban middle classes that priorities need to be
assigned in the use of foreign currency. Once people know
about an innovation that makes life easier, or more
pleasant, they want to acquire it if resources are
available. Most of these innovations occur in the ICs, but
once known in the 1.103, demand for them grows there also.
Priorities are justified by the criterion of social returns.
Accordingly, foreign currency should be used in purchases-
which maximize accrual to the society. A government
normally assigns priority to medicines, oil, and capital
goods, among others. In its view, returns on these goods
are greater than if each individual is allowed to ‘buy
according to means. Non adherence to this criterion would
have serious consequences in countries with a very
unbalanced distribution of income such as Brazil. In this
case the most well off portion of the population would have
access to a disproportionate amount of foreign currency in
detriment to the majority of the population.

In non-socialist countries the simple need of adoption
of those priorities is tantamount to the recognition of
failure in the efforts to democratize economic

opportunities. Be that as it may, the widespread existence

11

of black markets in LICs is an indication that the
government cannot effectively control or suppress the demand
for industrialized products, unless they push wage rates
further down. But this is only feasible up to a point due
to the risk of social unrest. The government is left with
two alternative paths: 1) Try to initiate its own production
(public or private), or 2) Allow the producing firms to
install plants within the country, and try to make the most
of it.

The first alternative could be very costly because it
involves duplication of effort.u Many things must be
rediscovered. Instead of using knowledge readily available,
the country must travel a road already travelled by others
and run the risk of staying far behind in that road. If the
country does not have a considerable market this alternative
is not realistic. The second alternative may not be
available to all countries as well. If the country is
small, and the majority of the people are poor, the market
is small; large firms are not impressed by small markets.
They are attracted to potentially sizeable markets such as
China, India, Mexico, Brazil, and the USSR. A small country
may find itself in the position of having to offer unusual
benefits to a multinational for the installation of a plant.

The Andean Pact in South America (Venezuela, Colombia,

 

12. Dahlman, Carl J., Ross-Larson, Bruce, and Westphal,
Larry E.; "Managing Technological Development: Lessons
from the Newly Industrializing Countries," Wgrld
Deyglgpmgnt, Vol. 15, N. 6, June 1987, pp. 759-775.

12

Ecuador, Peru, and Bolivia) is an attempt to create an ample
market to attract foreign direct investment, besides
expanding the market for their own industries.

Beside the fact that LICs operate in competitive
activities13 while 103 operate in areas of specialized
knowledge and relatively less (international) competition“,
the ICs can often easily substitute an input when its price
goes up. An example is sugar. The price of sugar went up
to $1500.00 a ton in 1976. Consequently, many industries in
the 103 started to use corn syrup and dozens of other
substitutes. In a two-year span, the price of sugar dropped
to $140.00 a ton, less than one tenth that of its peak.H

The example above illustrates the nature of demand and
the substitutability of LICs products. The nature of demand
explains in part why terms of trade deteriorate against the
latter. Except for some fossil fuels and minerals which
might have low price elasticity of demand in the short-run,
demand for agricultural products and low level manufacturing
is very responsive to price increases. High competition,

absence of privileged knowledge, and/or comparative

 

13. Even when the domestic markets have monopolistic
characteristics, in the international context, they
operate in areas of high competition.

14. The 105 operate in an environment more like monopolistic
competition. Firms are able to segment markets and
differentiate products in such a way as to lessen the
effects of the competition.

15. Barzelay, Michael; The Eoliticigeg Macketmggongmy;
Alcohol in Brazilislgnecsxmfiicatesx. University of
California Press, Berkeley, 1986, p. 135.

 

13
advantages make OILICs’ products highly substitutable. In a

contest to maintain a share of the global product, they come

out the losers.

Addressing Priorities

If terms of trade deteriorate for the OILICS even when
nominal oil prices remain stable, real prices go up because
the basket of goods necessary to pay for each caloric unit
of oil must increase. If energy remains a very expensive
and important input for those economies, the research effort
in the field should not diminish. If developing products
for which high demand exists is difficult, the alternative
might be to develop internal markets for alternative energy
sources. Research is needed in those countries where
governments keep adopting contradictory policies which
deepen the negative effects of an energy crisis instead of
alleviating them.“5 One example of such a policy is the
Brazilian government’s subsidy to hydroelectricity.
Hydroelectric power is not as cheap as it was initially
thought because the capital costs are enormous. The
construction of huge hydroelectric facilities to produce

power which is supplied at subsidized prices is partially

c~ “no. o....-......-........un--—c.-n-—u-. -.... ............ ... nu... N... .--- I-II-'1-Inq-o--A

16. DeLucia, R. J. & Lesser, M. C. Energy Policies in
Developing Countries. Enecsmeolioy 13(4). 1985. pp.
345-349; Lin, Ching-Yuan, ”Global Pattern of Energy
Consumption Before and After the 1974 Oil Crisis,"
Economiompevelonmentmano Cultural Change. 1984.;
MacKillop, Andrew; “Energy Sector Investment in LDCs:
The Credibility Gap Widens,“ Energy Policy, August

1986, pp 318-328.

 

14

responsible for the country’s external debt crisis, and the
decapitalization of the energy sector in the country.

The example above illustrates why continuing research
in the energy substitution field is needed in LICs.
Research in the field would hopefully demonstrate that the
assumptions behind such policies are not warranted; carrying
out the policy at its term could bring serious consequences
for the country's entire economy. This need is also voiced
by the World Bank:

The developing countries are in a period of

adj us tmen t to higher world energy prices and
increasingly widespread shortages of thelwood and
other tradi ti onal fuels. The recent: decline in

international energy prices and their short-term
unpredictability do not reduce the need to
continue planning on the premise of increased
energy prices in the longer term.17

Some authors articulate the need to make energy

planning an integral part of any development plan.”

Energy Substitution

One topic highly debated in the U.S. in recent years
is the question of substitutability” between energy and
capital in the production process. The substitutability

between inputs is thought to be important among economists

 

17. The Energy Transition in Developing Countries, The World
Bank, Washington D.C., 1983.

18. Foell, Wesley K., "Energy Planning in Developing
Countries," Egeggngolicy, August 1985.

19. "Substitutability" is used to refer to the degree of
easiness which one input is alternatively used in the
production process. A is said to be substitute for I
if A can be easily used in the place of B.

15

because it might determine the effectiveness of government
policies and hopefully influence policy changes. Suppose,
for example, that it is determined that capital and energy
are complements. A government policy of reducing taxes to
make capital less expensive in an energy crisis would lead
to an increase rather than a decrease in the expenditure on
energy. In such a case, a policy of subsidizing energy
would increase capital expenditures, and vice-versa. On the
other hand, if capital and energy are substitutes, a policy

of subsidizing energy prices would only delay technological

change. Lower energy prices would encourage the use of
energy instead of capital. The policy would be ineffective,
if not harmful. If capital and energy are substitutes, the

government should let market forces interact and firms make
their own decisions on input substitution.
It is not an easy task to test these ideas and

demonstrate complementarity or substitutability between

capital and energy. Several studies have been done and the
debate has sometimes been heated. Capital and energy can be
technological and/or economic substitutes/complements,

depending on the period being analyzed (short-run/long-run).
Furthermore, substitution is a micro phenomenon which cannot
be analyzed in the aggregate using methods designed to
analyze firm behavior. The hypothesis of this dissertation
is that the spectrum of input substitution varies
significantly from firm to firm, even when the same core

technology is used. The range of input substitution varies

16

with the degree of integration of the firm. The implication
is that elasticities, even when analyzed at the micro level,
cannot be used as a guide for macroeconomic policies.
Elasticities could be used in some cases for sector-specific
economic policies. Even though the elasticities should be
interpreted with care, because the methods being used up to
now do not produce unambiguous estimates.

Firms change the output mix in response to price
changes. This may not be the case in situations where
market prices do not reflect the real cost of inputs due to
market imperfections, existence (H? externalities, or
government intervention. The failure to identify the real
prices of inputs may distort the computation of
elasticities. In some cases the firm is forced to make
input changes independent of input prices , due to
regulation, strategic behavior, or the correction of a past
mistake. In such cases there will be no connection between
prices and quantities of inputs being used. Still, in the
long run, as the prices of energy increase, firms tend to
use more energy efficient machines at a higher capital cost.
Substitution is more difficult in those capital and energy
intensive activities when the time horizon for the
investment is long run. In such cases, short-run price
changes may cause the firm not to react, and the computed
elasticities may not indicate immediately the decisions made

by management. Fuel substitution is considerably easier to

17

accomplish than energy substitution.2° This, while helpful
in defusing short run energy crisis, may not help in

fostering technological changes.

Organization of the Thesis

An account is presented in Chapter 2 of the work done
in the field of energy substitution since 1973 when the
first studies of capital-energy substitution appeared. The
method is outlined in Chapter 3 and the data estimation
results presented in Chapter 4. In Chapter 5, the results

are discussed and the conclusions presented.

 

20. Fuel substitution, for example, is when coal is used
instead of Oil, or electriCity is used instead of coal,
but the caloric content remains roughly the same.
Energy substitution is when the caloric content of the
product is reduced while the quantity of other inputs
is increased. For example, if instead of 1 barrel of
Oil and 2 tons of wood being used to produce 1 ton of
paper, 1/2 barrel of oil and 2.5 tons of were used,
energy would be displaced by materials. Energy could
also be substituted for capital, in the form of a new
machinery.

CHAPTER 2

THE CAPITAL-ENERGY COMPLEMENTARY DEBATE

Early studies about energy' consumption in «different
sectors of the economy in the wake of the energy crisis in
the 19703 ignored the fact that energy use represents
essentially a derived demand. Firms demand energy as a
function of their output level. Nevertheless, they tend to
choose the mix of inputs which minimizes their total cost.
Accordingly, estimates of energy demand based only on the
levels of output could not be very accurate.‘ The main
weakness in input-output models is that they are not
grounded in a theory explaining the behavior of decision
makers—-in this case the firms; and in the way prices are
ignored altogether:

The most glaring defect of the Fbrrester-Meadows
models is the absence of any sort of fUnctioning
price system. I am no believer that the market is
always right, and I am certainly no advocate of
laissez-faire, where the environment is concerned.
But the price system is, after all, the main

---.o.-.-u.....—. oaIOy .. noun"... "nu ma... -..u.u...m......uu.

1. Casler, Stephen and Wilbur, Suzanne; "Energy Input-Output
Analysis," Resources and Energy. June 1984. pp. 187-
201; Constanza, Robert and Herendeen, Robert A.,
"Embodied Energy and Economic Value in the United
States Economy: 1963. 1967 and 1972." Resourcesmand
Eneggy, June 1984, pp. 129-163, Hannon, Bruce M.; "An
Energy Standard Of Value," Ins ennuaIS.ofMthememerican

"nun-g...” .-. u.

Academy of Political and SOCIal Science. Vol. 410.

v-‘mqsauoIWI ..

November 1973, pp. 139-153; and MADDISON (1987).

 

 

18

19

social institution evolved by capitalist economies

(and, to an increasing extent, socialist economies

too) for registering and reacting to relative

scarcity. There are several ways that the working

of the price system will push our society into

faster and more systematic increases in the

productivity of natural resources.2
It is argued that the profit maximizing behavior assumed in
economic theory, in spite of being a very simplifying
assumption, is better than no theory at all. The use of
econometric techniques makes sense only if there is a theory
behind the model.

Econometric studies attempt to explain input
substitution in the context of profit maximization or cost
minimization behavior tnr economic agents. These models
include prices of the inputs since prices affect the demand
for the inputs. Engineering studies demonstrate the
technological viability of physical substitution,3 but they
fail to make the connection with prices and the behavior of
the decision maker.‘

This dissertation accepts the view that substitution of

inputs is determined at any time by production technology

 

2. Solon, Robert; "Is the End of the World at Hand?“
gnallegge, March-April 1973.

3. Ross, Marc; ”Industrial Energy Conservation," natural
Besgutgeswqgutnal. Vol. 24. April 1984. pp. 369-404;
Marlay, Robert 0. "Trends in Industrial Use of Energy,"
Sgienge, vol. 226, December 14, 1984.

4. Hammond, Allen, L. (1977b), "Energy: Brazil Seeks a
Strategy Among Many Options," Science, Vol 195, no.
4278 (February): 566-567; Hannon, Bruce M.; An Energy
Standard of Value." [hemannals of the American Roadsmx
of Political and Social Science, Vol. 410, November

«"0"» ......

1973, pp. 139-153.

 

20

and prices of inputs. When the energy crisis hit the world
in the 19703, the absence of studies in the substitutability
of inputs, particularly energy, did not allow quick
formulation of impact analysis on higher energy prices in
the economy.

In response to the developments of the 19703, a
significant number of studies with the objective of
estimating the parameters of energy substitution for other
inputs appeared. Many of them were written by economists.
They were basically trying to determine if energy was easily
substitutable for other inputs. If 30, firms could shift
easily to a different input mix, the transition to a world
of higher energy prices would not be painful, and government
intervention would be unnecessary. The publication of these
studies was also an indication that economists had started
to pay more attention to theoretical and empirical research
on the issues of natural resource exhaustion.

The methodology employed involved jointly estimating
the demand functions for inputs derived from a production
function. Based on the resulting parameters, calculations
on the cross elasticity of substitution, input own-price
elasticity‘ of substitution, and the price elasticity of
demand could be determined. Conceptually, cross elasticity
of substitution is a measure of how the amount of product X
changes when the price of product Y changes. The input own-
price elasticity is measured against the input own price.

The price elasticity of demand measures, in general, how the

21

demand for product X changes if the price of Y changes. The
elasticity of substitution is the price elasticity of demand
weighted by the product cost share. Theoretically we should
expect the own elasticities of substitution to be always
negative because the law of demand tells us that if the
price of a product goes up, the quantity demanded of it
falls. For those inputs expected 1x) be substitutes, the
cross elasticities of substitution should be positive (If
the price of X .goes up, more Y is used). For the
complementary inputs, the cross elasticities should be
negative (If the price of X goes up, less Y is used).

In order to develop good theoretical ground, economists
normally estimate demand functions derived from production-
or cost functions. These functions are believed to
encompass all the relevant economic information about the
firm. They summarize the economic behavior of the firm.
The estimation of demand functions, derived from cost and
production functions, allows for testing their existence.
The major problem faced by researchers is finding out the
shape of those functions. 131 recent years several new
functions have appeared in the literature, but they have not
proved fruitful. One exception is the translog function.
In the absence of more appropriate forms the, Leontieff,
Cobb-Douglas, CES, and translog functional forms have been
widely used in the past. In recent years the translog,
which is a relatively flexible form, is the most widely used

in studies of input substitution.

22

Many of the studies, up to now, are highly aggregated,
involving the whole U.S. manufacturing industry; others are
disaggregated at the two to four—digit SIC levels. Only in
recent years have scholars devoted their attention to more
disaggregated studies. Advances in production theory,
conception of new computing techniques, and increasing
availability’ of statistical packages for micro computers
have made it easier in recent years to study input
substitution. using more sophisticated techniques not
available a few years ago.

One of the first studies done in the field of capital-
energy substitutability using translog cost functions
concluded that capital zuui energy were complements.s The
study used four inputs: capital (K), labor (L), material
(M), and energy (E). The model was estimated using data from
the U.S. manufacturing sector through the Iteractive Three
Stage Least Squares (I3SLS) estimation procedure. The
results of that study predicted a painful adjustment process
to higher energy prices for the U.S. economy. As investment
would decline in response to higher energy costs, unit costs
of output would rise and unemployment would increase until

the economy adjusted to a less energy intensive path.

 

5. Berndt, Ernst and Hood, David; "Technology, Prices, and
the Derived Demand for Energy," The ....... Review of Econqmigs
angmfitatistiqs. August 1975.

'Ifl‘oo-ODO-omun.

23

Energy complementarity was also found by Hudson and
Jorgenson.‘ at roughly the same time.

Griffin and Gregory,’ in spite of questioning the
existence of an aggregate cost function and the ability of
econometric techniques to depict such a function if one
existed, applied the same methodology used by Berndt and
Wood to a cross-section data set and obtained the opposite
result. The authors used pooled international data for the
manufacturing industry in OECD countries. They argued that
while short-run complementarity between energy and capital
may exist as production increases along an expansion path,
in the long run energy and capital are substitutes because
new equipment could be designed to achieve higher thermal
efficiency albeit at greater capital cost.

Other studies were as unsettling as these. Melvyn
Fuss° found complementarity in Canadian manufacturing data

pooled by region. Similar results were reported by Jan R.

 

6. Hudson, E. and Jorgenson, D.; "U.S. Energy Policy and

Economic Growth. 1975-2000." fisdliioutnal_ t_Economics.
Autumn, 1974, 5, pp 461-514.

7. Griffin, James and Gregory, Paul; "An Intercountry
Translog Model of Energy Substitution Responses,“
aggriggn Economic Reyieg, December, 1976.

8. Fuss, M. A., "The Demand for Energy in Canadian
Manufacturing: An Example of the Estimation of
Production Structures with Many Inputs," Journal of
Economettics. January 1977. 5. pp 89-116.

24

Magnus9 using Dutch manufacturing data and by Paul Swain and
Gerhard Friede1° using German data.
Humphrey and Moroneyll, using two-digit SIC data,

reported potential substitution between labor and natural

resources, and capital and natural resources in many
industries. They reported results with both translog cost
and translog production functions. This study was one of

the first to use disaggregated data by certain industries
and to estimate production functions. They also included
nonenergy natural resource inputs. Moroney and Toevs”,
using three and four digits SIC data, estimated translog
cost functions for several industries and found substitution
'between capital, labor, or both for industry specific

natural resource inputs.

 

9. Magnus, J. R., "Substitution Between Energy and Non-
Energy Inputs in the Netherlands, 1950-1974,"

Intense;isnal.§conomic_3axisu. 1979.

