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LIBRARY
5 Michigan State
3 or University

 

This is to certify that the
dissertation entitled

ANALYZING DYNAMICS OF TECHNOLOGICAL
ATTRIBUTES IN THE CANADIAN
SAWMILLING INDUSTRY:
NONPARAMETRIC AND PARAMETRIC APPROACHES

presented by

Asghedom Ghebremichael

has been accepted towards fulfillment
of the requirements for the

Doctoral. degree in Forestry

 

 

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ANALYZING DYNAMICS OF TECHNOLOGICAL ATTRIBUTES IN THE
CANADIAN SAWMILLING INDUSTRY:
NONPARAMETRIC AND PARAMETRIC METHODS
By

Asghedom Ghebremichael

A DISSERTATION
Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of
DOCTOR OF PHILOSOPHY
Department of Forestry

- 2007

ABSTRACT
ANALYZING DYNAMICS OF TECHNOLOGICAL ATTRIBUTES IN THE
CANADIAN SAWMILLING INDUSTRY:
NONPARAMETRIC AND PARAMETRIC METHODS
By
Asghedom Ghebremichael

The goal of this study was to analyze long-term dynamics of
technological attributes in the Canadian sawmilling industry over a forty-year
period (1961-2000). Specifying the production technology as a function of capital,
labor, energy, sawlogs (the sole raw material inputs), and a time trend variable,
nonparametric and parametric empirical methods were implemented jointly.
Nonparametric Method: Focusing on the annual level and growth rates of total
factor productivity (TFP) and on effects of tax incentives on capital formation and
TFP growth, the multilateral index procedure was applied. The average annual
growth rate of TFP over the study period was 2.0%. Parametrically, TFP was
decomposed into its main sources. Statistically significant results of two
regression models that involved (i) a quadratic function in output and (ii) a log-
linear functional form of output and a time trend variable revealed that output
growth and technological progress were the main determinants of TFP growth. In
addition, a Simulated analysis of the effects of raising capital cost allowance
(CCA) and investment tax credit (ITC) and reducing corporate income tax (CIT)

showed that mutually reinforcing effects of the tax incentives could spur capital

formation and TFP growth.

Parametric Method: The maximum likelihood estimation method with iterative
Zellner-efficient technique was applied to estimate a multivariate regression
system of four equations that involved an unrestricted translog form long-run cost
function and three of four cost Share equations. The long-run, nonhomothetic
cost function described the Canadian sawmilling industry’s production
technology. The Allen elasticities of input substitution indicated that the pairs of
labor/capital, labor/energy, capital/ material, and energy/ material, were
substitutes, while the pairs of labor/ material and capital/energy were
complements. Highly inelastic own- and cross-price elasticities of derived
demand for all the inputs indicated that the inputs were treated as “basic goods”.
Furthermore, it was observed that less than unity elasticity of total cost with
respect to output (0.249), a modest measure of scale economies (0.751), and
2.3% cost diminution rate, which is the dual measure of the prime TFP growth.
This joint implementation of the nonparametric method and the parametric
method made it possible to use dynamics of multiple technological attributes to
fully explore the dichotomy between the vertical shift in the production frontier,
realized through technological progress, and the input driven movements along
the frontier, realized through technical efficiency improvements. Important policy
implications of the empirical findings were highlighted. To rectify the inevitable

limitations of the study, long-term future research projects were proposed.

DEDICATION

To my parents, Ghebremichael Tirfe and Etai Zewdu, and to my wife, Gennet Selle.

iv

ACKNOWLEDGEMENTS

This is a product of many helping hands. Although it is difficult to list
everyone by name, I just have to say thank you all! But, I have to express my
greatest indebtedness to my Guidance Committee (GC) members, each of whom
was instrumental to the success of this project. I completed this research under
the guidance of four highly respected professors. For invaluable moral and
financial support, for contributions to the structure and contents of this
dissertation, and for bearing the responsibilities of chairing the GC, I am very
grateful to my supervisor, Dr. Karen Potter-Witter. Beyond the call of duty of any
member of the GC, Dr. Robert J. Myers, Distinguished University Professor of
econometrics, took graciously the responsibility of being my technical advisor on
the econometric aspects of the study. It was a great opportunity for me to take
Professor Myers’ graduate level econometrics course; and eventually to work on
this research closely with him. My gratitude to him is beyond words can express.
For contributions to the contents of the dissertation and for frequent words of
encouragement, I thank Dr. Sandra Batie and Dr. Larry A. Leefers, both of whom
were members of the GC.

The Michigan State University’s Main Library is a huge depository of
knowledge. I am thankful to every employee of the Library for the help I received
over the years of my study. But, my highest gratitude goes to those staff
members of the Computing and Technology Services Helpline. They set up a
long distance proxy server for me to be able to access the Library from the

comfort of my office in Edmonton, Alberta, Canada. I accessed all top scientific

journals published and distributed globally. l was able to print every single article
relevant to the work. That was a great deal of help, which expedited my research
work tremendously. Again, thanks everyone!

For playing crucial roles in building the database, I am very grateful to two
experts of Statistics Canada: Mr. Richard Landry, Chief of Capital Stock Section,
and Ms. Mychele Gagnon, Senior Economist, Capital Stock Section. For
constructive comments on different earlier versions of the manuscript, I am
thankful to my friends Dr. David M. Nanang and Dr. Shashi Kant. My intellectual
gratitude and debt goes to three prominent professors of economics at The
University of British Columbia: Dr. EI'WII'I W. Diewert, Dr. Michael W. Tretheway,
and Dr. Tae H. Oum, each of whom motivated and taught me that economic
theory, which is not interpreted and implemented with econometrics is of no use
to society.

My employer, the Canadian Forest Service (CFS), deserves special credit
for the success of my program. Without the full support and encouragement of
many individuals at the CFS, I would not have done it. My special gratitude goes
to my work supervisor, Dr. Bill White, who commented on an earlier version of
the manuscript and played instrumental role when my study leave was being
processed. Among other colleagues at the CFS, Dr. Tim Williamson’s detailed
comments are gratefully acknowledged.

Last, but not least, I am heavily indebted to my wife, Gennet Seile, who

made it all happen. We made it, Gennu!

vi

TABLE OF CONTENTS

LIST OF TABLES .......................................................................................................................... IX
LIST OF FIGURES ......................................................................................................................... XI
CHAPTER 1 INTRODUCTION ...................................................................................................... 1
1.1 THE CANADIAN FOREST SECTOR: A SHORT PROFILE ........................................................... 1
1.2 THE SAWMILLING INDUSTRY ..................................................................................................... 3
1.3 RATIONALE: PROBLEM STATEMENT AND KNOWLEDGE GAP ........................................... 8
1.4 GOAL, HYPOTHESIS, THEMES, AND RESEARCH QUESTIONS ............................................. 10
1.5 ORGANIZATION OF THE STUDY ............................................................................................... 14
CHAPTER 2 THEORETICAL FRAMEWORK ............................................................................. 15
2.1 KEY CONCEPTUAL TERMS ......................................................................................................... 15
2.2 THE NEOCLASSICAL EXOGENOUS GROWTH THEORY ........................................................ 20
2.3 THE QUEST FOR A MEANING OF THE SOLOW RESIDUAL ................................................... 28
2.4 THE NEED FOR JOINT IMPLEMENTATION OF THE TWO METHODS .................................. 32
2.5 ENDOGENOUS GROWTH THEORY ............................................................................................ 34
2.6 IMPERATIVES OF EFFECTIVE INSTITUTIONAL ARRANGEMENTS .................................... 36
2.7 THE THEORY OF PATH DEPENDENT TECHNOLOGICAL PROGRESS ................................. 39
2.8 THEORETICAL UNDERPINNINGS OF SELECTED STUDIES .................................................. 42
2.9 SUMMARY ...................................................................................................................................... 46
CHAPTER 3 METHODS .............................................................................................................. 50
3.1 THE PRODUCTION TECHNOLOGY ............................................................................................ 50
3.2 NONPARAMETRIC METHOD OF PRODUCTIVITY ANALYSIS .............................................. 52
3.2.1 Importance and Concepts ................................................................................................... 52
3.2.2 The Multilateral Index Procedure ....................................................................................... 5 7
3.2.3 Decomposing TFP into its Main Sources .......................................................................... 5 9
3.2.4 Taxation Policy Instruments, Capital Formation, and TFP ............................................. 61

3.3 THE PARAMETRIC METHOD: A NEOCLASSICAL COST FUNCTION .................................. 64
3.3.1 Specification .......................................................................................................................... 64
3.3.2 Production versus Cost Function Estimation .................................................................... 66
3.3.3 Functional Form .................................................................................................................... 67
3.3.4 Derived Demand Functions for Inputs ............................................................................... 70
3.3.5 Nature and Estimates of Technological Progress ........................................................... 73

A. Perspectives on Technological Progress: an Overview ................................................................. 73

B. Estimating Disembodied Technological Progress ........................................................................... 74

C. Hicks Neutral versus Biased Technological Change ...................................................................... 76

D. TFP Growth, Cost Elasticity, Returns to Scale, and Scale Economies ......................................... 78

3.3.6 Substitution and Price Elasticities of Inputs ....................................................................... 83

A. Economic Implications of Substitution Elasticities ........................................................................... 83

8. Which Measure of Elasticity? .............................................................................................................. 84

C. Approaches to Computing AES and MES ........................................................................................ 85

3. 3. 7 Estimation Techniques ........................................................................................................ 86
CHAPTER 4 THE DATA .............................................................................................................. 91
4.1 INDUSTRIAL OUTPUTS ................................................................................................................ 91
4.2 INDUSTRIAL INPUTS .................................................................................................................... 93

vii

CHAPTER 5 NONPARAMETRIC METHOD RESULTS - 98

 

 

 

 

 

 

 

5.1 HISTORICAL TRENDS IN THE DATA ......................................................................................... 98
5.1.1 Factor Shares in Total Cost ................................................................................................ 99
5.1.2 Input Quantities ................................................................................................................... 100
5.1.3 Output Shares in Total Revenue ...................................................................................... 102

5.2 PARTIAL FACTOR PRODUCTIVITIES ...................................................................................... 103

5.3 TOTAL FACTOR PRODUCTIVITY ............................................................................................. 106
5.3.1 Background ......................................................................................................................... 106
5.3.2 Nonparametric Measures of Gross Total Factor Productivity ........................... ' ........... 1 08
5.3.3 Effects of Selected Determinants on TFP Growth ......................................................... 111

A. Decomposing TFP into its Main Sources ...................................... 11 l
B. Taxation. Capital Formation, and TFP: a Simulation Analysis ...................................................... 1 13
CHAPTER 6 PARAMETRIC METHOD RESULTS ............... 122

6.1 RESULTS AND MODEL SELECTION PROCEDURE ................................................................ 122

6.2 SUBSTITUTION AND PRICE ELASTICITIES ........................................................................... 128
6.2.1 Factor Substitution Elasticities .......................................................................................... 128
6.2.2 Own- and Cross-Price Elasticities .................................................................................... 132

6.3 DECOMPOSED TFP GROWTH AND OTHER ATTRIBUTES ................................................... 133

6.4 COMPARISON WITH PREVIOUS STUDIES .............................................................................. 139

CHAPTER 7 SUMMARY OF THE FINDINGS 147

7.1 THE NONPARAMETRIC METHOD AND RESULTS ................................................................ 147
7.1.1 The Method ......................................................................................................................... 14 7
7.1.2 The Results ......................................................................................................................... 149

7.2 THE PARAMETRIC METHOD AND RESULTS ......................................................................... 153
7.2.1 The Method ......................................................................................................................... 153
7.2.2 The Results ......................................................................................................................... 155

CHAPTER 8 CONCLUSIONS, IMPLICATIONS, AND LIMITATIONS 161

8.1 CONCLUSIONS ............................................................................................................................ 161
8.1.1 Nonparametric and Regression Results ......................................................................... 161
8.1.2 Parametric Method ............................................................................................................. 164
8.1.3 Some Features of Strength ............................................................................................... 168

8.2 INDUSTRIAL POLICY IMPLICATIONS .................................................................................... 171
A. Some Perspectives on Canada’s Industrial Forest Policy ................................................... 1 7 I
8. Implications of the Key Empirical Findings ............................................................................ 1 73

8.3 LIMITATIONS AND FUTURE RESEARCH DIRECTIONS ....................................................... 177
8.3.1 Limitations ............................................................................................................................ I7 7
8.3.2 Future Research Directions .............................................................................................. I 78

APPENDICES 180

APPENDD< A. PRIMARY VARIABLES AND THEIR SOURCES, AND DERIVED VARIABLES ...... 181

APPENDIX B. TIME SERIES OF SELECTED EMPIRICAL RESULTS: SUMMARY ........................................... 183

APPENDIX C. PARTIAL AND TOTAL FACTOR PRODUCTIVITIES AND AGGREGATE OUTPUT AND INPUT

QUANTITIES ............................................................................................................................................ 187

APPENDIX D. SELECTED EMPIRICAL RESULTS WITH THE CHANGES IN TAXATION ................................. 189

REFERENCES ............... 193

 

 

viii

 

 

LIST OF TABLES

TABLE 1.1. AVERAGE ANNUAL OF CANADIAN TIMBER HARVESTED BY END-USE (MILLION M3) ...................... 4

TABLE 5.1 . AVERAGE ANNUAL INPUT COST SHARES AT TEN-YEAR INTERVALS FOR THE CANADIAN
SAWMILLING INDUSTRY ........................................................................................................................ 99

TABLE 5.2. AVERAGE ANNUAL CHANGES IN INPUT QUANTITIES AT TEN-YEAR INTERVALS FOR THE
CANADIAN SAWMILLING INDUSTRY .................................................................................................... 101

TABLE 5.3. AVERAGE ANNUAL OUTPUT REVENUE SHARES AT TEN-YEAR INTERVALS FOR THE CANADIAN
SAWMILLING INDUSTRY ...................................................................................................................... 102

TABLE 5.4. AVERAGE ANNUAL CHANGES IN PFPS AT TEN-YEAR INTERVALS FOR THE CANADIAN
SAWMILLING INDUSTRY ...................................................................................................................... 105

TABLE 5.5 AVERAGE ANNUAL CHANGES IN AGGREGATE OUTPUT, INPUT, AND GROSS TFP AT TEN- AND
FORTY-YEAR INTERVALS FOR THE CANADIAN SAWMILLING INDUSTRY: 1961-2000 ........................ 108

TABLE 5.6. GLS REGRESSIONS OF TFP WITH THE COCHRANE-ORCUTT ITERATIVE ESTIMATION
PROCEDURE FOR THE CANADIAN SAWMILLING INDUSTRY ................................................................ 112

TABLE 5.7. AVERAGE ANNUAL SHARES OF CAPITAL IN TOTAL COST WITHOUT AND WITH THE CHANGES IN
TAXATION AT TEN- AND FORTY-YEAR INTERVALS FOR THE CANADIAN SAWMILLING INDUSTRY ....... l 16

TABLE 5.8. AVERAGE ANNUAL CAPITAL INTENSITY AT TEN- AND FORTY-YEAR INTERVALS WITHOUT AND
WITH THE CHANGES IN TAXATION FOR THE CANADIAN SAWMILLING INDUSTRY ............................... 118

TABLE 5.9. AVERAGE ANNUAL VALUES OF TFPI AND TFP2 AND THEIR DIFFERENCE .............................. 120

TABLE 6.1. PARAMETERS OF SlX-TRANSLOG FORM COST FUNCTIONS ESTIMATED ACCORDING To
IZEF/MLE PROCEDURE FOR THE CANADIAN SAWMILLING INDUSTRY 1961 -2000 ......................... 124

TABLE 6.2. AES ESTIMATES FOR THE CANADIAN SAWMILLING INDUSTRY (STANDARD ERRORS IN
PARENTHESES): 1961 -2000 ............................................................................................................. 129

TABLE 6.3. MES ESTIMATES FOR THE CANADIAN SAWMILLING INDUSTRY (STANDARD ERRORS IN
PARENTHESEs): 1961-2000 ............................................................................................................. 131

TABLE 6.4. ESTIMATED OWN- AND CROSS-PRICE ELASTICITIES OF DEMAND FOR INPUTS IN THE CANADIAN
SAWMILLING INDUSTRY (STANDARD ERRORS IN PARENTHESES): 1961-2000 ................................. 132

TABLE 6.5. AVERAGE ANNUAL RESULTS OF KEY TECHNOLOGICAL ATTRIBUTES AT TEN- AND FORTY-YEAR
INTERVALS FOR THE CANADIAN SAWMILLING INDUSTRY .................................................................. 134

TABLE 6.6. DECOMPOSITION OF THE DUAL MEASURE OF THE PRIMAL TFP GROWTH AT TEN- AND FORTY-
YEAR INT ERVALS FOR THE CANADIAN SAWMILLING INDUSTRY: 1961-2000 .................................... 137

TABLE 6.7. AVERAGE ANNUAL RATES OF TECHNOLOGICAL CHANGE BIASES AT TEN- AND FORTY-YEAR
INT ERVALS FOR THE CANADIAN SAWMILLING INDUSTRY: 1961-2000 ............................................. 138

ix

 

TABLE 6.8. METHODOLOGICAL SUMMARIES OF THIS STUDY AND SELECTED STUDIES CONDUCTED ON
CANADIAN AND AMERICAN SAWMILLING INDUSTRIES ....................................................................... 142

TABLE 6.9. ALLEN PARTIAL OWN-ELASTICITIES (AES) OF INPUT SUBSTITUTION FROM THIS STUDY AND
FROM TWO SELECTED STUDIES ......................................................................................................... 143

TABLE 6.10. AES CROSS-ELASTICITIES OF INPUT SUBSTITUTION FROM THIS STUDY AND FROM FOUR
SELECTED STUDIES ........................................................................................................................... 143

TABLE 6. 11. OWN-PRICE ELASTICITIES OF DERIVED DEMAND FOR INPUTS FROM THIS STUDY AND FROM
SIX SELECTED STUDIES ..................................................................................................................... 144

TABLE 5. 12. CROSS-PRICE ELASTICITIES OF DERIVED DEMAND FOR INPUTS FROM THIS STUDY AND FROM

FIVE SELECTED STUDIES ................................................................................................................... 144
TABLE 6.13. TFP GROWTH FROM THIS AND FROM A SELECTED STUDY .................................................... 145
TABLE A.1. INDUSTRIAL OUTPUT DATA ...................................................................................................... 181
TABLE A. 2. INDUSTRIAL INPUT DATA ........................................................................................................ 182

TABLE B.1. FACTOR SHARES IN TOTAL COST WITHOUT THE CHANGES IN TAXATION FOR THE CANADIAN
SAWMILLING INDUSTRY: 1961-2000 ................................................................................................. 184

TABLE B.2. TRENDS IN INPUT QUANTITIES WITHOUT THE CHANGES IN TAXATION FOR THE CANADIAN
SAWMILLING INDUSTRY: 1961-2000 ................................................................................................. 185

TABLE B.3. OUTPUT SHARES IN TOTAL REVENUE WITHOUT THE CHANGES IN TAXATION FOR THE CANADIAN
SAWMILLING INDUSTRY: 1961-2000 ................................................................................................. 186

TABLE C.1. PARTIAL FACTOR PRODUCTIVITY INDICES WITHOUT THE CHANGES IN TAXATION FOR THE
CANADIAN SAWMILLING INDUSTRY: 1961-2000 ............................................................................... 187

TABLE C2. TRENDS IN AGGREGATE INPUT AND OUTPUT QUANTITIES AND TFP WITHOUT THE CHANGES IN
TAXATION FOR THE CANADIAN SAWMILLING INDUSTRY: 1961-2000 ............................................... 188

TABLE D.1. SHARE OF EACH INPUT IN TOTAL COST WITH THE CHANGES IN TAXATION FOR THE CANADIAN
SAWMILLING INDUSTRY: 1961-2000 ................................................................................................. 189

TABLE 02. SHARES OF CAPITAL IN TOTAL COST, WITHOUT AND WITH CHANGES IN TAXATION FOR THE
CANADIAN SAWMILLING INDUSTRY: 1961-2000 ............................................................................... 190

TABLE 03. CAPITAL INTENSITY WITHOUT AND WITH CHANGES IN TAXATION FOR THE CANADIAN
SAWMILLING INDUSTRY: 1961-2000 ................................................................................................. 191

TABLE 04. TFP1, TFP2, AND RATES OF THEIR MARGINAL DIFFERENCES FOR THE CANADIAN .............. 192

LIST OF FIGURES

FIGURE 1.1. SHARES IN TOTAL CANADIAN TIMBER HARVESTED BY END-USE: 1940-2002. ......................... 4
FIGURE 1.2. TRENDS IN CANADIAN TIMBER HARVESTED BY END-USE TYPE: 1940—02. .............................. 5
FIGURE 1.3. NUMBER OF ESTABLISHMENTS IN THE CANADIAN SAWMILLING INDUSTRY. .............................. 6
FIGURE 1.4. HISTORICAL TRENDS IN EMPLOYMENT IN THE CANADIAN SAWMILLING INDUSTRY ................... 6

FIGURE 1 .5. TOTAL SALARIES AND WAGES (TSW) AND TOTAL VALUE ADDED (TVADD) IN THE CANADIAN
SAWMILLING INDUSTRY .......................................................................................................................... 7

FIGURE 2.1. PRODUCTION FRONTIER, PRODUCTIVITY, TECHNICAL EFFICIENCY, AND SCALE ECONOMIES. 17
FIGURE 2.2. TECHNOLOGICAL PROGRESS OVER TWO PERIODS ................................................................. 18

FIGURE 2.3. ALLOCATIVE AND TECHNICAL EFFICIENCY ............................................................................... 19

FIGURE 5.1. INPUT COST SHARES IN TOTAL COST, THE CANADIAN SAWMILLING INDUSTRY: 1961-00. 100
FIGURE 5.2. TRENDS IN INPUT QUANTITIES FOR THE CANADIAN SAWMILLING INDUSTRY: 1961-00. ....... 101

FIGURE 5.3. OUTPUT SHARES IN PERCENT OF TOTAL REVENUE FOR THE CANADIAN SAWMILLING

INDUSTRY: 1961-00. ......................................................................................................................... 103
FIGURE 5. 4. TRENDS IN PFPS FOR THE CANADIAN SAWMILLING INDUSTRY: 1961-00. .......................... 105
FIGURE 5. 5. TRENDS IN OUTPUT, INPUT, AND TFP FOR THE CANADIAN SAWMILLING INDUSTRY: ........... 109

FIGURE 5. 6. SHARES OF CAPITAL IN TOTAL COST WITHOUTAND WITH THE CHANGES IN TAXATION FOR THE
CANADIAN SAWMILLING INDUSTRY: 1961-00. .................................................................................. l 16

FIGURE 5. 7. AVERAGE ANNUAL SHARES OF CAPITAL IN TOTAL COST WITHOUT AND WITH THE CHANGES IN
TAXATION AT TEN- AND FORTY-YEAR INTERVALS FOR THE CANADIAN SAWMILLING INDUSTRY ....... l 17

FIGURE 5. 8. CAPITAL INTENSITY WITHOUT AND WITH THE CHANGES IN TAXATION FOR THE CANADIAN
SAWMILLING INDUSTRY: 1961-00. .................................................................................................... 1 18

FIGURE 5. 9. AVERAGE ANNUAL CAPITAL INTENSITY AT TEN- AND FORTY-YEAR INTERVALS WITHOUT AND
WITH THE CHANGES IN TAXATION FOR THE CANADIAN SAWMILLING INDUSTRY. .............................. l 19

FIGURE 5. 10. TFP1 AND TFP2 FOR THE CANADIAN SAWMILLING INDUSTRY: 1961-00. ........................ 120

Xi

CHAPTER 1 INTRODUCTION
1.1 THE CANADIAN FOREST SECTOR: A SHORT PROFILE
Starting with the biological and physical potential of the forest resource-
base, this chapter highlights the socioeconomic importance of the sector and the

effects of business cycles on its performance over the years.

The Forest Resource-Base1 In its to the House of Commons, the The
Canadian Forest Service (2006b) stated that Canada’s forests account for up to
10% of the world’s forest cover, about 30% of the world’s boreal forest, more
than 25% of the world’s temperate rainforest, 25% of the world’s wetlands, and
20% of the world’s freshwater.

Canada’s land mass is estimated to be 979.1 million hectares, out of
which 402.1 million hectares are forestland and “other wooded land”. The
remaining 92 million hectares are characterized as “other wooded land”,
consisting of treed wetland as well as slow-growing and scattered-treed land.
Forestland is estimated to be 310.1 million hectares, of which 294.8 million
hectares is described as “commercial forest” (The Canadian Forest Service
2005)

Importance and Challenges In 2005, the Canadian forest products sector
created 339,900 in direct and 524, 1000 in indirect and induced jobs. In 2004, it

contributed Cdn$35.9 billion to the Canadian GDP, Slightly higher than that for

 

1The information in this section is from three sources of the CFS: ( 1) The State of Canada’s
Forests 2005-2006: Forest Industry Competitiveness; (2) The State of Canada’s Forests 2004-
2005: The Boreal Forest, and (3) Selected Forestry Statistics Canada, available at:
http://www2.nrcan.gc.ca/cfs-scf/selfor/defauIt.html,

2003, which was Cdn$33.7 billion. Canada’s trade in forest products reached an
historic high of Cdn$44.6 billion in 2004.

The sector’s role in the diversification and development of community-
based economies is also well documented. Researchers at the CFS estimate
that the sector supports nearly 350 rural communities throughout Canada. This is
in addition to providing significant employment opportunities in large urban
centers, such as Vancouver, Montreal and Toronto, where headquarters of the
multinational corporations that trade forest products are located. In total, there
were 361, 400 direct jobs in the sector in 2004.

However, even though it is one of the major engines that keep the national

economy in motion, the Canadian forest products sector is often adversely
affected by a variety of market and nonmarket forces. The effects are revealed
through industrial relocation, consolidation, mergers, acquisitions, plant closures,
and workforce layoffs. Consequently, industrial restructuring and rationalization
measures are frequent.
Structural Dynamics Within the forest sector, a number of industries,
predominantly the sawmilling industry, have been going through significant
structural changes. As firms strived to increase productivity and reduce
production costs, a rapid pace of mergers, acquisitions, and mill closures
occurred during 2004—2005. Generally, these types of industrial consolidation
measures are taken in order to gain efficiency and scale economies.

In addition to the mergers and acquisitions, the Canadian forest sector

experienced closures of 68 plants from September 2004 to May 2005. Most of

these were pulp mills and sawmill (CFS 2005). These closures were attributed to
a number of factors, which include the U.S.—Canada softwood lumber dispute;
relatively higher exchange rate of the Canadian dollar to the US dollar; high
energy costs; rising costs of delivered logs and high competition from offshore
producers.

1.2 THE SAWMILLING INDUSTRY

For the purpose of this study, the sawmilling industry is the 1980 Standard
Industrial Classification-Establishments 251 (SIC-E-251), which includes
establishments primarily engaged in manufacturing lumber, both rough and
dressed, Shakes and shingles, and other sawmill and/or planing mill products
(Statistics Canada 2005)? That is, the study covers the Shingle and Shake
Industry (SlC-E-2511) and the Sawmill and Planing Mill Products Industry (SIC-
E-2512).

Lumber is the most important product of the Canadian sawmilling industry.
Consequently, timber harvested for sawlogs, the sole inputs for lumber
production, increased steadily over the years (CFS 2005): from 32.6 million m3 in
1940 to 164.4 million In3 in 2002, while harvest for the other three uses -
pulpwood, fuelwood, and special uses declined steadily (Figs 1.1 and 1.2).

The utilization rate of harvested timber for lumber production was high in
the 19803 and 19903 (Table 1.1). For example, from an average annual of 34.1
million m3 (43.1% of the total harvest) during the period of 19403, it jumped to an

average annual of 146.0 million m3 (more than 87.2% of the total harvest) in the

 

2 http://www.Statcanca/englishI’Subvjectsv’Standardfsic.s’sice80-cIasse.htmtlZSI , accessed August, 2006.

 

19803. In 2001 and 2002, the latest years for which data were available, sawlogs

accounted for 83% and 84%, respectively (Table 1.1).