10. Frieda, Gerhard, "Die Entwicklung des Energieverbrauchs
der Bundes republik Deutschland und der Vereinigten
Staaten von Amerika in Abhangigkeit von Preisen and
Technologie," Karlsruhe: Institutewfgr Anggwgngte
§¥§L§m2flé12§§. June 1976-

 

11. Humphrey, D. 8. and Moroney, J. R., "Substitution Among
Capital, Labor, and Natural Resources Products in
American Manufacturing,“ Journal of Political Eggngmy,
83, February 1975, pp 57-82.

12. Moroney, J. and Toevs A., "Factor Costs and Factor Use:
An Analysis of Labor, Capital, and Natural Resources,"
Southern Economic Journal, 44, October 1977, pp. 222-
239.

25

Robert Halvorsen and Jay FordH found energy and non-
energy inputs to be predominantly substitutes. They used
data from the 1958 Census of Manufactures and estimated the
elasticities for eight two-digit industries.

In 1979, Berndt and WoodH returned to their previous
work of 1975 and tried to explain the disparity of results
obtained. by different authors but. mainly with those of
Griffin and Gregory. They distinguished between the
econometric and engineering interpretations of energy-
capital complementarity. Engineering studies supported the
hypothesis of E-K substitutability. Basically, a new, more
expensive machine may turn production less energy intensive.

Energy input share would drop while capital input cost share

would increase. The authors argued that their focus was on
net elasticities while other studies, finding E-K
substitutability, focused (n1 gross elasticities.u

Furthermore, they argued furthermore that the literature on
the subject deals mainly with two inputs and. in those
circumstances only substitution is possible. They go on to

state that the expansion effect may outweigh the

 

13. Halvorsen, Robert and Ford, Jay, "Substitution Among
Energy, Capital, and Labor Inputs in U.S.

Manufacturing," in Advgnceg in themggggomigs of Eneggx
gag Resggrces, Vol. 1, JAI Press, 1979, pp. 51-75.

 

14. Berndt, Ernst and wood, David; "Engineering and
Econometric Interpretations of Energy-Capital

Complementarity," 159 Ameriggn_§cgnomic Reyieg, June
1979.

15. Net measures of elasticities are the appropriate ones to
determine substitutability or complementarity. The
gross elasticities include the expansion effect.

26

substitution effect;15 a situation could emerge where E-K
may be gross substitutes and net complements. In their
view, this would be the most likely explanation for the
disparity in findings. They emphasize that if E-K are found
to be complements, a policy of reducing the price of capital
with tax incentives to encourage energy conservation would
increase the demand for energy instead of reducing it.
This, in the context of a four input economy would mean
lower demand for labor, materials, or both. There is no
disagreement about policy implications among the scholars
studying energy substitution. The burden of settling the
question of substitutability/complementarity in the Berndt-
WOod scenario is to a. great extent transferred to the
accuracy of the data. The available data are associated
with a level of output, and the models up to now have no
mechanisms to neutralize the output effect. The authors and
up saying that the complementarity problem remains
unsettled, largely because of the absence of' models to
explain the short and long run adjustment paths.

In 1981 James GriffinH provided. his version. of a
reconciliation attempt. He acknowledged that the matter

remained as unsettled as when the Griffin-Gregory results

 

16. Quantities of inputs would be affected more by the
effect of increase in production (expansion effect)
than by the input substitution effect itself.

17. Griffin, James, "The Energy-Capital Complementarity
Controversy: A Progress Report and Reconciliation
Attempts," in Berndt and Field (eds), Mggeling ang

measutinsiuatunal_Ba§Qutcs§i§uh§titution. HIT PFOSS.
Cambridge, 1981.

27

were first presented. No breakthroughs were reported, but
in Griffin’s view, the essence of the controversy was:

1. E-KI are complements or substitutes depending on
whether a short or long-run production relationship is being
measured. In the short-run, energy input per unit of
machine hours tends to be fixed. If“ other inputs are
substituted for energy and capital, capital and energy can
be short-run. complements. 131 the long run, energy' and
capital are expected to be substitutes.

2. It is argued that studies showing E-K substitution
measure only gross elasticity because one or more factors
have been omitted from the production function. Empirical
results indicate that energy and capital are gross.
substitutes but net complements.

3. Capital is not separable from other aggregates as
some studies have assumed. Capital should be disaggregated
into working capital and physical capital. Energy would act
as a complement to physical capital and a substitute for
working capital, and vice-versa.

The Allen Elasticity of Substitution (AE8)” between
energy and capital range from +1.07 in Griffin and Gregory
to +0.8 in Pindyck, and from -1.01 to +2.0 in Halvorsen and
Ford. These estimates are very different from the Berndt-

Wood estimate of -3.2. Consequently, Griffin argued that

 

18. Allen, R. G. D., Mathgmatiggl finalygis of Economists
London: Macmillan, 1938, 503-509.

 

28

pooled19 data are more appropriate to measure elasticities
because the price variations are greater not only among
countries but also within the countries included in the
study» In the US, the price variation in the periods
studied is very small, and thereby unable to yield reliable
results. In Griffin’s view, econometric evidence does run;
reject a short and long run dichotomy; the gross/net
elasticity distinction cannot offer a complete explanation.

Griffin questioned the wisdom of including working
capital into the production function. He argued that the
inclusion of working capital should be preceded by good
theoretical reasons to do so. He ended his review by saying
that E-K complementarity remained an unanswered but
important policy question.

Several other authors contribute to the debate. David
Stapleton3° examined the results from cross-section and time
series data, and concluded that cross-section data does not
always yield long-run elasticities nor does time-series data
always yield short-run elasticities. This study weakens

Griffin’s argument about the likely’ cause for divergent

 

.........

19. ”Pooled data" refers to the procedure of using data from
several countries to jOintly estimate functions through
dummy variable manipulation.

20. Stapleton, David, ”Inferring Long-Term Substitution
Possibilities from Cross-Section and Time-Series Data,‘
in Berndt and Field (eds), Modeling and Measuring
Ngtural Resources Substitution, MIT Press, Cambridge,
1981.

29

elasticity' estimates. Charles Struckmeyer21 argued. that
capital—energy’ complementarity is a short—run phenomenon
reflecting the fixed gxmpggt nature of factor employment in
a putty-clay technology.22 But if a specification is used
to measure the ezmantue choice of technique, capital and
energy are found to be long-run substitutes. Struckmeyer
argues, however, that neither the translog function nor the
putty-clay model are adequate representations of technology.
They do not capture the dynamic adjustments found in the
data.

Several problems remain to be worked out in the
methodology of estimating production and cost functions. In
order to omit some of the input series, authors have assumed
separability of inputs.23 With the separability assumption
the absence of one series would not affect the estimation of
the parameters for the others. Several authors, however,
argue that the separability assumption is not valid. In
later studies tests have been devised to validate the

separability assumption; results are mixed. Because

separability depends on the functional form, if the true

 

21. Struckmeyer, Charles, “The Putty-Clay Perspective on the
Capital-Energy Complementarity Debate," Ine_3eyieu_gf
Economic§_angi§tati§tics. 1987.

22. “Putty-clay” is used to describe the fact that firms are
free to choose the kind of technology they want to use.
Once they exercised that choice, they cannot change it
easily. So in a putty-clay technology model, inputs
are QE:QDL§ substitutes, but eg-post complements.

23. "Separability" means that the quantities of one input in
the production function is independent of the quantity
of the other inputs.

30

functional form is not known, or if the functional form
being used is not a reasonable approximation, separability
is a strong assumption.

The aggregation of inputs across firms bias the series
because firms have different degrees of vertical
integration. Anderson“ argues that it does not make much
sense to include intermediary inputs at the industry level.
This is a valid procedure only at the firm level. Kopp and
Smith35 used disaggregated data to study the performance of
translog functions. They argue that aggregated data in the
translog function does not properly describe the technology,
while disaggregated data provides a more appropriate
representation. ChungH proposes an. alternative ‘way of
estimating (AES) through a single cost-share equation.
While the estimation process is made easier, it does not
solve the basic problem of conflicting results. The
estimates remain mixed; he obtains negative and positive

parameters, similar to those already known.

 

24. Anderson, Richard 6., “0n the Specification of
Conditional Factor Demand Functions in Recent Studies
of U.S. Manufacturing," in Mggeling angwflgasgning

Natuggl Rggpgcce Substitgtion, edited by Ernst Berndt
and Barry 0. Field, pp. 119-144. Cambridge, 1981, MIT

Press.

25. Kopp, Raymond J.; and Smith, V. Kerry; “Measuring the
Prospects for Resource Substitution under Input and
Technology Aggregations," in Modelin ng angmngasgging

NELHIQLMB§§QQLQ§§”$29§L1L!_l2flgcaMDridgegfllT Press.
1981, pp. 145-173.

26. Chung, Jae Wan, "On The Estimation of Factor
Substitution in the Translog Model, ” Ihe 3gy1egmgf

Econceis§_ang_§tati§ticss 1987. PP- 409-417-

31

In a study involving several industries in Canada and
the U.S., Denny, Fuss, and Waverman37 found that in the U.S.
paper industry, energy and capital are complements (02,: = r
2.74), and energy and labor are substitutes (a;,r = 5.48).
The study, however» does. not capture» the effect of the
energy price shock since it comprehends only the period
1948-1971. In the case of Canada, the range is 1962-1975,
but still, it is not enough to capture the effect of the
first oil shock. The study shows substitutability between
energy and capital in the paper industry (03.: = 1.93);
energy and labor are substitutes in the short run (03,; =
0.39), and complements in the long run (03,; = -2.6I). For
Canada, the authors disaggregated energy among electricity,
fuel oil, coal, and natural gas. Significant
complementarity is found between electricity and fuel oil
(012,” = -0.299), substitutability between coal and fuel
oil (0:2.ci = 0.672), and substitutability between natural
gas and fuel oil (oua,:a = 0.124).

Aggregation, it is seen, presents serious problems for
the study of substitution of inputs. Different types of
data. have been aggregated which distort the parameters.
Aggregation not only presents problems on the input side,

but on the output side as well. Firms, responding to market

 

27. Denny, M.; Fuss, M., and Waverman, L. "Substitution
Possibilities for Energy: Evidence from U.S. and
Canadian Manufacturing Industries," in mggelingmgng
measunmflatural Resouroei§ubstitutiom edited by
Ernst Berndt and Barry C. Field, 1981, Cambridge, MIT
Press.

32

trends change the output mix. If energy prices double, for
example, prices of energy intensive goods would rise more
than the prices of less energy intensive goods. Demand for
energy intensive products would drop, while demand for less
energy intensive goods would rise. In order to respond to
this change in demand, firms would increase the production
of less energy intensive goods, and decrease production of
more energy intensive products. Elasticities in this
context could be misleading because two different outputs
are being compared. The methodology being employed assumes
that the same output is being analyzed.

Using the argument of changing output mix, John Solow28
express serious doubts about the entire process of
elasticity estimation as it is generally done. He looks at
input substitution in a general equilibrium context, as
opposed to a partial equilibrium approach, and concludes
that input substitution is basicallyr a. micro phenomenon
which cannot be analyzed using aggregated data. He argues

that price-induced changes in the composition of output can

cause either outcome in the aggregate -- substitution or
complementarity' -- even if no technical substitution is
possible. Changes in the relative incomes of U.S. consumers

as opposed to the rest of the world may be key in
determining if energy and capital are to become substitutes

or complements in the U.S..

 

28. Solow, John, “The Capital-Energy Complementarity Debate
Revisited," American Economic Review, September 1987,
pp. 605-614.

33

Solow’s article leaves two alternative ways of dealing
with the problem: a) Look for other models in which
aggregate data could be used to establish the relationship
between capital and energy, or b) Search for data at the
micro level and try to establish the elasticity estimates at
that level. A third alternative, of course, is to abandon
the effort altogether.

In the next chapter, the method used in the research

will be described in detail.

‘ul'

CHAPTER 3

ECONOMETRIC MODELS AND ESTIMATING PROBLEMS

The use of aggregate models is always troublesome.
Even the most sophisticated models cannot separate what is
needed from what is available. This dissertation took the
tack of studying input substitution at the micro level.

The search for data at the micro level is no easy task.
Firms consider most of the data needed for production and
cost function estimation as confidential and thus beyond the
reach of academic researchers. The reports produced for
public relations and stockholders do not have the necessary
details. Many firms manufacture more than one product, so
changes in the composition of output also occur at that
level. To obtain reliable data, the researcher must be
allowed free access to the books and internal reports, as
well as consulting with the employees who understand them.
Since this is always troublesome to them, it is not easy to
arrange.

Studying micro data, in a complete capital, labor,
materials and energy model (KLME) seemed, however, the most
promising line of research. In order to accommodate the
needs of the sponsor of my program, the approach was tried

in Brazil first. More than a hundred letters were sent, and

34

35
only six companies responded; four of them apologized
because they could not provide that kind of data.

The results were discouraging; it seemed like a change
in approach would be necessary. I started to look for data
at the industry level, when, luckily, I was introduced to
Indnstrias Klabin de Papel e Celulose s/a in Sao Paulo,
the holding company of a conglomerate involving paper,
mining, and packaging divisions. After the ‘matter was
discussed with members of the Board of Directors, I was
authorized to do research in three of their Brazilian paper
firms which are fairly representative of the nation’s paper
industry. I personally visited two of the mills, one in the

Western part of the Parana State, and the other in Guaiba,

Rio: Grande' do Sul State. I was allowed to talk with
technical personnel, take notes, look at the internal
reports, and books. I was to keep the data confidential and
not publish without first consulting them. It was a unique

opportunity to obtain valuable data which, hopefully, can
bring new information to the study of energy-capital
substitutability.

The most common method of measuring price responsiveness of
demand for any input is to measure the price elasticity of
demand. In its most simple form, in a production function Y
= f1X1,Xz), where Y is the output and X; and X; are inputs.

With prices P1 and P2, the elasticity of demand between the

36
two inputs is given by E1; = dln(X1/Xz)/dln(Pz/P1)‘. output

and other prices assumed to be unchanging. As E becomes
larger, the substitutions are easier between the two inputs.
If.E > 1, the share of input 1 becomes larger relative to
the share of input 2. If E < 1, the share of input 1
becomes smaller relative to the share of input 2. When
there are only two inputs, E21,: = 131.1, and there is no
ambiguity in the effects of a price change, they are
substitutes, unless a Leontieff type of technology is
deployed.2

The analysis of input substitution becomes more
complicated when there are more than two inputs. Inn such
cases, the elasticity measurement is not unambiguous since
several. partial derivatives are involved. A. greater» or
lesser number of derivatives are assumed to change depending

on ceteris paribus conditions. In this way, a large number

 

1. Suppose the two inputs are K and L. Elasticities are
derived in the following way:

8K dK/K L/K L/K L/K

E : -- : -—-- : —-—-- : ———-—— : _—_---

XL dL/L dL/dK dL/dO r/w
dK/dQ

where dK is the change in the amount of K, dL the
change in the amount of L, and do the change in the
amount of O. O is the output, r is cost of K, and w is
the cost of L. Prices enter the elasticity calculation
because the optimization condition requires that the
marginal product of the factor be equal to its
remuneration. The marginal products are dL/dQ and
dK/dO.

2. Inputs are used in fixed proportions. No substitution is
possible.

37

of elasticity measures are possible. The most common
elasticity concept used in cases of more than one input is
the Allen Elasticity of Substitution (ABS).3

It is standard in the literature to estimate the cost,

or production functions, and from those parameters estimate

the demand functions. The demand functions allow estimation
of elasticities. Implicit in the procedure is the
assumption that those functions exist. In order to validate

the assumption, tests are performed with the data and the
estimated parameters to check for their existence. When
those tests are performed the existence is, of course,
deferred to the accuracy of the data set.

While there are serious objections to the estimation of
production and cost functions, particularly because some of
the comparative statics hold only under optimization‘
conditions, the method is more appropriate in the context of
a single firm than in the aggregate. The adjustments in
production resulting from input price changes differ among
firms. In some cases, taking a very long period, and in
others, a short one. But in general, firms try to achieve
the mix of inputs which minimize their cost, even when the
adjustment process takes time. The problem is that most
firms cannot change their equipment overnight. In the paper

industry, for instance, it is common for a paper machine to

3. Allen. opclt pp. 503-509.

4. The firms are assumed to be continuously maximizing
profits or minimizing costs.

38

remain in use for more than 30 years. Even when energy
prices go up, and the paper produced by that machine ends up
being more expensive, liquidity constraints may prevent the
firm from changing tx> a new machine. So, the firm keeps
operating in a situation where it is not minimizing long run
costs, although it may be minimizing costs given the
technology in place. In order to compensate for higher
production costs firms cut costs in other areas like
overhead, for example. In such situations, the estimation
of production and cost functions may not yield. a fair
representation of technology. Some inputs, in such
situations, could present positive own price elasticities.

Another objection constantly raised is that the
technology is restricted in scale. For example, in the
translog function, the firm is assumed to exhibit constant
returns to scale. In order to achieve general results, the
assumption of constant, or decreasing returns to scale is
essential. It is well known, by experience, that this is
not the case. Firms may exhibit increasing returns to scale
in. a wide range of the output possibility' path, which
invalidates the comparative statics on which economics
relies heavily.