Table 1.1. Average annual of Canadian timber harvested by end-use (million m3)

 

 

 

 

 

Period Sawlogs Pulpwood Special Fuelwood Total Share Of
Use Harvest Sawlogs
%
1941-50 34.1 26.5 2.1 16.4 79.2 43.1
1951-60 44.1 36.4 2.0 8.5 909 48.5
1961-70 63.2 36.0 2.0 5.2 1062 59.5
1971-80 95-2 40-0 1-3 4'0 140.1 68.0
1981-90 146.0 30.0 2.5 5.0 167.5 87.2
1991-00 146.0 30.0 2.5 5.0 182.8 799
2001 154. 4 23.1 5.4 3.0 185.9 831
2002 164.4 26.0 3.3 3.0 196.6 83.6
Source: Selected Forestry Statistics Canada (Table l—1). Refer footnote 1 (previous
page).
100
90
80
A 70
0
2E 60
8 50 s I f I b
<0 30 ’ '- '
20

 

0 .
bpgaceoeeeeecec
.9 ,9 ,9" ,9" (IF .96 .9“ ,9" 9“" .339 .99 .99 (19°

Years

Figure 1.1. Shares in total Canadian timber harvested by end-use: 1940-2002.

 

 

 

 

Y
0 <0 0 9) Q

 

[—3— Sawlogs —-— Pulpwood + Special Use + Fuelwood]

Figure 1.2. Trends in Canadian timber harvested by end-use type: 1940—02.

The rapidly rising trend in timber harvested for sawlogs shows the
economic importance of the Canadian sawmilling industry. However, as pointed

out above, the industry has gone through several business cycles (Figs. 1.3

through 1.5).

1 ,600
1 ,400
1 ,200
1 ,000
800
600
400
200

Numberof establishments

 

Figure 1.3. Number of establishments in the Canadian sawmilling industry.

 

 

 

 

 

 

60.0
(D
250.0 x
(D W
U)
840-0 /
5
v30.0
(D
a) /
9.20.0
2 Wow/r“.
D.
510.0
LIJ
0.01TITTTITTI TTTTT ITTTTTTTITIITTTTTTTTTTIT

 

 

 

9,31,

'\ N ’\ o '5 Q) ’\ C
G B Q) '\ ’\ ’\ ’\ C
.9 ,9 .9 ,9 ,9 ,9 ,9 ,9

fo‘bNIx
QJ‘CQIQIQI
3,931,935.19

Years

Figure 1.4. Historical trends in employment in the Canadian sawmilling industry.

The ten-year historical trends in four major indicators - (a) the number of
establishments, (0) the number of employees, (C) total salaries and wages, and
(d) total value added, illustrate the effects of business cycles. From 1977 to 1978,

for example, the number of establishments and employees increased by 9%

(from 1,203 to 1,310) and 10% (from 62,199 to 68,616), respectively (Figs. 1.3
and 1.4). But, from 1988 to 1989, both the number of establishments and the
number of employees declined by nearly 12% and 5%, respectively.

While the growth rate of total salaries and wages was relatively slow over
the two decades of 1977 to 1997 that of total value added rose rapidly, with some

fluctuations (Fig. 1.5).

 

7000

6000~~r_f -- -e L --
_ +Tsw +TVADD .,

     

 

 

 

 

 

 

 

 

E 5000 . - ~

6

33 4000 —

O

2 3000 -

g l

3 2000 .

1000 —
O W I f I I I I I I I I I T I I I I I I T
(\«QIN‘DYJAQNQJ‘OA
,9 ,3 .93" .588 .833 .58" ,9‘" '9: .99 .39 .39
ears

Figure 1.5. Total salaries and wages (TSW) and total value added (TVADD) in
the Canadian sawmilling industry.

In summary, the Canadian sawmilling industry, which is the dominant
industry within the forest sector, went through a variety of industrial restructuring
measures that involved acquisitions, mergers, and plant closures from the early
19703 to the late 19903. The rapidly rising trends in timber harvested for sawlogs
and in total value added appear to indicate that the industry expanded production

operations (Figs. 1.1, 1.2, 1.5 and Table 1.1). Whether or not this led to

economies of scale is an empirical issue, which is examined in this study
(Chapter 6).
1.3 RATIONALE: PROBLEM STATEMENT AND KNOWLEDGE GAP

Public policy papers (e.g., CFS 2005)3, business reports and the media
commonly allege that the following proximate factors have negative impacts on
productivity and, hence, competitiveness of the Canadian forest products sector:
(i) new sources of timber supply from low cost, fast growing plantations in the
Southern Hemisphere; (ii) higher productivity levels achieved by Canada’s
traditional competitors in the marketplace; (iii) technological advances producing
specialized, engineered products (e.g., aluminum, composite Material, and plastic
products) that are substitute for solid wood products; (iv) globalization of the
marketplace; (v) environmental quality regulations; (vi) international trade disputes
— particularly the frequent softwood lumber trade dispute between the United
States and Canada; (vii) Canada’s international trade and environmental treaty
obligations; (viii) rapidly declining commercially Viable national timber supply; and
(ix) the demand Canadians place on their forest resources for a variety of goods
(e.g., paper, lumber, and plywood) and services (e.g., recreational activities,
carbon sequestration, aesthetic values, wildlife habitat, and soil and water
conservation).

It is true that all these peripheral issues influence the overall economic
performance of the sawmilling industry to some extent. But, the extensive
research literature shows that it is the dynamics of multiple attributes of the

production technology that primarily determine performance of an industry. This

 

3 See footnote 1.

is particularly the case for the Canadian sawmilling industry, which operates in
highly competitive international markets.

As described earlier, the sawmilling industry plays a very important role in
the Canadian economy. Given its importance, however, not much scientific
research has examined its production and cost structures, and thereby its
productivity performance. The available literature, most of which is from the
19803, shows that there is a wide gap of knowledge in terms of analytical depth
and statistical adequacy. For example, Nautiyal and Singh (1983) used annual
data for the 29-year period of 1952-1980 and estimated Cobb-Douglas (CD) and
constant elasticity of substitution (CES) forms of a restricted profit function for
each industry. They specified the industry’s production technology as a function
of capital stock, labor, and roundwood only, without taking into account the role
of energy. The authors concluded that the CD form represented the lumber and
the veneer and plywood industries best, while the CES explained the pulp and
paper industry. Several other studies that used annual data covering less than
20-year data-points estimated transcendental logarithmic (TL) forms of cost
functions to examine various aspects of the Canadian sawmilling industry’s
production technology during the early and mid-19803 (Section 6.4).

Using the multilateral index procedure, Ghebremichael et al. (1990)
conducted an inter-regional comparative analysis of productivity in the Canadian
sawmilling industry. These researchers were unable to carry out total factor
productivity (TFP) analysis, but estimated “variable factor productivity (VFP)”,

which is an aggregate quantity of output per unit of aggregate quantity of the

 

variable inputs: labor, energy, and Material. More recently, Latta and Adams
(2000) and Williamson et al. (2004) estimated restricted profit functions to
analyze derived demand for inputs and supply of outputs for the Canadian
sawmilling industry.

This study differs from previous studies in several ways, including (i)
coverage of a longer time frame, a forty-year period (1961-2000), (ii generation of
a price for capital services, using the perpetual inventory method, (a
methodology that accounts for opportunity cost of various capital assets); (iii)
database structure that details the multi-output and multi-input nature of the
industry; and (iv) a joint implementation of two major empirical methods, the
multilateral index procedure and econometric techniques, by which a wide range
of nonparametric and parametric empirical results were computed, interpreted,
and their policy implications explained.

The joint implementation of the two methods has provided comprehensive
information on the nature and dynamics of the industry’s technological attributes.
It was Ieamed that "our ignorance” of the meaning and the sources of total factor
productivity (TFP) was dispelled, because the empirical results from both
methods illustrated the dichotomy between the vertical shift in the production
function, explained by the level and growth rates of TFP, and the input driven
moment along the function, explained by various parametn'c results.

1.4 GOAL, HYPOTHESIS, THEMES, AND RESEARCH QUESTIONS
Goal: The goal of this study was to analyze long-term dynamics of technological

attributes that characterize the Canadian sawmilling industry’s production

10

technology. To that end, the following hypothesis was constructed; major
thematic areas were identified; and guiding research questions were formulated.
Hypothesis:

Over the forty-year study period (1961-2000), the sawmilling industry went
through several adjustments, such as mergers and plant closures; made
investments in R&D and/or purchased a variety of technologies, such as
machinery, equipment, and computer hardware and software; and, after
considering submissions of national organizations, such as the Canadian
Chamber of Commerce (2004), the Forest Products Association of Canada
(2006), and the Institute for Competitiveness & Prosperity (2006), the Canadian
government provided tax incentives in order to spur capital formation and
productivity.

Hence, it was hypothesized that these enabling conditions resulted in
technical efficiency improvements and technological progress, which could be
inferred through and gauged by the scale of and the trends in the nonparametric
and parametric empirical results, such as total factor productivity, cost diminution
rate (the dual measure of total factor productivity), economies of scale, capital
formation and intensity, and returns to scale.

Economists make clear distinction between technical efficiency
improvements and technological progress. Technical efficiency improvements
are revealed through increase in output without raising quantities or qualities of
inputs. They are believed to be results of various factors, such as learning-by-

doing, better management practices, structural adjustments made against shocks

1]

external to the industry, and innovation and diffusion of new technologies
invented elsewhere. Technological progress, on the other hand, is an increase in
output, which is realized through improvements in quality of inputs (e.g., human
capital through education and physical capital through inventions and
innovations) and investments in R&D (lntriligator 1965 and Romer 1990).
Thematic Areas and Guiding Research Questions:
Theme 1: Contributions of technical and technological progress to productivity

Trends in the levels and the growth rates of total factor productivity (TFP)
are good indicators of technical and technological improvements. Two questions
that deal with TFP are examined under Theme 1. The first question focuses on
the levels and growth rates of TFP: what were the trends in the levels and the
growth rates of gross TFP in the Canadian sawmilling industry over the forty-year
study period?

The second question deals with the sources of growth of the gross TFP:
what were the main sources of TFP growth ?
Theme 2: Multiple parameters that characterize the Canadian sawmilling
industry’s production technology

To examine technical improvements and technological progress over the
study period, the following conditions were postulated: (i) presence of economies
of scale and increasing returns to scale; (ii) less than unitary elasticity of cost with
respect to output, suggesting production cost increased at a lower rate than that
of output; (iii) combined contributions of both scale effects and rate of output

growth to TFP growth; and (iv) measurable rate of cost diminution, which is also

12

 

interchangeably referred to as a dual measure of the primal TFP growth or a
measure of disembodied technological progress.

In addition, own- and cross-price elasticities of derived demand for inputs
to examine substitutability or complementarity between pairs of inputs; input
substitution elasticities to observe the degree of ease in substituting one input for
another; and nature of technological change-bias to evaluate effects of factor-
saving and Hicks-neutral changes on employment and capital formation were
used to characterize the industry’s production technology.

Theme 3: Tax incentives to spur capital formation and productivity

Taxation policy instruments, such as capital cost allowance (CCA)4,
investment tax credit (ITC), and corporate income tax (CIT) influence capital
formation and productivity performance of an industry. Given the fact that this
research covers a forty-year period, during which several monetary and fiscal
policy changes occurred, assessing impacts of changes in fiscal and monetary
variables on capital formation and on TFP growth provides useful information for
policy making. Hence, the following research question was explored:

What would have been the effects of annual increases in the rates of CCA
and [TC and annual reductions in the rate of Cl T on capital formation and TFP

growth ?

 

4CCA is a tax deduction that Canadian tax laws allow a business to claim for the loss of capital
assets’ values due to wear and tear or obsolescence (Revenue Canada 2006): http://wwwcra-
_a_rc.qc.ca/menu-e.html. accessed October 4, 2006.

13

1.5 ORGANIZATION OF THE STUDY

The study is organized into eight chapters. Highlights of the Canadian
forest sector’s economic profile; the rationale for the study; and the hypothesis
and the guiding-research questions, classified under three major themes, are
discussed in Chapter 1. The various theoretical foundations of this study are
explained in Chapter 2. The nonparametric and parametric empirical methods
and the database are detailed in Chapters 3 and 4, respectively. In Chapters 5
and 6, empirical results of the nonparametric and parametric methods are
discussed, respectively. The main previous chapters are summarized in Chapter
7. Finally, conclusions, policy implications, the study’s limitations, and future

research directions are provided in Chapter 8.

14

CHAPTER 2 THEORETICAL FRAMEWORK

The preceding chapter has established the general direction of the study.
This chapter prepares the theoretical foundation for building the specific empirical
models that are explained in Chapter 3.

By necessity, this research uses concepts and techniques developed
under a wide spectrum of theories. Accordingly, several theoretical topics that
are particularly pertinent to this study are explored briefly in this chapter. The
topics include key conceptual technical terms, the neoclassical exogenous
growth theory, the endogenous growth theory, imperatives of effective
institutional arrangements, and path dependent technological progress. Finally,
several links between the theoretical framework in this chapter and the specific
methods described in Chapter 3 are summarized.

2.1 KEY CONCEPTUAL TERMS

In the economics of production, the following terms are used to describe
various attributes of technology: productivity, production frontier, technical
efficiency, allocative efficiency, technical change, scale economies, total factor
productivity, and feasible production set. Although these terms seem to be
deceptively very elementary for the specialist, it is appropriate to describe each
term here for the sake of clarity and ease of reference.

Productivity: There are two types: partial factor productivity (PFP), which is
aggregate output (in the case of a multi-output firm or an industry) per unit of the

quantity of a single input, such as labor; and total factor productivity (TFP), which

15

is aggregate output per unit of the aggregate quantity of all inputs (e.g., labor,
capital, energy, and Material).

Analyzing this aspect of the industry’s production technology is a major
part of this research. The methodology is detailed in Section 3.2 (Chapter 3).
Production frontier: Bounding all feasible production sets, i.e., all input-output
combinations, the production frontier represents maximum attainable output from
given set of inputs (Fig. 2.1)
Technical efficiency: Many members of the media, policy makers, and the
general public use productivity and technical efficiency interchangeably. This,
unfortunately, is wrong. To clarify the misconception, let there be a short-run
production function, with fixed capital input, K0, and a variable labor input, L, as

specified in Eqn. (2.1):

Q=f(K09L) (2-1)

Based on this short-run production function, these relationships can be

expressed geometrically (Fig. 2.1):

16

 

Technically (operationally) optimal scale efficiency

 

 

 

 

Production frontier

Q =f(K0, L)

 

 

Figure 2.1. Production frontier, productivity, technical efficiency, and scale
economies

In Figure 2.1 slopes of the rays 0R1, 0R2, and 0R3 represent average

QI-

productivity of labor, i.e., APL, = f, the steeper the ray, the higher the APL,-.

Thus, output Q3, with labor input L3, at the point of tangency, point E, is the
maximum possible output. At that point of tangency, APL is equal to the marginal
product of labor (MPL), described by the slope of the total production frontier.

That is,

MPL E f L = %—> = Slope of the total production frontier (2.2)

17

 

Thus, the point of tangency, point E, indicates technically optimal scale of
operation (Fig. 2.1). However, given the fact that changing a finn’s scale of
operation takes time, technical efficiency and productivity are often given short-
run and long-run interpretations. That is, dynamic interpretation of productivity
involves possible technological progress, which is revealed through an upward

vertical shift in the production frontier (Fig. 2.2).

Q A Vertically shifted production frontier

Production frontier pre-
technological progress

 

 

 

I—v

Figure 2.2. Technological progress over two periods

Allocative Efficiency: This refers to a least-cost combination of inputs (e.g., K
and L) to produce a given level of output, Q, under given prices of the inputs. It is

illustrated in Figure 2.3 and simple derivations that follow:

18

    
 

Isocost line

Isoquant curve

Q0

 

 

D
L* C/w L

Figure 2.3. Allocative and technical efficiency

C = rK + wL is a total cost, with r = capital rental price and W = labor price.

At point E, the point where the isocost line and the isoquant curve are tangent to
each other, their respective slopes are equal, meeting the following conditions for

allocative and technical efficiency (Fig. 2.3):

dQO = O =deL+deK :> —d—K=£ =MRTSLK (2.3)
a A

This condition is for the isoquant curve at point E.

And, for the isocost at the same point:

_MLK

TE — r (2'4)

Thus, producer’s equilibrium is attained at point E, whereMRTSLK :3.
r

That is, MRTSLK = marginal rate of technical substitution of labor for capital, must

19

be equal to the input price ratio for allocative and technical efficiencies to be
attained (Fig. 2.3).
2.2 THE NEOCLASSICAL EXOGENOUS GROWTH THEORY

The scope and complexity of the research on technological progress and
economic growth are described in this section. As an area of research, growth
theory is vast and diverse. For example, Jaffe et al. (2001) identify the following
ten major subject areas of research: (i) the theory of incentives for R&D; (ii) the
measurement of innovative inputs and outputs; (iii) the analysis and
measurement of positive extemalities, i.e., spillovers of R&D; (iv) the
measurement and analysis of productivity growth; (v) the process of diffusion of
new technologies; (vi) the effects of market structure on invention and
innovation; (vii) the failures of markets for inventions and innovations and the
challenges of designing effective institutional arrangements; (viii) the
socioeconomic impacts of publicly funded research projects; (ix) the economic
effects of the patent system; (x) the role of technological progress in endogenous
macroeconomic growth.

Solow’s (1957) seminal paper, Technical Change and the Aggregate
Production Function, has direct relevance to this study. In building his
macroeconomic production function model, Solow (1957) made the following
seven principal assumptions: (i) a national economy characterized by a constant
returns to scale production technology; (ii) perfectly competitive markets for both
inputs and outputs; (iii) national aggregate output that can be explained by the

amount of capital — particularly by aggregate value of the infrastructure - and the

20

knowledge-base of the productive workforce; (iv) real wages equal to marginal
productivities; (v) human capital (education, skills, and health of the workforce)
as a major driving force of economic growth; (vi) inputs other than capital and
labor were less important; and (vii) technological progress was Hicks neutral.

Solow concluded that technological change was a source of economic
growth in the United States. Specifically, he reiterated, “gross output per man-
hour doubled over the 1909 to 1949 period with 8.5% of the increase attributable
to technical change”. Notice that assumptions (i), (ii), and (iv) establish the
conditions for the application of Cobb-Douglas functional form and for the use of
Euler’s theorem.

Under these presumed conditions, Solow specified his “special case of
neutral technical change” to be estimated from an aggregate (macroeconomic)

production function as follows5:

Q = A(0f (K ,L) (2.5)

where Q is aggregate output of the economy (i.e., the GDP); K is productive
capital stock; L is the number of people in the workforce; A(t) is a measure of the
“cumulative effects of shifts over time”.

According to the formulation in Eqn. (2.5)6, the Hicksian parameter, A,
provides estimated measure of the shift in the production function at given levels

of K and L. In effect, it is expected to capture “technical change”, which is any

 

5 Solow (1957), Romer (1996), Jones (1998), Hulten (2001), and Link and Segel (2003) are the
main references for this section.

6 Other formulations are: (i) F[K',(AIL,)], which is referred to as “labor augmenting” or

“Harrod-neutral”; and (ii) F [(AIKI)’LI:I’ which is referred to as “capital augmenting” or

"Solow-neutral" (Jones 1998).

21

kind of shift in the production function: “slowdowns, speed ups, improvements in
education of the labor force, and all sorts of things will appear as technical
change” (Solow 1957). The aggregate production function model in Eqn. (2.5)
has two important features. Firstly, time is not directly involved in the production
function. This means that output changes over time only if the inputs into
production change. If output rises under given quantities of K and L, then it can
be inferred that there was disembodied technological progress. It means an
increase in output realized through industrial restructuring, not through increases
in inputs’ quality and quantity, while embodied technological progress refers to
increases in output realized through improvements in the quality of inputs -
particularly labor and capital (lntriligator 1965; You 1976, Romer 1990, and
Hulten 1992).

According to Solow’s theory, the Hicksian parameter, A, which is the
Solow residual TFP, is estimated using a nonparametric index number. This
approach does not impose any restriction on the production function. Totally
differentiating a logarithmic form of Eqn. (2.5) with respect to time and making

simple algebraic arrangements yields the result expressed in Eqn. (2.6):

aQ/at = [egg ] aK/az + [ 6Q= L, J 6L/at + aA/az

 

 

Q, 6K Q, K, 51 Q, L, A,
Q K 1; .21 <26)
'Q—=8QK F+8QLf+-A—

22

Thus,

A ' K L'

At Qt Kt Lt
Eqn. (2.7) shows that the growth rate of the Hicksian efficiency index, A, is
growth in real output minus the growth rates of capital and labor, both weighted

by their respective output elasticities ,gQ,(i = K, L). Note that the growth in real

output indicates movement along the production frontier, whereas the growth rate
of the Hicksian efficiency index, which is the so-called Solow residual, indicates a
vertical shift in the production frontier.

In this nonparametric formulation, the output elasticities with respect to K
and L are not observable. However, since Solow’s model is based on the
necessary condition for producer equilibrium in perfectly competitive markets for

inputs and outputs, real wage is equal to the marginal productivity of a given

 

 

input. That is,
59, _ _ We. , 8Q, _ _ Wu,
a—Iq = MPKI = R : WK! , and —a_L—t- = MPL! = P! : WL’ (28)

where Wcu and Wm are current dollar prices of labor and capital, respectively,

while WU and Wm are their real dollar values; Pt is output price; and the subscript,

6
t, is an index of a specific year. Then, substituting WL. and WK: for 5% and 21%

in the parentheses of Eqn. (2.6), yields:

23

_ L r
(a) SL: ‘ Q , share of labor in total-real value of output; and (b)

 

Q , share of capital in total-real value of output. Hence, again from
t

Eqn. (2.7), the Solow residual, SRt, can be calculated as follows:

m
U)
k
l
llQ-
l
at”
+
to;

TFP = '3‘ r _ Q ‘1? f (2.9)

t t
Eqn. (2.9) shows that the Solow residual TFP is output growth net of the sum of
inputs weighted by their respective shares in total-real output value. This means
TFP, in index number form, can be computed from prices and quantities.

SR is equivalent to the growth rate of the Hicksian efficiency index, A. But,
for lack of theoretical foundations, different researchers give it different
meanings. For example, Mawson et al. (2003) state that SR, measures “free
lunches associated with technological progress”, while Hulten (2001) calls it
something that is “a measure of our ignorance". In an extensive survey of the
literature, Lipsey and Carlaw (2004) identify three “main positions” of groups of
researchers who interpret the residual TFP differently as something that
measures: (i) the rate of technological change; (ii) only the “free lunches” or
“Manna from Heaven”; (iii) something useful, with no specific name; and (iv)
“supemonnal returns to investing in such changes — returns that exceed the full
opportunity cost of the activity” (Carlaw and Lipsey 2003; Lipsey and Carlaw

2004; Lipsey et al. 2005).

24

To make the exposition clearer, a specific functional form is handy. After
he experimented with various formulations, Solow (1957) used the following

generalized Cobb-Douglas functional form to draw conclusions:
Q = A(OKaL” (2.10)
where, assuming perfectly competitive markets for inputs and outputs and
constant returns to scale, and where a and B (a+8 = 1) are shares in real total
output value distributed to capital and labor, respectively. Furthermore, notice
that a and 8 are elasticities of output with respect to capital and labor,
respectively.

From Eqn. (2.10) the impact of technological progress on output can be

estimated as a residual growth rate of TFP by taking the natural logarithm of that

equation to formulate the following linear regression model with a stochastic

disturbance term, a:
an,=lnA(t)+aan,+,BlnL,+g, (2.11)

Notice that the Cobb-Douglas production function in Eqn. (2.10) has
unique features, which characterize it as a restrictive formulation. That is, (i)

technological change is simultaneously Hicks-neutral, Harrod-neutral, and Solow-
neutral; and (ii) the elasticity of input substitution, O'LK, is unity. Thus, a general

specification of the production function that permits flexible substitution of inputs,

similarto the one in Eqn. (2.12), is necessary (Link and Siegel 2003):

Q=F(K,L,t)=G[a(t)K,b(t)L] (2.12)

25

The generalized specification in Eqn. (2.12) provides Hicks-neutrality, if
a(t) = b(t), which means technological change is equally capital- and labor-
augmenting; Harrod-neutral, if a(t) = 1, implying technological change is only
labor-augmenting; Solow-neutral, if b(t) = 1, implying technological change is
capital augmenting.

In closing, highlighting the pitfalls of maintaining all Solow’s (1957)
assumptions in the measurement of technological progress and growth
accounting is in order. Arguments in the extensive literature (e.g., Nadiri 1970;
Boskin and Lau 1992; Prescott 1998; Hulten 2001; Lipsey and Carlaw 2004)
question particularly the validity of the restrictive assumptions of (i) constant
returns to scale; (ii) neutrality of technological progress; and (iii) profit
maximization, with perfectly competitive output and input markets. The following
is a summary of the arguments:

Firstly, for an economy in which aggregate real output and inputs are all
growing over time, it is difficult to identify separately the effects of returns to scale
and technological progress. It is possible either one can be used as a substitute
explanation for the other. Thus, given the likelihood of increasing returns to scale,
maintaining the hypothesis of constant returns to scale would result in an
overestimate of technological progress. Conversely, with the likelihood of
decreasing returns to scale, maintaining that hypothesis would result in an under-
estimate of technological progress. Moreover, if there are increasing returns to
scale, the assumption of constant returns to scale implies that the sum of output

elasticities with respect to the inputs is underestimated; and hence, at least one,

26

if not both elasticities, is underestimated, implying that the rate of technological
progress is overestimated. An additional implication is that the contributions of
capital and labor inputs to economic growth will also be underestimated. The
reverse would be true, if there are decreasing returns to scale. Examining
equations (2.7) and (2.9) should make these arguments clear.

Secondly, if technological progress is non-neutral, then the rate of
technological progress at time t will vary depending on the quantities of capital
and labor inputs at time t. Most importantly, technological progress over many
periods cannot be expressed simply as a smoothly cumulative sum of the
technological progress that has occurred over the individual periods, nor can it be
expressed simply as an average.

Thirdly, the assumption of profit maximization (or cost minimization), with
competitive output and input markets, implies the equality of the elasticities of
output with respect to capital and labor with their respective shares in total-real
output value. However, given the possibilities of market and nonmarket
constraints to instantaneous adjustments of inputs to their desired levels, the
output elasticities with respect to each input are likely to deviate from a given
input’s share in the real-total output value. Hence, an estimate of technological
progress obtained from Eqn. (2.9) will be subject to factor biases.

Furthermore, the estimated contributions of capital and labor inputs to
economic growth will be subject to biases. For example, if the output market is

monopolistic, then the input shares are likely to underestimate the output

27

elasticities, causing in turn an over-estimate of technological progress, if equation
(2.9) is used. The reverse Is likely to be true in a monopsonistic market.

To avoid all these problems, therefore, direct estimation of an econometric
model, such as that in Eqn. (2.11), is believed to be the best method. This is
because such econometric models do not require imposition of the assumed
restrictions as part of the maintained hypothesis in Solow’s model (Boskin and
Lau 1992).

Thus, given the fact that TFP growth is one of the major engines of
economic growth, the crux of the challenges lies in how to measure, analyze, and
interpret it. As the following sections show, the solution calls for an ongoing
research with a joint implementation of the nonparametric and parametric
approaches.

2.3 THE QUEST FOR A MEANING OF THE SOLOW RESIDUAL

The economic importance of TFP is well established. It is believed to be
an engine of economic growth. It is the cause and the consequence of the
evolution of dynamic forces that keep a given economy in motion (Nadiri 1970).
The forces include technological progress, quality of human and physical capital
accumulated over time, labor and management relations, and national and
international institutional arrangements. But, the debate on the exact meaning of
the Solow residual TFP and the techniques for measuring it continues.

The debate starts with a search for the correct definition of At: What is
TFP? What are its determinants? What are the scientific techniques for

measuring and analyzing it? As a start, assessing three general criticisms in the

28

literature directed at the validity of the key assumptions of Solow's (1957)
aggregate production function model is helpful.

Firstly, if the aggregate production technology is restricted to be constant
returns to scale, Le, a Cobb-Douglas form; and if each K and L is paid its
respective marginal productivity, then, by Euler’s theorem, the value of output
equals the sum of the payment to the inputs. This means the sum of the shares
of labor and capital in the total-real value of output in a given year, t, equals to
unity. Thus, there is nothing in the derivation steps in equations (2.5) to (2.9) that
requires constant returns to scale (Hulten 2001). In fact, Jorgenson and Griliches
(1967) demonstrate that the condition for constant returns to scale is needed only
to estimate, if there is any residual left as a return to capital.

Secondly, the marginal cost pricing, i.e., the marginal productivity
condition in Eqn. (2.8), rules out the likelihood of imperfect market competition (or
monopolistic competition), which leads to a price greater than marginal cost.
Under this market imperfection, Hulten (2001) argues that the Solow residual
was found to be a biased estimate of the Hicksian shift parameter, A, and “there
is no way out of this problem” within the Solow index approach.

Thirdly, the Hicksian formulation in Eqn. (2.5) is valid only if inventions
and/or innovations improved the marginal productivity of all the inputs at an equal
rate. This is very strong assumption that is bound to lead to a biased estimate of
A.