To those objections, one could be added which is more
serious: Successfully combining physical inputs to produce
an output is not, in a great number of cases, the key to a
firm’s success. In the spectrum of decisions with which the

manager is confronted with, the decision to substitute

39

physical inputs is not the crucial one in many cases.5 It is
unnecessary to substitute inputs, if the product is not
marketable, if the firm does not have an organization to
reach the markets effectively, if the new input source is
unreliable and unsustainable, or if the earnings vanish with
inflation. In the context of 1.103, it is not clear that
energy, in the long run, is the only input in need of
substitution. Organization, for example, is a scarce input.
In many cases the survival of the firm is threatened by
market conditions other than higher energy prices. In
countries like Brazil, the development of mechanisms to cope
tqitfii inflation is as important to the survival of the firm
as; the substitution of inputs whose prices have increased.
More profit is always better than less profit if all
(atluer things remain the same. It is logical to assume that
decision makers, if confronted with such a naive
:pzwaposition, would choose the alternative which brings more
3pzw3fit. This is relevant in the context of the firm but not
:18 (crucial as in neoclassical economics which relies heavily

on this assumption. The manager compares alternatives under

 

 

.-..—o-

In an interview with Dr. Jose Valentim Sartarelli,
General Manager of Eli Lilly Corporation of Brazil, on
July 26, 1988, he argued that for any firm to survive
in an inflationary economy such as Brazil, where price
levels increase at the rate of about 20% a month, the
financial management of the firm takes the highest
priority. Mismanagement in this area would make the
profits vanish overnight. Production is to a great
extent subordinate to finanCial management.
Alternating in priority is the relationship with
government bureaucracy vis-a-vis licensing procedures,
This takes which takes top management personnel a lot

of time and energy.

5-

40

which conditions are different. The decision to choose-
between more profit as compared to less profit, other things
being equal, is never faced. A decision, as such, would
never reach higher management, it can be made by any
employee which identifies such a possibility. Things do not
remain the same when a choice is made; most choices involve
alternatives which affect other variables. A great deal of
time and effort is devoted to identifying the alternatives,
establishing risks, and estimating returns. Decision-making
process takes into account the actions of the competition,
the actions of the government, the long-run objectives of
the firm, the potentiality of the markets, etc., some of
which may be more important than the combination of physical
inputs.

By including only physical inputs in the production
function important inputs are left out. This is easily
demonstrated in the construction industry where several
firms offer to build the same bridge, using the same
technology, at a similar price. The reasons for choosing a
particular firm are reputation, reliability, past history of
litigation, and client satisfaction rates. These are
intangible inputs which cannot be easily acquired. Even if

energy prices go up, it is not within the reach of the

firm’ 3 decision-makers to demand less energy and more
.. reliability , " in the short run . Intangibles such as
organization, reliability, reputation, and client

satisfaction, for example, are long-term commitments which

 

 

41

cannot be acquired in the short run. But they are clearly
inputs in the production process, and a key to the survival
of any business.

Suggestions to include other inputs in the production
function have been made but the difficulty in dealing with
the subject is holding back research. Meanwhile, it is
necessary to be realistic and deal with what is available.
This dissertation deals only with physical inputs in
studying substitution between capital and energy. A whole
spectrum of possibilities (substitution or complementarity)
exist which are different for each industry and for‘
particular firms within the industry. This is one of the
first studies using translog functions at the firm level;
consequently the method will also be evaluated. In addition
to the basic treatment of energy-capital substitution, four
inputs, K, L, E, M, will also be included making the
separability assumption unnecessary.

Following the suggestion of Toevs (1980), both the
translog cost and production functions will be estimated.
This allows illustration of the disparity between methods.
The translog function is widely used because the estimation
process can be made simple. It is a second order
approximation to any arbitrary function and offers
possibilities for testing its existence and properties.

Cost functions assume that firms are minimizing total

cost in the short-run, while production functions require

Ll'

42

the more stringent assumption of profit maximization.“ To
calculate the AES between factor 1 and factor j from a cost
function (Oi.J)p only the estimated. parameters and cost
shares of the production factors of the total cost are
needed. To estimate the same elasticities from production
functions (All), the matrix of estimated coefficients must
be inverted. Consequently, elasticity estimates from
production functions involve more complex computations.
Furthermore, if the data are not accurate, the distortions
in the estimated elasticities are more serious due to
greater manipulation of the data.

Hicks Elasticities of Complementarity (HEC) can be
estimated from the production function parameters when the
effect in factor prices caused by changes in quantities
available is needed. The HEC is useful in comparing the
effects of government policies. For example, when the
government intervenes to increase the supply of a particular
factor, the effects of that policy on the market prices of
products can be determined. In investigations of individual
firms, the HEC is not very useful, except for those

situations where the firm has monopsonistic power.7

 

6. Cost minimization requires the production function to be
locally quasiconcave, while profit maximization
requires the production function to be locally concave.
See Varian, Hal, Migggeccnqmic_finalx§is, Second
Edition, W.W. Norton & Company, New York, 1984, pp. 21-
25.

7. Monopsony is a situation where one economic agent is the
exclusive buyer of one input. Such a case can be
illustrated in the labor market by a large firm
established in a small town, giving employment to the

43

The translog cost function8 for four inputs, K, L, E,
and M (with symmetry and constant returns to scale) can be
specified as:

In C = ln(ao) + ln(Y) + axln(Px) + ailn(Pi) + azln(Pa)

+ anln(Pn) + iBII(lan)’ + thln(Px)ln(PL)
+ Blt1n(PI)ln(P£) + Bxu1n(Px)ln(Pn)
+ {Btt(lnPt)3 + Bttln(PL)ln(P:)
+ Bluln(P;)ln(Pn) + iB::(lnP:)3 +
+ Bsxln(P:)1n(Pu) + Qwa(1nPu)3o (1)
where:
C = total cost

Y = output level

P: = price of capital
PL = price of labor

P3 = price of energy

Pu = price of materials

ln = natural logarithm
311: parameters

a = parameters

 

majority of the local inhabitants. No major
alternative employer is available nearby. In such a
case the firm is said to enjoy monopsonistic power.
The situation of the Klabin plant in the Parana State
resembles in many ways such a situation.

8- The translog functional form was first presented in
Christensen, Laurits; Jorgenson, Dale; and Lau,
Lawrence; "Transcendental Logarithmic Production
Function Frontiers," lgssgsyiew of Eggggmigsmsng
SLQLLSLLQS. 55, February 1973, 29-45. Since the
authors first defined this production function,
variations of it have been the standard in the
literature for estimation of input substitution.

44

The assumptions of linear homogeneity in prices and
constant returns to scale, require that the following
restrictions hold:

ax + at + as + as = 1

Bus + BxL + BK: + Bin = 0
BIL + BLL + BL: + Btu = 0
Bus + Bis + Bar + Btu = 0

0 (2)

fits + BLM + Ban + Bun
Assuming a competitive market and cost minimization,
using Shepherd's Lemma’:
6C

Xi = p i = K, L, E, M0
GP:

 

where X. is the demand for factor 1.

Partial derivative of logarithms are equivalent to
elasticities. So if natural logarithms are taken of the two
sides of the cost function and the partial derivatives are
taken of the cost function in relation to P; (the price of
factor i), the result will be the sensitivity of total cost

with relation to the price of factor i (Pa):

 

9. The Shepard’s Lemma states that if xi(w,y) is the firm’s
conditional factor demand for input i, where y is the
optimal output level, and w is the vector of input
prices, if the cost function C is differentiable at
(w,y), then:

5C(W.Y)
x;(w,y) = ————————, i = 1,...,n.
8wi

For a more detailed derivation see Varian, Hal R.,
Microsconomic Anslxsis, second edition, 1984, w.w.
Norton & Company, New York, p. 54.

45
61n(C) BC Pi
__ = _— -- : C} + Bfli J lan ti
61n(Pi) 6Pa C ‘

where j = K, L, E, M.
Substituting GC/SP; = X: in the above equation:
P: X;
= as + zBijlnPj,i
C x

As PaXa/C is the share of the cost of input 1, Si, in
the total cost function, the following set of equations can
be derived which are equivalent to the demand functions for

each factor;

83 = PuK/C : a; + Bxxln(Px) + BxLln(PL) + Bxsln(Pg)
+ Bxuln(Pn)

SL = PLL/C = a; + Bngn(Pg) + BLLln(PL) + BLgln(Ps)
+ BtulanM)

S: = PsE/C = as + Bxsln(Px) + BLEln(PL) + Baaln(Ps)

+ Bsnln(PM)

SM = PHM/C = an + anln(PIl + Btnln(PL) + Bsnln(Pt)

+ Bnnln(PM) (3)
where the total cost is given by; C = PxK + PLL + PEE + PMM.
Si is the cost share of the input i in the total cost of
producing Y.

The above equations are much easier to estimate because
they are not complex algebraically and data about cost
shares and prices are more readily available than the larger
set needed to estimate directly a production or cost
finiction. The restriction imposed by the complexity of the

ecluations, however, has been greatly diminished in recent

46

years with the increasing availability of statistical
packages capable of handling simultaneous equation systems,
and non linear models. Once the parameters of the above
equations are estimated, elasticities of substitution can be
calculated and substitutability of inputs analyzed.

The AES between inputs i and j can be calculated in the

following way:

CCij
0i) =
CiCj
where
6C 630
Ci : —, Ci j : — o
6Pi 6Pi6PJ

Because symmetry was imposed in the production
function, by definition Oij = 05:. Using the translog cost
function, the AES are defined as:

Bli + (Si)2 - Si

 

 

as: = , i = K, L, E, M.
(Si):
(4)
Bi: + Slsi
0i.) = v inj : K: L! E! M! i¢J
$185
(5)

The AES varies according to the cost share of each input.
The price elasticity of demand 6:5 is defined as:
61n(xx)

Eij = f

OlnPj

 

and the price elasticities of demand are related to the AES
elasticities in the following manner:

$13 = SjOij.

In this way, even when. as; = 0,, by definition, price
elasticity of demand varies according to the cost share of
the input.
In the same fashion, the translog production function
can be defined as:
in Y = ln(ao) + axln(Xx) + aLln(XL) + asln(Xs)
+ anln(XMl + inrHlnXx)2 + Butln(Xx)1n(XL)
+ Bx:ln(Xx)ln(X£) + anln(Xx)ln(Xn)

+ iBLIJlnXL)2 + BLEln(XL)ln(Xg)

 

+ Btnln(XL)1n(an + $8;;(lnX:)2 +

+ Bsxln(X£)ln(XM) + iBMM(lnXu)2. (6)

Y = total output

Xx = quantity of capital input
X; = ” labor input

X; = " energy input
X" = ” material input

Bijz parameters

a = parameters

ln = natural logarithm
Given profit maximization,

6Y

P, = , i = K, L, E, M.
6Xi

 

The logs of both sides taking derivatives is equivalent

t1) finding elasticities. Thus:

48

6ln(Y) 6Y Xi

m ' 35.. 7’
where j = K, L, E, M.
Since 8Y/5Xs = Pia

PIXI/Y

= a: + EBIJInxJ.1

The equations below are

demand. functions if

output normalized at
S: = PxK/y = a:
St = PLL/Y 3 at
S: = FEE/Y = as
Su = PuM/y = au
To reiterate,

fTXITXLTXITXulo

total output Y.

we define S.

1:

.9.

+

4.

+

+

+

+

4.

equivalent to the

= as + XBiJlnXJ,1

substituting in the above we get:

factor’s

= P: X1 /Y with price of

Bxxln(Xx) + Briln(XL) + Bx:1n(XI)
Blu1n(XM)
Bltln(Xl) + BLL1n(XL) + Btsln(XI)
BLH1n(XM)
Bllln(Xl) + Btrln(XL) + Bzrln(xt)
B|u1n(Xu)
Buuln(Xx) + Biuln(XL) + Btuln(X:)
Buuln(Xu) (7)
the production function Y

S: is the cost share of each input in the

In the same way,

the assumptions of linear homogeneity

and constant returns to scale require that the following

restrictions hold:

a: + at +

8::
BIL
Bl!

Btu

+

+

+

BIL
Bit
BL:

Btu

a: + au = 1

+

+

+

+

BK: + Btu
BLE + Btu
Bx: + Dru

Btu + Buu

(8)

 

49

According to the AES, inputs are complements or
substitutes as 01) < 0 or 0:: > 0 respectively. The A33
will be calculated based on the production and cost
functions. The AES from the production function will be
Aa), to distinguish it from the AES calculated from the cost
function, on. The AH is obtained through the following
procedure:1°

IFTJI

IFI

Aij =

where Fl: is the cofactor of f1; in F, and F is the
following determinant, in a four input model:

0 f1 f2 f3 f4
f1 f1: f1: f1: fl‘
F = f2 f2: f1: f2: f2:

f3 f3: fa: f3: f3:

 

 

f: f4: f4: f4: f4!
where:
fa 1: S:

fil

Bl) + Ss’ - Si

f1: = Bl) + $185

In order to make sure that the data conforms to a cost
function, the test for positivity and concavity must be
performed. These are requirements for the existence of the
functions. The test for positivity is required to make sure

w

1C). Hamermesh, Daniel and Grant, James; “Econometric Studies
of Labor-Labor Substitution and Their Implications for
Policy," The Journal of Humsn Resources, XIV, 4, Fall
1979.

50

that there are no negative costs. This situation would rule
out the existence of a cost function. For the translog cost
function this is done by fitting the equation and ensuring
that there is no negative-fitted cost share.H

The test for concavity is needed to ensure that there
are no increasing returns to scale. In the presence of
increasing returns to scale the profit function may not have
a maximum. When the assumption of profit maximization does
not hold, the estimation of production functions and the
elasticities originated from the procedure may not be valid.

For the cost function quasi-convacity must be ensured
if the cost function is to have a minimum. Concavity/quasi-
concavity requirements do not hold for the translog function
globally, necessitating checks at every point.12 One way
to do this is to use a procedure called Cholesky
decomposition, first used. by Lau13 in this context. .A

function is concave if the Hessian matrix of second partial

 

11. Some authors like Jorgenson Dale, and Fraumeni, Barbara
M.; "Relative Prices, and Technical Change" in Mggsling
amifleasuring Natural ResourcLSubatitution. edited by
Ernst Berndt and Barry C. Field, Cambridge, MIT Press,
1981, pp. 17-47, consider satisfactions that the
average shares are non-negative.

 

12. Peter Schmidt does not attach too much importance to the
point by point check for concavity, probably because
the translog is a second order approximation, and it
does not satisfy concavity globally anyway.

13. Lau, Lawrence J., "Testing and Imposing Monotonicity,
Convexity and Quasi-Convexity Constraints," in
Egggggtign Egongmigs: A Dual Approach to Thsory and
aggligssigns, Vol 1, edited by Melvyn A. Fuss and
Daniel Mcfadden, 1978, Amsterdam, North Holland, pp.
409-453.

 

51

derivatives is negative semi-definite. This requirement is
achieved in the context of a translog cost function if all
Cholesky values are less than or equal to zero at each
sample point. An alternative way of doing it is to check
for the eigenvalues. For quasi-concavity, the number of
non-positive eigenvalues must be greater than or equal to
(n-l) where n is the order of the symmetric matrix. For
concavity, all eigenvalues must be non positive.

The share equations (ST) derived from the cost and
production functions, as a result of the mathematics of the
derivation, are deterministic. There is no reason, however,
to expect deterministic behavior from stochastic variables.
The decision-makers in a firm make mistakes. A firm cannot
adjust input mix overnight as a result of changes in prices
and. market conditions, and the data. contain measurement
errors which justify for adding error terms to the equations

so that econometric techniques can be used to estimate the

parameters. The error terms are assumed to have means of
zero and constant variances across the sample. This may not
always be the case, but small departures will not

significantly distort the results.u
The error terms of the equations (3) and (7) above are
correlated because the increase in the cost share of one

input implies the reduction in the cost share of at least

 

14. Chavas, Jean Paul and Segerson, Kathleen; "Stochastic
Specification and Estimation of Share Equations
Systems," Journsl of Econometrics, July 1987, pp. 337-
358.

52

one competing factor. Ihi these cases, the ordinary least
squares technique does not yield efficient estimates. The
Zellner Seemingly Unrelated Regression Estimation (SURE) is
used because it improves the efficiency of the estimates by
plugging back the covariance matrix into ‘the estimation
process. When the covariances between the error terms are
zero, SURE will be equivalent to OLS. The assumption of no
serial correlation within equations must still hold.

As a brief summary of what has been done in the field,
an updated synopsis taken from Chung” is presented in

Appendix A.

 

15. Chung. crisis...

CHAPTER 4

DATA AND ESTIMATION

The data used in this study refer to three paper
enterprises of the Klabin Group in Brazil: Industrias
Klabin de Papel e Celulose s/a (IKPC), Riocell s/a
(RIOCELL), and Papel e Celulose Catarinense s/a (PCC). The
first firm acts as a holding company for the Group in spite
of the fact that this relationship is not formally defined
in the structure. The headquarters of Klabin are located in.
830 Paulo, and its plant is located in the Monte Alegre
Farm in Telemaco Borba in the west of Parana state. The
Group controls several other firms besides PCC and RIOCELL;
some of them in other states. In addition to its paper
companies, the conglomerate has 'packaging, forestry, and
mining divisions.

The three firms cited above were chosen from among the
others in the group because the paper producing activity
could be clearly separated from the other activity. The
reason to limit the study to one activity, and one product
is to minimize the phenomenon of changing output mix in

response to market demand as described by Solow.1 The

 

1. 3010", 9.2.2.9312..-

53

54

phenomenon, in this case, was minimized but could not be

eliminated because even within paper manufacturing,‘ there

were variations in the product. For example. every plant
produces at least four types of paper. The composition of
the final output may also be changing over time. Paper

production is, however, the most disaggregated level for
which data can be readily obtained. It is possible to pick
only one type of paper, but it would take a long time to
determine the specific inputs used. Furthermore, those
determinations would never be exact, because many inputs are
jointly used.

The data were taken from internal management reports
together with records of specific units in the plants,-
accounting records, and cost accounting reports. Data for
more) than five years were «difficult to assemble because
reports changed considerably; while more detailed data were
included in recent years, some series of data were
discontinued. There are very good cost accounting reports
for the recent years, but similar data for earlier years are
not available. Because this study relies on time series
analysis, the length of the time series is important. This
research concentrates on those series for which the longest

period of time could be covered.

DATA.

The three firms researched have different management
teams and different reporting techniques. The data are

necessarily in different degrees of completeness, accuracy,

55

and aggregation. The most complete data set exists for the
Klabin mill in Monte Alegre, Parana. More time was spent in
that plant and its offices reviewing reports. Time series
were obtained for:

-output levels

—product prices

-depreciation

-financial costs

-number of employees

-cost of labor

-electricity (prices and quantities)

-coal (prices and quantities)

-fuel oil (prices and quantities)

-black liquor2 (quantities)

-firewood (prices and quantities)

-wood (prices and quantities)

-caustic soda (prices and quantities)

-whitewash (prices and quantities)

—sodium sulfate (prices and quantities)

-chloro (prices and quantities)

-water (prices and quantities)

-sulphur (prices and quantities).

 

2. Black liquor is a residual from the wood digesting
process. One of the processes of decomposition of the
wood for transforming it into paper is through the use
of chemicals. When the wood is dissolved and the
fibers finally separated, what remains is a
chemical/wood residue which when treated can be
effectively used as fuel.

56

The data were obtained (with the exception of a few series),
for the period of January, 1982 to December, 1987.

The first major difficulty was the transformation of
prices and values into a common, measurable monetary unit.
Inflation in Brazil has been a problem for decades. In
recent years, the inflation rates have been consistently
above 100 per cent3 and currency unit changes have been a
common occurrence. This poses a dilemma for firms, because
they cannot plan if they do not have a stable unit of value.
Those firms which have a trained staff plan everything in
dollars or in any of the various fixed value currencies the
Government has created over the years. There are Standard
'Units of Capital (UPCs), Readjustable National Treasury
Bonds (ORTNs), National Treasury Bonds (OTNs), Fiscal OTNs
and Standard Reference Units (URPs) among others. Several
index tables are available, each one with its own approach
and directed to a specific sector or activity. The reports
at IKPC company started with cruzeiros, went to ORTN, then
cruzados, and finally dollars. These changes were either
caused by an overhaul in currency denominations, or required
by soaring inflation rates. Planning for the future has
been done in dollars for several years, but reports remained

in cruzeiros/cruzados until 1986. To report in dollars is a

 

3. The World Bank, Bgszil: A Mscrogconomic Evsl at on tithe
Cruzsdo Plan. Washington, 1987; Baer, Werner; "The
Resurgence of Inflation in Brazil, 1974-86, ngld

anelsament. VOl- 15. N-8. 1987-

57'

more demanding task. The transformations must be made by
trained people, or the numbers are grossly distorted.

All data used in this study were transformed into
January, 1982 dollars. Brazilian firms need to maintain two
accounting systems, one in local currency to comply with
corporate tax laws and another which accurately reflects the
real value of assets and profits. It was a monumental task
to convert all values into 1982 dollars. Nevertheless, the
transformed data are not free from distortions because they
reflect the sharp internal price fluctuations caused by
exchange rate lag. The official exchange rate is fixed by
the Central Bank. Depending on how they practice catching
up with inflation, prices are lowered or increased sharply.
During strong inflationary periods, internal prices become
very high if the Central Bank does not devalue the currency
fast enough. 11' it devalues it faster than inflation,
internal prices fall. The record shows that the Central
Bank always plays tricks with the exchange rate to allow the
government to achieve short run political goals.‘

Planning in dollars does not solve a firm’s problems
because tricks with the exchange rate distort company
operations in any circumstance. Swift movements in exchange
rate cause sharp fluctuations in a firm’s liquidity because

those changes affect contracts already signed but not yet

 

4. The President of the Central Bank is selected by the
Finance Minister. So the Central Bank has no autonomy
to follow a sound monetary policy. It has to yield to
the interest of the politician in charge.

58
fulfilled. They also affect a firm’s decision to buy

locally or to buy imports, and its competitiveness in the
international market.

It would be interesting to disaggregate labor and
energy to see which segments of labor are being substituted
for which group of inputs. This would provide a picture of
the evolving labor market contrasted with patterns of energy
use. A disaggregation, however, is not possible for labor
because labor use reports by wage level use different
criteria across the years. There are some reports
classifying the labor force by wage level (minimum wages
earned) but, because the wage rate fluctuates considerably,
acute fluctuations in the numbers within each category
occur. Minimum wage readjustments by the government do not
coincide with the timing of wage rate readjustments for the
industry. Thus, in the period preceding wage rate increases
by firms in the paper industry, wage rates are very low (in
terms of minimum wages earned), and the low-paying
categories are inflated.5 In months when pay rises, almost
everybody moves up in the scale (they earn more minimum wage
units) with the lower categories dropping sharply in

numbers. So, an analysis of the labor force by skill level

 

5. For example, minimum wages category X has an inordinately
high number of employees because inflation has eroded
wages, and government readjusted minimum wages before
firms readjusted the salaries of their employees. Wage
increases are normally intended to compensate for past
inflation. In the months when the firms give a wage
increase, fewer people will be classified in the
category X.

59

will take considerable time to complete. The disaggregation
of energy was possible in three categories, except for
RIOCELL which was subdivided in only two categories.

In order to find a common factor for energy
aggregation, all energy inputs were transformed into Tons of
Oil Equivalent (TOE),‘ using the coefficients published by
the Ministry of Mines and Energy.7 A good share of electric
power used in the plants is produced internally using fuel
oil, coal, firewood, or black liquor. Only the electricity
purchased from public utilities was included because the
caloric content of the electricity produced internally was
accounted for in the fuels used to generate it (coal, oil,
firewood, etc.). Power shortages in this industry can be.
disastrous. Firms maintain several backup systems for power
because the public utilities supplying energy are
unreliable.

The other material inputs can also be disaggregated.
But as was the case for labor, this task is beyond the scope
of this study and will be left for a future undertaking.

The data used in the estimation process for each firm
are: share of labor in total cost of production (3;), share
of energy (8;), share of materials (Sn), share of capital
(Sr); and levels of use of energy (X3), materials (Xu),

labor (XL), and capital (Xx). For the materials series,

 

6. The equivalency is in caloric content.

7. Balanco Energetico Nacional, 1987, Minisssrio dgs Minss e
Emma. PP - 119-120 -

60

inputs were added up in tons. In the labor series, the
number of workers was used” For the physical capital
series, a composite index to resemble the number of machine
hours was calculated. The composite index was based on the
level of output, total electricity used (acquired and
generated internally), and tons of steam generated.
Physical capital has been very stable in recent years,
except for RIOCELL. For the others, there has been no major
addition of equipment. There have been changes in boilers
and a biomass plant° built at IKPC. The series, in index
numbers format, are shown in Appendix B.

In order to estimate the parameters using SURE, the
prices and quantities are transformed into index numbers and
then into natural logarithms so that the data conform to the
model.

The basic equations are estimated with the restriction
that the elasticity between input 1 and j are the same as
the elasticity between input j and i: ani=o;;. This
restriction, in fact, is part of the model because of the
way the cost and production functions are set up. The
demand equation systems to be estimated for each firm are:
Qgggpwl. Cost Function - 4 inputs, K, L, E, and M.

(1) St = an 4- Bx: lnP: + BK: lan 4’ BIL lnPL +

Btu 1nPu + e;
(2) Su = on + Bus lnP; + Bur lan + But lnPL +

Buu lnPu + e:

 

8. This is a facility to prepare wood residues for burning.

61
(3) Sr. = as + Bra 11113: 4’ Bax lan. 4' BEL lan. +

Btu lnPu 4' ea

(4) St

at + BIN lnPr + BL; lan + Btu lnPL +
Buu lnPu + e4
The results of the estimation for the three firms are shown
in Tables 1, 2, and 3.
Grggpwg. Production functions - 4 inputs; K, L, E, and M.
(1) Su = Cl + Bl! lnXx + BIL IHXL + Bx: lnXs
Bxu lnXu + e;
(2) S: = at + But lnXx + BLL lnXL + BLS lan +
Btu lnXu + e:
(3) S. = a: + Br: lnX. + 8;; lnXL + Bag lnX; +
Bsu lnXu + e;
(4) St = au + Btu lan + BLH lnXi + Btu lnX: +
Buu lnXu + e;
The results of the estimation for the three firms are shown
in Tables 4, 5, and 6.
Grggpmg. Cost Functions - 6 inputs with energy disaggregated
in 3 categories: Biomass (E1 ) , Fossil fuels (E2 ) ,
Hydroelectricity (E3), and K, L, M:
(1) 331 = as: + Bsi.ailn(P:i) + Bxi.szln(Ps2) +‘
Bti.saln(P::) + Bll,lln(Pl) + BII.L1n(PL) +

Bsi.uln(Pu) + e;

(2) Se: as: + Bsz.niln(P:1) + sz.:2ln(P::) +
Baz.saln(Pns) + Bsz.xln(PI) + sz.t1n(PL) +

Baz.uln(Pu) + e:

62

(3) SE: = as: + BE:,£11D(PII) + B:3,lzln(P£z) +
Baa.saln(P:3) + Bra,xln(Px) + Bla.tln(PL) +

B:3.uln(Pu) + 83

(4) St = as + 83,;1ln(P:1) + Bg,gzln(P£2) +
Bx.saln(Psa) + Bl,xln(Px) + Bl,L1n(PL) +
Blaflln(PM) + e.

(5) SL = at + Bt.liln(Psi) + Bt.lzln(Psz) +

Bi,saln(Psa) + Bi.rln(Px) + Bt,lln(PL) +
Br.uln(Pu) + es
(6) Su = Cu + Bu.siln(P31) + Bu,szln(Prz) +

Bu.raln(P33) + BM.lln(Pl) + Bu,tln(Pt) +
Bu.uln(Pu) + es

The results are presented in Tables 7, 8, and 9.

figggpm_4. Production Functions - 6 inputs, energy dis-

aggregated as in item :3. For the) production function,

instead of prices quantities (X;) are used in the share

equations as regressors. The results are presented in

Tables 10, 11, and 12.

E_ls_s.t.i.ci.t.x_.Eatima_tss

The AESs are shown for each group (for the three firms)
in Tables 13 to 24.

As important as estimating their elasticities is
finding their significance. This procedure consists
basically of estimating a confidence interval. One chooses
the level of confidence that one wants to have about the

probability that the estimated elasticity will fall within

63

the interval; if it falls within the interval,
"significance" is said to have been reached. The most
common level of significance chosen in scientific research
is 95 per cent (a=0.05).° This is called statistical
significance, as opposed to a theoretical or conceptual
significance. Statistical significance has a very narrow
interpretation. If an a=0.05 is chosen, the statistical
significance indicates that, given the sample used in the
study, with 95 percent certainty, the coefficients are
likely to be within the estimated interval. In the
discussion below, the term significant and significance are
used to refer to statistical significance.

The confidence interval may be estimated by several
methods. The first, and most frequently used is to assume
that the input shares in the total cost are not stochastic.
This assumption simplifies significantly the computation of
the variances, which can be obtained by the formula:

1
VAR(G)J) = --- VAR(B:J)
S; S)
The shares, however, are clearly stochastic and the
intervals generated by this formula are not appropriate. A

more appropriate method assumes that the shares are
stochastic. The estimated elasticity can be written as

functions of the shares and the regression coefficients:

 

9. a being the tail of the distribution. This is the area
we want to exclude.

64
6,, = f(§1 3§Jffil1)

This is a non-linear relationship. Assuming that the
function is continuous and twice differentiable in the
neighborhood of the mean, the variance of the estimates can
be approximated by:10

A 6f .. 6f 6f .. A
VAR(G) 5) z 2 --;- VAR(Bi 3) + 2): -; —A- COV(B: :BJ)
SB; 3” GB.) BB)

To any elasticity G,,, this would be translated into:

 

 

2 A 2 A 2
A 1 A -B|: A -B:J
VAR“); 3) = 77—A— VAIHB: j) + VAR(S() + ..
Si 3.) S) ’3.) S) S) 3

 

1 -B13 A A
VAR(SJ) + 2 7—7— A A COV(BIJ,SI)
SIS) 3133:

 

A A
COV(BIJ:SJ)

cov<§..8.)

 

 

A A A
The COV(B; J ,S: ) and COV(B. 3 ,S; ) are assumed to be
zero. In this case, three terms are left and the estimated

variances are reasonable approximations.

 

10. Kmenta, Jan; glsments of Economstrics, The MacMillan
Company, New York, 1971, pp. 443-444.

65

In order to facilitate the task of connecting the
results, Tables 25 and 26 summarize the results for the
four-input estimates euui six-input estimates respectively.
To allow a brief comparison with selected results found in
the literature. Table 27 presents the elasticities
published in a few selected studies. This study is
interested. mainly i1: the energy-capital coefficients and
elasticities, but a discussion of the other estimates is
illustrative because it would tell something about the
method itself. The other inputs estimates can be compared
to theory and/or previous studies for disparities. If
disparities are present, an explanation for that should be

provided.

Thewfigurmlnputwfistimatss

Cgst Function

The input own price elasticities are expected to be
negative, meaning that as the price of the input increases,
the use of the input diminishes. For the cost function
estimates, only eight from the twelve elasticities were
negative. For the PCC company, the energy and materials own
price (elasticities (05.: and. au.u) have the ‘wrong sign,
whiLe for the RIOCELL company, the energy and capital own
elasticities (05,5, and Ox,x) are also positive. From the
four estimates with wrong signs, only the capital elasticity
for the RIOCELL company is significant at the 5 per cent

level.

66

Two of the energy-capital (05.x) elasticities are
positive (IKPC anui PCC companies) indicating substitution
between energy and capital, while the same elasticity for
the RIOCELL company is negative and significant indicating
complementarity between the two inputs. Worth mentioning is
the fact that the capital/labor elasticities (OI,L) are all
positive and significant. The labor-materials (0L.u)
elasticities are all positive but only for IKPC is it
significant.

Rroductionlfiunction

The elasticities calculated from the production
coefficients show that nine of the twelve input own price
elasticities (Aa.s) are negative, and three of them have the
wrong sign. The estimates of the IKPC company remain
consistent with all input own price elasticities, that is,
negative. For the PCC company, the energy estimate remains
positive, but the capital estimate (63,3) turns from
negative and significant ix: the cost function 1x) positive
but not significant in the production function. The case of
the RIOCELL company remains consistent also~ Only the
capital elasticity is positive, repeating in the production
function the result of the cost function estimation. In
general, input demand is responsive to its own price
increases, as indicated by the negative numbers of the input
own price elasticities. In other words, as the relative

price of an input rises, less of it is used.

67

The energy-capital (Gs,x) estimate for IKPC company
remains consistent, that is, positive; reinforcing the case
of substitutability of inputs in that company. The estimate
for the PCC company shifted signs from positive to negative,
but both of them are not significant. The case of RIOCELL
remained negative and significant. .Based on 1flue cost and
production functions, energy capital are substitutes in the
IKPC company, complements i1: the RIOCELL company, and rum;
defined in the PCC company.

For both IKPC and RIOCELL companies, the capital/labor
estimates (GILL) change signs. Only the coefficient for
IKPC is significant. These sign shifts are problematic and
indicate that there are inconsistencies present in the
method, or in the data. The signs for labor/materials
(GL.u) remain positive across methods.

All the energy/labor (Ga,L) estimates are not
significant in the cost function while in the production
function two of them are positive and significant. That is
the case for PCC and RIOCELL companies, indicating that
there is some degree of substitutability between energy and

labor.

ThewSixWInputmEstimates

Costmfiunction

The transformation from four to six inputs is a result
of the disaggregation CM? energy into three categories: E1
(fossil fuel), E2 (biomass), and E3 (hydroelectricity).

This categorization is arbitrary; there is no special reason

68
beyond the fact that fossil fuels are clearly non-renewable
while biomass and hydro are usually considered renewable.
In the case of RIOCELL company, hydroelectricity was dropped
because it was negligible; there is some indication that the
translog function method is sensitive to small input shares.

Twelve of the input own price elasticities are negative
(0,,3). Those not conforming with the theory are:

IKPC company
- Fossil fuels
- Biomass
PCC company
- Labor
- Materials
RIOCELL company
- Capital

Only the capital estimation for RIOCELL company is
significant.

An interesting fact is that the energy own price
elasticity' for the IKPC company' (Gs,s) was negative and
significant when the estimation was done with four inputs.
In the cost function with six inputs, the estimates for the
three disaggregated series (E1, E2 and E3) are not
significant, but only 033,33 is negative. The remaining own
input price elasticities are negative for IKPC.

The elasticities for fossil fuels/biomass (Gan.zz) are
positive for the PCC and RIOCELL companies indicating

substitutability between the two energy groups in those

69

companies. The same elasticity is negative for the IKPC
company reflecting complementarity between the two energy
groups.

Substitution between biomass and capital (021.3) was
found only in PCC and RIOCELL companies. The biomass-
capital elasticity for the IKPC company is negative and not
significant. All the elasticities between biomass and the
other inputs (0:1,; and Gsx,u) for the three companies were
not significant.

The elasticities between fossil fuels and
hydroelectricity (052,;3) were negative and significant for
the two companies for which they were estimated (IKPC and
PCC), indicating complementarity in the use of those two
energy groups. Substitutability between fossil fuels and
capital (ze,x) was found only in the IKPC company. For PCC
and RIOCELL the elasticities were negative and significant,
indicating complementarity for these companies.

The hydroelectricity/capital (633,3) elasticities
indicate substitutability between the two inputs for IKPC
and PCC companies. The capital/labor elasticities (G;,;)
are positive for IKPC and RIOCELL, and negative but not
significant for PCC. These results remain consistent with
the literature which usually finds substitutability between
capital. and labor (Table 27). The elasticities between
labor and material (Gt,u) are consistently positive across

methods and disaggregations.