In an attempt to solve the problems associated with the Solow formulation,

Hulten (2001) using the following more general formulation that allows

29

improvements in technology to augment the marginal productivity of each input

independenfly:

Q, = F(0(,K,,)3,L,) (2.13)

Link and Siegel (2003), who specified the formulation in Eqn. (2.12),
supported Hulten’s (2001) formulation, which is specified in Eqn. (2.13). It is

factor augmentation production technology, replacing the Hicksian parameter, A,
with two augmentation parameters: or and [3. Then, retaining all the other

assumptions of Solow, except the constant returns to scale, the residual can be

expressed as:

aa/at +5“ afl/at
, fl,
2' ,8 (2.14)

SR, = SK,

 

 

t t

Thus, SRt, the Solow residual, is now the output-value share weighted average of
growth rates of the input augmenting parameters; and still it measures changes
in TFP.

However, the intellectual “debate”, “criticism”, and/or “concern”, does not
end here. In general terms, Domar (1961) argued against previous studies, which
concluded that “80-90% of output growth per unit of labor in the United States”
was attributable to technological progress, measured in terms of the SR(, “the
remaining 10-20% being all that capital (and land) could claim”. Domar argues

that the SR(, “which does not even have a scientific name and theory behind it”,

30

does not take into account contributions of all inputs and attributes that
characterize a production technology.

That is, it does not value effects of several technological attributes, such
as economies of scale and scope; enhanced quality of the workforce acquired
through improved health, education, and skills of the labor force; effective and
efficient management; and changes in product mix. Moreover, “the heavy weight”
assigned to the contributions of labor productivity in macroeconomic models is
misleading, because partial productivity of labor (PPL) is a function of all inputs7.

In addition, the various names given to SR( by different researchers
appear to add more confusion. For example, Domar (1961) identifies the
following six names used by different researchers: “output per unit of input”,
“efficiency index”, “total factor productivity”, “change in productive efficiency”,
“technical change”, and “ a measure of our ignorance”.

Furthermore, in the very recent literature, pioneered by Richard G. Lipsey
and associates, TFP is described as a measure of “supemorrnal gains”,
associated with investments in R&D (Carlaw and Lipsey 2003; Lipsey and
Carlaw 2004; Lipsey et al. 2005). These authors interpret the “supemorrnal
gains” as gains that are over and above the opportunity costs of expenditures
made mainly in R&D.

In sum, the quest for a universally accepted interpretation of TF P goes on.

For the purpose of this study, however, TFP growth is an indicator of output

growth realized through combined effects of production scale and technological

 

7This aspect is explored fully in Section 3.2 (Chapter 3).

31

 

progress. These two mutually reinforcing effects cause a vertical shift in the
frontier of the production technology.
2.4 THE NEED FOR JOINT IMPLEMENTATION OF THE TWO METHODS

The steadily growing literature shows that joint implementation of the
nonparametric and parametric methods can “dispel our ignorance” (e.g., Domar
1961; Griliches and Jorgenson 1967; Hulten 2001; Carlaw and Lipsey 2004;
Lipsey et al. 2005). As Hulten (2001) puts it, “both approaches can be
implemented simultaneously, thereby exploiting the relative simplicity and
transparency of the nonparametric estimates to serve as bench-marks for
interpreting the more complicated results of the parametric approach”.

The intuition is that empirical results from both the nonparametric and
parametric methods can illustrate “the dichotomy between the shift in the
production function and the factor—driven movement along the function” (Hulten
2001). Thus, the justification for joint implementation of the two methods is based
on the strengths and limitations of each method. The nonparametric method has
the following merits: (i) it allows multiregional and international comparisons; (ii)
enables measurement of growth rates and levels of productivity; (iii) is easily
understood by policy makers, business executives, and other non-specialists; (iv)
avoids the problems often associated with specification and estimation of
econometric models; (v) displays results that reveal data anomalies, unlike
statistical approaches that tend to conceal irregularities; and (vi) enables the
researcher to examine efficiency in terms of a wide range of measures, such as

historical trends and cycles in the data and the productivity indices (Freeman et

32

al. 1987; Frank et al. 1990; Ghebremichael et al. 1990; Ghebremichael and
Nanang 2004). The main drawback of this procedure is that it does not provide
the several parametric measures of production technology and technological
change that an econometric model does.

But, it is clear that an econometric method also has pitfalls. They include
the challenges associated with (i) identifying all potentially “correct” explanatory
variables in order to build credible model, starting with a correct specification of
the production technology; (ii) choosing the right flexible functional form and
estimation techniques; (iii) identifying, explaining, and diagnosing simultaneity
problems”; and (iv) many other statistical challenges.

In summary, the resolution of that debate appears to rest on the joint
implementation of both methods. Empirical work that combines these two
methodologies is expected to explain “the measure of our ignorance” (Hulten
2001). It is also expected to address concerns of many researchers — particularly
those of Jorgenson and Griliches (1967) - who argued that the residual ought to
vanish if all explanatory variables are paid their respective marginal
productivities; and that the aggregate measures of K and L inputs possess
embedded qualities obtained from R&D expenditures.

Out of the extensive intellectual debate on how to model, measure, and
analyze economic growth, a new growth theory, endogenous growth theory, is

gaining some momentum in the academic world. The complex models of this

 

8 For example, in a simple production function, K and L on the right hand side of a regression
equation depend on the dependent variable, Q, the level of which is endogenously decided by
management. Based on the level of Q, management decides what amounts of K and L should be
used, leading to simultaneity problem.

33

theory focus mainly on how R&D contributes to TFP growth and thereby to
economic growth. The theory is highlighted next.
2.5 ENDOGENOUS GROWTH THEORY

As pointed out above, the neoclassical exogenous growth theory assumes
that effects of inventions and/or innovations are exogenously determined under
given R&D expenditures. But, this is far from reality. A more realistic approach is
to recognize that R&D makes significant contributions to the growth of TFP
endogenously (e.g., Romer 1986, 1990; Hulten 1992; Jones 19953, b; Jones
1998; Griliches 1998; Aghion and Howitt 1999; Hulten 2001). It is instructive to
observe that these and other researchers use more or less similar specifications
of endogenous growth models to explain implications of endogeneity of
technological progress for the measurement and interpretation of TFP.

For example, Hulten (2001) specifies the following variant of the
generalized Cobb-Douglas functional form of the production function to illustrate

the workings of the endogenous growth model:

Q,=A0K7(K/3Lf) a+fl=1; fl+7=1 (214)

According to the formulation in Eqn. (2.14), capital, K, has two effects: (i) a one
percent increase in K raises output of its owner-user by a percent; and (ii) a

spillover effect on the output of other users. Furthermore, observe

thata+ ,8 =1, implying constant returns to scale in the K variable across all

producers; and )6 + 7 :1 implies K and L are also subject to constant returns to

scale. In addition, this formulation exhibits increasing returns to scale. However,

34

it is consistent with competitive equilibrium, because each producer operates
under the assumption of constant returns to the inputs that the producer monitors
and controls.

But, what does the new formulation in Eqn. (2.14) imply for the residual
TFP, computed from the formulation in Eqn. (2.9)? Notice that the residual is
derived from the Hicksian production function formulation in Eqn. (2.5), while the

formulation in Eqn. (2.14) is a special case of that function in which the output
elasticities are constant (Cob-Douglas) and the efficiency term, AOKf”, replaces

the Hicksian efficiency parameter, A.

The associated residual, like that in Eqn. (2.9), is equal to the growth rate
of capital weighted by the spillover effect. The analogous TFP residual continues
to measure costless gains to society — the “Manna from heaven” - realized
through innovations (Hulten 2001). But, the “Manna” is associated with the
extemality parameter,a, instead of the Hicksian efficiency parameter, A.
According to the New Growth theory, therefore, the approach to estimating the
residual is not a nonparametric approach. It is a parametric approach, which is a
reflection of a given process.

In short, the new endogenous growth theory supports the following five

economic policy prescriptions: (i) that government policies that stimulate

35

competitiveness in the marketplace result in economic growth; (ii) that there are
potential increasing returns from higher levels of capital deepeningg; (iii) that
private investment in R&D is the central source of technological progress; (iv)
fully specified and protected property rights and patents can provide the incentive
to engage in R&D; and (v) that investment in human capital (education and
training of the workforce) is a necessary ingredient of economic growth.
2.6 IMPERATIVES OF EFFECTIVE INSTITUTIONAL ARRANGEMENTS
Arguing on the importance of institutional arrangements for productivity
measurement and analysis, the Nobel Prize Laureate, Douglass C. North (1993),
criticizes the “biased tendency of neoclassical economists”. He reiterates that
institutions, which are “the rules of the game of an economy”, play determinant
roles in the process of productivity growth and, hence, national wealth. He makes

his point as follows:

.. ..that institutions matter .and that they must be integrated with
classic sources of productivity change if we are to understand the long-run and
for that matter short-run performance of economies.

Consisting of “formal rules, informal constraints (norms of behavior,
conventions, and self imposed codes of conduct), the enforcement
characteristics that humans impose on their dealings with each other, institutions
are “the humanly devised constraints on human interaction” (Noth 1993).

Institutions are “constructs of the human mind” that cannot be seen, felt, or

 

9 Capital deepening is the process of capital stock accumulation at a faster rate than the growth
rate of the labor force, while capital widening is the process of accumulating capital stock at the
same rate as the growth rate of the labor force so that the capital labor ratio remains constant
(Pearce 1992).

36

measured (North 2002). In effect, without effective institutions, public and private
policies cannot be implemented effectively and efficiently.

Recent and extensive literature shows that effective institutional
arrangements, enhanced investments in R&D, and technological progress are
the main sources of productivity and thereby economic growth (e.g., Romer
1990; North 1993; Lipsey et al. 2005). Technological progress is realized through
intentionally planned investments made by profit maximizing private firms. But, if
a given technology is patent free, it is nonrivalrous and nonexcludable. This is
particularly important when one takes into account the quality of human capital,
the embodied knowledge base.

Economic theory suggests that the existence of nonconvexity, due to
nonrivalriness and nonexcludability, perfectly competitive market structure for
technology (knowledge) cannot be supported. This by itself calls for effective
arrangements of relevant institutions for intellectual property rights. Romer ( 1990)
developed his model under the following three premises to argue against the
conditions under which the aggregate production function-based economic
growth model of Solow (19957) was expected to work: Firstly, he concurred that
technological progress is an engine of economic growth. Secondly, technological
progress arises because rent seeking (profit maximizing) economic agents that
respond to market incentives make decisions to invest in R&D and other
opportune areas that result in endogenous technological progress. Thirdly,
marginal costs for innovative techniques (i.e., innovations) are zero: once they

are created they can be used over and over free of any marginal cost (e.g.,

37

computer software). Romer (1990) draws the following three conclusions: that
the stock of human capital determines the rate of economic growth; that
integration into world markets would increase growth rates; and that having a
large population was not sufficient to generate growth, as the Solow model
implies.

In Canada, activities of firms, trade unions, and other socioeconomic
organizations are constrained by federal and/or provincial institutional
arrangements. Specifically, the institutional arrangements that govern
sustainable forest ecosystem management deal with complex issues whose
effects can be examined within the framework of the forestland tenure system.
This system stipulates that 93% of Canada’s forest resources are publicly owned,
while private woodlot owners manage the remaining 7% (The Canadian Forest
Service 2006b).

The Canadian Constitution enunciates that the federal, provincial, and
territorial governments have specific roles in sustainable management of forest
ecosystems. The 10 provinces and three territories have legislative jurisdictional
authority over the conservation and sustainable management of 77%, while 16%
is under the federal govemment’s purview. About 80% of total timber harvesting
by private companies takes place in the publicly owned forests (The Canadian
Forest Service 2006b). Institutional arrangements on timber harvesting contracts
made between provincial/territorial governments and companies place legally
binding obligations on the companies to pay harvesting fees, and to submit plans

that ensure sustainable forest management in return for the right to harvest

38

timber. The management plans must be submitted to government authorities for
approval before the start of harvesting operations.

Frequent changes in institutional arrangements of the contracts occur in
the Canadian forest policy, because of conflicting interests of three bodies: the
governments that attempt to obtain maximum economic rent of forest resources;
the companies that seek to maximize profits; and the labor unions that aspire for
secured jobs and fair wages.

Furthermore, due to the jurisdictional mandates, the national constitution
on forest tenure system accords to the federal and provincial/territorial
governments to develop a national forest policy regime. This varies often with
provincial, territorial, and local community development goals and objectives. A
variety of ideas and institutional arrangements on sustainable forest ecosystem
emerge from a complex of interests of governments, industries, local
communities, and labor unions.

For illustrative purposes, this study focuses on key fiscal policy
institutional arrangements. Specifically, effects of changes in taxation policy
instruments on capital formation and total factor productivity growth are analyzed
[Section 532(8)].

2.7 THE THEORY OF PATH DEPENDENT TECHNOLOGICAL PROGRESS

Recent literature shows that the theory of path dependence plays an
important role in the study of technological progress and economic growth
(Ruttan 2001). Depending on the subject matter under review, path dependence

is used to explain two concepts: “history matters”, a very broad and “trivial”

39

conception which means “everything has causes” and institutions are self-
reinforcing social constructs. This is a well focused concept with scientific
explanatory power.

Reiterating the importance of historical facts that describe path

dependence for evaluation of industrial performance, Rosegger (1986) states,

“Performance evaluation does not deal in scenarios of what might have been, it

deals with the “facts” of the past. What performance evaluation aims at is an
understanding of the technological and economic factors, internal or external to
the entity being evaluated, that caused observed changes in such variables as
the productivity of inputs, costs, prices, and profits”.

Generally, path dependence is used to explain general conceptions, such
as (i) specific patterns of timing and sequence matter; (ii) starting from similar
conditions, a wide range of social outcomes may be possible; (iii) large
consequences may result from relatively “small” or contingent events; (iv)
particular courses of action, once introduced, can be virtually impossible to
reverse; and consequently, political development is often punctuated by critical
moments orjunctures that shape social life (Pierson 2000).

That is, if historical events affect long-run equilibrium patterns, an
economic system is path-dependent. Big events, such as plagues, catastrophes,
wars, and major inventions and/or innovations, affect the steady state of an
economy (Bassanini 1997). It is clear that technological changes in the Canadian
forest products sector are part of Canada’s economic history. The Canadian
economy evolved from one that was a natural resource dependent, exporter of
primary products (e.g., lumber, fur, and fish), to its current position of a high-tech
dominated economy. With no doubt, there are historical forces that drove this

technological advancement. In effect, cumulativity and specificity of path

40

dependent technological changes result in irreversibility and self-reinforcing
mechanisms that amplify effects of historical events (Pierson 2000).

Moreover, TFP growth, considered as an upward vertical shift in the
production frontier, is path dependent and several forces, such as technical
change and capital deepening are considered to be always at work
simultaneously (Givon 2006). Technological advance that occurs sequentially
causes differences in measured TFP changes.

The challenge is in understanding and explaining those forces. Ruttan
(1997) argues that induced innovation, evolutionary theory, and path
dependence are sources of technological change. Evolutionary economic theory
posits that technological change is driven by continual creation of technological
variety through inventions, innovations, and diffusion processes. Generally it is
conceptualized that dependence of current technology on past and existing
knowledge tends to move firms, regions, and nations along well defined
technological trajectories (Essletzbichler and Winther 1999).

In the forest products sector, historical records of major events, such as
outbreak of wildfire, diseases, and endemic insects adversely affect timber
supply, leading to changes in market demand and supply. Such events are
incentives that stimulate search for all sorts of new technologies through R&D
investments. Under these supply side shocks, research projects similar to this
one would focus on enhancing productivity in timber harvesting and in sawmilling

operations.

41

In short, there can be no doubt that technological change is path
dependent. It can be driven by either supply side or demand side forces or by a
combination of both. The key to the concept is time path: “technological change
evolves from earlier technological developments” (Ruttan 1997). On the
importance of the theory of path dependence, Hirsch and Gillespie (2001) make

the following convincing argument:

Path dependence deserves credit for bringing history back into
analysis of economic and technological development, stimulating economists
and other social scientists to address the limitations of their largely ahistorical
models. Path dependence points out the paradox of researchers using
history as a data bank and source of economic variance, even while
simultaneously assuming that history does not fundamentally differ from, and
has no implications for, the present.

Thus, this study, which covers a forty-year period (1961-2000), places the
dynamics of the key technological attributes that characterize the Canadian
sawmilling industry’s production technology into their historical perspectives.
Particularly, the historical trends in gross TFP have reflected path dependence of
technical improvements and technological progress.

2.8 THEORETICAL UNDERPINNINGS OF SELECTED STUDIES

In this section, selected studies whose theoretical underpinnings
contributed significantly to the processes of building the empirical models used in
this study, are highlighted. In analyzing dynamics of technological attributes in an
industry, computation of real capital stock and its rental price is the most
challenging part. Rental price of capital depends on accurate measurement of its
real capital stock, the asset market price, the rate of return, the rate of
replacement, and the tax structure of a given economy. In a seminal paper,

Christensen and Jorgenson (1969) pioneered a technique called perpetual

42

inventory procedure for establishing aggregate quantity and price indices of
various vintages of capital. This method has become a standard tool used by
public and private organizations. For example, in its ongoing program of
database building for capital stock in current and constant dollar values, Statistics
Canada (2001) uses the perpetual inventory method, with which it is possible to
calculate rental price and to adjust stocks and prices for relative utilization of
capfiaflo.

Productivity change is both the cause and consequence of the evolution of
dynamic forces operative in an economy — technical progress, accumulation of
human and physical capital, enterprise, and institutional arrangements (Nadiri
1970). Measurement and interpretation of its dynamic behavior at the
microeconomic and macroeconomic levels require the understanding of many
complex factors. In its partial factor productivity (PFP) and total factor productivity
(TFP) forms, productivity is the main measure of technological progress
(Kennedy and Thirlwall 1972). Regarding methodologies of measuring and
analyzing productivity parametrically, Kennedy and Thirlwall (1972) caution about
the drawbacks of the Cobb-Douglas form, which has restrictive assumptions of:
(i) neutral technological progress; (ii) unitary elasticity of factor substitution; (iii)
constant returns to scale; and (iv) disembodied technological progress, as in the
case of Solow’s growth model.

The challenges of formulating an effective econometric functional form
and aggregation lie at the heart of applied production economics (Chambers

1988). Christensen et al. (1973) developed the transcendental (TL) logarithmic

 

1° The math of this procedure is summarized in Section 4.2 (Chapter 4).

43

production and price possibility frontiers. These frontier functional formulations
are quadratic in the logarithms of the quantities of inputs and outputs.
Christensen et al (1973) demonstrate that the TL frontiers provide accurate
global approximations for many of the production and price frontiers used in
econometric studies of production".

Christensen (1975) challenged those who used partial factor productivity
(PFP) for decision-making. He stated, “Thus, I do not believe that l have to
convince this audience of the importance of total factor productivity concept”
(TFP). With that assertion, Christensen derived and explained various conceptual
index number approaches to the measurement and analysis of TFP.

Christensen et al. (1980) conducted a comprehensive international
comparison of economic growth over the period of 1947-73. The study covered
nine countries: Canada, France, Germany, Italy, Japan, Korea, the Netherlands,
the United Kingdom, and the United States. The primary objective of the study
was to separate growth in real input from growth in TFP in order to account for
growth in real product for each country. The production technology was assumed
to be characterized by constant returns to scale; and was specified as a function
of capital, labor, and a time-trend variable only. The authors concluded that
variations in aggregate economic growth for the period 1960-73 were associated
with variations in the growth of real input; and that the rapid growth in real
product was associated with rapid growth of both real capital input and real labor

input

 

1‘ More explanations on the effectiveness of the TL form of the dual cost function are given in
sub-section 3.3.3 (Chapter 3: Methods).

44

Applying the Tomqvist index procedure, Christensen and Cummings
(1981) analyzed real product, real input, and productivity in the economy of the
Republic of Korea for the period of 1960-73. Their findings revealed that the
average annual growth rates of real output, real input, and TFP were 9.7%, 5.5%,
and 4.1%, respectively.

Bemdt and Watkins (1981) carried out a rigorous analysis of energy prices
and productivity trends in the Canadian manufacturing sector for the period of
1957-76. They estimated a long-run TL cost function; and found that capital was
substitutable for labor and energy; and that labor and energy were substitutes for
each other. However, they cautioned that the aggregated nature of the data
made their findings less credible.

Rao and Preston (1983) analyzed the causes of inter-temporal variations
in factor intensities and TFP in major Canadian industry groups, such as
agriculture, forestry, mining, and the manufacturing sector. The authors
estimated a TL form total cost function; and found out that many of the industries
experienced 15 to 20 percent slowdown in TFP growth after 1973.

As discussed in Section 2.2, Solow’s (1957) pioneering work associates
technological progress, i.e., TFP growth, with time derivative of an aggregate
production function. Although a useful conceptualization, Solow’s formulation is
not appropriate for actual measurement and analysis of productivity (Caves et al.
1982b). Since index number procedures entail comparisons of discrete points in
time, using discrete data points, the procedures require a discrete approximation

to continuous time derivative. Caves et al. (1982a) demonstrated that

45

“superlative index” numbers could be used for making multilateral comparisons.
By permitting the first order TL parameters to differ across economic entities, the
authors developed “superlative” output and input indices; and formulated 3 TL
multilateral productivity index. Continuing with refinement of their work, Caves et
al. (1982b) developed an index number construction procedure for making
comparisons under very restrictive general circumstances. Malmquist input,
output, and productivity comparisons were defined for structures of production
with arbitrary returns to scale, substitution possibilities, and biases in productivity
change. For TL production structures, Tornqvist output and input indices were
shown to be equal to the mean of two Malmquist indices. The Tomqvist
productivity index, corrected by a scale factor, was shown to be equal to the
mean of two Malmquist productivity indices.
2.9 SUMMARY

To lay a strong foundation on which the empirical models for this study are
built, the pertinent theoretical framework is detailed in the previous sections. That
is, the challenges associated with economic growth theory in general and with
the measurement, analysis, and interpretation of TFP in particular are detailed.
This section summarizes that discussion and links it to the empirical methods,
which are explained in Chapter 3.

What are the elements of TFP? Conversely, what does TFP measure?
Conceptually, it is believed that the residual TFP captures changes in the amount
of output that cannot be attributed to a given set of inputs. lntuitively, it measures

vertical shift in the production frontier. But, many factors affect the shift. They

46

include technical innovations, organizational and institutional changes, shifts in
societal preferences, fluctuations in demand, changes in input shares in the total-
real value of output, omitted variables, and measurement errors. Hence, the
residual TFP cannot be interpreted as technological change (Hulten 2001;
Carlaw and Lipsey 2003; Lipsey and Carlaw 2004; Lipsey et al. 2005).

To the extent that productivity is affected by the rate of inventions,
innovations, and diffusions of new technologies, it is commonly accepted that
TFP captures the costless part: “the Manna from Heaven” or “free Iunch”. It may
measure the so called “supernorrnal gains”; and it may also reflect spillover
extemalities from R&D projects elsewhere and effects of enabling institutional
arrangements, such as taxation policy instruments and well-defined property
rights and patent rights.

Furthermore, the residual is a nonparametric index number designed to
estimate one parameter in the larger structure of production, the efficiency shift
parameter, A(. It uses prices to estimate marginal products in order to accomplish
this. Thus, the various factors comprising TFP are not measured directly, but are
lumped together as a “left-over” factor (hence the name residual). They cannot
be factored out within the pure TFP framework; and this is the source of the
“famous epithet”, as Hulten (2001) puts it, “a measure of our ignorance”.

In addition, the Divisia index must be path independent to be unique. The
discrete-time counterpart of the Divisia index, the Tomqvist approximation, is an

exact index number, if the underlying production function has the TL form. The

47

problem of path dependence is one of uniqueness, which is not the same thing
as measurement bias.

The two conditions for path independence are the existence of an
underiying production function, and marginal productivity pricing. Although they
are usually assumed for convenience of measurement, neither constant returns
to scale nor Hicksian neutrality are absolutely necessary conditions. It is only
when the various assumptions are met that the residual is a valid measure of the
shift in the production frontier. However, it generally understates the importance
of productivity change in stimulating the growth of output, because the shift in the
production frontier generally induces further movements along the function as
capital increases.

Finally, the literature shows that the quest for the exact meaning and the

theory of the residual TFP remains open. In Hulten’s (2001) words:

The residual is still, after more than forty years, the workhorse of
empirical growth analysis. For all the residual flaws, real or imagined, many
researchers have used it to gain valuable insights into the process of
economic growth. Thousands of pages of research have been published, and
more are added every year. Total factor productivity has become a closely
watched government statistic. Not bad for a forty-year old.

In short, the positive value of the TFP residual outweighs the
negatives. The residual has provided a simple and internally consistent
intellectual framework for organizing data on industrial performance and
economic growth; and has provided the theory to guide economic
measurement (Hulten 2001).

Despite the lack of universally accepted theory behind it, the

residual TFP is the best available yardstick to measure and analyze

48

performance of a given economic entity, such as a firm and an industry.
For instance, a complete picture of the industrial dynamics of an
economy would require correctly measured and analyzed TFP residuals.
In addition, whatever limitations a TFP model has are equally applicable
to any other model, be it an econometric or any other empirical model.
This challenge, therefore, calls for joint implementation of the

nonparametric and parametric methods, as done in this study.

49

CHAPTER3 METHODS

Chapter 2 has established the ground for building the two empirical
methods. Sufficient justifications of the need for joint implementation of the
nonparametric and the parametric (econometric) approaches to analyze
industrial technologies are presented in that chapter. Here, the two methods
used in this study are described. First, the production technology of the Canadian
sawmilling industry is specified in Section 3.1, while the importance and concepts
of productivity are highlighted in Section 3.2. Then, the workings of the two
empirical methods: (i) the nonparametric method, which involves application of
the multilateral index model and (ii) the econometric method, which involves
estimation of a long-run dual-cost function, are described in sections 3.3 and 3.4,
respectively.
3.1 THE PRODUCTION TECHNOLOGY

Microeconomic theory of production deals with the process of combining
and coordinating productive resources and services, which are collectively called
inputs. What to produce, how much to produce, and the optimal combination of
all inputs are the key issues in any production process. These issues are of
concern to an industry as well as to a society. Hence, a production function can
be defined as a mathematical specification of the various technical production
possibilities a firm faces. For given levels of inputs, a production function is
expected to represent the maximum output(s) in physical terms.

In general, the concern of production economics is not only choice of

effective and efficient techniques of production, but also how choices are

50

influenced by changes in technology. Mathematical specification of the
production function can range from simple algebraic functions, such as a function
relating corn yield to fertilizer dosage, to highly complex systems of equations,
such as a detailed model of corn plant growth and response to nitrogen
fertilization (Beattie and Taylor 1985). The degree of mathematical complexity of
the production function depends on the complexity and scale of the production
process and the degree of the desired accuracy. But, cost and manageability of
the research must be taken into account. In most cases, cost effectiveness
determines the socioeconomic and scientific merits of a research project.

For the purpose of this study, the following production function was
assumed to explain the production technology of the Canadian sawmilling

industry:

Qt =f(Kt,Lt,Et, MfiTt) (3.1)

where Q = aggregate of the three types of output: (i) lumber, (ii) shakes and
shingles, and (iii) all marketable sawmilling operations’ byproducts that include
wood chips, sawdust, slabs, edgings, and shavings, which are sold to pulp mills;
K, L, E, and M are capital, labor, energy, and sawlogs, which are the sole raw
material input, respectively; T is a time trend variable, which is expected to

capture disembodied technological progress, measured by TFP (Solow 1957;
Bemdt and Watkins 1981; Chambers 1988; Griliches 1998; Diwan and
Chakraborty 1991 ); and the subscript t stands for a specific year during the study

penod.

51

The trend variable, T, is a poor indicator of technological change, because
it is used under the presumption that technological progress is smooth and
steady. If the goal is to obtain an exact measure of technological dynamics, this
problem is quite serious. But, if the goal is to test for the existence of
technological change and statistical significance of its impact on production cost,
this approach is valid (Nautiyal and Singh 1985). Furthermore, Chambers (1988)

argues for the validity of using T as follows:

“This approach is sometimes disparaged as being a measure of our ignorance than
anything else. But, even if it is true, should one be upset at being able to measure
one’s ignorance?”

Hence, in this study, T is expected to provide information on the presence
of technological progress over the forty-year study period. Previous studies,
which are all of the 19803, used the specification in Eqn. (3.1) (e.g., Singh and
Nautiyal 1985; Nautiyal and Singh 1985; Martinello 1985; and Meil and Nautiyal
1988)

3.2 NONPARAMETRIC METHOD OF PRODUCTIVITY ANALYSIS
3.2.1 Importance and Concepts

A. Importance

The importance of productivity for the future growth of living
standards, defined as GDP per capita, is becoming increasingly
recognized. ...Productivity growth really is our economic destiny. But, the
Achilles heel of Canadian economic performance in recent years has been
weak productivity growth, a disconcerting development (Sharpe 2006)12

In general terms, productivity is the core of the science of economics.