70

Productionmfunction

Fourteen (M? the seventeen input (Mfll elasticities are
negative, repeating the early results from the four-input
model and the six-input cost function. The elasticities not
conforming to the theory are:

IKPC company
- 0:3,53
- Gx,l
PCC company
- Gas,£3
Only the estimate for the IKPC company is significant.

All the elasticities between biomass and fossil fuels
(0:1,53) are positive and significant, indicating
substitutability between the two groups of inputs. The
elasticities between biomass tnui hydroelectricity (031,53)
are negative; it is significant only in the case of IKPC
company. This gives a mixed result because, in the case of
the cost function, the elasticities between biomass and
hydroelectricity' are different. The elasticity for PCC
company is positive and significant, and for IKPC it is
negative and not significant.

The elasticities between biomass and capital (651,3)
also provide mixed results. The estimates for the RIOCELL
company remain consistent from the cost to the production
function, indicating substitutability between biomass and
capital; they are significant. The estimates for the IKPC

company are negative in both the cost and production

71

functions and are not significant. The estimates for the
PCC company shift signs from positive and significant in the
cost function to negative and significant in the production
function.

The complementarity between fossil fuels and

electricity (0:2,;3) is once more shown tnrzi negative and

significant estimate for IKPC company. The same elasticity
is positive for PCC, but not significant. This estimate
does not exist for RIOCELL company because the

hydroelectricity variable was dropped.

Another major shift in signs occurs for the PCC company
in the case of the fossil fuels/capital (Gsz,x) elasticity.
From .negative and significant in the cost function, it
shifts to positive and significant in the production
function. The estimates for the RIOCELL company remain
consistent with negative and significant elasticities across
methods. In the case of the IKPC company, 0:2,: is positive
and significant in the cost function and negative and not
significant in the production function--an ambiguous result.
Also ambiguous are the results of biomass with the other
labor and material inputs.

The estimation of the hydroelectricity/capital (653,3)
elasticities seem to be consistent across methods, revealing
significant substitution between hydroelectricity and
capital. The relationship between hydroelectricity and the
other inputs, labor and materials, is not clear. Also, in

the capital/labor elasticities (G;,L), there seems to be a.

72
major shift in the case of the RIOCELL company. The
significant estimates for GK,L have been primarily positive,
but in the five-input case for RIOCELL, it shifts from
positive and significant to negative and significant.

The only elasticity estimate which remains consistently
positive across methods and firms is the labor/materials
(Gi.u) elasticity. The substitutability between labor and
materials seems unequivocally established in this study.

Comparing the results obtained here with those found in

previous studies (Table 27), one can see that they are not

very' different. The labor/material elasticity' has been
found to be positive most of the time. The same applies to
capital/materials and capital/ labor. But the results are

not as consistent when the other elasticities estimated in

this study are compared. From seven significant
capital/materials (Gx,u) elasticities, only" four are
positive. From nine significant capital/labor (G;,L)

significant elasticities, only seven are positive.

The results in general are mixed and do not by
themselves establish substitutability between inputs
unambiguously. The study, however, does provide evidence
that some assumptions underlying government policies in the
energy sector are not warranted.

The tests required to check for the existence of cost
and production functions (positivity' and. concavity) were

performed. All the regressions satisfied the positivity

73

requirement, but only the following regressions complied
with the concavity requirements:H

RIOCELL - Production, 5 inputs

RIOCELL - Cost, 4 inputs

RIOCELL - Production, 4 inputs

PCC - Production, 6 inputs

PCC - Production, 4 inputs

All the test results for IKPC company were undefined.
The test was also undefined for PCC company for the cost
function with 4 and 6 inputs, and for RIOCELL company cost
function with five inputs. This is reason. enough. for
looking at the estimates from those regressions with care.

In the next chapter, the results will be further

discussed and concluding comments presented.

 

11. These tests are necessary to rule out negative costs and
increasing returns to scale in the production function.

'744

TABLE 1: IKPC
ESIJIIIE iEUAIllXPIEEIIEFt IEEiTIIPIAVITEEB ()1? 13, 1C, 1., 1414I) 11 - (3()E§1? IFIJPTCTIYI(317
JAN/82 to DEC/87 (Asymptotic t-ratios in parenthesis)

 

Equation 01 81.5 81,: Bi,1 B..n :2 F

 

(1) (Se) 0,3040. 0.0980: 0.0767: -0.1122' -0.0630* 0.53 (7.59
(3.75) (7.42) (5.10) (-14.40) (~3.04)

(2) (5:) 0.1360’ 0.0767‘ ‘0.0948* '4.0E-7 0.0180 0.27 9.92
(20.17) (5.18) (‘4.02) (-0.05) (0.62)

(3) (31) 0.3060‘ -0.1122' -4.0E-7 0.14604 -0.0338 0.61 39.05
(78.87) (‘14.40) {-0.05) (12.34) ('1.79)

(4) (5.) 0.2520: -0.0640t 0.0100 -0.0330 0.0790: 0.37 0.03
(42.62) (-3.04) (0.62) (-1.79) (4.20)

 

i = E, K, L and M
* Significant at the 5 per unit level.

TABLE 2: PCC
EflJIIE: ItAIlAfldEEPEflZ IESKP114AKFI§3 (DI? 13, It, 1., A09!) P1 - ()CE?!‘ FfiJbKDTIICli
JAN/82 to DEC/87 (Asymptotic t-ratios in parenthesis)

 

Equation as 81,: 81.: Bi,L 81.0 a? F

 

(1) (8:) 0.3670‘ 0.2780‘ '0.0090 '0.1540‘ '0.1154‘ 0.89 125.55
(4.15) (30.14) (‘1.78) (-14.58) (‘8.27)

(2) (5;) 0.0530‘ -0.0090 '0.0025 -3.0E-6 0.0118* 0.02 1.61
(26.44) {-1.78) (-O.49) (-0.03) (1.97)

(3) (St) 0.4060’ '0.1540’ '3.0E-6 0.2048’ -0.0507' 0.75 73.67
(108.75) ('14.58) ('0.03) (15.10) ('8.49)

(4) (Sn) 0.1720’ -0.1155’ 0.01184 ‘0.0507* 0.15434 0.78 44.00
(71.90) {-8.27) (1.97) (‘8.49) (18.78)

 

1. == IE, Ii, 14 1311C! 11

4 Significant at the 5 per unit level.

'755

TABLE 3: RIOCELL
SURE PARAMETER ESTIMATES OF E, K, L, AND M - COST FUNCTION
JAN/82 to DEC/87 (Asymptotic t-ratios in parenthesis)

 

Equatlon a; B1,: 81.x 81.1 B..u :2 F

 

(1) (3:) 0.4720: 0.2240: -0.1300i -0.0434: -0.0509 0.57 10.52
(5.72) (9.08) (-4.901 (-3.00) (-1.55)

(3) (5:) 0.1470‘ '0.1300‘ 0.20184 -3.0E-7 -0.0716 0.33 10.73
(6.13) ('4.90) (5.25) ('0.03) (-1.42)

(21(51) 0.1036‘ -0.0434‘ '3.0£'7 0.04804 -0.0047 0.08 2.78
(6.40) (-3.00) ('0.03) (2.80) (-0.17)

(4) (Sn) 0.2770t -0.0509 -0.0716 -0.0047 +0.1274t 0.09 2.04
(16.90) (-1.50) (-1.42) (-0.17) (4.51)

 

i = E, K, L and.M
* Significant at the 5 per unit level.

TABLE 4: IKPC
SURE PARAMETER ESTIMATES OF E, K, L, AND M - PRODUCTION FUNCTION
JAN/82 to DEC/87 (Asymptotic t-ratios in parenthesis)

 

Equat1on a. 81.: 87,: 81.1 81.: ADJ 8’ F

 

(1) (5c) 0.2820‘ -0.0610 -0.0340* 0.0640* 0.0310 0.12 4.44
(31.37) (-1.21) ('3.70) (1.96) (1.05)

(2) (3%) 0.1870‘ -0.0340* 0.0700‘ 0.0027 -0.0387‘ 0.96 579.77
(88.15) (-3.70) (23.88) (0.31) (-5.80)

(3) (SL) 0.3030‘ 0.0640‘ 0.0027 0.0241 -0.0910* '0.03 0.22
(36.51) (1.96) (0.31) (0.72) ('3.15)

(4) (Sn) 0.2280‘ 0.0310 -0.0387 -0.0910 0.09804 0.63 16.21
(3.12) (1.05) (-5.80) (‘3.15) (4.24)

 

i = E, K, L and.M
* Significant at the 5% level.

76
TABLE 5:

I’CICZ

SURE PARAMETER ESTIMATES OF E, K, L, AND M - PRODUCTION FUNCTION
JAN/82 to DEC/87 (Asymptotic t-ratios in parenthesis)

 

 

Equation 01 87,: 81.: 81,1 81,u 807 82 F

(1) (3:) 0.30908 0.46908 ‘0.0640* ‘0.2170‘ -0.1880* 0.58 34.41
(31.20) (9.67) (“6.49) ('5.13) (-4.74)

(2) (SK) 0.0550‘ '0.0640‘ 0.0814‘ ‘0.0097 -0.0084* 0.69 55.51
(27.67) (-6.49) (11.58) (~0.97) (-1 49)

(3) (31) 0.4590‘ '0.2170* ‘0.0090 0.2170* 0.0090 0.26 9.49
(44.98) (-5.13) (‘0.97) (4.51) (0.21)

(4) (SI) 0.1770t ‘0.1880* ‘0.0080‘ 0.0090 0.1880* 0.51 10.36
(2.11) (-4.74) (‘1.49) (0.21) (10.70)

 

i = E, K, L and M
* Significant at the 5% level.

TABLE 6: RIOCELL
SURE PARAMETER ESTIMATES1OF E, K, L, AND M - PRODUCTION FUNCTION
JAN/82 to DEC/87u (Asymptotic t-ratios in parenthesis)

 

 

EQUation a) 81.: 85.x 07,1 Bi,u ADJ 83 F

(1) (85) 0.3770‘ 0.21303 '0.1360‘ ‘0.0124 -0.0650‘ 0.65 43.54
(28.63) (6.71) ('10.79) {-0.88) (‘4.49)

(2) (SK) 0.1860x '0.1360’ 0.24404 -0.0350¥ ‘0.0730* 0.93 325.66
(27.18) ('10.?9) (27.55) ('5.42) (‘9.05)

(3) (31) 0.2290* ‘0.0124 ‘0.0350‘ 0.06704 '0.0196‘ 0.47 21.25
(24.74) (‘0.88) ('5.42) (7.28) (‘2.01)

(4) (5.) 0.20803 '0.0650‘ '0.0730‘ ‘0.0196‘ 0.15768 0.57 12.42
(14.63) (“4.49) ('9.05) (‘2.01) (18.21)

 

i = E, K, L and.M
" NOV/82, DEC/82, JAN/83, FEB/83 excluded from sample.
' Significant at the 5% level.

TABLE 7:
SURE PARAMETER ESTIMATES CF E1.

77

IKPC

1312,

E3, K, L, AND M
COST FUNCTION - ENERGY DISAGGREGATED JAN/82 to DEC/87
(Asymptotic t-ratios in parenthesis)

 

 

 

Equatlon a) 01.01 87.52 B(,£3 85.x 01.1 01,! AD) 92 F

(1) (5:1) 0.1617’ 0.2020‘ -0.0858‘‘ -0.0156* -0.02353 ‘0.0547‘ -0.0226 0.64 27.34
(35.04) (12.22) (-5.78) (-2.05) ('5.28) (-6.46) (-1.06)

(2) (522) 0.0827‘ ‘0.0858‘ 0.11934 -0.0234* 0.0464‘ -0.0297’ '0.0265’ ‘0.05 0.21
(16.83) ('5.78) (7.53) ('2.81) (5.36) ('3.94) (‘2.94)

(3) (853) 0.0610* '0.0156‘ '0.0234‘ 0.05524 0.01958 -0.0235* ‘0.0121‘ 0.51 16.33
(22.70) ('2.05) ('2.81) (7.58) (3.40) ('5.28) ('2.20)

(4) (51) 0.1330* -0.0235‘ 0.0463‘ 0.01954 :0.0354 0.0016 -0.0085 0.25 5.79
(19.97) (-5.28) (5.36) (3.40) (-1.85) (0.14) (-0.28)

(5) (31) 0.3070* -0.0547‘ -0.0297‘ -0.0235* 0.0016 0.13863 -0.0322 0.64 27.05.
(66.18) (-6.46) (-3.94) (-5.28) (0.14) (11.78) ('1.75)

(6) (SH) 0.2530‘ -0.0226 -0.0265 '0.0121 -0.0085 ‘0.0322 0.1020‘ 0.19 1.88
(25.45) (-1.06) (-2.94) (-2.20) (°0.28) (‘1.75) (3.13)

i =IL K,l.mm1M

* Significant at the 5% level.

'75)

TABLE 8: PCC
SURE PARAMETER ESTIMATES OF E1, E2, E3, K, L, AND M
COST FUNCTION - ENERGY DISAGGREGATED JAN/82 to DEC/87
(Asymptotic t-ratios in parenthesis)

 

EQUatlon a) 81.51 B1.£2 81,55 81,: 81.1 81,0 ADJ 82 F

 

(1) (551) 0.2730' 0.07104 0.1470* 0.0100 0.0050 -0.1600‘ -0.0720* 0.83 73.96
(67.04) (3.02) (9.74) (1.40) (1.00) (-12.33) ('5.22)

(2) (852) 0.0400‘ 0.1470* -0.0219 '0.0177‘ ~0.0325* '0.0226‘ ‘0.0521‘ 0.04 1.71
(11.92) (9.74) (-1.56) (-3.15) (-5.60) (‘2.31) (-4.47)

(3) (853) 0.0307‘ 0.0102 -0.0177* 0.0117 0.0101* 0.0052 -0.0195‘ 0.28 6.57
(18.11) (1.40) ('3.15) (1.84) (2.33) (1.00) ('5.20)

(4)(s() 0.0503: 0.0052 0.0325: 0.0101: 0.0190: 0.020111 0.02m 0.15 3.55
(22.01) (1 00) (-5.60) (2.33 (2.69) (-3.84) (4.55)

v

(5) (51) 0.4290¥ -0.1600‘ ~0.0226* 0.0052 -0.0281‘ 0.24908 -0.0435‘ 0.87 96.55 ‘
(134.91) (-12.33) ('2.31) (1.00) ('3.82) (19.09) (-4.14)

(6) (SH) 0.1770* -0.0720* -0.0521* -0.0197¥ 0.0261* '0.0435‘ 0.1612* 0.63 7.37
( ) ('5.22) (-4.47) (-5.20) (4.55) (-4.14) (17.08)

 

i 21L K,I.and14
* Significant at the 5% level.

'71)

TTIKIBIilg 59 3 I? [()(3131414
SURE PARAMETER ESTIMATES OF E1, E2, K, L, AND M
COST FUNCTION - ENERGY DISAGGREGATED JAN/82 to DEC/87“
(Asymptotic t-ratios in parenthesis)

 

Equat1on a1 01.!) Bx,£2 87,4 01,1 81,4 ADJ R? F

 

(1) (641) 0.3140: 0.0420 0.0500: 0.0214 -0.00804 -0.0529 0.29 7.91
(21.44) (1.08) (2.14) (0.71) (-4.00) (-1.14)

(2) (5(2) 0.1530‘ 0.05804 0.0617‘ -0.1539‘ 0.07044 -0.0362 0.15 4.08
(12.06) (2.14) (2.46) (‘6.90) (4.60) ('1.56)

(3) (3%) 0.0810‘ 0.0214 -0.1539* 0.21064 0.0069 -0.0850* 0.58 24.81
(4.77) (0.71) ('6.90) (5.41) (0.32) ('2.39)

(4) (81) 0.1850* -0.0880‘ 0.07044 0.0069 0.0001 0.0115 0.39 12.02
(16.93) (‘4.80) (4.60) (0.32) (0.007) (0.63)

(5) (SH) 0.2670* -0.0329 -0.0362‘ -0.0850‘ 0.0115 0.1426‘ -0.09 0.56
(2.06) (‘1.16) ('1.56) (-2.39) (0.63) (5.92)

 

1. == 13, 11, l. auncl 11
" NOV/82, DEC/82, JAN/83, FEB/83 excluded from sample.
3 Significant at the 5% level.

80

TABLE 10: IKPC
SURE PARAMETER ESTIMATES OF E1, E2. E3. K) L. AND M
PRODUCTION FUNCTION - ENERGY DISAGGREGATED JAN/82 to DEC/87
(Asymptotic t-ratios in parenthesis)

 

Equat10n a) 81.21 81.52 81.15 81.: 31.1 15,4 ADJ 9’ F

 

(1) (5(1) 0.1390‘ 0.04305 '0.0201‘ -0.0258‘ -0.0416* 0.0461‘ -0.0022 0.06 1.98
(17.16) (2.04) ('3.03) ('2.26) (-3.88) (2.58) (-0.08)

(2) (3(2) 0.0673‘ *0.02014‘ 0.04404 -0.0091 -0.0083 0.0003 -0.0067 0.68 31.55
(35.68) (-3.03) (6.32) (-1.24) (-O.91) (0.045 (-1.35)

(3) (5:3) 0.06404 -0.0258‘ -0.0091 0.0656‘ '0.0149 -0.0417* 0.0260* 0.05 1.83
(18.85) ('2.26) ('1.24) (3.84) ('0.98) (-3.88) (3.35)

(4) (34) 0.17404 -0.04163 -0.0083 -0.0149 0.2770x -0.0198 -0.1920¥ 0.83 72.00
(45.96) (-3.88) (~0.91) (-0.98) (10.32) (-0.98) (-13.57)

(5) (5() 0.3220‘ 0.0461’ 0.0003 -0.0417‘ -0.0198 0.0523 -0.0373 -0.07 0.05
(35.82) (2.58) (0.04) ('3.88) (‘0.98) (1.90) (‘1.15)

(6) (SH) 0.2319* ~0.0022 -0.0067 0.02604 °0.1920¥ '0.0373 0.2120‘ 0.43 3.87
(2.52) (*0.08) ('1.35) (3.35) (-13.57) (-l.15) (7.74)

 

izEl’ E2, E3, K,L8MM.
* Significant at 5% level.