Although the Solow residual, detailed earlier, is accepted as a measure of the

 

’2 Presentation of Andrew Sharpe, Executive Director, Centre for the Study of Living Standards,
to the panel session on “Human Capital, Technology, and Innovation” at the Conference on
Canada’s Competitiveness and Prosperity, organized by the Institute for Competitiveness and
Prosperity, Ottawa, Ontario, March 10, 2006.

52

shift in the frontier of production technology, it does not explain the importance of
productivity improvement as a source of economic growth. Researchers attribute
part of the historically observed growth rate of capital stock (i.e., steady
increases in capital formation) to productivity growth.

In its broadest sense, however, productivity is the amount of aggregate
output per unit of aggregate quantity of inputs. Enhanced productivity is an
indicator of efficient and effective utilization of scarce economic resources (e.g.,
labor, various vintages of capital, and natural resources) to generate goods and
services.

In summary, there are multiple direct and indirect (spin-off) benefits that
society gains from improvements in industrial productivity. They include the
following: (i) mitigation of accelerated depletion of natural resources; (ii)
minimizing environmental damages caused by industrial operations; (iii) saving in
the use of the productive services of scarce economic resources, i.e., minimizing
consumption of a given input per unit of output; (iv) minimizing impacts of
inflation on performance of a given economy by off-setting rising wage-rates and
other input prices; and (v) improvement in the competitiveness of national
industries in the global marketplace. Consequently, public policy makers and
industry executives pay special attention to strategies that lead to productivity
improvement (Sharpe 2006).

In addition, the growing number of national and international productivity
research centers shows the importance of productivity growth for social welfare

improvement. Examples of national and international centers include the

53

European Association of National Productivity Centers, the Asian Productivity
Association, the American Productivity Association, and the Japanese
Productivity Association.

B. Concepts

While the computation techniques are discussed in the next section, the
concepts and the challenges associated with measuring and analyzing
productivity are briefly discussed here. As detailed in Chapter 2, whatever “label”
is placed on it (e.g., “measure of our ignorance” or “Manna from Heaven”), TFP
is considered as more illuminating indicator of technological progress than partial
factor productivity (PFP), which is productivity of a single input (Ghebremichael
and Nanang 2004).

As detailed in the previous chapter, an analysis of TFP is considered as
economic growth accounting. This conception is based on the pioneering work of
Solow (1956, 1957). TFP indices are used to measure the residual growth in
output not accounted for by the growth in inputs. That is, TFP growth rate is
defined as the rate of aggregate output growth minus the rate of aggregate input
growth.

Many researchers are reluctant to calculate and report PFPs, because of
the lack of credibility associated with them. However, an extensive literature
reveals that business executives, policy makers, and academic researchers find
trends in and levels of partial productivity of labor (PPL) of particular interest for
various reasons (e.g., Solow 1957; Daly and Rao 1985; Gordon 1987; Frank et

al. 1990; Ghebremichael et al. 1990; Ghebremichael and Nanang 2004). But, this

54

is misleading, because aggregate productivity cannot be attributed to a single
input, because production is a function of all inputs (Ghebremichael et al. 1990;
Ghebremichael and Nanang 2004). If, for example, high partial productivity of
energy (PPE) is observed, it can be due to either intensive use of labor, capital,
or Material.

In short, PFPi, partial factor productivity of input i, is a function of the

inputs that constitute the production technology, as specified below:
PFP-t = f(Kt,L,,Et,M,) (3.2)

Keeping in mind the above caveat, PFP of each of the four inputs and the
TFP are analyzed in this study. Analyses of both types of productivity are based
on the production technology specified in Eqn. (3.1). That is,

PFfit = *Q—t (3.3)
xit

where PFP“ = partial factor productivity of input i (= K, L, E, M); Q = aggregate
quantity of the three types of output specified for Eqn. (3.1); x), = quantity input i;
and the subscript t depicts a specific year during the study period.

In general terms, TFP is a measure of productivity of all inputs combined.

It can be defined as a ratio of aggregate output, Q, to aggregate input, Xt:
T FPt E — (3.4)

Depending on the structural characteristics of the production technology in
question, TFP has the following three types of quantitative measures

(Ghebremicahel et al 1990; Ghebremichael and Nanang 2004):

55

(1) In line with Solow’s (1957) conception, if the production technology is
characterized by constant returns to scale (CRTS), TFP is specified as a function

of the technological change index term only. That is,

TFP: = f (Tz) (3.5)

(2) If the technology is homothetic, but does not produce at CRTS, then TFP is a

function of both output and technological change”:

TFP=f(Qt,Tt) (3.6)

(3) While the above measures are used to assess a homothetic14 production
technology, TFP of a nonhomothetic technology is a function of all inputs and

technological progress, which is expected to be captured by T:
TF1"; =f(KtaLtaEtaMtht) (3.7)

Although there is no universally accepted interpretation of the quantitative
results of TFP, Chambers (1988) provides the following three interrelated
interpretations: (i) average product of an aggregate input, as expressed in Eqn.
(3.4); “(ii) a measure of the rate of technical change; and (iii) an index of input
effectiveness in producing output before and after technical change, that is, if
technical change makes the aggregate input more productive, the TFP index is

greater than 1; if the aggregate input becomes less productive TFP is less than

 

'3 A homothetic function Is a monotonic transformation of a homogeneous function. Hence, even
functions that do not necessarily exhibit CRTS, such as the Cobb-Douglas and the CES
functions, can have homothetic isoquant maps (Nicholson 2002).

4 A production functions whose isoquants are parallel radials of each other is called homothetic.
It is characterized by a constant marginal rate of technical substitution along any ray from the
origin. Consequently, input-price ratio does not change under this condition of production
equilibrium.

56

1; and in the absence of technical effects on the aggregate input, TFP is equal to
1” (Ghebremichael and Nanang 2004)..

Recall that the fundamental challenges in measuring, analyzing, and
interpreting TFP are explained in Chapter 2. One of the major challenges is
aggregation of various inputs and outputs accurately. For example, “one cannot
obtain a meaningful measure of all inputs by simply adding number of workers,
quantities or dollar values of fuels, Material, etc.” (Ghebremichael et al. 1990;
Ghebremichael and Nanang 2004). To overcome this difficulty, economists have
devised methods of aggregating various quantities measured in different units
into meaningful input and output indices. The procedure is discussed next.

3.2.2 The Multilateral Index Procedure

To evaluate methods and results of fourteen TFP studies conducted on
the US. agricultural sector, Trueblood and Ruttan (1995) categorized the
methods of those studies into three: index number, production function, and non-
parametric (e.g., data envelopment analysis). They concluded “that many
economists prefer the Divisia index”, because it is believed to be “theoretically
consistent with flexible production functions and avoids the problems associated
with estimating those functions” (Ghebremichael and Nanang 2004).

However, the Divisia index cannot be used for discrete (annual) data,
because it is based on the following three impracticable presumed conditions:
that a continuously twice-differentiable production function characterized by an
instantaneous growth process exists; that the production function is

homogeneous of degree one; and that each input is paid its marginal productivity

57

(Star and Hall 1976). Since economic data are observed in discrete time
quantities, some form of approximation is needed.

Christensen and Jorgensen (1969) derived a procedure known as the
multilateral index procedure, which is the Tomqvist discrete time approximation
to the Divisia index procedure. Caves et al. (1982a,b) refined the work of

Christensen and Jorgenson (1969) to the following formulation:

—’ 1%(5 Ellan (3)1233“ “(an Q)
=exp _ Rir+ Ri :_ __ Rrs+ Rt 3—
7”? 2i=1 2i=1
(3.8)
1 4 — ~ 1 4 — ~
-exp — 2 (SC/'1 +Sq)(lnXfl—XJ)_— 2 (SC/'5 SG)(lans_ 1)
2j=1 2j=1

where Q. - aggregate quantity of outputs, i = 1, 2, 3 [i.e., lumber, shakes and

l

shingles, and all of the industry’s tradable by—products), as described under Eqn.

(3.1); X; = aggregate quantity of the inputs, j = 1, 2, 3, 4 (Le, K, L, E, M]; SR,=
share of output i in total revenue over the entire sample; SC]. : share of input j in
total cost over the entire sample; §R,= an arithmetic mean value of the share of

output i in total revenue over the entire sample;SCj = an arithmetic mean value

~

of the share of input j in total cost over the entire sample; Q, = geometric (natural

~

logarithm) mean of output i over the entire sample; X j: geometric (natural

logarithm) mean of inputj over the entire sample. The subscripts s and tdepict

observations at the base and the current years, respectively.

58

According to the multilateral-translog-index formulation in Eqn. (3.8), TFP
can be defined as a residual of the revenue-share weighted aggregate output
quantity of the three outputs left after accounting for the cost-share weighted
aggregate quantity of the four inputs that are assumed to characterize the
production technology of the Canadian sawmilling industry. The exponential
values of the right hand of Eqn. (3.8) provide the weighted aggregate quantities
of inputs and outputs (Ghebremichael and Nanang 2004).

3.2.3 Decomposing TFP into its Main Sources

As discussed earlier, if the technology exhibits constant returns to scale,
TFP is considered only as a function of technological change over time, as
specified in Eqn. (3.5). That is, TFP growth can be equated to technological
progress. In the absence of constant returns scale, however, TFP reflects a
combination of scale and technological effects, because “it does not distinguish
between pure productivity gains (i.e., shifts in the underlying isoquants or isocosts)
and efficiency gains resulting from increases in the scale of operation”
(Ghebremichael and Nanang 2004). In other words, the production technology is
homothetic that is characterized by economies or diseconomies of scale that can
be expressed as in Eqn. (3.6).

In addition to scale effects, there are many other inputs that affect
productivity. They include quality of human capital (knowledge and skills of the
workforce), managerial efficiency, government regulations, and relationship
between labor and management. Because of these reasons, the commonly used

practice is to decompose growth of the gross TFP into scale effects and pure

59

technological change effects.

But, non-parametrically measured TFP can only be decomposed using
statistical (parametric) techniques. Caves et al. (1981) suggested the model
expressed in Eqn. (3.9), which appears misleadingly simple. It has been used in
several studies (e.g., Freeman et al. 1987; Ghebremichael et al. 1990;
Ghebremichael and Nanang 2004). It is a log-linear regression model for

decomposing TFP into output and technological progress effects:
lnTFR=a+flan,+I97:+g, (3.9)
Thus, Eqn. (3.9) states that logarithmic value of the aggregate output, Q,
and a time dependent technology variable, T, can explain growth in TFP, given the
error term, 8,. Obviously, both ,6 and Hare hypothesized to be positive in order to
validate the fact that growth in TFP is a function of output growth and technological
progress, respectively. In this formulation, 8 is interpreted as an elasticity of TFP

with respect to Q given that all other conditions remain unchanged. I9 is a
marginal effect of technology on TF P, ceteris paribus.

In addition, the following second-degree polynomial, Le, a quadratic
function in output, is believed to be statistically effective indicator of the marginal

effect of output on TFP:

TFP=a+fl1Qt+flZQt2+8t (3.10)

While 81 is expected to be positive, showing the direct relationship between output
and TFP, [32 would indicate the rate (acceleration) at which TFP rises/declines as

output rises/declines.

6O

Eoonometricians, such as Gujarati (2003), argue that such relatively simple
models are effective enough to shed light on important economic phenomena. A
sample of studies that used the log-linear approach to decompose gross TFP
include Freeman (1987); Ghebremichael et al. (1990); Gum and Yu (1998); and
Ghebremichael and Nanang (2004).

However, an elaborated econometric model is required to decompose TFP
into its major quantifiable sources. For this purpose, Denny et al. (1981) derived an
econometric formulation from a long-run-dual cost function. This is described in
Subsection 3.3.5, (Section 3.3), where the parametric method is explained.

3.2.4 Taxation Policy Instruments, Capital Formation, and TFP

On the importance of tax incentives and the relevant policy instruments,

the Canadian House of Commons’ Standing Committee on Industry (2000)

concluded as follows:

Canada’s imbalanced corporate tax structure has been identified as
contributing to poor investment rates and slow productivity growth in
certain key industries.

It is clear that taxation comprises policy instruments that affect the way in
which scarce economic resources are allocated in the public and private sectors.
For example, investment incentive taxes (e.g., enhanced rate of investment tax
credit, reduction of corporate income tax, and accelerated rate of capital cost
allowance), are expected to stimulate investments in R&D that encourages
invention, innovation, and diffusion of new technologies; and improvement in the
quality of human capital. Investments in these two major strategic areas of

economic growth coupled with private saving and government expenditures on

61

infrastructure can collectively boost the processes of capital formation“, which
raises TF P. That is, in the parlance of economic growth theory, tax incentives are
expected to stimulate savings, which in turn enhance capital accumulation and
formation, which determine productivity growth (Kaldor 1957).

In 2004, The Canadian Chamber of Commerce (CCC), in its policy
release, 2004 Policy Resolutions, Finance and Taxation, argued strongly that
Canada’s effective tax rates on capital, which incorporated income tax, capital
taxes, sales taxes on capital components and depreciation allowances that
directly affected capital investment, were well above those in the United States
and in a number of other countries, including the United Kingdom, France,
Sweden, and Ireland. The CCC emphasized that Canada’s high “effective tax
rates on capital particularly could impede capital formation, which is critical to
improving productivity and Canada’s standard of Iiving”.

The Institute for Competitiveness & Prosperity, an independent think-tank,
which was established in 2001 to serve as “the research arm” of Ontario’s Task
Force on Competitiveness, Productivity, and Economic Progress, in its 2006
annual report urged the three levels of government in Canada (federal,
provincial, and municipal) to cut taxes on capital investment significantly. The
Institute argued that reducing taxes on capital investment increases the rate of
return on capital and encourages investment in physical capital, such as
machinery, equipment, and software as well as in human capital. Its specific

recommendations include elimination of federal and provincial taxes on existing

 

'5 Capital formation means net addition to existing real capital stock, after the removal of
depreciation cost allowance.

62

business capital, because they are levied “even if the business is not profitable”;
and consequently, the Institute argued, the propensity of the private business
sector is dampened.

However, empirical studies (e.g, Barro 1990; King and Rebelo 1990;
Jorgenson and Yun 1990; Kneller et al. 1999; Quadrini 1999) caution that the
distributive role of taxation policy instruments in the demand side of the economy
should not be overlooked. In fact, Kneller et al. (1999), in their detailed empirical
study on “fiscal policy and growth” in the OECD, concluded that “distortionary
taxation reduces growth, whilst non-distortionary taxation does not; and that
productive government expenditure enhances growth, whilst non-productive
expenditure does not”. The authors treated income and property taxes as
“distortionary” and consumption (i.e., expenditure-based) taxes as “non-
distortionary”. They argued that the later do not reduce the retum on investment,
although they might affect the labor/leisure choice. Furthermore, in evaluating the
impacts of the Tax Reform Act of 1986 on US. economic growth, Jorgenson and
Yun (1990) concluded that the most promising avenue for tax reform was to
include income from household assets in the tax base, while reducing tax rates
on business income.

In any case, the focus of this study is the supply side of the Canadian
economy. It is understood that taxation policy instruments, such as capital cost
allowance (CCA)16, investment tax credit (ITC), and corporate income tax (CIT),

influence productivity performance and thereby competitiveness of the Canadian

 

16CCA means the actual cost of a depreciable capital asset, accounting for depreciation,
obsolescence, or depletion (Revenue Canada 2006): http://wwwcra-
arcqcca/E/pub/tp/it285r2/it285r2-e.html, accessed Oct. 25, 2006.

63

sawmilling industry. Depending on the way they are implemented, taxes have
either negative or positive impacts on capital formation, which is one of the
determinants of TFP. That is why public policy makers and the private business
sector often negotiate in search for possible optimal tax rates. For instance,
“accelerated depreciation allowance”, can be considered as interest-free loan to
firms with the goal of increasing capital accumulation in the economy (Mankiw
and Scarth 1995). It was in accordance with this macroeconomic theory’s line of
reasoning that the Forest Products Association of Canada (2006), in its
submission to The House of Commons Standing Committee on Finance during
the “2006 pre-budget consultations”, argued strongly for “accelerated” CCA. Its
argument was that Canada’s forest products industries needed to be helped in
order to maintain competitive positions in the global marketplace.

Therefore, given that this research covers a forty-year period, during
which several monetary and fiscal policy changes had occurred, assessing the
effects of changes in the key fiscal policy instruments on TFP is warranted.
Effects of changes in three important taxation policy instruments on capital
formation and on gross TFP performance of the industry are examined in this
study: increases in CCA and ITC and reduction in CIT.

3.3 THE PARAMETRIC METHOD: A NEOCLASSICAL COST FUNCTION
3.3.1 Specification
The following neoclassical, long-run-total cost function is dual to the

production function in Eqn. (3.1):

64

Ci=gz(QnWKtaWLnWEzaW/14'T) (3-11)

t’ t
where C = long-run cost; W" = price of input i (= K, L, E, M); T = trend variable
whose role is as described in Eqn. (3.1); and the subscript t depicts a specific
year during the study period.

Eqn. (3.12) is based on the assumption that solving a general optimization
problem is feasible. That is, given the exogenously determined output level, Q,
and input prices WK, WL, W5, and WM” firms in the sawmilling industry choose
optimal combination of K, L, E, and M that would minimize total cost of

production: C = WKK +WLL+WEE+WMM , subject to the technological
constraint: Q = f (K,,L,, E), ,M,;T,). That is, duality theory posits that, subject

to given constraint conditions there exists a dual cost function corresponding to
the primal production function in Eqn. (3.1).
Key Assumptions: Existence of the following four basic conditions are
assumed: (i) competitive markets for both inputs and outputs where cost
minimizing firms are price takers; (ii) constant returns to scale implying that
equiproportional change in all inputs would lead to equiproportional change in
total cost, which establishes the condition where the share of an input in total
cost is equal to its price elasticity; (iii) adjustments for least-cost combination of
all inputs are feasible, i.e., solution to the general optimization problem is feasible
; and (iv) technical efficiency exists in the industry.

Moreover, to meet the theoretically required conditions, the cost function
in Eqn. (3.11) is expected to be characterized by positive and non-decreasing in

the vectors of output level and input prices; positively and linearly homogenous

65

as well as concave and continuous in input prices; and twice-continuously

differentiable with respect to input prices.

3.3.2 Production versus Cost Function Estimation

Generally, it can be argued that either the production function in Eqn. (3.1)
or the cost function in Eqn. (3.11) can be estimated to investigate the
technological attributes of the Canadian sawmilling industry. However,

Binswanger (1974a), Christensen and Greene (1976), and many other

researchers argue that cost function estimation is more effective, because it has

several advantages over production estimation that include the following:

- The serious problem of multicollinearity among input quantities that arise in
estimating a production function does not exist among input prices.

- It is most likely that government policy measures regarding timber harvesting,
such as the annual allowable harvest rate restrictions imposed by the
provinces, would lead to situations where exogenous forces determine output
levels.

- Since firms in the sawmilling industry compete with other firms in the
economy for the same inputs, output levels and input prices are exogenously
determined.

- Recent developments in duality theory have enhanced the appeal of the cost
function estimation approach.

. Functional forms that meet theoretical requirements for estimating cost
functions have been developed and verified over the years. In addition to their

ability to represent very general production functions, even though they

66

cannot be derived from explicit production functions, such functional forms
enable the researcher to compute various parameters that characterize a
given production technology, such as derived demand for inputs, substitution
elasticities between given pairs of inputs, own- and cross-price elasticities ,
and economies of scale.

3.3.3 Functional Form

Estimation of a cost function requires selection of an appropriate
functional form that is sufficiently flexible to accommodate the various properties
of a production technology. The literature shows there are several flexible
functional forms that include the generalized Leontief (GL), the transcendental
logarithmic (TL), the generalized Cobb-Douglas (GCD), and the generalized
square root quadratic (GSRQ). According to Caves and Christensen (1980) it is
not clear how the practitioner can choose among these forms. Among the
required properties, a functional form should not impose a priori restrictions on
input substitution possibilities and on variations in economies of scale.

Guilkey et al. (1983) concurred with the conclusions of Christensen et al.
(1973) that the “TL form provides a dependable approximation to reality provided
that reality is not too complex”. Specifically, the TL form places no a priori
restrictions on substitution possibilities among all the factors of production; and it
allows scale economies to vary with level of output (Christensen and Greene
1976)

Moreover, as highlighted in Section 1.3, its extensive application indicates

that the TL form has become a standard tool of researchers (e.g., Christensen

67

and Greene 1976; Nautiyal and Singh 1983; Nautiyal and Singh 1985; Martinello
1985; Frank et al. 1990; Kant and Nautiyal 1997; Baardsen 2000). The TL used
in this research takes the following form of the long-run cost function specified in

Eqn. (3.11):

lnC =a0+7Q(an)+Z,B,.ln( W.)+ iip,(1W,)(1nW)

i=1

Nlr—

+iyig (an,)(an)+?lz-yQQ (an)2 (3-12)
+4T+§anr2+£4.(1nm)(r)+eg.(lng)(r>

where £1.36,” by symmetry for i, j (= K, L, E, M); n = 4, the number of inputs;

and all the terms containing T imply technological effects. Notice, the subscript, t,
which depicts a specific year during the study period, is not included in Eqn.
(3.12) for brevity.

In order to correspond to a well-behaved production function, a cost function
must be homogeneous of degree one in input prices. That is, for a fixed level of
output, total cost must increase equiproportionally for equiproportional increase

in all input prices. This means that the following restrictions must be met:

Zfli =1 (3.13)

i

ZViQ :0 (3.14)
i

(3.15)

2 ’61]: Z 1817:2917": 0
i=1 j=1

68

No restrictions are imposed with respect to the substitution possibilities
between pairs of inputs; the extent of economies of scale; the degree of
homotheticity; and the particular form of technological change.

In accordance with microeconomic theory, it is hypothesized that for global
concavity of the cost function own-price elasticities of substitution,0'ii, ought to

be negative at all points (Bemdt and Watkins 1981). No restrictions need to be

imposed on the cross-price elasticities of substitution, 00', because they can be

either positive, suggesting substitutability, or negative, suggesting
complementarity.

A homothetic production structure is further restricted to be homogeneous,
if and only if, the elasticity of cost with respect to output is constant. For the TL
cost function, therefore, homotheticity and homogeneity restrictions are imposed

as follows:

homotheticity: 71g = O (3.16)

where i = K, L, E, M.

The particular restriction in Eqn. (3.16) implies that a homothetic cost function
could be written as a separable function of output and input prices (Pindyck

1979)

For homogeneity, the following restrictions need to be imposed:

7QQ =71Q :0 (3.17)
In addition, elasticities of substitution must be restricted to unity by eliminating

the second-order and cross-partial terms in the input prices in Eqn. (3.12):

69

18H = 16,-)- = 0 (3.18)

3.3.4 Derived Demand Functions for Inputs
One of the important features of the cost function estimation approach is
that the derived demand functions for inputs can easily be obtained using
Shephard’s lemma, which uses the envelope theorem. That is,

61nC(.)= 8C Ki- W,X,. :
alnw, 8W, C C

=fl.+7,-Q(1nQ)+Z:3,/3a(ani)+giTT

 

SCI
(3.19)

aC(-)
6W.

 

where x, = , and Si stand for an input i quantity and a share in total cost

of an input i (= K, L, E, M), respectively.
From Eqn. (3.19), a system of four cost share equations, each of which
represents cost minimizing-optimal derived demand for a given input, can be

formulated as follows:

Sc. =13. +7.8 (InQ)+/3.,.(1n Winnaan W,)+flKE(ln W.)+fl...(1nm,)+6,.fl (3.20)

S... = 13. +1.9 (InQ)+fl..(ln W.)+ri,,,.(1n WK)+/3.E(In W.)+fl...<1nWM)+0.TT (321)

S = fl. +7.8 (1n Q)+fl..<1n WEN/3.. (In Wow... (111%)ng (1n WM)+6..T (3.22)

S... =4, +7.49(InQ)+fl,....,(1n%)+flM,.anWK>+4m<1niVn+flME<1nw+awT (323
Hence, the optimal demand function for input i (= K, L, E, and M), is a

function of all input prices, level of output, and disembodied technology. Notice

that the system of four equations: (3.20) to (3.23) represents the standard

70

conditional factor" demand functions for K, L, E, and M, respectively. That is, the
demand for anyone of the inputs depends on the level of output, prices of all
inputs that are involved in the production process, and the prevailing technology.
Then, under the above-imposed restrictions, the unrestricted TL model in Eqn.
(3.12) and the four restricted models, i.e., the four share equations (3.20) to
(3.23), which are nested in the unrestricted TL model, form a system of five
equations”. Furthermore, it should be noted that each of the input demand
functions in equations (3.20) to (3.23) possesses important economic
interpretations.

Again, application of Shephard’s lemma simplifies interpretation of the
input demand functions. Shephard’s lemma states that the partial derivative of
the long-run-dual cost function with respect to a given input’s price gives the

quantity of that input. That is, from Eqn. (3.11):

 

6 ,W W ,W ,W ;T
x, = g(Q K’ L E M ),i=K,L,E,M (3.24)
5W.-

Hence, as was pointed out earlier, Eqn. (3.24) shows that the cost-
minimizing optimal derived demand for the ith input is a function of all factors that
characterize the dual-long-run cost function: the prevailing structure
(coordination) of the production technology, the level of output, the prices of all

inputs, and the state of technology depicted by T. Then, an important question

arises: What are the economic and technological effects of changes in optimal

 

‘7 Following the convention of microeconomic theory, the terms factor and Input are used here
interchangeably to refer to any means of production (e.g., labor and capital).
18 The system estimation technique is described in Subsection 3.3.7.

71

demand functions for inputs in response to changes in the exogenously
determined output and input prices?

The sensitivity of the derived demand for input x; to a change in the price
of x,- is measured by the cross-price elasticity of demand, Sir" derived from the
relevant demand equation i.e., from the share equations in (3.19) to (3.22):

alnx,
8,, =
‘1 aanj

 

(3.25)

where output quantity and prices of all other inputs, Wj, (i i j) are fixed. Thus, a

cross-price elasticity measures the percentage change in the cost minimizing
demand for x, in response to the price of input x,-, when gross output, Q, and all
other input prices are held fixed. This takes effect after all input quantities are

allowed to adjust to their new cost minimizing levels (Bemdt and Watkins 1981).
Since 81-]- ¢ Ejl', positive 81-]: implies inputs x,- and x,- are substitutes; negative
81-]- implies they are complements; and 81",“ = 0 reveals xi and x; are

independent. The necessary condition for concavity curvature of the production

function is met when all own-price elasticities, gii’ are negative”.

 

'9 For more details, refer Bemdt and Watkins (1981 ).

72

3.3.5 Nature and Estimates of Technological Progress
A. Perspectives on Technological Progress: an Overview

Neoclassical economic theory classifies the effects of technological
progress into two categories: embodied and disembodied. Embodied
technological change is realized through improved quality of inputs (e.g.,
knowledge and skills of the workforce). In other words, long-run endogenous
economic growth is driven by technological progress realized through - among
other things - R&D efforts of profit-maximizing economic agents (e.g., firms within
the Canadian sawmilling industry). This implies that government subsidies to
R&D and other incentives, such as increased investment tax credit, can stimulate
long-run economic growth. However, Jones (1995) cautions that technological
change that spurs long-run economic growth should be explained by parameters
of both endogenous (e.g., R&D) and exogenous (e.g., population) forces. The
advent of word processor computer technology is a good example of embodied
technological progress (Betts 1998).

By contrast, technological change that results in an inward shift of
isoquant contours of a given production function over time, with no changes in all
inputs, is called disembodied technological change. In other words, more output
can be produced without any change in inputs. Disembodied technological
change is generally attributed to technical change, which means improvements in
production techniques and/or organizational behavior that enhance productivity
of existing inputs. Thus, technological progress is disembodied, if existing

machinery and equipment or the whole range of productive capital stock can be

73

made more efficient by implementing new knowledge. For example, a new
version of software, once installed on an existing computer, can increase the
computer’s efficiency without any need for new computer and related equipment.

Learning-by-doing, which means that an industry learns better ways of
doing things 11‘because of knowledge accumulated through experience, is
considered as disembodied technological progress. This is because new capital
equipment is not required. Such technical progress is a result of a series of
incremental improvements discovered by workers and mangers on the
production line.

Thus, innovative production techniques that do not require new capital
equipment characterize a disembodied technological progress. It is disembodied
in that it is assumed to spread itself quickly evenly across all plant and equipment
of firms operating in an industry (Betts 1998). This is particularly believed to be
the case if the innovation is developed in-house, so that there are no royalties
paid to an outside inventor. In effect, unpatented technical progress becomes
general knowledge quickly and firms adopt the idea at little or no cost.

B. Estimating Disembodied Technological Progress

Given the justifications for incorporating a time trend variable, T, into
equations (3.1) and (3.11) to capture technological change, differentiating Eqn
(3.12) with respect to T yields the dual measure of TFP (Bemdt and Watkins
1981). That is,

-alnc(.)
6T

 

EECT 2—[9T +677T+§6fl1nWi +6QTan] (3.26)

74

Technological progress is defined here as rate of total cost
diminution,8CT, over time, ceteris paribus. A negative sign is attached to the

partial derivative equation to ensure that a positive value of technological
progress is achieved in a situation where production cost is falling

(Bhattacharyya et al. 1997).
The right hand side components of Eqn. (3.26) reveal that SCT comprises

the following three components (Baltagi and Griffin 1988; Bhattacharyya et al.
1997)

0) Pure technological change (PTC) =

—(6T + 9TTT) (3.27)

(ii) Nonneutral, factor-augmenting technological change (NTC) =

n
— 2977111”? (3.28)
i=1

(iii) Scale-augmenting technological change (STC) =

—-(6IQT 1n Q) (3.29)

PTC represents effects of knowledge advancement, i.e., a disembodied
technological change. Note that, since time is considered as an indicator of
knowledge, PTC is measured only by the terms containing T, whose coefficients
are expected to capture marginal effects of disembodied technological change

[Eqn. (3.27)].

75

NTC is an estimate of the effects of changes in input prices as well as
subsequent input substitutions on cost diminution, which are believed to be
effects of embodied technological change [Eqn. (3.28)]. Observe that NTC is
captured by the sum of the product of time and input price interaction parameters
and the logarithmic value of the input prices.

Finally, STC represents part of the reduction in production cost attributable
to increase in output realized through exploitation of scale economies [Eqn.
(3.29)].

C. Hicks Neutral versus Biased Technological Change

The nature of technological change-bias has important implications. For
example, the impact of new technology on employment and wages depends
crucially on whether the innovation is Hicks neutral or biased. Consider, for
example, a small-scale sawmill which uses capital (K) and labor (L) to produce a
planned (optimal) amount of lumber, 0', per year. A Hicks neutral technology is
one that increases productivity of both K and L proportionately. That is, the
isoquant moves toward the origin along the expansion path to produce Q. at a

possible least-cost combination of K and L without changing the marginal rate of
technical substitution of labor for capital. (MRT S L K ). Consequently the ratio of
the price of labor to that of capital remains unchanged. That is, the ratio of wage
rate to that of rental price of capital and the MRT S M remain constant along the

expansion path, the locus of tangencies of isoquants and isocosts.
What is the tradeoff between technological progress and employment? “Is

it inevitable that Hicks neutral technological progress will lead to layoff of

76

workers? The answer is “no”” (Betts 1998). After the sawmill has adopted the
technology, it is very likely that its output will rise and it will be able to sell more of
it at a competitively lower price, passing on the cost savings to consumers, who
are willing to buy more of the lumber. This will be the case even if all firms in the
sawmilling industry adopt the new technology. Alternatively, Betts (1998) argues
that even if only one of the firms adopts the cost-saving new technology, the
likelihood is greater that employment at the innovative firm will rise, because the
cost reductions will cause demand for the lumber output to rise, leading to a
possible increase in employment.

By contrast, a technological change is said to be “Hicks-biased”, if, holding
input prices constant, it changes the ratio of one input used to that of another
input. For example, If the K to L ratio rose after technological progress, this would
mean a “labor-saving” technological change. Thus, it is likely that this type of
technological change will lead to involuntary unemployment, ceteris paribus. In a
sense anybody who would like to work, even at a lower wage that maintains the
original (optimal) ratio of labor price to that of capital cannot find a job (Betts
1998)

As specified, the TL cost function in Eqn. (3.12) does not constrain the
technology to be either Hicks neutral or constant returns to scale. Thus, Hicks
neutral technological change specification will require the restriction that all the
interaction terms of the input prices with the time variable, T, be eliminated from

Eqn. (3.12). As it stands, therefore, Eqn. (3.12) represents non-neutral

77

technological change. That is, a biased technological change is feasible. This
condition meets one of the requirements for empirical purposes.

The technology is Hicks neutral, if 6?,7.=0 in Eqn (3.26). For no

technological change, all parameters on the right hand side of Eqn (3.26) should
be equal to zero. On the other hand, a rejection of Hicks-neutrality of
technological change suggests biased technological change, which means that
the technology is such that it saves more on some inputs than on others.
Binswanger (1974b) derives the following formula for estimating bias in

utilization rate of a given input:

 

B 285,, 1
.- 6T Sc- (3.30)

where B) is the bias, T is technological change variable, as described earlier, and
SC,- is the share of input i in total cost. For the TL cost function in Eqn. (3.12), the

rate of bias can be estimated easily from the following equation (Bhattacharyya

etaL1997)
6.
B,- 2 ET— (3.31)

CI
The meanings of the measure of bias are as follows: B,- > 0 implies input i-

using; 8; < 0 implies input i-saving; and B,- = 0 implies Hicks neutral.

D. TFP Growth, Cost Elasticity, Returns to Scale, and Scale Economies
Given estimates of the parameters of the system of equations (3.12) and

three of the four share equations (3.20) through (3.23), gross TFP growth can be

78

decomposed into its parametric sources. Recall from the discussions in Chapter 2
that the index approach to the measurement and analysis TFP growth analysis,
which is fundamentally based on Solow’s (1957) pioneering work, is based on
several restrictive assumptions, such as constant returns to scale; marginal cost
pricing; and perfectly competitive markets for both inputs and outputs. If these
assumptions are violated, the residual TFP growth is a result of the effects of
several factors that include (i) non-constant returns to scale, (ii) market
imperfections, (iii) economies of scale, (iv) input substitution, (v) product mix, (vi)
R&D; (vii) human capital; and (viii) managerial efficiency.

Thus, in order to decompose the gross TFP into its main sources, structural
information about the production technology is needed. This information can be
obtained by estimating a cost function, which provides separate effects of scale
economies and technical change. To accomplish this, Denny et al. (1981) derived
the formulation in Eqn. (3.32) from a translog functional form of a dual-long-run
cost function. This formulation provides several useful parametric measures that

characterize the production technology:

 

TF P growth

'1_ alnc(.) dan _ alnc(.)
(3an dT ET

I—
.—

= 1—(79 +2719 an7 +7QanQ+69TTHQ

—

 

{6, +6.,.,T+ £30,, 1118/, +69, mg) (3'32)
i=1

:(1_8CQ)Q—8CT

where ECQ = elasticity of total cost with respect to the aggregate output;

79

8C, = the dual measure of the primal TFP growth rate due to disembodied

technical progress is a measure of the rate of total cost diminution with input
prices and output quantity fixed. That is, in the context of a cost function, TFP is
equivalent to cost diminution, the percentage reduction in total cost resulting from
technological progress and organizational improvements under given output
quantity and input prices (Bemdt and Watkins 1981 ).

Eqn. (3.32) contains two important components on which TFP growth

depends: the first term which represents the scale effect is a function of ECQ and

the growth rate of the aggregate output, Q, and the second component, ECT, is

the dual measure of the primal TFP growth, which is total cost diminution
parameter (Bemdt and Watkins 1981).

One important condition is implicit in Eqn. (3.32): the formulation is based
on the assumption that the Canadian sawmilling industry departs from the
condition of constant returns to scale and perfect competition in input and output
markets. This departure relaxes the condition that restricts TFP growth to be

explained only by technological change. If this assumption was violated and the

production technology exhibits constant returns to scale, then 8C9: 1.

Consequently, the whole scale effect disappears, leaving only am. This outcome

makes the primal and the dual measures of TFP equivalent (Bemdt 1991).

Another well-known and useful economic parameter, retums to scale

(RTS), can be derived easily from SCQ. This is possible, because the TL

formulation of the total cost function given in Eqn. (3.12) is a nonhomothetic, which

80

research community uses it in analyzing industrial technologies also (e.g., Bemdt
and Watkins 1981; Nautiyal and Singh 1985; Freeman et al. 1987; Kant and
Nautiyal 1997).

Economies of scale (ES) are other measures that characterize a production
technology. Again, although they are more applicable at a firm (plant) level, the
literature shows they are widely used for gaining additional characteristics of
industrial production technologies (e.g., Daly and Rao 1985; Nautiyal and Singh
1985; Banskota et al. 1985; Singh and Nautiyal 1986; Baltagi and Griffin 1988; and
Bhattacharyya et al. 1997).

In the context of estimating a cost function, Christensen and Greene (1976)
state that it is appropriate to express ES in terms of the relationship between total
cost and output along the expansion path, where input prices are constant and
costs are minimized at every output level. That is, the natural way to express the
extent of ES is that as the proportional increase in cost resulting from a

proportional increase in the level of output, i.e., the elasticity of total cost with

respect to output. Thus, ES can be expressed as one minus ECQ. That is,

6111 .
ES=1———£(—)
aan
=1—[yQ +yQQ +éyinnWij (3-35)
=1-8CQ

where ES > 0 implies economies of scale; ES < 0 implies diseconomies of

scale; and ES 2 0 implies constant returns to scale, i.e.,.e‘cQ =1.

82

3.3.6 Substitution and Price Elasticities of Inputs
A. Economic Implications of Substitution Elasticities

The degree of substitutability among productive factors (i.e., all means of
production) has far reaching economic implications. Clearly, the whole spectrum
of the literature on production economics reveals that the main purpose of the
concept of production function is to describe the substitution possibilities among
the inputs so that a given output level can be produced efficiently. With
justifications for importance of the degree of technical substitutability of
productive inputs, Sato (1977) demonstrates and provides “a more general and
more meaningful class of CES production functions, i.e., non-homothetic CES
functions”.

Historically, Blackorby and Russell (1989) attribute the origin of input
substitution elasticities to John R. Hicks (1932) who introduced it “for the purpose
of analyzing changes in the income shares of labor and capital in a growing
economy”. Pessoa et al. (2005) elaborate that their interest in estimating
elasticity of substitution between capital and labor stemmed from the fact that it
determines the quantitative effect that investment distortions have on per-capita
income. It is instructive to observe that these authors explore the correlation
between per-capita income and TFP under a variety of substitution elasticities
between capital and labor.

Arrow et al. (1961), in their classic paper, Capital-Labor Substitution and
Economic Efficiency, demonstrate the importance of input substitution elasticities

in a wide economic sphere, which includes the following five areas: the pure

83

theory of production, the functional distribution of income, technological progress,
international differences in efficiency, and the sources of comparative advantage.

The authors particularly reiterated the “fundamental economic significance
of the degree of substitutability of labor and capital”. It was in this classic paper
that Arrow et al. (1961) discovered the celebrated Constant Elasticity of

Substitution (CES) production function. Their research question was, “For what

functional form would 0'9. be constant but not be constrained to equal unity?”

They also disentangled the theory of production economics from the Cobb-
Douglas unitary-constant elasticity trap and concluded, “Our empirical results
imply that elasticities of substitution tend to be less than one, which contrasts
strongly with the Cobb-Douglas view of the world.”

In summary, a measure of the degree of input substitution has very
important economic policy implications. But, it appears there is no a universally
accepted measurement and analysis methodology. The following remarks show
why there is fuzziness regarding which of two measures of input substitution
elasticity is more credible than the other: the Allen partial elasticity of substitution
(AES) or the Morishima partial elasticity of substitution (MES)?

B. Which Measure of Elasticity?

The AES, credited to Allen (1938) and the MES credited to Morishima
(1967) are widely used measures. Yet, neither of them is universally accepted as
a best measure. For example, Blackorby and Russell (1989), have strong
objections regarding the credibility of AES. These authors, with some

mathematical demonstration, argue that the AES is not a measure of the “ease”

84

of input substitution or curvature of the isoquant; provides no information about
relative factor shares, the purpose for which the elasticity of substitution was
originally defined; and cannot be interpreted as a (logarithmic) derivative of a
quantity ratio with respect to a price (or the marginal rate of substitution). They

further make the following assertion:

As a quantitative measure, it has no meaning; as a qualitative measure, it adds
no information to that constrained in the (constant output) cross-price elasticity.
In short, the AES is (incrementally) completely uninformative.

However, the literature shows extensive use of AES more than MES,
establishing its credibility. Many highly regarded researchers calculate and report
AES, not MES (e.g., Parks 1971; Berndt and Wood 1975; Pindyck 1979; Nautiyal
and Singh 1985; Meil and Nautiyal 1988; Kant and Nautiyal 1997). Moreover,
AES estimates are necessary for calculating own- and cross-price elasticities,
which in turn are used for calculating the MES, as the formulas in equations
(3.37) and (3.38) show.

C. Approaches to Computing AES and MES

A

For the TL cost function, the AES (0'.

U. ) is calculated from the following

 

 

formulae:
0; = fig LEGS”

C" 0' (3.36)
i,j= K,L,E,M i¢ j;
and the own-utilization elasticity of a factor:

-+S?—S_ ,
0': = )6" SC; Cl 1: K,L,E,M (3.37)
Ct

85

Blackorby and Russell (1989) concluded that the MES preserves the
important features of the Hicksian concept in the multi-input setting; and is
sufficient for assessing effects of changes in price or quantity ratios on relative
input shares. An MES is calculated as the difference between the cross-price and

the own-price elasticities of derived demand for a given input:

M _ M _
0-,]- — 81'; _ 8i,“ and O-j)‘ — 8,] _ 8].]. (3.38)
where
8.. = S of” and 8.. = Sof’ (3 39)
r} j y u r u '

where 8]., and 8,, are the cross-price and own-price elasticities of demand for an

input, respectively.
3.3.7 Estimation Techniques

It is feasible to estimate the parameters of the TL total-cost function in
Eqn. (3.12) and each of the cost share equations. (3.20) to (3.23), using ordinary
least squares (OLS) equation by equation. However, the OLS estimates of each
equation will risk the problem of multicollinearity; and restrictions on cross-
equation parameters must be imposed. In other words, since many of the
coefficients in the unrestricted TL form long-run cost function and those in each
of the share equations are the same, it is imperative that all these equations be
estimated as a system simultaneously. This should be done not only to attain

higher effectiveness of the models through minimized determinants of the cross-

products’ matrix, but also to obtain the estimates of a0,9r,6TT,yQ and yQQ, which

all appear only in the unrestricted TL form long-run cost function in Eqn. (3.12).

86

Because they are derived from partial differentiation of the long-run TL
cost function in Eqn. (3.12, the cost share equations are not constrained by
stochastic terms of their own. Moreover, following Zellner (1962), it is assumed
that the disturbance terms have a joint normal distribution; and the four cost
shares sum to unity at each observation, leading the disturbance terms to add up
to zero at each observation. It should be expected also that the disturbance term
in the unrestricted TL total cost function in Eqn. (3.12) to be correlated with the
random errors of the share equations, which are nested in it.

Thus, to ensure maximum efficiency, estimating the unrestricted TL total
cost function and three of the four input cost share equations as a multivariate
regression system, applying the maximum likelihood estimation (MLE) method is
the optimal approach. Note that MLE applied to a multi-equation system, such as
a system of Eqn. (3.12) and three of the four share equations (3.20) to (3.23),
chooses the set of parameters by minimizing the determinant of the residual

cross-products’ matrix (Bemdt 1991). That is, MLE minimizes the
determinantle'el .

Zellner’s seemingly unrelated estimator, abbreviated as ZEF, also called
in the literature as seemingly unrelated regression estimator (SURE) or the
minimum chi-square estimator (Bemdt 1991), is considered an efficient
procedure. This is particularly the case if the iterative Zellner-efficient estimator,
typically termed as IZEF is used under the assumption of no hetroskedasticity or

autocorrelation within equations (Pindyck 1979; Bemdt 1991).

87

Virtually all econometric computer programs, such as SAS, Stata, Limdep,
SHZAM, and Microfit, which are capable of estimating parameters in systems of
equations by MLE generate the value of the maximized log-likelihood function.
SHAZAM©, the widely used econometrics software (White 2003)20 is used for this
research. It is capable of estimating a system of linear equations with linear
restrictions imposed on the coefficients within and/or across equations. The
software handles easily many types of system of linear equations, such as IZEF
and I3SLS. The estimation is iterated until the parameters converge or until the
maximum number of iterations specified (White 2003).

Any one of the four share equations from (3.20) to (3.23) can be dropped
arbitrarily from the system to avoid singularity of the contemporaneous variance-
covariance matrix. Accordingly, Eqn. (3.23) was excluded from the estimation
procedure. Results obtained using this procedure are invariant to which equation
is dropped from the system of the cost share equations. As Zellner (1962) notes,
it is assumed that the error term in each equation is homoscedastic and non-
autocorrelated. In short, this procedure has become a standard for this type of
study (e. g., Christensen and Greene 1976; Meil and Nautiyal 1988; Frank et al.
1990; Kant and Nautiyal 1997; Baardsen 2000). Moreover, the procedure
provides additional degrees of freedom, without adding any unrestricted
regression coefficients.

Restrictions based on economic theory that are imposed on the long-run

TL cost function are detailed in Subsection 3.3.3. Accordingly, six models are

 

2° Copyright © 2003 by Ken J. White, the University of British Columbia, Version 9, Professional
Edition, was used in this study.

88

tested for capability to describe the Canadian sawmilling industry’s production
technology. Model I is the unrestricted long-run TL cost function in Eqn. (3.12).
The test models are Model II for Hicks-neutrality of technological change; Model
”I for presence of technological change; Model IV for homotheticity; Model V for
homogeneity; and Model VI for unitary elasticity.

Each of the six models in the multivariate regression system was
estimated simultaneously, using the IZEF procedure. Finally, the likelihood ratio
test approach was used to test the various theoretical restrictions. Likelihood
ratio test is a more general method that does not utilize least squares and does
not rely on the normality of the error term (Pindyck and Rubinfeld 1998).
However, the likelihood ratio test procedure summarized in Eqn. (3.40) was

applied assuming that the error term is distributed normally. The procedure is

based on the notion that, for large sample size, the test statistic,3., follows the
chi-square, )8, distribution.

8 = 2(ULLF - RLLF) ~ 1,}, (3.40)21

where ULLF and RLLF are the maximized values of the unrestricted and the
restricted log-likelihood functions, respectively, while m, the subscript of x2,

indicates the number of the imposed restrictions, which are used as degrees of
freedom. Multiplying the parenthesized value in Eqn. (3.40) by two approximates

the LR to chi-square distribution (Wooldridge 2006). The testing procedure

 

21This formulation is expressed in different ways in the literature. For example,
—2[L (,BR) — L(,BUR )] ~ 1,3,; ( Pindyck and Rubinfeld 1998) and —2(1n L0 —- In LI ) ~ 1:, (Berndt
1991)

89

involves a simple comparison of the calculated value of 12 with its critical

value, I: , at a 5% level of significance. That is, if it is greater than 222’ then, the

null should rejected.

It is understood that the traditional F-test and the likelihood ratio test
should generate similar results for linear models involving large sample sizes.
But, although it may be difficult to apply, depending on the type of software being
used, the likelihood ratio test is more appealing because “it does not require an

assumption of normality” (Pindyck and Rubinfeld 1998).

90

CHAPTER 4 THE DATA

Covering a forty-year period (1961-2000), the database includes multiple
data sets, each of which comprising several variables. The output and input
variables, including implicit derivations of some of the required variables, as well
as all sources, are summarized in this chapter. Descriptions and sources of the
output and input variables are detailed in Table A1 and Table A2 (Appendix A),
respectively.

4.1 INDUSTRIAL OUTPUTS

For the purpose of this study, the sawmilling industry is Sector 251 of the
1980 Standard Industrial Classification (SlC-E-251), which includes plants
primarily engaged in manufacturing lumber, both rough and dressed, and other
sawmill and/or planing mill products (Statistics Canada 2005)”. That is, the
study covers the Shingle and Shake Industry (SIC-E-2511) and the Sawmill and
Planing Mill Products Industry (SlC—E-2512).

Accordingly, the industry is treated as a multi-output industry: lumber (Qt),
shakes and shingles (Q2), and an aggregate of all the sawmilling operations’
byproducts (03). Byproducts include wood chips, veneer cores, slabs, edgings,
sawdust, and shavings.

Lumber (SIC-E-2512): The annual series of output (Q1) were collected from
Table l-4 of Selected Forestry Statistics Canada, The Canadian Forest Service
(2006a). The quantities and values of shipments that were used to the derive

implicit annual price series were collected from the Canadian Forest Service

 

22 httgflwww.statcan.ca/englislt/Subjcots/StandardisicfsiceSO-classe.htm#25l , accessed August, 2006.

91

(2001), Table I6 of Selected Forestry Statistics Canada Special Edition —
Historical Series and from Statistics Canada Catalogue No. 35-204 and 35-250.
A series of IPPI (1992 = 100) for the Wood Industries Group (SIC-25-E)
was collected from The Canadian Forest Service (2001), Selected Forestry
Statistics Canada Special Edition — Historical Series, Table V-1 for 1961-99 and
from Statistics Canada Catalogue No. 62-011 for year 2000. These indices were
used to convert the current dollar prices into real dollar prices.
Shakes and Shingles (SIC-E-2511): The annual series of value added in
production activities were collected from Selected Forestry Statistics Canada,
Information Reports: E-X-34 (1984), E-X-48 (1995), and Statistics Canada
Catalogue No. 35-204, 35-250, and 31-203 for 1961-69. Industrial product price
indices (IPPI) (1992 = 100) for these products (SlC-E-2511) were collected from
The Canadian Forest Service (2001), Selected Forestry Statistics Canada
Special Edition — Historical Series, Table V-1 for 1961-99 and Statistics Canada
Catalogue No. 62-011 for year 2000. The commonly used implicit quantity
derivation procedure (e.g., Christensen et al. 1980; Bemdt and Watkins 1981;
and Christensen and Cummings 1981) was used to obtain output quantity (02)
by dividing value added by real price.
Wood Residues: An annual series of quantities (03) of wood residues sold to
pulp mills and their current dollar prices were collected from Manning (1972) for
the period of 1961-68; and from The Canadian Forest Service (2001), Selected
Forestry Statistics Canada Special Edition — Historical Series, Table I-3 for the

period of 1970-99. The quantity and price values for 1969 were determined from

92

the average values of 1968 and 1970; and the single data point for 2000 was
estimated based on the forty-year historical series. The IPPI (1992 = 100) series,
which are described above, under lumber, were used to deflate the current dollar
price series.
4.2 INDUSTRIAL INPUTS
A. Capital
Stock and Implicit Price by Asset Type: Statistics Canada (2001) classifies
the stock of capital input in the sawmilling industry into three major asset
categories: building construction (e.g., plants and offices), engineering
construction (e.g., roads, dams, and bridges), and machinery and equipment.
For three data points (1998-2000), there was a problem in acquiring capital data,
because of the incompatibility between the Standard Industrial Classification of
1980 (SIC-E 1980) and the North American Industrial Classification System
(NAICS), which came into effect in 1998. Experts at the Investment and Capital
Stock Section of Statistics Canada (2006) 23 advised that the annual expenditure
totals on each of the three assets, which were reported in NAICS 3211: Sawmills
and 3219: Wood Preservation, were equivalent to the expenditures in SIC-251 of
1980.

The experts advised further that the current and constant dollar values by
type of asset in NAICS 321114 (SIC 2591): Wood Preservation and in NAICS
321911 (SIC 2543): Wood Window and Door Manufacturing were included in the

NAICS 3211 and NAICS 3219 totals. However, the experts recommended that,

\

23 Personal communications with Richard Landry, Chief, Capital Stock Section, and Mychele
Gagnon, Senior Economist, Statistics Canada.

93

accounting for only within the range of 1% and 2% of the total capital stock value,
these components were insignificant. Accordingly, the total expenditures (sum of
NAICS 3211 and NAICS 3219) on the three capital assets were obtained from
Statistics Canada in current and constant dollars.

Following the commonly used procedure, current dollar expenditures were
then divided by the constant dollar expenditures to yield prices for each asset
type. These prices were required for computing the rental price for each asset.
Rental Price of Capital: The perpetual inventory method, pioneered by
Christensen and Jorgenson (1969), was used to compute rental price of capital.
The data required for calculating the rental price include the following rates:
corporate income tax (CIT), investment tax credit (ITC), Scotia McLeod average
weighted bond yield (r), and capital cost allowance (CCA). They were obtained
from the database of Ghebremichael and Nanang (2004).

The procedure for computing rental price is summarized in equations (4.1)
through (4.5):

K, =(l—d,)K,__l +1, (4.1)
where K, = real capital stock; KM = real capital stock from the previous year
adjusted for depreciation values; I) = annual real-dollar investment flow; and d, =
geometric rate of physical depreciation of a given capital asset. The subscript t
stands for an end of a specific year within the study period.

The present value of depreciation, used for the purpose of taxation, is

calculated from Eqn. (4.2):

94

6(1+’;)U2
tail 2
(r. +5)

 

(4.2)

where p = present value of depreciation; 6 = capital cost allowance (CCA); r =
Scotia McLeod average weighted bond yield, representing the opportunity cost of
capital (i.e., cost of financing capital); and the subscripts i and t stand for a capital

asset and a year, respectively. A tax multiplier is calculated as follows:

= 1'kit'utiuir

 

Init (4-3)

1 - u,
where m is tax multiplier, while Kr), and u), stand for ITC and CIT, respectively.
Furthermore, the capital gains rate must be calculated. It was estimated
using a 5-year moving average of the natural logarithm of an asset’s price. That
is,
((33)
PA,.,_5

., = (4.4)
77, 5

 

Finally, following Christensen and Jorgenson (1969), the rental price of an

asset was generated from the following formula:
pit = mit(’iP/4it—1 + diPAit _77:PAtt) + TIPAit (45)
where p = the rental price; PA = price of a given capital asset i (= machinery

and equipment, engineering, and building); d = rate of physical depreciation of
an asset, computed using the double declining method; 77 = capital gains rate

from Eqn. (4.4); 1 = property tax rate used only for building components.

95

This approach to computing rental price of a capital asset has important
economic implications. The rental price calculated with the formula in Eqn. (4.5)
captures the true opportunity cost i.e., user cost, of a capital asset. This is
because the equation takes into account effects of capital cost allowance,
corporate income tax, investment tax credit, property tax, interest cost of the
funds tied up in the physical asset, economic depreciation, and capital gains and
losses due to changes in an asset price.

B. Labor: Two sets of labor input in production and in management activities
were identified. The values for each set were collected from the The Canadian
Forest Service (2006a), Table Ill-11A in Selected Forestry Statistics Canada
(details in Table A2). The annual number of workers in production (LP = labor in
production) was subtracted from the total number of employees in both
production and management to determine the total number of employees in
management and administration (LM = labor in management). Similarly, wages in
production (WP) were subtracted from total salaries and wages reported for both
production and management to obtain total wages in management (WM). Then,
WP divided by LP provided labor price in production (W1), while WM divided by
LM provided labor price in management and administration (W2). Finally, a

weighted average price of labor, WL,, was calculated as follows:

_ WlLP+ WZLM
LP+ LM

 

W L (4.6)

In Eqn. (4.6), LP + LM = QL, total quantity of labor input.
C. Energy: The quantity of energy was derived implicitly. Total cost of fuels and

electricity were collected from the Canadian Forest Service (2006), Table Ill-11A

96

in Selected Forestry Statistics Canada (details in Table A2). Then, industrial
energy consumption price indices were collected from Economic Reference
Tables (old title) and Fiscal Reference Tables (current title) of the Department of
Finance Canada (2006) for deriving implicit energy quantity.

D. Raw material: A complete annual quantities of harvested sawlogs, the sole
raw material inputs, were collected from the Canadian Forest Service (2006a),
Selected Forestry Statistics Canada, Table l-1 (details in Table A2). Implicit
prices were derived from quantity and value of shipments collected from various
issues of Statistics Canada Catalogue Number 25-201.

All previous studies used the term “roundwood” or simply “wood” as one of
the four inputs that described the production function of the sawmilling/lumber
industry (e.g., Martinello 1985; Nautiyal and Singh 1985; Singh and Nautiyal
1986; Meil and Nautiyal 1988; and Meil et al. 1988; Puttock and Prescott 1992).
Although not clearly stated, it is believed that the term “roundwood” in these
studies is supposed to mean sawlogs; because, based on end-use, Statistics
Canada classifies harvested timber into four categories of roundwood: sawlogs
(logs & bolts), pulpwood, other industrial roundwood (e.g., railway ties and

poles), and fuelwood and firewood (The Canadian Forest Service (2006)“.