81

TABLE 11: PCC
SURE PARAMETER ESTIMATES OF E1, E2, E3, K, L. AND M
PRODUCTION FUNCTION - ENERGY DISAGGREGATED JAN/82 to DEC/87
(Asymptotic t-ratios in parenthesis)

 

Equation 01 81.01 01.02 81.03 81.: 31.1 31.! 807 R? F

 

(018:1) 0.0400: 0.04204 0.0352: 0.0101: 0.0004 0.04701 -0.0074 0.90 131.17
(33.07) (24.50) (0.03) (-0.40) (-2.99) (-7.10) (-1.22)

(2) (5:2) 0.2670‘ 0.0352‘ 0.5940* -0.1850* '0.0305* ‘0.2740* -0.1380‘ 0.71 36.81
(45.72) (6.03) (16.91) ('11.64) ('3.14) (-8.19) (-4.50)

(3) (3:3) 0.01914 -0.0162* -0.1857* 0.2350* '0.0253‘ -0.0067' '0.0008 0.76 47.78
(12.05) (‘8.48) (-11.64) (11.08) ('4.49) (-2.99) ('0.22)

(41(5):) 0.0532* 000684 003054 002534 0.0875* 0.0024 -0.0273* 0.69 33.49
(29.96) ('2.99) (-3.14) (-4.49) (10.54) (0.23) ('4.81)

(5) (81) 0.4560’ :0.0470‘ -0.2740* ‘0.0067* 0.0024 0.31303 0.0135 0.50 15.47
(65.62) (‘7.10) (8.19) ('2.99) (0.24) (7.26) (0.39)

(0)(574) 0.1032 000730 013004 -0.0000 0.02734 0.0135 0.1599: 0.40 4.20
(1.00) (-1.22) (-4.50) (0.22) (-4.01) (0.39) (0.09)

 

izEl, E2, BI, K, 1.38de.
* Significant at 5% level.

82

TABLE 12: RIOCELL

SURE PARAMETER ESTIMATES CF E1, E2, K, L, AND M
PRODUCTION FUNCTION - ENERGY DISAGGREGATED

JAN/82 to DEC/873* (Asymptotic t-ratios in parenthesis)

 

Equation 01 01.21 81.02 85.71 81.1 81.11 AN 92 F

 

(1) (321) 0.3040’ 0.1620t -0.0380* -0.0610* -0.0134 '0.0480* 0.62 28.57
(31.94) (10.05) ('4.54) (‘7.05) (-1.36) (‘4.00)

(21(562) 00950" 003804 0.1130* -0.0750‘[ 0.02404 -0.0243* 0.84 90.22
(14.19) (‘4.54) (12.93) (-10.93) (4.40) (-4.19)

(3) (3%) 0.1880* -0.0610* -0.0750* 0.25904 ‘0.0507‘ -0.0721‘ 0.94 318.34
(27.02) (-7.05) ('10.93) (28.70) (-8.08) (‘3.18)

(4) (3() 0.2100‘ :0.0134 0.02404 *0.0507‘ 0.06003 '0.0214 0.32 9.04
(23.28) ('1.36) (4.40) ('8.08) (6.55) (‘1.93)

(5) (80) 0.20303 -0.0480* '0.0243* -0.0721* -0.0214 0.16589 0.56 7.64
(2.47) (-4.00) (-4.19) (-3.18) (‘1.93) (18.80)

 

i =El’ E2, E3, K, Ila-rid".
3 Significant at 5% level.
" NOV/82, DEC/82, JAN/83, FEB/83 excluded from sample.

TABLE 13:

83

IKPC

SURE ESTIMATED ALLEN ELASTICITIES OF SUBSTITUTION. (AES)

COST FUNCTION (E. K. L. AND M) JAN/82 to DEC/87
(Asymptotic t-ratios in parenthesis)

 

 

AES Estimate MIN MAX

0:; '1.29 1.54 -0.97
(-3.38)

or: -21.88 -44.22 -5.57
(-3.15)

OLL -0.67 -0.71 -O.48
(-1.83)

ouu -1.58 -2.15 -1.05
(-3.77)

or: 3.87 2.28 6.03
(3.43)

GEL -0.23 -0.61 0.07
(-1.52)

OIM 0.15 -0.76 0.50
(0.50)

OIL 0.99 0.99 0.99
(3921.97)

oxu 1.67 1.37 2.18
(1.73)

OLM 0.61 0.42 0.73
(2.78)

 

* Significant at the 5% level.

SURE ESTIMATED ALLEN

TABLE 14:

ELASTICITIES OF SUBSTITUTION.

COST FUNCTION (E, K, L, AND M) JAN/82 to DEC/87
(Asymptotic t-ratios in parenthesis)

84

PCC

 

 

AES Estimate MIN MAX

0:: 0.47 0.10 1.58
(0.55)

our -20.19 -38.76 -7.65
(-10.29)

ULL -0.18 -0.22 -0.01
(-0.52)

ouu 1.36 -0.48 5.08
(0.54)

or: 0.49 0.06 0.76
(1.65)

05L -0.03 -0.30 0.18
(-0.24)

osu -1.07 -1.89 -0.44
(-2.56)

OIL 0.99 0.99 0.99
. (238.69)

oxu 2.56 1.61 3.42
(2.92)

UL" 0.17 -0.51 0.52
(0.74)

 

* Significant at the 5% level.

(AES)

SURE ESTIMATED ALLEN ELASTICITIES OF SUBSTITUTION.
COST FUNCTION (E, K, L, AND M) JAN/82 to DEC/87
(Asymptotic t-ratios in parenthesis)

85

TABLE 15: RIOCELL

(AES)

 

 

AES Estimate MIN MAX

0:: 0.10 -0.11 1.36
(0.14)

aux 34.48 -0.23 542.79
(13.19)

OLL -3.45 -4.20 -1.79
(-2.83)

ouu -0.82 -17.07 -2.99
(-0.90)

or: -1.61 -15.34 -0.06
(-3.31)

OIL 0.13 -0.22 0.66
(0.41)

osu 0.35 -1.10 0.68

(0.32) -

GIL 0.99 0.99 0.99
(3525.41)

oxu -1.28 -l4.64 0.21
(-1.38)

UL" 0.86 0.77 0.94
(1.18)

 

* Significant at the 5% level.

86

TABLE 16: IKPC
SURE ESTIMATED ALLEN ELASTICITIES OF SUBSTITUTION. (AES)
PRODUCTION FUNCTION (E, K, L, AND M) JAN/82 to DEC/87

(Asymptotic t-ratios in parenthesis)

 

 

AES Estimate AES Estimate
A3,; -2.26* A£.L 0.53
(-3073) (1069)
Ag,g -33.49* A£,u -0.11
(-7045) (-0034)
AL,L -3.62* AK,L '1.34‘
(-9073) (-5025)
Au.u -7.46* Ag," 9.738
(-14.92) (24.04)
AE.K 4.75* AL,u 3.62*
(9.69) (9.48)

 

* Significant at the 5% level.

TABLE 17: PCC
SURE ESTIMATED ALLEN ELASTICITIES OF SUBSTITUTION. (AES)
PRODUCTION FUNCTION (E, K, L, AND M) JAN/82 to DEC/87
(Asymptotic t-ratios in parenthesis)

 

 

AES Estimate AES Estimate
A...' 0.31 A... 1.634
(0.21) (5.24)
A‘n‘ 26022 AS,” -4029:
(1076) (-4091)
AL,L ‘4029* A"L 2048‘
(-9031) (5059)
AM,” -4072* AK," '10.740*
(-1.53) (-14.03)
A2,: -1.88 AL,M 7.303
(-1.73) (11.25)

 

* Significant at the 5% level.

87

TABLE 18: RIOCELL
SURE ESTIMATED ALLEN ELASTICITIES OF SUBSTITUTION. (AES)
PRODUCTION FUNCTION (E, K, L, AND M) JAN/82 to DEC/87“
(Asymptotic t-ratios in parenthesis)

 

 

AES Estimate AES Estimate
A505 -4023* AE,L 2017*
(-5026) (8027)
A3,: 8.23* A£.u 9.93*
(2.21) (34.62)
AL. I. -10035* A‘, I. -0074*
(-6.32) (-1.67)
Au.u -17.68* Au.u -0.10*
(-17.95) (-0.21)
A5,: -5.15* AL.u 4.194
(-10.48) (13.44)

 

‘* NOV/82, DEC/82, JAN/83, FEB/83 excluded from sample.
* Significant at the 5% level.

TABLE 19:

88

IKPC

SURE ESTIMATED ALLEN ELASTICITIES OF SUBSTITUTION. (AES)

COST FUNCTION

DISAGGREGATED ENERGY INPUT

 

 

(E1, E2, E3, K, L, AND M) JAN/82 to DEC/87
(Asymptotic t-ratios in parenthesis)

AES Estimate MIN MAX

0:1.s1 4.07 0.43 20.16
(1.03)

032.52 31.92 8.38 89.05
(1.54)

033.33 -1.77 -3.41 3.93
(-0.50)

0|.I -13.98* -26.24 -4.31
(-4.87)

OL,L -0.74* -0.80 -0.55
(-2.16)

ou.u -l.24* -l.45 -0.88
(-2.06)

031.3: -10.94* -29.78 -4.33
(-2.63)

031.33 -0.52 -2.53 0.15
(-0.66)

031.: -0.64 -1.87 0.38
(-0.98)

031.2 -0.13 -0.80 0.28
(-0.50)

0:1.u 0.43 -0.45 0.71
(0.86)

032.33 -5.71* -13.49 -2.49
(-2.10)

032,: 11.18! 3.99 19.56
(2.28)

0:2,; -0.83 -1.57 -0.20
(-1.45)

0:2,u -0.91 -2.35 -0.19
(-1.29)

033,: 3.858 2.37 5.93
(3.30)

als.t -0.03 -0.47 0.27
(-0.12)

0:3.u 0.36 -0.12 0.62
(1.13)

0:,3 1.05* 1.01 1.11
(3.26)

al,u 0.68 0.45 0.82
(0.70)

at.u 0.631 0.46 0.75
(3.02)

 

* Significant at

the 5% level.

89

TABLE 20: PCC
SURE ESTIMATED ALLEN ELASTICITIES OF SUBSTITUTION. (AES)
COST FUNCTION - ENERGY DISAGGREGATED
(El: E2, E3, K, L, AND M) JAN/82 to DEC/87
(Asymptotic t-ratios in parenthesis)

 

 

AES Estimate MIN MAX
021.:: -1.74* -2.51 -0.89
(-3.03)
052.52 -61.90¥ -318.90 -10.14
(-4.92)
0:3,:3 -17.29* -20.35 -13.08
(-0.37)
03.: -10.948 -12.15 -6.10
(-2.66)
02,; 0.06 -0.004 0.51
(0.17)
0u.u 1.48 -0.36 5.66
(0.60)
051.52 19.92* 5.31 79.16
(2.73)
_0£i,£3 2.11* 1.61 3.20
(2.68)
0:1,: 1.37* 1.20 1.75
(3.69)
031.1 -0.45 -1.33 -0.09
(-1.67)
03:.u -0.73 -1.68 -0.20
(-1.66)
032.33 -14.673 -45.16 -2.13
(-2.09)
022,: -18.96¥ -55.19 -3.05
(-2.18)
052.2 -0.59 -3.60 0.47
(-0.81)
0:2.u -8.884 -27.17 -1.45
(-2.23)
083.: 6.82* 3.29 13.98
(2.32) -
Ol3,L 1.36* 1.20 1.78
(3.94)
0:3.u -2.69 -6.05 -0.62
(-1.94)
OI,L -0.31 -l.26 0.42
(-0.68)
0u.u 4.313 2.35 6.35
(3.48)
02.u 0.32 -0.30 0.59
(1.41)

 

* Significant at the 5% level.

90

 

 

 

TABLE 21: RIOCELL
SURE ESTIMATED ALLEN ELASTICITIES OF SUBSTITUTION. (AES)
COST FUNCTION DISAGGREGATED ENERGY INPUT
(E1. E2, E3, K, L, AND M) JAN/82 to DEC/87::
(Asymptotic t-ratios in parenthesis)
AES Estimate MIN MAX
031.0: -2.57* -4.27 -0.99
(-3.24)
002.32 -2.45 -3.05 4.03
(-0.62)
ox.x 36.293 -0.18 568.79
(11.10)
02,; -5.85* -9.59 -2.32
(-8.13)
au,u -0.52 -0.75 -2.96
(-0.54)
031.32 3.46* 1.91 6.61
(2.51)
031,: 1.64* 1.21 4.52
(3.05)
031.2 -1.64 -3.38 0.11
(-1.60)
0:1.u 0.36 -1.23 0.74
(0.87)
032,: -10.60* -135.54 -2.20
(-4.48)
0:2.L 5.46* 2.10 7.73
(2.65)
0:2.u -0.47 -3.21 0.51
(-0.48)
03,; 1.33* 1.06 3.51
(2.33)
0x,u -1.71* -17.57 0.07
(-2.09)
02,u 1.338 1.12 1.56
(2.72)
*3 Nov/82, Dec/82, Jan/83, and Feb/83 excluded from the
sample.

4 Significant at the 5% level.

91

TABLE 22: IKPC
SURE ESTIMATED ALLEN ELASTICITIES OF SUBSTITUTION. (AES)
PRODUCTION FUNCTION DISAGGREGATED ENERGY INPUT
(E1, E2, E3, K, L, AND M) JAN/82 to DEC/87

(Asymptotic t-ratios in parenthesis)

 

 

AES Estimate AES Estimate
A31.£1 -13.71* A:2,33 -44.50*
(-14097) (-22013)
Asz,gz -197.26* A32.l “0.90
(-29.80) (-0.51)
Afl3,§3 54004* A529L 17013*
(11.39) (37.83)
AM). 3949 AEZ." -1076‘
(0020) (-5014)
AL.L *0.62 A33,g 9.04:
(-2044) (4053)
Au.u -1.69 A:3,L -10.84‘
(-2.09) (-21.64)
As:.sz 54.474 Ara,u 9.644
(60.60) (19.09)
AEI'ES '11006‘ A‘.L -0052
(-10.24) (-0.89)
A31,| -2.01 AK,M ‘1.77
(‘1091’ (-1011)
A:1,L 0.73 AL,u 0.12
(2.06) (0.35)

All.M 0.22

(0.36)

 

* Significant at 5% level.

92

TABLE 23: PCC

SURE ESTIMATED ALLEN ELASTICITIES OF SUBSTITUTION. (AES)

PRODUCTION FUNCTION - DISAGGREGATED ENERGY INPUT

(El! E2, E3,

K, L, AND M)

JAN/82 to DEC/87

(Asymptotic t—ratios in parenthesis)

 

 

AES Estimate AES Estimate
A51,51 ~251.26* A32.£3 1.02
(-11.37) (0.17)
As2.32 -1.96 A32,x 5.89*
(-0.55) (6.82)
A53,:3 5.84 Agz,L -3.82*
(0.06) (-8.18)
Al.l ~1.89 Asa," 2.98*
(-0.11) (3.74)
A2,; -7.92* Ara,x 0.32
(-13.51) (0.05)
Au.u -19.68* Aga,L 0.33
(-7.43) (1.72)
A31,32 29.70* Aga,u -4.223
(17.40) (-0.60)
A81.E3 0.02 AI,L 13.263
(0.004) (27.75)
A51,g -62.67* AK,M -27.21*
(-30.34) (-10.88)
A51,L 32.134 At,u 14.22*
(25.63) (33.81)

A:1.u -46.40*

 

* Significant at 5% level.

SURE ESTIMATED ALLEN ELASTICITIES OF SUBSTITUTION.

93

TABLE 24: RIOCELL

PRODUCTION FUNCTION - DISAGGREGATED ENERGY INPUT
K, L, AND M) JAN/82 to DEC/87n
(Asymptotic t-ratios in parenthesis)

(El:

E2: E3!