 

24 http://www2.nrcan.gc.ca."cfs-sc E/sclfor/defaulthtml, accessed October 05, 2006.

 

97

CHAPTER 5 NONPARAMETRIC METHOD RESULTS

The previous four chapters have established the necessary groundwork
for the empirical work. In this chapter, the nonparametric empirical findings
generated with the multilateral index model are discussed. The parametric results
are discussed in Chapter 6. First, historical trends in the data are analyzed in
Section 5.1 to make preliminary observations that are helpful in interpreting the
nonparametric empirical results.

5.1 HISTORICAL TRENDS IN THE DATA

The first step involved analysis of input and output quantity indices as well
as input shares in total cost and output shares in total revenue. This preliminary
analysis is crucial, because it reveals anomalies in the data, allowing the
researcher to take remedial measures; enhances credibility and scope of the
empirical findings; and provides useful insights into the dynamics of technological
attributes, such as partial and total factor productivity measures (Frank et al.
1990, Ghebremichael et al. 1990, Ghebremichael and Nanang 2004).

In this section, the historical trends in factor shares in total cost, the
Tomqvist quantity indices of inputs, and output shares in total revenue, are
discussed. While average annual results and graphs are used for the discussions
here, the complete time series of the results of cost shares, input quantity
indices, and revenue shares, respectively, are reported in Tables B1, 3.2, and

33 (Appendix B).

98

5.1.1 Factor Shares in Total Cost

Total cost refers to the long-run cost of production, which includes annual
expenditures on the factors of production, which are capital, labor, energy, and
sawlogs (raw material). A factor’s share in total cost is the ratio of the annual
expenditure on that input to the annual total cost of production.

Input-cost shares provide useful information on resource allocation by
revealing the inputs that account for the greatest proportion of the total cost of
production. Cost shares signal inputs that should be targeted for cost
minimization and productivity improvements. As expected, the raw material
accounted for the largest average annual share of 69% over the study period
(Table 5.1). Energy accounted for the least average annual share (roughly 1.5%
to 3.0%), followed by capital, which accounted for an average annual share
ranging from 8% to 10%; and labor’s share declined from more than 46% in the

19603 to roughly 21% in the 19908 (Table 5.1 and Fig. 5.1).

Table 5.1. Average annual input cost shares at ten-year intervals for the
Canadian sawmilling industry

 

 

 

Shares (%)
Period Capital Labor Energy Material
1961-70 8.64 46.26 1.51 43.59
1971-80 7.55 40.35 1.83 50.27
1981-90 9.72 31.82 2.86 55.60
1991-00 8.43 20.74 2.21 68.62

 

 

99

 

   
  

1000/0 - ‘ ' 1, Eff-",1 - '- "'~2'1':.i'

 

80%

  
   
    
   

' Material

60% Energy

Capital if

Shares

  
  

40% - . .

20%

 

0% . 1 . . ,
\ bi ’\ o 15 e o q. <o is x is '\ o
.9" .96 .98 {5‘ .53\ .é‘ ,é‘ .939 @‘b .99 .99 .99 .99 (19°

Years

Figure 5.1. Input cost shares in total cost, the Canadian sawmilling industry: 1961-00.
When analyzing an industrial cost structure, it is important to bear in mind that

changes in cost shares embody movements in both the price and the quantity of
all inputs. Even if there is no change in the price of a given input (e.g., labor), a
change in its cost share can also be influenced by changes in the prices of other
inputs (Freeman et al. 1987). Thus, it is imperative to think of changes in cost
shares as being made up of two components: one that depends on the given
input’s own price and quantity and the other on the prices and quantities of all
other inputs.
5.1.2 Input Quantities

Table 5.2 summarizes ten-year average annual changes in quantities of

the inputs, while Figure 5.2 presents their trends over the forty-year period.

100

Table 5.2. Average annual changes in input quantities at ten-year intervals for
the Canadian sawmilling industry

 

 

 

 

 

 

 

 

 

 

Changes (%)
Period Capital Labor Energy Material
1961-70 1.95 0.26 3.14 2.47
1971-80 2.63 1.57 5.15 2.14
1981-90 0.41 -0.80 -0.04 1.31
1991-00 1.08 1.72 -0.31 1.86
3.00 2 - . _.
82.50~ ~ ,, , ~ ~ ~ — m “A ~-- 4* E,
O.
‘.T 2.00~ V - _. 2 _-_.-,-_2_- ..
5:31.50~~ ~9- 4 77v . ‘9 J's”.--
33 1.001 “ - -‘-— -— m ,_-_2 2- 4+ _- W
(D
.0
E 0.503 ~~ ~ , 2 2 ~ 2 - 2
0.00—1Wij—IIIIIIITIIIITIIIIIIIIIIIIT—TIIITfT—V—T"
'\ bi ’\ Q ’5 Co 0.) (I, 95 ‘b '\ l>i ’\ Q
.99 ,9“) .96 .53‘ ,{S‘ ,é‘ ,93‘ .93" ,3‘8 .9‘" .9? .39 .99 .99

Years

 

 

+ Capital + Labor -*- Energy -—-— Material

 

 

Figure 5.2. Trends in input quantities for the Canadian sawmilling industry: 1961-
00.

Generally, input quantities trended upwards over the study period (Fig.
5.2). During the decades of the 19603 and 1970s, capital input increased at an
average annual rate of 2%. In the 19803, however, its growth rate was low, just

0.4%. This is despite the appearance of some improvements in investments in

101

the 1990s. In the two decades of the 19603 and 19703, labor input averaged
0.3% and 1.6%, respectively, while energy input increased at the rates of 3.0%
and 5% (Table 5.2 and Fig. 5.2). The raw material input (the sawlogs) maintained
an average annual growth rate of 2% during the first two decades of the 19603
and the 19703. But, the average annual growth rate of sawlogs’ utilization during
the 19803 and 19903 was less than 2%. This indicates that there were
slowdowns in production operations during the two decades.
5.1.3 Output Shares in Total Revenue

As detailed in Section 4.1, the Canadian sawmilling industry is a multi-
output industry. For the purpose of this study, the sawmilling industry is a
multioutput industry, producing three main components: lumber, shakes and
shingles, and wood residues. An output’s share in total revenue indicates the

scale of its commercial importance.

Table 5.3. Average annual output revenue shares at ten-year intervals for the
Canadian sawmilling industry

 

 

 

Shares (%)

Period Lumber Shakes & Shingles Wood Residues
1961-70 85.13 1.34 13.53
1971-80 87.14 1.42 11.45
1981-90 81.09 1.01 17.90
1991-00 80.73 0.71 18.56

 

 

102

 

100%
-/ // // -//// /%_i
80% f’:”////// ’///

60%

Shares

40%

20%

 

0%
\u’\orbeoit,<o<o~rx’\o
bee'\’\'\’\eeeoooo
,9\o\o\o\o\o@\o\o\o@\o\o@

Years

Figure 5.3. Output shares in percent of total revenue for the Canadian sawmilling
industry: 1961-00.

Accounting for more than 80% share in total revenue, lumber was the
industry’s most important product (Table 5.3 and Fig. 5.3). Wood residues, the
byproducts of sawmilling operations, accounted for the second largest annual
revenue shares, ranging from 14% to 19%. By contrast, shakes and shingles
appear to have been losing their relative economic significance over the years.
They accounted for just 1% of the total revenue in the 19603 and 0.7% in the
19903 (Table 5.3).

5.2 PARTIAL FACTOR PRODUCTIVITIES

In this section, the levels of partial factor productivities (PFPs) and their
average annual growth rates are examined. Graphs and ten-year-period average
annual changes are used for the discussion, while Table C.1 (Appendix C)

presents the complete time series of the PFP indices.

103

For the reasons detailed in B of Subsection 3.2.1, many researchers are
reluctant to report empirical findings of PFPs. However, policy makers, industry
executives, labor unions, the media, and some researchers focus on PFPs. For
example, partial productivity of labor (PPL) is always given special attention.
Researchers (e.g., Bemdt and Watkins 1981; Freeman et al. 1987; Oum and
Tretheway 1989; Ghebremichael et al. 1990; Oum et al. 1990; Baldwin and
Dhaliwal 2000) argue that PFP of a given input is a good indicator of a given
input’s contribution to the growth of an industrial aggregate output.

Based on this concept, the major public agencies in North America, the
US. Bureau of Labor Statistics and Statistics Canada, calculate and record
annual series of PPL. They call it simply “labor productivity". However, focusing
on PPL misleadingly implies that other inputs, such as capital, energy, material,
and technological progress make less important contributions to output growth.

Levels and growth rates of the PFP of each of the four inputs are used
here to provide additional insights into the production structure and productivity

performance of the Canadian sawmilling industry over the years, 1961-2000.

104

Table 5.4. Average annual changes in PFPs at ten-year intervals for the

Canadian sawmilling industry

 

 

 

 

 

 

 

 

 

Changes (%)

Period PPK PPL PPE PPM
1961-70 3.37 5.04 2.24 2.78
1971 -80 3.20 3.87 1.07 3.23
1981-90 3.86 4.87 4.09 2.67
1991-00 3.17 2.49 4.72 2.31

4.50

4.00 ~~ . , - , - ~ ~ ~ - -~ ~ — - ——
A350 2 2 , ,- - 4 4 4 -, .4 _- 4--- 4- .- ——I
8
.4 3.00« , , e . ~ -.-2 ~ -2--- - -. 2 -~ ,_.2
ll
\- 2 2.... - ~— —~ —- -— ;_
8 50 lfm ,/'
F; 2.00 ~~ 2 2.. »— ”.4 4—‘~- — 22, 2.22 — 2 4»
g 1.50 -2 — ~ ~~ é”; "V m—4 2 J I
5 1,00 5 _;M E E 2 _ 42 - -

0.50 .._-_ 2- _ _.. L.__ . . 22..-. -_ __ __ . __ _ ._ _

0.00 I I I I I I I I I T I I F I I I T T IIIIIIIIIIIIIII T IIIII

.98" New .96 $6 .939 .556) .é‘g 9‘6" \o‘bfi 3‘6!) ,3?" Ned, 335‘ $090

 

RPPK -f—PPL +PPE +PPMJ

 

Figure 5. 4. Trends in PFPs for the Canadian sawmilling industry: 1961-00.

As described earlier, PPK, PPL, PPE, and PPM stand for partial
productivities of capital, labor, energy, and Material, respectively. Differing in
growth rates, all PFPs took upward trends over the study period (Table 5.4 and
Fig. 5.4). These trends indicate that either use of each input declined steadily

over the study period or the industry had experienced technical and/or

105

technological improvements. This is the crux of the difficulty associated with
interpreting PFPs.

The average annual growth rate of PPK remained within the range of 3%
and 4% over the four periods, while that of PPL was within the range of 5% in the
19603 and 2% in the 19903 (Table 5.4). The growth rate of PPE ranged from a
low of 1% in the 19703 to roughly 5% in the 19903, while PPM maintained an
approximate rate of 3% during each of the three decade-periods of the 19603,
the 19703, and the 19803 and just over 2% during the 19903 (Table 5.4 and Fig.
5.4).

PF Ps can easily be related to their respective quantities that are utilized in
the production process. Obviously, the higher the quantity of a given input used,
the lower the PFP of that input. Consider, for example, trends in PPE. The rapid
growth in its consumed quantity (Fig. 5.2) has resulted in its lowest partial
productivity (Fig. 5.4). By contrast, the Canadian sawmilling industry attained a
high PPL (Table 5.4 Fig. 5.4) since labor input has been relatively low and
steadily declining (Fig. 5.2).

5.3 TOTAL FACTOR PRODUCTIVITY
5.3.1 Background

What were the levels and growth rates of the gross TFP in the Canadian
sawmilling industry over the forty-year study period? And, what were the main
sources of TFP? These are the two interrelated research questions posed under

Theme 1 in Section 1.4. The discussion in this section addresses these

106

questions. First, as a brief reminder of the details given in Chapter 2, highlighting
the complexities that underlie measurement and analysis of TFP is in order.

Growth in TFP is the difference between aggregate output growth
weighted by revenue shares and aggregate input growth weighted by cost
shares. If the technology exhibits constant returns to scale, TFP is considered
only as a function of technological change. Thus, its growth is interpreted here as
a measure of “supemonnal” gains associated with investments in R&D that lead
to technical and technological improvements (Lipsey and Carlaw 2004). In the
absence of constant returns scale, however, the gross TFP index reflects a
combination of scale and technological effects, because it does not distinguish
between pure productivity gains (i.e., shifts in the underlying isoquants or
isocosts) and efficiency gains resulting from increases in the scale of operation.

There are many quantitative and qualitative productive inputs each of
which is capable of influencing TFP growth. They include managerial efficiency,
government regulations, labor and management relations, human capital
(knowledge and skills), R&D expenditures, and taxation policy instruments. Thus,
TFP growth has to be decomposed into scale effects and pure technological
change effects. This aspect of the analysis is detailed in Chapter 6, where the
parametric results are discussed.

Moreover, the model formulated in Eqn. (3.8) shows that TFP is a residual
that cannot be attributed to an aggregate of given quantity of inputs. In effect, the
TFP results discussed here cannot be attributed to the four inputs of capital,

labor, energy. and material that are assumed to characterize the Canadian

107

sawmilling industry’s production technology. With these caveats in mind, the
nonparametric, index form TFP results are discussed next.
5.3.2 Nonparametric Measures of Gross Total Factor Productivity

The complete forty-year series of TFP results that were generated using
the multilateral index model formulated in Eqn. (3.7) and aggregate output and
input quantities are reported in Table 0.2 (Appendix C). A summary of average
annual changes in aggregate output and input quantities and that of the gross
TFP along with a graph that depicts annual series of these three variables are
used for the discussion here.

Aggregate output has been rising at a faster rate than that of aggregate

input, leading to a modest growth rate of TFP (Table 5.5 and Fig. 5.5).

Table 5.5 Average annual changes in aggregate output, input, and gross TFP at
ten- and forty-year intervals for the Canadian sawmilling industry: 1961-2000

 

 

 

 

Average annual changes (%)

Period Output Input TF P
1961-70 5.33 2.69 2.45
1971-80 5.85 4.23 1.26
1981-90 4.23 1.11 2.98
1991-00 4.24 3.58 0.62
1961-00 4.56 2.52 1.89

 

108

 

6.00

5.00 —

1.00)

4.00 , - ~ - A -

3.00-. - - ~ ~ - ~

lndexes(1961

:“ N
o o
o o
I

I

I

‘1

fl

I

I

 

 

 

0.00 IIIIIIIIIIIIITIIIIIIIIIIIIIITWTTIIIIIII

«'5 «9 «9 99’ 6° ‘8’ 9"
<3 ,9 ,3 .9 ,9 .9 .9

'\ bi ’\ Q
Q) Q) Q) ’\
r9 '3’ r9 '3’ '\

bi ’\ Q
<3 o o
,9 No.9

Years

 

+Output +lnput +TFP]

 

Figure 5. 5. Trends in output, input, and TFP for the Canadian sawmilling
industry:

1961-00.

Examination of the growth rates by decade indicates different efficiency
scenarios in production processes. During the decade of the 19603 (1961-70),
more than 5% average annual growth in aggregate output and approximately 3%
in aggregate input growth resulted in roughly 2.5% growth in TFP (Table 5.5).
During the decade of the 19703 (1971-80), although aggregate output rose at an
average annual rate of 6%, a relatively faster growth rate than previous years,
aggregate input quantity also grew at a relatively faster rate of more than 4%.
Consequently, the industry’s TFP growth rate was at 1.3%, which is considerably

lower than previous years. Furthermore, the Canadian sawmilling industry

109

experienced considerably sluggish TFP growth of 0.62% in the 19903 (Table
5.5). The forty-year average annual growth rates also show similar trends:
roughly 5% and 3% for aggregate output and aggregate input, respectively,
resulting in approximately 2% average annual growth in TFP (Table 5.5).

What are the causes of the industry’s TF P fluctuation and sluggishness? It
is understood that TFP performance of the Canadian sawmilling industry is linked
to the North American economic climate -- particularly to that of the United
States. Nearly 90% of Canada’s lumber is exported to the US. market. If there
were productivity slowdowns in the American economy, then stagnation in
housing starts sets in, leading to substantial decline in demand for Canadian
lumber. Extensive literature shows that this is the scenario that prevailed in the
early 19703 and in the 19803 up to the mid-19903 (e.g., Wolf 1996 and Hulten
2001)

Covering the 19703 and the 19903, researchers at the Brookings Institute
(e.g., Griliches 1989; Bosworth and Perry 1994; Nordhaus 2002) studied
productivity performance of the American economy. They attributed “productivity
stagnation in the early 19703” to a number of market and non-market forces that
include (i) rising energy prices; (ii) a high inflation rate; (iii) declining investments
in R&D; (iv) “deteriorating” quality of human capital; (v) “depleted possibilities for
invention”; and (vi) “societal laziness”.

Thus, economic conditions in the US. coupled with performance of the
Canadian economy should have had significant effects on the Canadian

sawmilling industry’s TFP performance.

110

5.3.3 Effects of Selected Determinants on TFP Growth

The results discussed above deal with the trends in gross TFP indices.
Here, parametric and nonparametric approaches are used to assess effects of
variables that are commonly deemed as major determinants of TFP. The
parametric results from the stochastic regression models are discussed first.
Then, to shed some light on the research question under Theme 2, effects of tax
incentives on TFP growth and capital formation are analyzed.
A. Decomposing TFP into its Main Sources

Effects of output growth and time dependent technology are commonly
accepted main sources of TFP growth. To minimize autocorrelation effects, the
GLS method, with the commonly used Cochrane-Orcutt iterative estimation
procedure, was used to generate the results reported in Table 5.6. The GLS
method “rids an equation of pure first—order serial correlation and in the process
restores the minimum variance to its estimation” (Studenmund 2006)”.

The two regression models, which are formulated and detailed in
equations (3.9) and (3.10) (Subsection 3.2.3), are rewritten below for ease of
reference; and results of each model are reported in Table 5.6.

Model 1:

TFP=a+fl1Qt+fl2Qtz+8t
Model 2:

lnTFP =a+flan, +67: +8,

 

25 In SHAZAM, the AUTO command performs this procedure.

111

Table 5.6. GLS regressions of TFP with the Cochrane-Orcutt iterative estimation
procedure for the Canadian sawmilling industry

 

 

 

 

 

 

Model 1 Model 2
Variable Parameter (t-ratio) Parameter (t-ratio)
Constant 0.6510 (6.7290)" 0.0261(1.0770)
0 0.4429 (60670)“ --------
02 -0.0353(-2.847)'“ --
LnQ 0.2887(6.2680)“‘
T 0.0062(3.055)“'
Test statistics:
R2 0.9811 0.9870
ow 1.6320 1.7945

 

 

 

Note: ... Indicates significance at the 1% level.

The two regression models performed fairly well. The estimated
coefficients are highly significant; and their signs meet the hypotheses that were
set forth in accordance with economic theory; the R2 of each model is more than
98%; and the Durbin-Watson (DW) is 1.632 for Model 1 and 1.795 for Model 2
(Table 5.6). Hence, as expected, TFP growth is highly dependent on output
growth and technological progress.

Results of the regression for Model 1 show that the marginal effect of
increase in aggregate output on TFP growth is 0.4429, ceteris paribus. But, the
coefficient on 02 reveals that TFP rose (accelerated) with output at a declining
rate of 3.5%.

According to Model 2, the log-linear model in the aggregate output,

elasticity of TFP with respect to Q, is roughly 0.3. This means that a 1% increase

112

in Q would generate approximately 0.3% average annual growth in TFP, ceteris
paribus. The coefficient on T, on the other hand, indicates the expected marginal
effect of technological progress on TFP growth. It shows the average annual TFP
growth rate was 0.62% over the study period, ceteris paribus.
B. Taxation, Capital Formation, and TFP: a Simulation Analysis

The research question under Theme 2 poses the following question:
What were the effects of annual increases in the rates of capital cost allowance
and income tax credit and annual reductions in the rate of corporate income tax
on capital formation and on TFP growth? The following discussions on the
simulation procedure and empirical results are intended to address this research
question.
3.1. Assumptions and Procedure
Assumptions

This analysis is based on the assumption that all three simulated fiscal
policy actions would lead to enhanced rate of capital formation and improved
TFP performance. These potential improvements were expected to be reflected
through a higher share of capital in total cost; a higher capital intensity in the
production technology; and a slightly lower gross TFP due to the fact that
aggregate output and the other three inputs (labor, energy, and Material) are
fixed. This is because capital formation increases the available capital stock,
which in turn raises the aggregate input quantity. Consequently, the post-policy
TFP (TFP2) should be expected to be slightly lower than the pre-policy TFP

(TFP1)

113

Procedure

A brief on the empirical procedure is provided here. In order to get
measurable differences between the without and the with policy actions, the
following relatively significant changes were made on each, taxation instrument
arbitrarily:
CCA: For building and engineering assets, the CCA rate was doubled from 4% to
8% for the 1961 to 1987 period; and from 5% to 10% for the 1988 to 2000 period.
For machinery and equipment assets, it was doubled to 40% from a constant rate
of 20% over the study period (1961to 2000).
ITC: Assuming a 5% benchmark, the ITC rate was raised from 0% to 5% for the
1961 to 1974 period; doubled from 5% to 10% for the 1975 to 1978 period; from
7% to 14% for the 1979 to 1986 period; and from 5% to 10% for the year of 1987;
raised from 0% to 5% for the 1989 to 1995 period; and doubled from 5% to 10%
for the 1997 to 2000 period.
CIT: A reduction of 50% of the original rate that varied between 43.40% and
53.41% over the study period was made.
Asset Prices: Following the pre-taxation change techniques, which are
summarized from Eqn. (4.1) through Eqn. (4.5), annual rental prices of each of
the three capital assets were re-calculated. Then, quantity weighted capital
service price and a total cost of capital were re-computed. Finally, the multilateral

index model in Eqn. (3.7) was re-run to compute TFP2.

114

8.2. Results with Changes in Taxation

The share of capital in total cost and capital intensity are discussed first.
These measures are good indicators of capital formation.

Cost Shares

These shares are implicit measures of capital formation as a result of the
simulated tax incentives, which are expected to stimulate investment. The
complete annual series of the cost shares of all inputs with the changes is
reported in Table 0.1 (Appendix D), while those shares of capital for without and
with the changes along with percentage differences are reported in Table D2
(Appendix D).

Higher average annual shares of capital in total cost associated with the
changes in the taxation policy instruments than those without indicate that the tax
incentives enhanced capital formation (Fig. 5.6 and Table 5.7). The average
annual shares of capital in total cost without the changes ranged between 8%
and 10%, roughly, whilst those with the changes ranged between 12% and 14%

(Table 5.7).

115

 

 

 

 

 

0.0 fiITIIITITIIIIIIIjTIIIIIIIIIIIIIIIIIIIIII

ixbiAQ’be
bbbAAA
gaggeo

«9‘ 951"?)6393Q’9N 986‘s“
ix ix CZ’ix‘bixg gixq’ixqixq

ix ix ()9
Years

 

[:0- Without +With

 

 

Figure 5. 6. Shares of capital in total cost without and with the changes in
taxation for the Canadian sawmilling industry: 1961-00.

Table 5.7. Average annual shares of capital in total cost without and with the
changes in taxation at ten- and forty-year intervals for the Canadian sawmilling
industry

 

 

 

Changes (%)
Period Without With
1961-70 8.6 11.9
1971-80 7.5 12.0
1981-90 9.7 13.5
1991-00 8.4 11.7
1961-00 8.6 12.3

 

 

116

 

   

 

 

   

1961-70 1971-80 1981-90 1991-00 1961-00
Pefiods

Without I With

Figure 5. 7. Average annual shares of capital in total cost without and with the
changes in taxation at ten- and forty-year intervals for the Canadian sawmilling
industry

The forty-year average annual (1961-00) also depicts similar outcomes.
The highest capital formation occurred during the period of 1981-90 (Fig. 5.7).
Capital Intensity

Capital intensity is a term commonly used in economics to describe real
capital stock per worker in a production process (Pearce 1992, Mankiw and
Scarth 1995). High capital intensity indicates a production technology
characterized by more machinery, equipment, etc; and presumably, higher
productivity.

Complete annual series of capital intensity results, without and with
changes in the taxation policy instruments, are reported in Table D3 (Appendix

D).

117

Table 5.8. Average annual capital intensity at ten- and forty-year intervals without
and with the changes in taxation for the Canadian sawmilling industry

 

Without (real $) With (real $)

 

2297.24
4557.23
13538.17
21219.02

 

10402.91

3275.10
7625.31
19643.58
30510.82
15263.70

 

 

 

Penod
1961-70
1971-80
1981-90
1991-00
1961-00
40000
35000 ~
a 30000 -
E, 25000 —
-_‘-=_- 20000 4 e
3% 15000 ~ -
0 10000 ~
5000 ~ -4-

 

Ann-.1,“

 

 

OIIIIWIIIrrIfiTIIIIIIIIIIIIIIITVTTIIIIITTI

quQeeewoe
eee«'\'\’\<o<b<oe
,3 ,9 ,9 ,9 ,9 ,9 ,9 ,9 ,9 .9 ,3)

Years

ix “009°

9
,9 ,9 .19

 

L—i—Without +With

 

 

Figure 5. 8. Capital intensity without and with the changes in taxation for the Canadian

sawmilling industry: 1961-00.

118

Capital intensity with the changes in the three taxation policy instruments
shows steady growth significantly above that without the changes (Table 5.8 and

Fig. 5.8).

30.00
25.00
20.00
15.00
10.00 <

   

5.00 .

  
 

 

 

Real capital stock per worker
(thousands)

we ,
1961—70 1971-80 1981-90
Periods

I, VWthout I With

0.00 —

Figure 5. 9. Average annual capital intensity at ten- and forty-year intervals
without and with the changes in taxation for the Canadian sawmilling industry.

The intensity with changes followed rapidly rising trends (Fig. 5.8). The
average annual intensity of the 19603 (1961-70) was real $2,297.24 per worker
for the without and real $3,275.10 per worker for with the Changes (Table 5.8). By
contrast, in the 19903 (1991-00), it was real $21,219.02 per worker for the
without and real $30,510.82 per worker for with the changes. Over the forty-year
study period (1961-00), average annual intensities were real $10,402.91 per
worker for the without and real $15,263.70 per worker for with the changes

(Table 5.8).

119

The highest intensity with the changes occurred during the period of 1991-

00 (Fig. 5.9). It appears that the economic climate during that period was

conducive for the industry to invest in various types of capital assets.

Total Factor Productivity (TFP)

For comparative purposes, a complete annual series of both TFP1 and

TFP2 are reported in Table 04 (Appendix 9)-

Table 5.9. Average annual values of TFP1 and TFP2 and their difference

 

 

 

 

 

 

 

 

 

Marginal
Period TFP1 (without) TFP2(with) difference (%)=
(TFP2-TFP1 )x100
1961-7O 1.1541 1.1512 -0.2877
1971-80 1.4239 1.4011 -2.2861
1981-90 1 .7446 1 .7099 -3.4721
1991-00 1 .9054 1 .8642 -4.1243
1961-00 1.5570 1.5316 -2.5425
2.50 -2. ~— ~ ~

8

O.

‘.T

ES

92

71’

o

X

8

E 0.50 -

0.00 IIIIIIIIIIIIIIIIIITIIIIIIIIIIIIIIIITIII
\bAQ‘btbcb’I/fo‘bNbiAQ
Q>©Q>«’\’\«Q>QD%QQQ>Q

.9 ,9 ,9 ,9 ,9 ,9 ,9 ,9 .9 ,9 ,9 .9 9 (,9
Years

 

 

+TFP2 +TFP1

 

 

Figure 5. 10. TFP1 and TFP2 for the Canadian sawmilling industry: 1961-00.

120

As expected, TFP2 is slightly lower than TFP1 (Fig. 5.10). This is a result
of higher capital formation, motivated by the tax incentives. Consequently, the
aggregate quantity of the inputs increased significantly, while the aggregate
output and the other inputs (labor, energy, and material) were unchanged. The
highest average annual difference between TFP2 and TFP1 (over 4%) occurred
during the 19903 (1991-00), the period during which capital intensity was the
highest (Table 5.9 and Fig.5.9).

As detailed in Section 3.2, TFP growth is the revenue-share weighted
aggregate output growth minus the cost-share weighted aggregate input growth.
Under these conditions, therefore, the multilateral index model, which is
summarized in Eqn. (3.8), has generated the expected results: a larger share of
capital in total cost, a higher intensity of capital, and a relatively lower TFP; which
are all results of the tax incentives.

In closing, a caveat on the above findings is in order. To examine impacts
of changes in various taxation policy instruments on the supply and the demand
sides of the Canadian economy, inter— and intra-industry transaction models,
such as the commonly used computable general equilibrium (CGE) model, need
to be developed.

Therefore, it can be concluded that robustness of the multilateral index
techniques and the reliability of the findings have been achieved. The arguments
of think tank organizations, such as the Forest Products Association of Canada
(2006) and the Institute for Competitiveness & Prosperity (2006) for increases in

CCA and ITC and for reduction of CIT are justifiable.

121

CHAPTER 6 PARAMETRIC METHOD RESULTS

The parametric method, estimation of a long-run dual neoclassical cost
function, is described in Section 3.3. The empirical models’ specification, the
translog functional formulation, the estimation techniques, and the various
parametric measures that can characterize the Canadian sawmilling industry’s
production technology are detailed in that section.

In this chapter, results of this parametric empirical method are reported
and discussed. The procedure for selecting the best model out of the six
empirical models, factor substitution and price elasticities, and decomposition of
TFP growth into its parametric sources along with other technological attributes
are summarized and discussed in sections 6.1, 6.2, and 6.3, respectively. Finally,
results of this study are compared with those of previous studies in Section 6.4.
6.1 RESULTS AND MODEL SELECTION PROCEDURE

As detailed in Subsection 3.3.7, Model I, which is the unrestricted TL form
of the long-run total cost function, and the first three of the four cost-share
equations: (31.20) to (3.22), formed a system of four equations. Eqn. (3.23) was
dropped out of the system arbitrarily. The systems approach is used to deal with
cross equation restrictions and the variance-covariance matrix.

The optimal procedure is to simultaneously estimate the long-run cost
function and the three selected cost share equations as a multivariate regression
system. Resulting in more efficient parameter estimates than would be obtained
by applying OLS estimation to each model, including the cost share equations in

the estimation procedure has the effect of adding many additional degrees of

122

freedom without adding any unrestricted regression coefficients (Christensen and
Greene 1976).

Efficacy of six models in describing the Canadian sawmilling industry’s
production technology was tested. The models are the unrestricted TL form cost
function (Model I), Hicks neutrality (Model II), no technical change (Model III),
homotheticity (Model IV), homogeneity (Model V), and unitary elasticity (Model
VI). The empirical results of each model are summarized in Table 6.1, followed
by the meaning and significance of disembodied technological progress and the
procedure for selecting the best model that described-the industry’s production

technology are discussed successively.

123

Table 6.1. Parameters of six-translog form cost functions estimated according to

IZEF/MLE procedure for the Canadian sawmilling industry 1961-2000

 

Models and their Estimated Coefficients

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

124

 

 

 

Para- (Asymptotic t-ratios in parentheses)
meters I II III IV. V VI
Unrestricted Hicks- No Tech. Homo- Homogenei Unitary
TL neutrality Change theticity -ty elasticity
Const. 20.620 23.209 19.029 20.944 21.024 16.698
a0 (26.580) (13.360) (22.240) (25.960) (27.900) (256.100)
Output: 1.089 ... 1.681 ... 1.496 ... 0.287 0.267 ” 0.398
70 (4.962) (7.810) (18.070) (2.158)“ (2.412) (1.720)
Labor 0881 , -1.065 ... -0.615 ... -0.974 ... -0.988 ... 0.501 ...
BL (5948)" (-3.775) (-4.159) (-6.172) (-6.562) (58.100)
Capital 0.144 0.908 .. -0.060 0.118 0.127 0.125 ...
BK (1.218) (2.832) (-0.444) (0.977) (1.112) (23.760)
Energy -0.075 -0.061 -0.142 -0.0569 -0.054 0.013 ...
E (-1.810) (-0.260) (-3.390) (-1.367) (-1 .344) (8.655)
Materi- 1.812 1.219 1.817 1.913 1.915 ... 0.361 ...
3,, [3,, (15920)“ (4.216)“ (17150)“ (14.770)“ (14.730) (32.700)
Time, 0.022 .. -0.005 ----- - 0.038 ... 0.038 0.075 ...
9T (2.322) (-0.687) (3.077) (3.174) (8.211)
BLL 0.196 0.191 m 0.173 0.207 0.208 .. ----
(12.620) (7.116) (12.440) (12.170) (12.560)
BKK 0.025 .. 0.103 .. 0.006 0.018 0.022 ----
(2.060L (2.463) (0.421) (1 .834L (1 .889)
BEE 0.014 ... 0.019 0.011 ... 0.014 0.014 ... ----
(4.735) (0.653) (3.568) (5.227) (5.162)
BMM 0.223 ... 0.217 ... 0.216 ... 0.226 ... 0.225 ... ----
(12.700) (3.819) (15.340) (13.080) (13.050)
700 0.134 2.223 -0.119 ... -0.229 '
@263) (2.790) (-3.220) (-0.422) ---- ----
OTT -0.001 0.004 --—-- -0.002 -0.001 ...
(-1 .123) (3.284) (-1 .776) (-3.956) -----
BLK 0.004 -0.046 0.018 0.005 0.004
«meg (-1 .860) (1 .733) (0.508) (0.431) -----
BLE 0.008 .. 0.011 0.014 ... 0.005 0.005
(2.059) (0.572) (4.230) (1.251) (1 .226) --------
BLM -0.208 ... -0.156 ... -0.205 ... -0.217 ... -0.217 ...
...... 415.179). - _ - 1.5-.351)- _- 0:19.850)- - 1.1-13.4.79). - ..(-1.4.149). - ..l .—:-.—_-: _ - -

 

Table 6.1 (cont’d). Parameters of six-translog form cost functions estimated
according to IZEF/MLE procedure for the Canadian sawmilling industry 1961-

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

2000
135.57”? """ "it '''''' "ii """" lTI. """ \7"'""'Tri """""
meter Unrestrict Hicks- No Tech. Homo- Homogenei Unitary
...... _ _-.e.d_T.L_ - _. 9255932 - _ 9.119099. - _ intensity. - _ .-_ty. - - _ - _. 995.590- _.
BKE -0.018 ... -0.013 ” -0.019 ... -0.019 -0.018 ---
(-4.655) (-0.531) (-4.481) (-4.991 *** (-5.007)
BKM -0.011 -0.044 .. -0.005 -0.008 -0.008 -----
(-1.023) (-1 .325) (-0.435) (-0.797L (-0.743)
BEM -0.005 -0.017 ” -0.006 -0.000 -0.000 ----
(-1.279) 0554) (-1.671) (-0.101) (-0.108)
9LT 0.000 ----- ---- -0.001 -0.002 -0.009 ...
(0.072) (-0.899) (-0.909) (-7.087)
OKT 0.000 ------ ----- 0.001 0.001 0.001
(0.298) (1.626) (1 .601 ) (1.242)
BET 0000 -—--- ----- -0.000 -0.000 —0.000
-0.356) (-0.050) £0048) (0315)
GMT 0000 ~------- ------ -0.000 -0.000 0.008 ...
(-0.204) (-0.1 12) (-0.083) (5.015)
.YL Q -0.110 ... -0.132 ... -0.109 ... ----- ---— 0.026
(-3.931) (-8.529) (42.880) (0.771)
YK Q 0.010 0.016 0.006 ---- ---- -0.026
(1.706) (0.943) (0.856) (-1.239)
YE Q 0.004 0.010 0.009 —--—-- —-— 0.009
(0.238) (0.707) (4.670) (1.535)
7M Q 0.096 0.106 ... 0.095 ... ~--------- 2...... -0.009
(4.700) (3.835) (12.650) (0223)
e QT 0.003 -0.096 -- 0.018 0.009 .. -0.006 ...
(0.125) @039) (0.846) (2.554) (-6.739)
Restri- None 3 6 3 4 6
cfions
Log of 525.590 492.923 518.213 523.815 523.736 482.058
likelihood
funcfion
Calgulated —----- 65.334 14.754 3.550 3.708 87.064
1
Critical ----- 7.81 12.59 7.81 9.49 12.59
2
I
m: and indicate statistical significance at the 1% and 5% levels, respectively.

Disembodied Technological Progress: First, a brief on each model’s result of

disembodied technological progress is in order. Disembodied technological

125

progress is revealed through the coefficient on the time trend variable (T), which
is included in models I, II, IV, V, and VI. Thus, according to the asymptotic t-ratios
of the coefficient on T, each of models I, IV, V and VI has the capability of
capturing statistically significant 2.2%, 3.8%, 3.8%, and 7.5% average annual
rates of disembodied technological progress over the study period, respectively
(Table 6.1).

The 2.2% average annual rate of disembodied technological progress is

consistent with the 2% growth rate of the “residual” TFP, which was generated
with the application of the multilateral index model of the nonparametric method
(Table 5.5). This is an encouraging outcome, which verifies credibility of the data, ‘
robustness of the results, and scientific merit of the two methods.
Model Selection Procedure: Model II results show that the Hicks-neutrality null
hypothesis is rejected at the 5% level of significance in accordance with the log
likelihood ratio (LR) test (Table 6.1). Furthermore, the LR test statistics show that
neither the no technological change hypothesis (Model lll) nor the unitary
elasticity hypothesis (Model VI) can be accepted at the 5% significance level.
Obviously, rejection of the no technological change hypothesis suggests
presence of technological change over the study period, while rejection of the
unitary elasticity hypothesis means that a Cobb Douglas functional form cannot
describe the industry’s production technology.

In contrast, neither the null hypothesis on homotheticity (Model IV) nor that
on homogeneity (Model V) can be rejected. These results indicate that either a

homothetic or homogeneous model can describe the Canadian sawmilling

126

industry’s production technology. Nautiyal and Singh (1985) reached at the same
conclusion. They stated that the production structure of the “Canadian lumber
industry” was homothetic and homogeneous.

The outcome that a homothetic technology characterized the Canadian
sawmilling industry over the study period is encouraging, as it shows that both
the input price ratios and the output level determined cost minimizing input
combinations. This verifies specification of the industry’s total production cost as
a function of input prices and output level.

The LR test results reveal that the Canadian sawmilling industry’s
production technology was characterized by disembodied technological progress
and by homotheticity and homogeneity. Hence, the most appropriate model is
one characterized by disembodied technological change, statistically significant
technological change, homotheticity, and homogeneity.

The objectives of this study, however, involve investigation of the
dynamics of various technological attributes. Thus, Model I, the nonhomothetic,
unrestricted TL form long-run cost function, was selected as the one that meets
the objectives. This decision to select Model I is based on two main reasons.
Firstly, it is a “full technology model” (Stevenson 1980). In other words, it is a
model with sufficient information necessary for conducting complete analysis of
the production technology. Secondly, the results of Model I (Table 6.1) show that
all of the estimated coefficients, which are required for computing the various
measures of technological attributes: factor substitution elasticities, price

elasticities of derived demand for inputs, economies of scale, elasticity of cost

127

 

with respect to output, TFP growth, and cost diminution rate, are statistically
different from zero.

Economic theory also suggests that a cost function is well behaved if it is
concave in input prices and if its input demand functions are strictly positive. The
TL form long-run cost function does not satisfy these globally (Bemdt and Wood
1975). Hence, it was necessary to check the fitted TL cost function for positivity
and concavity. Positivity is satisfied, if the fitted cost shares are positive. Tests of
the fitted cost shares, which are input demand functions, revealed that the
positivity conditions were satisfied at each annual observation. Concavity of the
TL long-run cost function is satisfied, if the Hessian matrix of the second-order
partial derivatives is symmetric and negative semidefinite (Varian 1984). While
the Hessian is symmetric by assumption, its negative semidefiniteness was
checked for each annual observation and mean values; and was found to be
true.

Finally, the TL form long-run total cost function, Model I, which
characterizes the Canadian sawmilling industry’s production technology as a
nonhomothetic, is consistent with the objectives of this study and with economic
theory requirements. The following technological attributes of the industry are,
therefore, analyzed using the estimated parameters of that model.

6.2 SUBSTITUTION AND PRICE ELASTICITIES
6.2.1 Factor Substitution Elasticities
Equations (3.36) and (3.37) were used to calculate the AES results that

are reported in Table 6.2, while equations (3.38) and (3.39) were used to

128

 

calculate MES that are reported in Table 6.3. Because both are easily influenced
by the magnitude of a given input cost shares over the study period, they were
calculated at the mean value of input cost shares over the entire sample.

Major previous studies (e.g., Bemdt and Wood 1975; Pindyck 1979;
Nautiyal and Singh 1985; Singh and Nautiyal 1986; and Kant and Nautiyal 1997)
used AES to analyze degrees of technical substitutability between pairs of inputs.
For the reasons discussed earlier, this study also focuses more on AES results

than on MES.

Table 6.2. AES estimates for the Canadian sawmilling industry (standard errors
in parentheses): 1961-2000

 

 

 

Input j
Input i Labor Capital Energy Material
Labor -0.236 1.091 2.183 -0.189 ..
(0.139) (0.250) (0.574) (0.077)
Capital -5.508 -6.104 0.831
(0.797) (1.526) (0.165)
Energy -1 3.842. 0.573
_ (7.327 (0.333)
Symmetric
Material -0.096
(0.064)

 

 

Notes: ... and " indicate significance at the 1% and 5% levels, respectively.

In accordance with economic theory, the own-partial elasticities of
substitution are all negative (Table 6.2). The AES results reveal that between the
pairs of labor/capital, labor/energy. capital/ material, and energy/ material are

positive, suggesting that these input pairs were substitutes to each other. On the

129

rrsfl—u ‘an-amu‘

other hand, the AES between the pairs of labor/ material and capital/energy are
negative, implying complementarities between these in pairs (Table 6.2).

The substitution elasticities of the labor/capital and labor/energy input
pairs are greater than unity, implying that it was relatively easy for the industry to
substitute labor for capital and energy. Moreover, statistically significant degrees
of substitutability between labor/capital (1.091) and labor/energy (2.183) as well
as the significant complementarities between labor/ material (-0.189) and
capital/energy (-6.104) were possible over the study period (Table 6.2). The own-
elasticities of substitution of labor and Material are less than unity and are
statistically not different from zero, suggesting that demand for these inputs was
not responsive to either their marginal productivity ratio or to their price ratio.

These findings are also consistent with economic theory in that productive
inputs are expected to be “neither perfect substitutes nor perfect complements”
(Sherif 1983). Moreover, AES findings of other studies were more or less the
same as those of this study. For example, Martinello (1985) found all other pairs
of inputs to be substitutes, with the exception of Material and energy; Nautiyal
and Singh (1985) and Singh and Nautiyal (1986) found labor/capital;
labor/energy; and labor/ material to be substitutes; Kant and Nautiyal (1997)
found pairs of all four inputs, i.e., capital, labor, energy, and Material, to be

substitutes.
The magnitudes of O'KK andO'EE, which are -5.508 and -3.847,

respectively, might appear to the casual reader to be unrealistically high (Table

6.2). But, these results are consistent with findings of several other researchers,

130

who conducted empirical research on manufacturing industries and other
sectors, using the method used in this study. For example, Binswanger (1974c)
found -26.573 for fertilizer in the US. agricultural sector; Berndt and Wood
(1975) reported -10.66 for energy in the US. manufacturing sector; and Pindyck
(1979) reported -16.96 and -27.21 for the energy sector in the national

economies of Canada and the US, respectively.

Table 6.3. MES estimates for the Canadian sawmilling industry (standard errors
in parentheses): 1961-2000

 

 

 

lnputj
Input i Labor Capital Energy Material
Labor n.a. 0.443 0.807 0.205
(0.115) (0.205) (0.067)
Capital 0.809 n.a. -0.073 0.778
(0.118) (0.221) (0.110)
Energy 0.324 .. 0.156 .. 0.291
(0.152) (0.169) n.a. (0.149)
Material -0.488 0.485 0.351 n.a.

 

(0.069)” (0.1 10)“ (0.069)“

Notes: (i) and .. indicate significance at the 1% and 5% levels, respectively.
(ii) n.a. means not applicable.

According to the MES results, the pairs of capital/energy and
material/labor are complements; and all other input pairs are substitutes (Table
6.3). This is in contrast to the AES results (Table 6.2). Thus, there are technically
inherent features that characterize the difference between AES and MES. The

main difference between the two is that AES is always symmetric (e.g.,

0',“ = 0“) (Table 6.2). MES does not meet this condition. Moreover, MES

131

does not provide own-substitution elasticities, as AES does. However, Blackorby
and Russell (1989) argue that for more than two inputs, the MES is symmetric, if
and only if, the inputs converge to the same constant, in which case the
production function is a member of the implicit CES-Cobb-Douglas family. In any
case, as pointed out earlier, in this study conclusions are based on the AES
results.

6.2.2 Own- and Cross-Price Elasticities

The negative values of own elasticities of substitution, O',,, (Table 6.2) and

of the own-price elasticities of demand, 8,,, (Table 6.4) reveal that the necessary

condition for global concavity of the dual cost function is met (Bemdt 1991).

Table 6.4. Estimated own- and cross-price elasticities of demand for inputs in the
Canadian sawmilling industry (standard errors in parentheses): 1961-2000

 

Input j (= L, K, E, M) Prices

 

 

 

Input i Labor Capital Energy Material
Labor -o.079 0.134 0.044 -0.099
(0.046) (0.031) (0.011) (0.040)
Capital 0.364 -0.676 -0.123 .. 0.435
(0.083) (0.098) (0.031) 0.086)
Energy 0.728 -0.749 -o.270 .. 0.300
(0.192) (0.187) (0.148) (0.175)
Material -0.063 0.102 0.012 -0.050
(0.026) (0.020) (0.007) (0.034)

 

Note: and .. indicate significance at the 1% and 5% levels, respectively.

Although most of the estimates are statistically significant, both the own-

and the cross-price demand elasticities are inelastic (Table 6.4). The cross-price

132

elasticities between the pairs of capital/energy and energy/capital show
complementarities; while the pairs of labor/capital, labor/energy, capital/labor,
capital/material, energy/labor, and material/capital were substitutes (Table 6.4).
These results are consistent with those observed in many previous studies of the
sawmilling industry (e.g., Banskota et al. 1985; Nautiyal and Singh 1985;
Martinello 1985; Singh and Nautiyal 1986; Meil et al. 1988; Puttock and Prescott
1992)

The highly inelastic nature of the own- and the cross price elasticities
indicates that each input was treated as a “basic” good during the study period.
In other words, the Canadian sawmilling industry experienced very limited
possibilities for substituting one input for another (Table 6.2). It is believed that
this condition is one of the sources of inefficiency in the industry’s production line.
6.3 DECOMPOSED TFP GROWTH AND OTHER ATTRIBUTES

In this section, decomposition of TFP into its main determinants and the
nature of several technological attributes are summarized in Table 6.5, followed
by interpretive discussions on the major attributes: elasticity of total cost with
respect to output, scale effects, technological progress, TFP growth, returns to

scale, and economies of scale.

133

Table 6.5. Average annual results of key technological attributes at ten- and
forty-year intervals for the Canadian sawmilling industry

 

 

 

Scale Technological TFP growth: Returns Economies
CQ effects: progress (I _ 8 ) Q _ g to scale: of scale:
from _ ' CQ CT 1_ 8
E qn. (1 ECQ )Q 8C, frozm from 1/8CQ f CQ
Period (3.34) from Eqn-(3° 6) Eqn. (3.32) from Em?“ 35)
Eqn. (3.32) Eqn. ‘1 - -
(3.33)

(1) (2) (3) (4) (5) (6) (7)
1961-70 0.230 0.041 -0.021 0.062 4.356 0.770
1971-80 0.231 0.051 -0.023 0.074 4.324 0.769
1981-90 0.245 0.022 -0.023 0.045 4.087 0.755
1991-00 0.292 0.024 -0.024 0.048 3. 422 0. 708
1961—00 0.249 0.034 -0.023 0.057 4.017 0.751

 

 

Note: First the logarithmic mean values of the input prices and of the aggregate output quantity
that appear in the right hand side of the identified formulas were computed for each interval
period. Then, these mean values were multiplied by their respective coefficients from Model I
(Table 6.1).

Interpretations and implications of the technological attributes summarized

in Table 6.5 are as follows:

Elasticity of Total Cost
The elasticity of total cost with respect to output, 8 CQ, [Column (2)] is a

measure of the degree of responsiveness of total cost to changes in total output, is

positive as one would expect. That is, the higher the output the higher the

production cost.

ECQ plays important role in characterizing the production technology: if the

production function exhibits increasing returns to scale (IRTS), then8CQ <1,

134

 

I,
i.

implying that doubling of output would less than double total cost under given input

prices; if the production technology experiences constant returns to scale (CRTS),

then 8CQ = 1, suggesting that doubling output would equiproportionately double

total cost given that input prices remain unchanged; and, finally, if the production

technology exhibits decreasing returns to scale (DRTS), then ECQ >1, hence,

doubling output would more than double total cost under given input prices.

Results for all the ten- and forty-year interval periods reveal that total cost
was inelastic (Table 6.5). That means production cost responded to increases in
output at a slower rate, implying IRTS. For example, a 1% rise in aggregate
average annual output over the study period would have resulted in only 0.25%
rise in total cost, ceteris paribus.
Scale Effects

The scale effects (SCEs), [Column (3)] are products of economies of scale
and the average annual growth rate of the aggregate output. Given that the
industry’s technology was characterized by IRTS, the positive nature of these
results is as should be expected. These results contribute to TFP growth
[Column (5)]. The average annual SCEs were 3.4% over the study period.
Technological Progress

Technological progress [Column (4)] is inferred through the rate of cost
diminution, which is also referred to as the dual measure of the primal TFP
growth under fixed input prices and output quantity (Bemdt and Watkins 1981).

Consistent with the theoretical concept, the results are all negative. Over the

135

.K‘

-Yt‘i‘fln-J ~;-l'.

 

study period, for example, the average annual cost diminution rate was 2.3%.
That is, technical progress did indeed contribute to TFP growth.
Growth in TFP

The TFP growth results comprise effects of mutually reinforcing two
important factors: scale effects and cost diminution rate. Thus, the relatively high
average annual growth rate of 5.7% over the study period is a joint effect of the
two factors (Table 6.5). This result is more than double of the approximately
2.0% growth rate, which was generated with the nonparametric, multilateral index
procedure (Table 5.5).

Overall, parametric results show that the industry gained measurable TFP
growth in the 19603 and in the 19703, with average annual rates of 6.2% and
7.4%, respectively [Column (5)]. However, there were slowdowns in the 19803
and 19903, with the ten-year interval average annual growth rates being 4.5%
and 4.8%, respectively.

Returns to Scale

Returns to scale (RTS) [Column (6)] are inversely related to the elasticity
of cost with respect to output. That is, the lower the elasticity of cost the higher
the RTS. As highlighted earlier, the consistently greater than unity results verify
that the industry gained IRTS over the study period.

Economies of Scale

Economies of scale [Column (7)] indicate a declining range of a long-run

average cost, resulting from expanded level of output. Economic theory suggests

that there are internal and external economies. Internal economies are attributed

136

 

1F“ ”‘1 "" ‘

to expansion of a firrn’s production operations through technological progress,
managerial improvements, risk spreading or combination of two or all three
factors (Pearce 1992). External economies arise from the expansion of industrial
operations through various actions that include acquisitions and mergers.

Following Christensen and Greene (1976), economies of scale (ES) were
calculated as unity minus ECQ. A positive value of ES implied that the industry
gained economies of scale over the study period. This outcome is consistent with
the above discussed less than unity ECQ results recorded for the ten- and forty-

year intervals (Table 6.5). For the forty-year study period, for example, the
average annual ES value was 0.751. Several other studies reached at the same

conclusion (e.g., Banskota et al. 1985; Nautiyal and Singh 1985).

Table 6.6. Decomposition of the dual measure of the primal TFP growth at ten-
and forty-year intervals for the Canadian sawmilling industry: 1961-2000

 

Period Pure Non-neutral Scale- Elasticity of cost

technological technological augmenting with respect to

change (PTC) change (NTC) technological time dependent
change (STC) technological

progress: ECT

 

(1) (2) (3) (4) (5)

 

1961-70 -0.021 0.001 -0.001 -0.021
1971-80 -0.021 0.001 -0.002 -0.023
1981-90 -0.021 0.001 -0.003 -0.023
1991-00 -0.021 0.001 -0.004 -0.024
1961-00 -0.021 0.001 -0.003 -0.023

 

 

Sources: Eqns. (3.25, (3.26), (3.27), (3.28) for PTC, NTC, and STC, respectively

137

 

KW

PTC is expected to capture pure technological progress achieved through
enhanced quality of human capital (knowledge and skills). Hence, the negative
results indicate contributions of PTC to total cost diminution at an average rate of
2% per year (Table 6.6). By contrast, the positive values of NTC indicate effects
of input augmenting technological changes, resulting in a 0.1% annual increase
in total cost, while the scale augmenting technological changes (SCT) lead to an

average annual decline of 0.3% in total cost (Table 6.6). The dual measure of the

primal TFP growth, 6‘”, which is the sum of PTC, NTC, and STC shows an

average annual rate of 2.3% diminution in total cost over the study period (Table

 

6.6).

Table 6.7. Average annual rates of technological change biases at ten- and
forty-year intervals for the Canadian sawmilling industry: 1961-2000

 

 

 

 

Period Capital Labor Energy Material
(1) (2) (3) (4) (5)
1961-70 0.002 0.000 -0.007 0.000
1971-80 0.003 0.000 -0.005 0.000
1981-90 0.002 0.000 -0.003 0.000
1991-00 0.002 0.000 -0.005 0.000

1 961-00 0.002 0.000 -0.005 0.000

 

Note: The formula in Eqn. (3.34) was used for the calculation.

 

The production technology of the Canadian sawmilling industry was
characterized by capital-using, energy-saving, and Hicks-neutrality on labor and

material (Table 6.7). That is, technological change resulted in rising demand for

138

capital; declining demand for energy; and had no effect on the individual demand
functions for labor and material, ceteris paribus.

An input bias technological change has important economic implications.
For example, the technology’s Hicks-neutrality on labor and material implies that
technological change in the Canadian sawmilling industry used labor and
material proportionately to produce an optimal output, Q', leaving the marginal
rate of technical substitution of material for labor or vise versa as well as the
price ratio of the two inputs fixed. That is, the isoquant moved inward (toward the
origin) along the expansion path in the production process of Q. at a least-cost
combination of the two inputs.

These findings are more or less consistent with those of previous studies.
For example, Martinello (1985) found technological change in the industry to be
labor and round wood (material) saving and capital and energy using. Stier
(1980, 1985) observed capital using and labor saving technological change bias
for US. forest products industries.
6.4 COMPARISON WITH PREVIOUS STUDIES

In this section, empirical findings for key technological attributes from this
study and other selected studies that were conducted on the Canadian and
American sawmilling/lumber industries are summarized and evaluated. The
extent to which each study has been cited in the literature and methodological
similarity with this study were the main criteria for selecting the studies.

A caveat on the consequences of comparing empirical results from

different studies is instructive. Different studies must not be compared literally,

139

based on the face values of parametric coefficients. Doing so is misleading and,
in most cases, confusing, because of possible differences in the following and
other conditions: (i) data structures, (ii) sample size (e.g., length of time period),
(iii) regional and international variations in social, economic, industrial, and
environmental policy instruments, (iv) accessibility to and structure of markets,
and (v) efficiency and effectiveness of raw material delivery and utilization. These
and other similar conditions are sources of incomparability of industrial- empirical
studies (Ghebremichael et al. 1990, Ghebremichael and Nanang 2004).

In general terms, there are “scientific requirements” every empirical
econometric model must meet to be validated. Although there is no “magic
formula” for selecting the most effective and efficient econometric model, there
are “alternative general philosophies” that can be used successfully (Myers
2004). The following five statistical criteria for selecting an effective econometric
model are commonly considered as necessary: parsimony other things being
equal the simplest model could be the best; identifiability. whether numerical
estimates of the parameters of a structural equation can be obtained from the
estimated reduced-form coefficients, i.e., the endogenous and exogenous
variables are identified correctly during the process of building an econometric
model; statistical adequacy. effective and efficient explanatory power; (iv)
consistency with social, biological, and physical theories; and predictive power;
how far apart the predicted values based on estimated parameters are from the

actual data (Gujarati 2003; Myers 2004).

140

 

Thus, the selected previous studies and this study have to be evaluated in
light of these statistical criteria as well as the relevance of each study’s results for
policy making; not on the basis of “face values” of estimated parameters. For the
purpose of this section, the following three common categories of research
findings are selected: input substitution elasticities, price elasticities of derived
demand for inputs, and growth in TFP.

The information is classified into two parts. First, each study is
characterized by author and publication year, model specification, functional
form, and sample size (Table 6.8). Then, each study’s empirical findings on the
basis of the above-identified parameters are summarized in the five tables that

follow Table 6.8.