 

 

AES Estimate AES Estimate
A£1,§1 -87086* A5135. 18049*
(-55.86) (62.19)
A:z.sz ‘152-86* Aei.u -29.48*
(-23.33) (-84.08)
Au.u -34.48* A52,| -82.53*
(“8.70) ('73.22)
A8403. -12084* AEZ.L -23037’
('8.61) (-31.76)
Au.u -47.61* Asz,u 69.44
(-45.79) (157.83)
4431,32 103.98* Alhl. '15.60*
(141.04) (-25.84)
Ag,u 31.96* AL,M 16.97*
(52.51) (48.25)
Aa:,x 53.553
(131.69)

 

** NOV/82 to FEB/82 excluded from sample.

1 Significant at 5% level.

(AES)

94

TABLE 25: SUMMARY - FOUR INPUTS (E, K, L, AND M)
Summary of Allen Elasticities from the Cost and Production
Functions IKPC, PCC, RIOCELL

 

 

 

 

Cost Production

Elasticity

IKPC PCC RIOCELL IKPC PCC RIOCELL
03.: -1.29* 0.47 0.10 -2.26¥ 0.31 -4.23*
03.: -21.88t —20.19* 34.48* -33.49t 26.23 8.23!
GL.L -0.67 -0.18 -3.45* -3.623 -4.30t -10.35t
Gu.n -1.58* 1.36 -0.82 -7.46¥ -4.72* -17.68t
05,: 3.87* 0.49 -1.61* 4.753 -1.88 -5.15t
05.; -0.23 -0.03 0.13 0.63 1.63! 2.173
02.x 0.15 -1.07* 0.35 -0.11 -4.303 9.93:
03,; 0.993 0.99! 0.99* -1.34t 2.48: -O.74
Ga." 1.67 2.56* -1.28 9.731 -10.753 -0.10

GL.H 0.61* 0.17 0.86 3.63* 7.31* 4.19*

 

TABLE 26:

SUMMARY - SIX INPUTS (E1:

95

E2:

E3:

K, L, AND M)“
Allen Elasticities from the Cost and Production Functions
IKPC, PCC, RIOCELL

 

 

 

 

Cost Production

Elasticity

IKPC PCC RIOCELL IKPC PCC RIOCELL
031.31 4.07 -1.74* -2.57* -13.71* -25l.26* -87.87*
032.32 31.92 -61.90* -2.45 -197.26* -1.96 -152.87t
033.33 -1.77 -17.29 - 54,04: 5,34 -
63.: -13.98* -10.94¥ 36.298 3.49 —1.89 -34.49*
01,; -0.74* 0.06 -5.85¥ -0.62t -7.92* -12.848
On." -1.24* 1.47 -0.52 -1.69 -19.68* -47.613
G:1.:2 -10.94* 19.97* 3.46* 54.47* 29.70* 103.983
GEI.£3 -0.52 2.11* - -11.06* 0.02 -
G:1.l -0.64 1.371 1.64* -2.01 -62.67# 53.553
Gax.L -0.13 -0.45 -1.64 0.79 32.133 18.49!
Gsx.n 0.43 -0.73 0.36 0.22 -46.40* -29.49t
Gs2.£3 -5.71* -14.67* — -44.50* 1.02 -
652.: 11.183 -18.96t -10.60* -0.90 5.893 -82.531
GEZ.L -0.83 -0.59 5.468 17.131 -3.82* -23.373
G:z.u -0.91 -8.88* -0.47 -1.76* 2.983 69.443
0:3,: 3.85*, 6.82* - 9.043 0.32 -
Gsa.L -0.03 1.36* - -10.84¥ 0.33 -
G:a.n 0.36 -2.69* - 9.64* -4.22* -
GI,L 1.05* -0.31 1.33* -0.52 13.261 -15.60t
0;," 0.68 4.31! -1.71t -1.77 -27.21* 31.96!
03.x 0.63* 0.32 1.33* 0.12 14.22* 16.97*

 

1* For RIOCELL E:

3 Significant at 5% level.

was dropped because it was negligible.

96

 

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ousuauoau; 0:» a“ weapon»: couuaafiomnsm mo nouuuouunuqm
an «Sane

CHAPTER 5

COMMENTS AND CONCLUSION

One important implication here is that policy—makers
cannot, in general, rely only on estimated elasticities as a
point of departure for macroeconomic policies.1 Those
estimates can at best provide some guidance for sector-
specific policy-making. Elasticities vary from firm to.firm
even when they belong to the same industry. A wide spectrum
of input mixes is available to firms in spite of the fact
that in many cases the core technology is the same. The
realm of feasible input mixes widens with the degree of
integration of the firms. Firms with a high degree of
integration in their activities have more options in the
combination of inputs. This will become clear as the
structure of the activities in the firm is further
explained.

The production function being studied here is eggpgst
in nature. The core equipment is in place, and this means

that the process cannot be fundamentally changed. In

 

1. Macroeconomic policies generally assume elasticities are
in the extremes (0 or m), or 1. If the true
elasticities were known, they could provide some
guidance to policy making. Since we are not positive
about the range of elasticities, other parameters must
be also used.

97

98

economics jargon, it is a putty-clay technology meaning that
gzzantg the inputs are substitutable, but exgpost they are
fixed. This study refers to actual data of production,
which means that the technology has been chosen. The option
of choosing an alternative production technique is not being
considered. In highly integrated firms, however, even when
the core technology is in place, input mix can be changed
significantly. To illustrate the point, the paper industry
itself can be used as an example.

The paper industry is very integrated vertically. The
production process starts with a natural resource (trees)
and ends with the manufactured product ready for consumption
(paper). The basic output can be further transformed into-
more elaborate products like specialty papers, packaging,
and. cardboards among others. The» major transformation,
however, occurs within the paper mill.

Even if the paper machine, the single most important
piece of equipment in the firm, is chosen to represent the
technology being used, there remains room for change in the
associated. activities. The firm: has different ways of
performing several activities such as:

1. The transport of the pulverized wood from the
grinding unit to the cooking/digesting unit which can be
done by trucks or by conveyor belts.

2. The wood segments can be transported from the
storage path to the grinding unit by trucks or by conveyor

belts.

99

3. Tree branches may be left in the forest as
fertilizer, or used as fuel.

4. The digesting process can be done through chemical
or heating processes.

5. The residues of chemical decomposition can be
treated and used as a fuel, or released into the
environment.

6. Electric power can be generated internally or
purchased from public utilities.

7. The wood/chemical residues may go through a process
of secondary recovery from which additional paper fiber
could be generated.

8. A variety of fuels may be chosen to generate steam:
coal, fuel oil, firewood, black liquor, wood residues, tall
oil, diesel, and gas.

The above illustrates the fact that even when the core
technology is the same, several jobs can be done
differently. Depending on how these tasks are performed, a
different input mix will emerge.

Because of the ex399§t nature of the production
function ‘being studied, the capital productivity is not
captured in the estimation process. Except for the RIOCELL
company, no major addition of equipment was made in the
period studied. The addition of one paper machine, for
example, would produce a sharp» increase in the output.
Major increases in the output are not possible with only

changes in how some tasks are performed. The latter is

100

rather associated with input substitution. The addition of
a secondary recovery' process would increase the use of
capital, and reduce the input of raw material (wood). This
is shown by the estimated AES for the IKPC company whose
major changes were the installation of a recovery boiler and
a biomass plant. The capital/materials (Gx,u) elasticity is
positive in the cost and the production functions,
indicating substitutability between capital and materials.
The G3... for the RIOCELL and PCC companies is ambiguous.
The labor/materials (6;,3) elasticity is positive throughout
the methods, indicating easy substitution between labor and
materials. The above elasticities indicate that
'substitution of inputs is possible even in an ex;ngg&
production function. The putty-clay characterization of
technology is not appropriate in cases of highly integrated
activities.

A general pattern of input substitution cannot, be
established. The paper industry operates with long time
horizons, adjusting slower to economic changes than any
other industry. Equipment has a life span of more than 20
years, and major equipment substitutions have to be planned
years ahead. The paper industry is an excellent
representation of an industry in which input substitution is
difficult and slow. The present study encompasses only five
years; a short span for analysis of the industry. Studies

of less capital and energy intensive industries may find

101

more substitutability between energy and capital, as well as
among other inputs.

There are a number of discrepancies between the methods
of estimating demand functions originating from cost and
production functions. These might be an indication of
problems with the method, and/or problems with the data.
The number of inconsistencies, however, is rather small
considering the number of parameters estimated; especially
when one considers that the translog cost and production
functions are not duals of one another.

Estimating of elasticities of substitution from demand
functions based on production and. cost functions is an
attempt to measure how much the use of one input is affected
by the price of other inputs. This in turn should
facilitate the development of more accurate predictions of
demand for inputs. Energy demand forecasts based on energy
consumption as a fixed proportion of output (E/Y)2 have not
fared well because they do not take into account
substitutability among inputs. In this regard, econometric
studies undertaken in the past several years provide some
guidance about energy—capital substitutability
possibilities. The studies have also provided consistent
estimates of capital/labor substitutability, and similar
measures of the effects on demand of changes in input own

prices.

 

2. E = energy, Y = output.

102

The controversy about energy and capital
substitutability has been going on for about 13 years. Many
studies have tried to establish substitutability in the
aggregate for the whole manufacturing industry, for specific
sectors, or industries. The studies do not produce
unambiguous estimates of energy-capital substitutability.

The recent argument by John Solow that estimating
production and cost functions with aggregate data may be
invalid, must be taken into account. That is one of the
reasons why this study focuses primarily at the micro level;
another reason is the difficulty of obtaining data in LICs
at the macro or industry level. However, the ambiguity
observed in aggregate level studies remains at the micro
level. While it is evident that demand is responsive to
price changes, the substitutability between energy and
capital could not be unambiguously established in the
sample.

The estimation. of jproduction and. cost functions is
sensitive to the level of disaggregation. Highly
disaggregated models make studies more interesting because
there is a clearer distinction between substitutes, and the
method is more precise. But computation costs may increase
significantly. In this study, for example, if energy in
Group 2 were disaggregated into coal and fuel oil, the
elasticities would have been evaluated differently because
fuel oil is heavily substituted for coal in this industry.

Once these two fuels are aggregated, the process of

103

substitution is run; captured. Furthermore, elasticities
calculated from the disaggregated cost function (6 inputs)
are not comparable to elasticities found in the cost
function (4 inputs) for those inputs which remain unchanged.
Changes in elasticities should be analyzed longitudinally,
that is, how they change in time instead of how they change
across aggregations. Each elasticity bear a relationship
with the others, and disaggregation into more inputs
generate conceptually different elasticities.

Energy groups are physical substitutes. This can be
seen in Figures 2, 3, and 4, for the IKPC, PCC and RIOCELL
companies. The installation of a new coal burning boiler in
the RIOCELL company explains the sharp increase in the-
consumption of fossil fuels. The elasticities being
calculated in this study measure these relative changes in
energy consumption against changes in relative prices. The
pattern of physical substitution should provide an idea of
the trend in relative price changes. There are situations,
however, in which this is not the case, as explained below.

Since investment in IKPC and PCC companies was very low
in the past years, there was not much potential for
energy/capital substitution. The investment made in the
RIOCELL company was not related to a technological
improvement, but rather to the addition of a whitening
facility. Before 1983, RIOCELL produced only natural paper.
In other words, there was a change in the output mix in this

company in 1983.

104

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107

In order to take advantage of the exceptionally good
market conditions. for paper' in the last few (years, the
Klabin group has chosen to acquire existing firms. They
reorganize them to conform with the management style of the
holding company which tries to achieve higher input
productivity.3 As a major paper producer, the Klabin group
has no problem in marketing its products. It has a
significant market share 'within the country and it has
expanded considerably ix: foreign markets :hi recent years.
Its production capacity has reached its limit and it still
has the potential to capture more markets. That is why it
makes sense to acquire other firms. Investment in new
equipment might take several years to be transformed into
increased production. By then, market conditions may not be
as good. This strategy allows the group to take immediate
advantage of increased demand and higher paper prices. This
strategy also affects the composition of factors within the
firm, as new externally acquired capacity is not reflected
in the firm’s production. Instead capital is being diverted
from the internal operations of one firm to the other. To

have a better picture, the whole group should be analyzed as

 

3. Those are smaller firms, and they are in such a situation
because they could not compete effectively in
international markets when the country entered into the
recent crisis. As the internal market shrunk because
of the crisis, they found themselves in an increasingly
weak position. Those firms which could compete
effectively in foreign markets gained strength and are
now in a position to acquire the smaller. The smaller
ones have neither the structure nor the organization to
venture into foreign markets.

108

one producing unit. But in this case, there would be no
homogeneity in the output. The estimation process would
also be running into the problem of changing output mixes
pointed out by Solow.‘

As previously mentioned, some (M? the estimated
functions do not comply with concavity requirements. This
may cast some doubts on the estimates of those functions.
This situation indicates that the method needs to be
perfected. The data should not be forced to fit into an
existing model. Rather, the model should be broad enough to
explain the dynamics contained in the data. The data should
not be made to conform with a concave function if in reality
the function is non-concave. The method is not appropriate
in such cases because it cannot explain the behavior of the
variables.

In several occasions, the behavior of the firms do
not conform to the theory. Thus, the analysis must be
complemented in order to provide a better understanding of
why this is the case. Following are some explanations for
non-concavity of some functions; and each one will be
further explained later:

1. Late reaction to higher oil prices due to lags

in the firms adjustment process.

2. The market price of oil does not reflect the true

cost of using oil.

 

4 . SoloW. 0901!: 1987 .

 

109

3. Technological change takes a long time to implement.
It is not induced by short-term price fluctuations
but, rather, the long-run trend in relative factor
prices.

4. Increased local demand for biomass and coal pushed

up their relative prices.

5. Presence of increasing returns to scale in the

production functions.

The late reaction to oil price increases may be
explained by the firms’ continued effort to substitute oil
for other energy sources, even when oil prices were going
down. This can be seen in Figure 5 for the IKPC company
which shows decline in the use of oil at the same time that
oil prices were declining. This happens because the
affected companies could not do much in the short-run. They
took measures to substitute oil, but these measures take
several years to be operationalized. When the changes began
to be operational, oil prices started to go down. Thus,
adjustment lags explain why substitution happened in a
period when it was not justifiable economically.

An alternative explanation is that entrepreneurs were
adjusting the prices of oil by an uncertainty premium. The
supply of oil has greater probability of being disrupted in
Brazil than in other countries because of the debt crisis.
Firms were taking this risk into consideration when they
decided to substitute oil for biomass. Oil prices were

being adjusted by an additional risk premium.

110

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111

A paper machine may remain in use for about 30 years.
This may explain the slow reaction of this industry to sharp
input price fluctuations. Decisions to change technology
take several years to be implemented. By the time the new
equipment starts to affect production, conditions may have
changed. This happened to some degree in the decision to
substitute fuel oil.

The fact that many industries were looking for domestic
sources of energy may have pushed up the prices of local
inputs since increased demand for any input drives prices
up. More biomass was being used by the companies in a
period when biomass prices were going up; less fuel oil was
being used at a time when oil prices were going down. This
behavior goes against the core~ of :neoclassical economic
theory, but it can still be rationally explained.

The results may be further distorted because the firms
may be operating in a range of increasing returns to scale.
Estimation of a simple Cobb-Douglas production function with
four inputs (K, L, E, and M) using non-linear least squares
as expressed by the formula:

Y = AE'KflLtM'
where:
= output
= energy

— capital

rmmx:
l

labor

3
u

materials;

112

with aggregated data for the three firms results in the

following parameter:

A = 0.16
a = 0.60‘
B = 0.053‘
t = 0.29‘
9 = 0.45‘
where:
t : significant at the 1 percent level,
** = significant at the 5 percent level, and

*** = significant at the 10 percent level.

The four marginal products sum to 1.39, indicating the
presence of increasing returns to scale.5 The input with
the highest marginal product is energy, followed by
materials and labor. The input with the lowest marginal
product is capital. This is explained by the ex;pggt nature
of the production function. The machinery is already
installed and operating with little room for changes in the
technology. But this is not saying that the input mix
cannot be changed.

Estimation of the Cobb-Douglas function in its
linearized form:

lnY = lnA + alnE + Ban + tlnL + ilnM

yields results similar to the non-linear form:

 

5. If the sum of the marginal products is more than one,
that means increasing returns to scale. If they sum to
one, it represents constant returns to scale, and if
they sum less than one, the firm is in a range of
decreasing returns to scale.

113

lnA = -2.35‘
a = 0.59‘
3 : 0.06"
t = 0.36‘
4 = 0.48‘

The presence of increasing returns to scale is confirmed by
the sum of marginal products (1.49).

If energy is disaggregated into biomass (E1), oil
derivates (E2). hydroelectricity (E3), and coal (E.), the
production function becomes:

lnY = lnA + axlnEx + azlnEz + aalnEa + aglnE. + Ban +

tlnL + anM
and the estimates are:

lnA = -2.09"

a: = 0.37‘
a: = 0.02

as = 0.13"‘
a. = 0.04

B = 0.06"

t = 0.33*

9 = 0.47‘

In such a case, materials become the input with the higher
marginal product. Again, the sum of marginal products is
higher than one (1.42). In an exgagte production function,
the marginal product of capital is likely to increase

considerably.

114

One reason why the firms are exhibiting increasing
returns to scale may be the fact that the managers are
making a great effort to increase labor productivity. All
three firms have been increasing labor productivity over the

past years, as shown in Table 28.

Table 28
Input Productivity. Aggregated Data
(IKPC, PCC and RIOCELL)

 

 

1982-1987
Labor! Capital** Materialsttt Energy+
1982 6.66 0.021 0.210 1.31
1983 7.49 0.025 0.189 1.13
1984 10.29 0.031 0.193 1.26
1985 10.88 0.033 0.191 1.26
1986 10.99 0.030 0.189 1.24
1987 11.13 0.026 0.193 1.28

 

* Tons of paper per worker.
** Tons of paper per dollars.
t** Tons of paper for ton of materials.

+ Tons of paper per ton of oil equivalent (TOE).

Energy efficiency declined slightly from 1982 to 1987.

The efficiency of materials declined from 1982 to 1983,

remained roughly constant for the remaining years.

productivity increased over the period.

productivity
productivity,

other

factors,

of

and roughly' unchanging productivity“ of the

explain

combined

why the

with

Cobb-Douglas

increasing

Capital
The increases

capital

production

115

function captures increasing returns to scale in the data.
Average product per worker has been increasing over the
years. This means that marginal product has been on the
rise, and wage rates should. have risen. According to
economic theory, firms pay workers their marginal product.
This is the case for the aggregated data (all three firms),
as shown in Table 29, in spite of not being the case when

each firm is analyzed individually.

Table 29

Wage Rate
Average Cost Per Worker
JANUARY, 1982 Dollars

 

 

Year Cost

1982 $654.50
1983 $633.85
1984 $635.48
1985 $664.63
1986 $703.42
1987 $710.42

 

A competing explanation lfin? the inconsistency between
the disaggregated and aggregated data is provided by
organization theory. Any organization tends to deteriorate
over time. People tend to do things in the way in which
they are accustomed, they tend to resist change, and they
tend to not accept new assignments which are interpreted as
an increase in the amount of work they have to do. In order
to take care of new tasks, the organization tends to hire

new people. Over time, the organization becomes inefficient

116

because there is duplication of

effort, lack of

coordination, and conflicts over authority. In order to

remedy this, reorganization is necessary from time to time

to increase reorganizations,

efficiency. In these many
duplicated tasks and tasks which are no longer necessary are

eliminated.

In such situations, jobs are cut zuui workers

are reassigned. The paper firms in this study are in the
process of reorganization.

In the more capital intensive firms, labor productivity
should be higher because each employee has more machinery
available with which to work.

This is found to be the case

in the firms studied, as shown in Table 30. The Riocell
company is the most capital intensive, followed by IKPC and

PCC companies.

TABLE 30

LABOR PRODUCTIVITY
(Tons per worker)

 

 

1982-1987
YEAR IKPC PCC RIOCELL
1982 6.71 3.68 11.16
1983 7.15 3.92 16.54
1984 9.19 5.11 20.61
1985 9.73 5.34 22.14
1986 10.44 5.42 18.22
1987 10.8 5.53 17.45

 

Accordingly, the wage rate should be higher in the firms
where labor productivity is higher. This is not the case,

as shown in Table 31. Starting in 1983, relative wages in

117
the RIOCELL and PCC companies reflect their relative capital

intensity, but IKPC company is still out of line. The
explanation for this may be due to the labor market since
the companies are located in different regions. The
headquarters of the IKPC company is located in the more
competitive labor market of Sao Paulo. Furthermore,

overhead, which should be part of a separate holding company
is part of the IKPC payroll. This pushes the average wage

up because overhead salaries are above average.

TABLE 31

WAGE RATE
AVERAGE COST PER WORKER
(January, 1982 Dollars)

 

 

YEAR PCC RIOCELL IKPC
1982 726 503 820
1983 498 597 671
1984 442 510 585
1985 461 602 617
1986 569 639 759
1987 588 723 748

 

The method used in this study does not capture the
dynamics of the data. Thus, the search for new methods to
explain the mechanism of adjustment among inputs and prices
must continue. The estimation of energy demand through
the use of production and cost functions represents,
however, an improvement over estimates based on energy

consumption as a fixed ratio of output. It has been shown

118

that energy demand is responsive to price changes, and
fitted demand equations predict future energy demand quite
well. This is shown in Figures 1 through 34 in Appendix C.
The assumption that energy and capital are substitutes
underlying macroeconomic policies aimed at lowering the
price of capital to promote its use and reduce the use of
energy is not warranted. Similarly, the assumption that
energy and capital are complements underlying policies aimed
at lowering the prices of fuels to promote capital spending
is not warranted. Furthermore, the assumption that energy
groups are substitutes, underlying policies aimed at
promoting the substitution of a particular fuel for another
is not warranted. Some fuel groups show complementarity
rather than substitutability.

Since the results provide inconclusive evidence of
energy-capital substitution, it is not correct to assume
either energy-capital complementarity or substitutability in
the formulation of macroeconomic policies. This assumption
underlies some government policies in the energy sector of
OILICS like the subsidy to some types of energy, when their
prices go up, to avoid a recession. The assumption behind
this policy is that energy and capital are complements.
Furthermore, factor prices manipulation distorts the choice

of appropriate factor proportions.o

 

6. White, Lawrence J.; "The Evidence on Appropriate Factor
Proportions for Manufacturing in Less Developed
Countries: A Survey,"
Change, October 1978.

uQ-u-ueaowu

mun-o.

119

In Brazil, for example, the government subsidizes
hydroelectricity. The assumption behind.ii: is that fossil
fuels and hydroelectricity are substitutes. If the
conclusions of this study are correct, subsidizing

electricity to induce substitution of oil would lead to an
increase in oil consumption as fossil fuels and
hydroelectricity are shown to be complements.7 Three out of
four 652,53 are negative, and the only positive one (PCC) is
not significant at the 5 per cent level. These results are
consistent with the findings of Denny et. al.‘3 in their
study of the Canadian paper industry. In that case, the
effect of a decline in the price of electricity entailed an
increase in the use of electricity associated with an
increase in the use of oil. These results indicate that
subsidizing the price of hydroelectricity in order to
encourage the substitution of fuel oil for hydroelectricity,
would not work in the Brazilian paper industry. Policies
aimed at promoting the substitution of oil would work better

if coal was used to replace oil, as the Canadian study

shows. The present study did not disaggregate oil from
coal, but the data show that there is considerable
substitution between the two energy sources.
Hydroelectricity and capital (Gsa,x) are found to be

 

 

7. The BraZilian policy of subsidizing alcohol to encourage
substitution of 011 did not produce the expected
results. It is not known if a substitution analyses
was conducted prior to the adoption of the policy.

8- Denny 81- al. 0130111 . 1981-

120

substitutes. The policy of subsidizing electricity would
only delay technological changes, because firms would
withhold capital spending during the period they enjoy a
lower electricity cost.

Another implication of this study is that capital and
labor are shown to be substitutes. Thus government policies
aimed ar lowering the cost of labor would increase the share
of labor, and decrease the share of capital in the industry.
Again, this is not the policy followed by the Brazilian
government which through increasing payroll taxation is
making labor more expensive, encouraging the use of capital,
and discouraging the use of labor.

Elasticities vary across firms, industries, countries.
and time. This is partially illustrated by the energy-
capital elasticity of the three firms in this study (Figures
6, 7, and 8). Only a constantly updated table of
elasticities would provide a useful guide for sector-
specific policy-making. Elasticities are also affected by
the share of each input in total cost, and by structural
changes occurring at any particular time and place.

The study of elasticities should be more useful for
policymakers if they were calculated for long periods of
time for any given industry. The number and types of inputs
should be kept constant in order to make the estimates
comparable. In such a case, the policy—maker would have
access to a vast number of elasticity estimates so as to

evaluate the impact of policies for different sectors. This

121

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124
can be done with a computer program which would
automatically calculate the elasticities once the data were
entered into the system.

Research should.tx3 done within specific industries to
check for similarities and differences among them in the
pattern of input substitution, with special focus on the
capital/energy' coefficients. More importantly, however,
research which includes intangible inputs into the
production function is needed along with a more intensive
search for methods allowing the exitence of non-concavity

and discontinuity in the production function.

APPENDIX A

125

 

 

table 1. - sci-cud swan on Factor abstimtim: Firdinss and Whey
Assueptions and Type of Equation
Country Data and Production or test on VA and hethod of
Author and Industry miservations Cost Function Separability Estimation Main Results
Berndt and U.S. line series Linear homogeneous NA SURE (11,, 11.). (K, or 11,: L)
Christensen (1973) manufacturing 1929-68 and separable ISSLS = substitutes
Um. 1,, L), x] IZEF
Hudson and U.S. 9 industrial Time series Homogeneous and NA SURE (KzE) = coepleeents
Jorgenson (1974) sectors 1947-71 separable NUDE (L:E) = substitutes
[K7 Ll E! H]
Berndt and U.S. Tine series Linear hoeogemous VAS under SURE (K:L),(K:N),(L:E),
Hood (1975) nanufacturing 1947-71 and separable LSR ISSLS (L:H),(E:H) : abstitutes
(11, L, E, H] (K:E) = ooepleeents
Humphrey and U.S. 2-digit Cross section Linear hoeogeneous NA SURE (K:L),(K:N),(L:N)
Horoney (1975) eanufacturing 1963 and separable IZEF = abstitutes
W. L. N). 1]
Griffin and Cross- Pooled data Honothetic and VAS SURE (K:L),(K:E),(L:E),
Gregory (1976) country (9) in 1955, ’60, separable IZEF = substitutes in H!
eanufacturing ’65 and ’69 [Y, WI. PL, Pg), R., t) (M) = come-ants in 841 -
Halvorsen (1977) U.S. 2-digit Cross section Linear hoeogeneous NA SURE (E,:E,) = substitutes
eanufacturing 1971 and separable IZEF
IE, 4 energy costs]
Fuss (1977) Canada Pooled data Hoeothetic and NA SURE (K:L),(K:H),(L:E).(L:H),
manufacturing 1961-71 separable IZEF (E,:E,~) = substitutes
[11, L, H, E(6)] EIV (K:E),(E:N) = comleeents
Halvorsen and U.S. 2-digit Cross section Hoeothetic and NA SURE (E, :Ei).(E:X) : substitutes
Ford (1979) eanufacturing 1958 separable IZEF
(M. Li. Li. 5(3)). X]
Pindyck (1979) Cross- Pooled data Noeothetic and NA SURE (K:L),(K:E).(L:E)
country (10) 1963-73 separable IZEF : substitutes
[f(K, L, E(4)), 11] (E,:E,) = nixed results
Field and U.S. 2-digit Cross section Linear hoeogeneous NA SURE (11,:E) = comleeents
Grebenstein (1980) Ianufacturing 1971 and separable IZEF (11,:E) = substitutes
[f(K1lKJILIE)IH]
Viton (1981) U.S. urban Cross section Hoeothetic and NA SURE (LzF) = substitutes
transportation 1958 separable IZEF
(R. L. Fl
Hazilla and U.S. 34 Tine series Hoeothetic and NA SURE (E:K),(E:L).(E:l)
Noon (1984) producing sector 1958-74 separable IZEF : nixed results

[K(-). L1 ). E1). H1 )1

126

 

Kulatilaka (1985) U.S. Time series NA NA SE NAc
eanufacturing 1947-71 (K; L, E, I] NIV
Chung (1987) U.S. Time series Non-hoeogeneous VAS under SE (KILLLKIUJKM)
eanufacturing 1947-71 and separable LSR and NSR DIN (L:E),(L:)1),(E:H)
if, L, E, H] IZEF : substitutes
Notes:
fype of Equation: L, = Labor 1 (i = production workers or non-production workers in case
SURE = seeeingly unrelated equations of Halvorsen and Ford)
SE = Single equation " = energy '
heth of Estieation: E; = energy 1 (i 2 coal, liqiid petroleue, fuel oil, natural gas,
EIV : Efficient instrueental variable method electricity, and actor gasoline in case of Fuss; electricity, fuel
13818 = iteractive three-stage least squares nethod oil, and gas in case of Nalvorsen and Ford; oil, gas, coal, and
IZEF = Zellner’s iteractive efficient eethod electricity in case of Pindyck)
NUDE : Halinvaud's eininue distance estimator eethod F : fuel
ZEF : Zellner’s efficient eethod N = eaterials
va = non-linear instrueental variable technique N = natural resources
DTN : Durbin's two-stage eethod N; = natural resources i (nonfuel einerals)
Variable: I : nonresource intereediate inputs
K = capital = rolling stock
K; : capital 1 (i = moment or structures in case of 0,)( = Other inputs
Berndt and Christensen; phySical capital or Separability:
working capital in case of Field and Grebenstein) VAS = value-awed separability
K : quaSi-fixed capital LSR = linear separability restrictions
L = labor NSR = nonlinear separability restrictions

NA = not available

a In general, a cross section analysis yields long-run effects, whereas a tile series analySis yields short-run effects.

b This coluen takes no account of other separability tests.

c The estieation of factor substitutions is not a prieary concern in this paper, Kulatilalta rejects the validity of the full
static (long-run) equilibriue approach taken by all of the previous studies.

APPENDIX B

Nth/Yr
1982

1983

1984

1985

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TABLE 1:
FOUR INPUTS

IKPC

PM SHRRE SHRRK SHHRL SHEEN E

100.

00

99.34

139.
72.
104.
94.
101.
95.
101.
98.
95.
113.

101

74

128.
81.
104.

110.

106.

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101.

106.

114.

67.

142.

103.

114.

109.

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106.56

110.82
104.04
107.16
107.79
102.68
97.22
68.69
109.90
101.55
102.64
112.19
117.97
113.31
115.28
120.02
119.87
115.17
116.83
105.79
117.85
115.87
102.32
121.75
120.75
118.95
119.62
122.95
131.05
132.31
139.32
120.13
139.07
130.18
137.92
136.13
140.82
130.42
112.52
131.90
121.74
129.31

101.39 99.
109.83 100.

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113.28 97.50 87.94 115.58
110.83 97.02 93.53 120.04
103.23 107.11 126.67 1m.67
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119.20 95.99 112.07 $.69
110.35 1$.37 103.38 111.34
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99.01 111.39 128.61 81.19
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109.72 105.59 137.43 92.50
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77.23 89.57 66.35 70.76
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91.38 1$.69 72.39 60.50
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87.45 99.97 53.31 57.30
99.03 104.07 .05 62.58
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1$.38 102.81 .67 59.43
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107.35 97.29 58.94 61.50
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1$5 87.19 99.57 64.51 62.25
92.35 109.‘ 55.58 59.$
83.97 99.26 56.56 55.18
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69.53 115.62 77.75 51.23
65.07 113.54 66.77 60.79
68.20 107.78 69.91 53.40
70.76 $.69 63.58 57.41
71.$ 117.63 59.33 64.19
65.07 111.20 85.74 61.60
71.26 87.49 $.51 58.84
67.09 94.12 $.69 67.83

TABLE 2: PCC
FOUR INPUTS

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TABLE 3:
FOUR INPUTS

83E$2€38l38l322853

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3m 9m 9m. m E
0.13 0.20 0.23 100.00
0.12 0.19 0.20 104.14
0.11 0.20 0.23 87.73
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0.02 0.18 0.5 129.34
0.02 0.14 0.30 150.50
0.02 0.30 0.25 63.43
0.03 0.27 0.3 59.60
0.04 0.27 0.34 49.03
0.02 0.22 0.25 122.16
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0.12 0.17 0.30 170.”
0.09 0.15 0.29 1%.30
0.12 0.12 0.25 2‘15
0.13 0.11 0.30 1%.10
0.15 0.13 0.23 161.62
0.12 0.14 0.27 113.5
0.15 0.16 0.29 144.03
0.13 0.12 0.29 1,313
0.28 0.10 0.25 157.36
0.24 0.09 0.8 181.82
0.” 0.14 0.17 104.56
0.3 0.14 0.21 139.04
0.27 0.11 0.24 33.20
0.29 0.11 0.24 200.59
0.33 0.11 0.23 159.93
0.28 0.10 0.24 210.43
0.28 0.10 0.25 15.75
0.29 0.11 0.21 1%.15
0.27 0.12 0.20 2CD.21
0.29 0.11 0.20 203.61
0.28 0.12 0.23 235.60
0.34 0.13 0.19 173.71
0.30 0.11 0.23 191.52
0.30 0.17 0.12 171.76
0.30 0.15 0.21 1%.63
0.31 0.12 0.22 28.79
0.31 0.12 0.23 202.93
0.31 0.12 0.22 ”.28
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TABLE 4: IKPC

SIX INPUTS
L Fl “1
100.00 100.00 0.14
99.51 5.% 0.16
100.19 62.78 0.10
100.72 101.59 0.14
1m.68 107.73 0.16
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101.63 102.00 0.16
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100.34 102.5 0.14
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89.44 102.52 0.18
87.55 99.27 0.22
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85.35 107.01 0.5
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5.5 137.93 0.15
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89.39
85.98
78.67
83.87
76.35
68.21
78.63
87.66
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63.59
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70.68
64.38
58.69
59.91
57.70
53.74
57.64
55.22
52.27
57.31
56.30
52.00
58.88
56u09
55.24
48.47
44.95
41.21
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76.33
68.16
72.65
75.92
70.20
77.96
75.51
75.10
71.84
79.18
65.31
56.33
49.39
58.59
63.67
77.14
86.94
93.47
90.20
88.98
85.71
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100.49
90.89
99.97
104.07
104.40
102.81
98.50
97.29
100.63
99.55
110.24
107.69
99.57
109.48
99.26
126.63
115.62
113.54
107.78
90.69
117.63
111.20
87.49
94.12
72.32
51.82
115.41
111.94
107.70
106.95
109.53
109.17
111.89
106.14
103.07
94.16
99.19
128.20
90.06
82.26
89.97
72.10
101.91
123.21
103.60
95.85
96.61

PL
65.64
60.43
54.54
84.12
77.40
76.59
78.42
70.66
61.66
86.50
76.83
96.92
74.02
64.34
59.02
87.59
78.46
70.51
73.98
68.71
63.99
95.06
83.73

118.16
112.13

80.45
83.38
80.26
81.70
89.32
89.61
90.13

106.25
118.04
110.10
111.28

92.38

108.24
110.16
102.30

98.22
87.35
77.93
82.70
79.73
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101.54
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67.24
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111.64
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116.34
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116.33 110.
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TABLE 5:

SIX INPUTS

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112.
103.
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128.
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112.67
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99.07
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89.67

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1984

1985

1986

1987

0.05
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0.05
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0.05
0.03
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0.41
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.14
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101.
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101.
91.01
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86.27
103.05
96.90
98.30
108.13
102.44
92.57
100.68
110.65
106.51
119.59
106.74
103.80
93.82
70.56
85.13
93.68
85.81
88.43
98.42
102.75
82.83
87.06
78.02
81.29
77.34
86.18
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100.57

99.29
116.56

93.75
106.68
110.17
111.66
113.28
103.34
110.60
102.38
121.08
100.65
104.78
108.68
106560
104.96

97.60
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100.59

95.51
109.83
103.59
104.24
113.86
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95.63
104.97
114.71
108.25
123.18
110.43
107.76
100.58

92.11

96.15
103.68

94.08

96.36
102.81
116.25
108.63
108.50
106.27
105.30
107.03
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138

3.:

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1
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117.
114.
108.
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111.41
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109.55
118.30
109.81
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136.34
120.49
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TABLE 6:
FIVE INPUTS

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APPENDIX C

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