141

ft.“ _ 1 m‘ m‘ blun— ‘h‘fiififi

Table 6.8. Methodological summaries of this study and selected studies
conducted on Canadian and American sawmilling industries

 

 

Author(s) Model specification Functional Sample

(year) form range

Nautiyal Long-run cost function: Translog 1965-81

and C=f(QiWK9WLiWEiWM;T)

Singh

(1985)

Martinello Long-run cost function: Translog 1963-82

(1985) C=f(Q,WK,WL,WE,WM;T)

Banskota Total cost function for cross-sectional data:: Translog 1978

etal. C: ,W ,W,W ,W cross-

(1985) “Q K L E M) sectional

Singh Long-run total cost function: Translog 1955-

and C:f(Q’WK’WL’WE’WM;T) 1982

Nautiyal

(1986)

Stier Restricted (two exogs. variables) cost Translog 1958-74

(1980) function:

C=f(Q,WK,WL;T)

Abt Variable (short-run) cost function: Translog 1963-78

(1987) VC = f(Q, K, WLaWM ; T) pooled
data

Puttock Variable (short-run) cost function: Translog 1980-84

and VC = f(Q,K,W,,WE,W,,) pooled

Prescott data

(1992)

This Long-run cost function: Translog 1961-00

StUdy Ct =gt(Qr’WKr’WLt’WEr’WMr;T)

 

 

The following five tables show discrepancies among the seven selected

previous studies in reporting the required parametric results. Examining each

study’s model specification reveals that database structural limitations were the

sources of the discrepancies (Table 6.8). In contrast, this study reports all the

142

 

required parameters. For example, only Nautiyal and Singh (1985) and Singh

and Nautiyal (1986) reported partial own-Allen elasticities of input substitution

(Table 6.9).

Table 6.9. Allen partial own-elasticities (AES) of input substitution from this study

and from two selected studies

 

 

Author(s)/study year 0'22 0m 0'55 UMM
Nautiyal and Singh (1985) -1.95 -8.61 -13.40 -0.88
Singh and Nautiyal (1986) -3.29 -2.14 -10.56 -0.16
This study 024 -5.51 -13.85 -0.10

 

 

Table 6.10. AES cross-elasticities of input substitution from this study and from

four selected studies

 

 

Author(s)/study year 02K 0'25 ULM 0105 01014 GEM
Nautiyal and Singh 0.93 0.49 0.60 3.56 1.24 1.36
(1985)

Martinello (1985) 0.23 1.36 0.00 0.04 0.58 1.93
Banskota et al. 1.73 1.35 0.06 1.97 -0.05 0.78
(1985)

Singh and Nautiyal 2.58 4.49 0.24 -0.40 -0.62 -0.02
(1986)

This study 1.09 2.18 -0.19 -6.10 0.83 0.57

 

 

143

Table 6. 11. Own-pnce elasticities of derived demand for inputs from this study

and from six selected studies

 

 

Author(s)/study year 5,, gKK 555 gMM
Nautiyal and Singh (1985) -0.48 -1.21 -1.32 -0.44
Martinello (1985) -0.24 -0.30 -1.12 -0.37
Banskota et al. (1985) -0.36 -0.76 -0.07 -1.09
Singh and Nautiyal (1986) -0.86 -0.24 -1.04 -0.69
Puttock and Prescott -0.49 n.r. -2.20 -0.20
(1992)

Abt (1987), US. Western -0.39 n.r. n.r. -0.20
region

This study 008 -0.68 -0.27 -0.05

 

 

Table 6. 12. Cross-price elasticities of derived demand for inputs from this study

and from five selected studies

 

 

Author(s)/study year ELK gLE gLM 3K5 gKM gEM
Nautiyal and Singh 0.13 0.05 0.03 0.34 0.63 0.69
(1985)

Martinello (1985) 0.03 0.21 0.00 0.01 0.24 0.81
Banskota et al. (1985) 0.63 0.49 0.02 0.27 -0.01 0.06
Singh and Nautiyal 0.29 0.44 0.13 -0.04 -0.33 -0.01
(1986)

Abt (1987) 0.01 n.r. 0.39 n.r. -0.19 n.r.
This study 0.13 0.04 -0.09 -0.12 0.44 0.03

 

 

144

 

Table 6.13. TFP growth from this and from a selected study

 

 

Author(s) (year) TF P growth (%)
Martinello (1985) 4.3
This study 5.7

 

Although all of the studies estimated TL form cost functions, the above five
tables of results show that they differ in several ways. Their differences include
model specification details. For example, Stier (1980) specified the production
technology as a function of capital and labor only, while Abt (1987) specified it as
a function of capital, labor, and material only. Moreover, Abt (1987) and Puttock
and Prescott (1992) estimated restrictive variable cost functions. Consequently,
these researchers were unable to analyze the important technological attributes,
such as price elasticity of derived demand for an input, Allen elasticity of factor
substitution, and TFP growth. The missing parameters are crucial for
characterizing an industry’s production technology, which is the ultimate goal of
such studies.

In terms of model specification, Nautiyal and Singh (1985), Martinello
(1985), and Singh and Nautiyal (1986) are similar to that of this study. But, they
also differ from this study and among themselves in analytical depth. For
example, Martinello (1985) did not report AES, but reported TFP growth. Nautiyal
and Singh (1985) and Singh and Nautiyal (1986) reported results on AES, but did

not report TFP results.

145

By comparison, this study possesses features that establish its
uniqueness. They include the following: (i) coverage of a longer time frame
(statistically sufficient sample size); (ii) generation of capital rental price, using
the perpetual inventory method, a methodology that accounts for opportunity cost
of various capital assets, such as machinery and equipment); (ii) a database
structure that details the multioutput and multiinput nature of the Canadian
sawmilling industry; and (iv) the scope of the empirical work, which involves
implementation of two major methods, generating a range of nonparametric and

parametric empirical results.

146

CHAPTER 7 SUMMARY OF THE FINDINGS

This chapter summarizes the two methods and their respective findings. It
was in accordance with recommendations made in the rapidly growing literature
that the two major empirical methods were jointly implemented in this study. The
methods are the nonparametric method, which involved application of the
multilateral index procedure; and the parametric method, which involved
simultaneous estimation of a multivariate regression system of translog form
long-run cost function and three out of four cost share equations that are nested
to the long-run cost function. Sections 7.1 and 7.2 summarize the nonparametric
and parametric methods and results, respectively.

7.1 THE NONPARAMETRIC METHOD AND RESULTS
7.1.1 The Method

Productivity is considered as the core of the science of economics. It is
one of the main engines of economic growth. Researchers attribute the
historically observed increases in capital formation to productivity growth.

There are two forms of productivity: partial factor productivity (PFP) and
total factor productivity (TFP). PFP is real-aggregate output per unit of a given
input quantity (e.g., labor), while TFP is real-aggregate output per unit of real-
aggregate input. Although public and private agencies, such as Statistics Canada
and the US. Bureau of Labor Statistics, analyze and record PFPs - particularly
partial productivity of labor, it has neither scientific nor practical merits, because
output is a function of all inputs and technological change. Hence, the main focus

of this study was on the levels and growth rates of TFP.

147

Growth in TFP is the difference between the growth in revenue-share
weighted real-aggregate output and the growth in cost-share weighted real-
aggregate input. For the purpose of this study, TFP growth is an indicator of
technical improvements and technological progress over the study period.

Measurement and interpretation of the dynamics of TFP require a clear
understanding of many complex factors that influence it. They include R&D
expenditures, inventions, innovations, the rate of technological diffusion,
institutional arrangements, nature and effectiveness of organizations, societal
preferences, natural resource endowment, market demand and supply
conditions, and relationship between labor and management.

Thus, the various terms used to define TFP reveal the challenges to
measure and analyze it and the lack of universally accepted scientific definition
I”, ..

for it. The labels frequently placed on TFP include “a residue a measure of our

71 u

ignorance , Manna from Heaven”, and a measure of “supemorrnal returns” to
investing in R&D — returns that exceed the full opportunity cost of an investment.
In addition to the application of the multilateral index procedure, using the
original data, to measure and analyze the PFPs and TFP, two supplementary
analyses were conducted. The first involved regression of the gross TFP on
output and a time dependent technological variable, while the second dealt with
the application of the multilateral index procedure to simulate effects of raising

capital cost allowance (CCA) and investment tax credit (ITC) and reducing

corporate income tax (ITC) on capital formation and on TFP growth.

148

7.1.2 The Results

First, historical trends in the data are summarized. Then, results without
the changes in taxation are discussed, followed by a discussion on the effects of
the Changes in the tax rates.

Historical Trends in the Data

The first step in applying the multilateral index model to analyze TFP is to
examine closely the trends in the input cost shares in total cost and output
shares in total revenue, the aggregate quantity of inputs and aggregate quantity
of outputs, and the prices of inputs and outputs.

Although researchers often overlook this step, close examination of the
key variables’ behavior over time is crucial as it reveals anomalies in the data.
This allows the researcher to take remedial measures; it enhances the credibility
and scope of the findings; and it provides useful insights into the dynamics of the
technological attributes being analyzed.

On average, aggregate output rose at a faster rate than aggregate input
over the forty-year study period (1961-00). This gave a clear indication that the
industry attained measurable TFP. For example, during the 19603, the output
quantity grew at an average annual rate of 5%, while the aggregate input quantity
increased at a rate of 3%. The average annual growth rates over the study period
also showed similar trends of 5% and 3% for aggregate output and aggregate
input, respectively.

Average annual shares in total cost varied by type of input: the share of

capital remained nearly constant, within the range of 8%, while that of labor

149

declined substantially from more than 46% in the 19603 to 21% in the 19903, a
very important preliminary indicator of a labor-saving production technology. The
share of energy remained steady, within the range of 2%. The share of raw
material (sawlogs) accounted for the largest share and jumped from 43% in the
19603 to 69% in the 19903. These results suggest that targeting raw material for
cost minimization would have been advisable for the industry.

Similarly, the output shares in total revenue revealed that lumber is the
dominant product of the Canadian sawmilling industry. It accounted for average
annual of more than 80% of the total revenue over the study period. The share of
wood residues (wood chips) ranged between 12% and 19%, while that of shakes
and shingles was roughly 1%.

Partial Factor Productivities

Partial factor productivities (PFPs) of capital (PPK), labor (PPL), energy
(PPE) and Material (PPM), were analyzed. All PFPs trended upward, iindicating
that either use of each input declined steadily or the industry had experienced
technical and/or technological improvements over the study period. The ten-year
interval average annual growth rate of PPK ranged between 3% and 4%; that of
PPL between 3% and 5%; that of PPE between 1% and 5%; and that of PPM
between 2% and 3%.

Total Factor Productivity

When the multilateral index model is used, growth in total factor

productivity (TFP) is the difference between the revenue-share weighted output

quantity growth rates and the cost-share weighted input quantities. Overall, TFP

150

followed upward trends in output and input quantities over the forty-year study
period. The average annual growth rate of TFP over the study period was 2.0%.
However, rapid annual fluctuations were observed.

Output and Time Dependent Technology as Sources of TFP Growth

Output expansion and technological progress are commonly identified as
major sources of TFP growth. To examine their effects, two regression models
were estimated. The first model used the quadratic form in output, while the
second used the natural log of output and time trend variable. The GLS method
with the Cochrane-Orcutt iterative estimation procedure was used in order to
minimize the potential problem of autocorrelation.

Overall, both models performed reasonably well. The estimated
coefficients were highly significant, except for the constant in Model 2; and their
signs met the hypotheses that were set forth in accordance with economic theory
(Table 5.6). The R2 of each model was more than 98%; and the Durbin-Watson
(DW) statistics were 1.632 and 1.795 for Models 1 and 2, respectively.

According to the results of the first model, the marginal effect of increasing
aggregate output on TFP growth was more than 44%, ceteris paribus. But, the
coefficient on 02 was -0.0353, indicating TFP rose (accelerated) with output at a
declining rate of 3.5%.

In the second model, the coefficient on InQ (= natural log of aggregate
output) was interpreted as an elasticity of TFP with respect to Q. For example, a
1% increase in Q would generate approximately 0.3% average annual growth in

TFP, ceteris paribus. The coefficient on T, on the other hand, indicated that the

151

marginal effect of technological progress on TFP growth. It showed that the
average annual TFP growth rate was 0.62% over the study period.
Effects of Changes in Taxation Policy Instruments

The analysis of effects of raising CCA and ITC and reducing CIT on
capital formation and on TFP growth was based on the hypothesis that all three
fiscal policy measures would lead to an enhanced rate of capital formation and
TFP. This hypothesis was expected to be supported through three outcomes: a
higher share of capital in total cost; a higher intensity of capital in the production
technologY; and a slightly lower gross TFP due to fixed aggregate output and
inputs (labor, energy, and Material).

Since capital formation increased capital stock, which in turn raised
aggregate input quantity, the with policy change TFP (TFP2) was expected to be
slightly lower than that without policy change TFP (TFP1). The results are
summarized as follows:

Cost Shares: Cost shares were considered as implicit measures of capital
formation due to the tax incentives. As expected, capital formation rose
substantially. Over the study period, the average annual share of capital in total
cost with the changes was estimated at 12.3%, while that without the changes
was 8.6%. This outcome suggested an enhanced capital formation.

Capital Intensity: High capital intensity was expected to indicate a production
technology characterized by more machinery, and equipment; and hence, higher
productivity. It was observed that capital intensity increased steadily with the

changes in taxation. Over the study period, the average annual real-capital stock

152

 

per worker was estimated as $15,263.70 with the changes compared to
$10,402.91 without the changes.

Effects on TFP: Higher capital formation, motivated by the tax incentives, raised
aggregate quantity of the inputs significantly, while the aggregate output and the
other inputs were unchanged. As expected, TFP2 was slightly lower than TFP1.
The gap between the two measures (i.e., TFP2 minus TFP1) ranged from a least
average annual rate of 0.3% in the 19603 and 4.1% in the 19903.

7.2 THE PARAMETRIC METHOD AND RESULTS

7.2.1 The Method

The parametric approach involved specification and optimization of a dual-
long-run neoclassical cost function. It was assumed that solving a general
optimization problem was feasible. That is, given exogenously determined output
level and input prices, firms in the sawmilling industry would choose the optimal
combination of the inputs of capital, labor, energy, and material, subject to the
technological constraint.

There are several reasons why estimating a dual-long-run cost function
was considered more effective than estimating a production function. Firstly,
there is no serious problem of multicollinearity among input prices as there is
among input quantities. Secondly, government policy measures regarding timber
harvesting (e.g., the annual allowable harvest rate restrictions imposed by the
provinces) are very likely to lead to situations where exogenous forces determine
output levels. Thirdly, since firms in the sawmilling industry compete with other

firms in the economy for the same inputs, output levels and input prices are

153

exogenously determined. Fourthly, recent developments in duality theory have
enhanced the appeal of the cost function estimation approach. Fifthly, effective
functional forms, such as the translog (TL) and the generalized Leontief (GL) that
meet theoretical requirements for estimating cost functions have been developed
and verified over the years.

In addition to their ability to represent very general production functions,
the commonly used functional forms, such as the TL form, enable the researcher
to compute several parameters that characterize a given production technology.
The TL functional form has been found to be more reliable than the other forms
in providing a credible approximation of a given technology. It has two important
advantageous properties over other forms: in that it places no a priori restrictions
on substitution possibilities among all the factors of production and it allows scale
economies to vary with the level of output. Accordingly, the TL functional form
was used in this study.

To ensure maximum efficiency, a multivariate regression system of four
equations that included the unrestricted TL total cost function and three of the
four input cost share equations was estimated, applying the IZEF/MLE. By
imposing required restrictions on the long-run TL form cost function, six models
were tested for their capability to describe the Canadian sawmilling industry’s
production technology. Model I was the unrestricted long-run TL cost function.
The restricted-test ones were Model II for Hicks-neutrality of technological
change, Model III for presence of technological change, Model IV for

homotheticity, Model V for homogeneity, and Model VI for unitary elasticity.

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The six models in the multivariate regression system were estimated
simultaneously. The likelihood ratio (LR) test procedure, which does not utilize
least squares and does not rely on the normality of the error term, was used to
test the specified theoretical restrictions. Based on the results of the LR tests and
the objectives of the study, Model I, which possesses relatively full technological
information, was selected as the model capable of describing the Canadian
sawmilling industry’s production technology.

The estimated parameters of Model I were used to analyze several
technological attributes that include the elasticities of Input substitution, the own-
and cross-price elasticities of derived demand for inputs, the elasticity of total
cost with respect to output, scale effects, the dual measure of TFP growth in the
absence of scale effects, TFP growth in the presence of scale effects, returns to
scale, economies of scale, and technological change biases.

7.2.2 The Results
Input Substitution Elasticities

The degree of substitutability among all factors of production has far
reaching economic implications. Generally, the purpose of the production
function is to describe the substitution possibilities among inputs so that a least-
cost combination of inputs is attained to produce a given level of output most
efficiently.

Because, the Allen elasticity of substitution (AES) has been found to be
more credible than the Morishima elasticity of substitution (MES), only the AES

results are summarized here. The estimates of AES revealed that the pairs of

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labor/capital (1.091), labor/energy (2.183), and capital/ material (0.831) were
substitutes to each other. In contrast, labor/material (-0.189) and capital/energy (-
6.104) were complements. Notice that substitution of labor for capital and labor
for energy were relatively easier than any other input pairs; and there were
significant complementarities between labor/ material and capital/energy.

Moreover, it was observed that the own-elasticities of substitution of labor
and material were less than one and were statistically not different from zero.
This results suggest that demands for these inputs were not responsive to either
their marginal productivity ratio or to their price ratio. In short, the AES findings
made logical and economic sense, because productive inputs were expected to
be “neither perfect substitutes nor perfect complements”.

Price Elasticities of Derived Demand for Inputs

The cost-minimizing, optimal-derived demand for the ith input is a function
of all inputs that characterize the dual-Iong-run cost function, the prevailing
coordination structure of the production technology, the level of output, the prices
of all inputs, and the state of prevailing technology.

The own-price elasticities were inelastic, with values of -0.079, -0.676, -
0.270, and -0.050 for labor, capital, energy, and material, respectively. The
cross-price elasticity between capital and energy (-0.123) shows
complementarity between these inputs. All other cross-price elasticities were

positive, suggesting that those input pairs were substitutes.

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The highly inelastic nature of the own- and the cross price elasticities
indicated that each input was treated as a “basic” good. In effect, the low values
of price elasticities suggested presence of input price “rigidity”.

Elasticity of Total Cost
To observe degree of responsiveness of total cost of production to

expansion of production operations, the elasticity of total cost with respect to

output, ECQ, was calculated. Its average annual rate over the study period was

0.249, indicating that the Canadian sawmilling industry’s production technology
exhibited increasing returns to scale (IRTS) over the study period. For example, if
the average annual of the aggregate output had increased by 1%, total cost
would have increased by only 0.25%, ceteris paribus, implying IRTS.
Scale Effects

Scale effects were calculated as unity minus elasticity of total cost with
respect to output multiplied by the rate of output growth. All ten and forty-year
interval annual averages showed positive scale effects. For example, the
average annual measure for the forty-year study period was 0.034. This positive
value of scale effects and the inelastic nature of total production cost indicated
that the industry had gained economies of scale.
The Dual Measure of the Primal TFP Growth

Change in total cost with respect to time is also referred to as the dual
measure of the primal TFP growth under fixed input prices and output quantity.
Equivalently, it is also referred to as cost diminution, i.e., a percentage reduction

in total cost brought about by technological progress.

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Consistent with the theoretical conceptions, the rates were negative. For
example, over the study period, the average annual cost diminution rate was
-2.3%. This result suggested that technological progress contributed to a modest
average annual TFP growth.

Combined Effect of Production Scale and Cost Diminution on TFP Growth

The total of scale effects and cost diminution rate yielded TFP growth. Its
growth rates in the 19603 and in the 19703 were 6.2% and 7.4%, respectively.
But, there were slowdowns in the 19803 and 19903 that led to 4.5% and 4.8%
rates of growth, respectively. Over the forty-year study period, the average -
annual growth in TFP was approximately 5.7%. These findings were consistent
with the other parametric findings, such as the inelastic nature of production cost,
increasing returns to scale, economies of scale, and the modest rate of cost
diminution.

Returns to Scale

Returns to scale (RTS) are inversely related to the elasticity of total cost
with respect to output. The lower the elasticity of cost, the higher the RTS,
implying the industry gained increasing returns to scale (IRTS) over the study
period. The average annual RTS for the study period was 4.02, which implied an
IRTS. Generally, if elasticity of cost with respect to output is less than unity, then,
doubling output should result in less than doubling of total cost; and hence, IRTS.
Economies of Scale

Theoretically, economies of scale(ES) are estimated along the expansion

path, where input prices are constant and total cost is minimized. In other words,

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a positive ES value indicates declining range of a long-run average cost of
production. In this study, unity minus elasticity of total cost with respect to output
is interpreted as ES. All of the ten- and forty-year interval annual averages were
positive. For example, a result of 0.751 per year over the forty-year study period
revealed that the industry had gained measurable ES.

Measures and Effects of Technological Change Biases

The nature of technological change-bias has important socioeconomic
implications. For example, effects of a new technology on employment and
wages depend on whether the new technology is Hicks-neutral, labor-using or
labor-saving. The concept of a factor-using new technology means hiring more of
a given input, while a factor-saving new technology means hiring less of a given
input

At the mean value over the entire study period, the production technology
of the Canadian sawmilling industry was characterized as capital-using (0.002)
and energy-saving (-0.005); but as HICKS-neutral (0.000) for labor and material
inputs. This outcome meant that demand for capital increased while that for
energy declined over the study period, holding prices of other inputs and output
constant.

In contrast, technological change did not have measurable effects on the
demand for labor and material, ceteris paribus. That is, the Hicks-neutrality
outcome means that technological change resulted in proportionate use of labor
and material to produce the optimal output, leaving the marginal rate of technical

substitution between these two inputs and their price ratio unchanged.

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Comparison with Previous Studies

Because there is no study other than this present study that implemented
the parametric and nonparametric methods jointly, only results of the previous
studies that used the parametric method were compared with those of this study
(Section 6.4),

Discrepancies were observed among the selected previous studies in
terms of the reported empirical parameters. Structural limitations of data were the
main sources of the discrepancies. Restrictive cost functions were specified for
several of the selected studies. To Characterize the industry’s production
technology, each study reported results for limited number of parameters.

By contrast, this study not only that it specified a long-run cost
function and reported several parametric results, but also implemented the
parametric and nonparametric methods jointly. Thus, it was possible to fully
explain the dichotomy between the vertical shift in the production technology

frontier and the input driven moment along the frontier.

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CHAPTER 8 CONCLUSIONS, IMPLICATIONS, AND LIMITATIONS

This study started from the hypothesis that enabling conditions, such as
industrial restructuring and rationalizations that enhanced R&D expenditures
coupled with tax incentives resulted in technical efficiency improvements and
technological progress in the Canadian sawmilling industry. The hypothesis was
tested through the estimated magnitudes of and trends in total factor productivity,
capital formation and intensity, scale effects, economies of scale, returns to
scale, input substitution elasticities, and price elasticities of derived demand for
inputs, using the nonparametric and parametric methods.

Conclusions are drawn in Section 8.1. In Subsection 8.1.1, results of the
nonparametric method are used to draw related conclusions, focusing on
addressing the research questions under Themes 1 and 2. Then, in Subsection
8.1.2, results of the parametric method are used to examine the conditions
postulated under Theme 3 and to draw conclusions accordingly. In Subsection
8.1.3, the strength and limitations of this study are highlighted. Policy implications
of the empirical results and future research directions are discussed in Sections
8.2 and 8.3, respectively.

8.1 CONCLUSIONS

8.1.1 Nonparametric and Regression Results

Levels and Growth Rates of Gross TFP: The first research question under
Theme 1 deals with the inquiry into the levels and growth rates of gross TFP.
Results from the multilateral index model showed that TFP followed upward

trends throughout the forty-year study period (1961-2000). The forty-year

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average annual growth rate was 2.0%. However, annual growth changes
revealed significant fluctuations where deep troughs and high peaks were
observed.

What should be of concern to the industry is that its TF P performance was
better in the earlier periods (19603 and 19803) than in the later years of the
19903, when it was sluggish. For example, TF P declined substantially from 3.0%
during the period of 1981-1990 to a marginal average annual growth of 0.62%
during the period of 1991-2000.

TFP is a closely watched parameter of industrial performance and
economic growth. Economists attribute the declining trends in the Canadian
industrial productivity since the early 19703 to several factors, which include the
following: rising energy and labor prices; insufficient R&D expenditures; declining
supply of economically accessible and commercially valuable timber;
environmental quality regulatory restrictions; and international trade disputes,
such as the US. — Canada softwood lumber trade dispute. Thus, also effects of
these and similar factors need to be taken into account to conduct a detailed
study on TFP.

Sources of TFP Growth: The second question under Theme 1 poses
Challenges in identifying the main sources of TFP growth. To address that
question, results of two regression models are summarized as follows:

Output Effect: Regression of TF P on the aggregate output revealed that the later
(i.e., the explanatory variable) had a marginal effect of 0.4429 on TFP. This

meant that output accounted for more than 44% of TFP growth. Thus, it can be

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inferred that strategies focused on expanding production would have improved
efficiency, leading to economies of scale.

Output and Time Dependent Technological Progress: The log-linear regression
model revealed that elasticity of TFP with respect to output was 0.289. That is, a
1% increase in output would have led to approximately 0.3% growth, ceteris
paribus. Furthermore, the same model showed that the elasticity of TFP with
respect to technological progress over time was 0.62%. This suggests that
inventions and innovations through R&D might have played important roles in
improving TFP performance of the industry. Thus, the results show that output
growth and technological progress jointly contributed to TFP growth.

The parametric results reported in Table 6.1 validate this conclusion. The
results of the coefficients on the time trend variable in the four models of the
translog form total cost function: the unrestricted, the homothetic, the
homogeneous, and the unitary elasticity revealed that the industry recorded
average annual growth of TFP within the range of 2% and 3% over the forty-year
study period.

The average annual TFP growth obtained with the implementation of the
multilateral index model is equal to the growth obtained by estimating the
unrestricted translog cost function. Both methods estimated a 2% growth rate of
TFP. This is an encouraging outcome that indicates credibility of the data,
robustness of the empirical results, and the scientific merit of the joint

implementation of the two methods.

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Effects of Changes in Taxation Policy Instruments: The business community
and policy makers argue that tax incentives are often required to spur capital
formation and thereby to enhance productivity and competitiveness. To address
the research question under Theme 2, a simulated analysis of the effects of
increasing capital cost allowance (CCA) and the investment tax credit (ITC) and
of reducing corporate income tax (CIT) was conducted. The results showed that
these tax incentives could indeed stimulate capital formation (i.e., net
investments in various capital assets and R&D), leading to TFP growth.
8.1.2 Parametric Method

The key outcome of the parametric analysis was that a dual-long-run,
nonhomothetic, translog form cost function described the Canadian sawmilling
industry’s production technology. Thus, the parametric results of that cost
function were used to examine the conditions postulated under Theme 3 and to
draw conclusions as follows:
Elasticity of the Total Cost: Reflecting the modest gains of economies of scale
and returns to scale, the elasticity of the total cost of production with respect to
output was less than unity. For example, the average annual elasticity over the
study period was 0.249. This value meant that cost increased proportionately
less than the proportionate increase in output, such that a 1% rise in output
would have resulted in only 0.25% increase in total cost, ceteris paribus.
Economies of Scale: Economies of scale are attained within the declining
range of the long-run average cost curve. One minus elasticity of total cost

provided estimates of economies of scale. An average annual result of 0.751

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suggested that the industry had gained modest economies of scale over the
forty-year study period.

Returns to Scale: Estimated as a reciprocal of the elasticity of total cost with
respect to output, the industry recorded significant increasing returns to scale.
Consistent with previous studies, the average annual RTS over the study period
was 4.02.

Determinants and Rate of TFP Growth: TFP growth was decomposed into two
main detenninants: scale effects and cost diminution rate. The sum of the effects
of these two technological attributes revealed that the average annual rate of
TFP growth was 5.7% over the study period. Thus, combined effect of the
mutually reinforcing forces of production scale and cost diminution resulted in
measurable TFP growth.

The Dual Measure of the Primal TFP: The change in total cost with respect to
time, which is the diminution rate of production cost, is referred to as the dual
measure of the primal TFP growth under given input prices and output. A
negative value of this measure is an indicator of technological progress. Over the
study period, —2.3% average annual value of this measure implied modest
contribution of technological progress to TF P growth.

Price Elasticities of Derived Demand for Inputs: While they were statistically
significant, both the own- and cross-price elasticities showed that input demands
were price inelastic. This outcome indicated that each input was treated as a
“basic” good; and that input price “rigidity” prevailed in the industry over the study

period. However, there were opportunities for substituting one input for another to

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a limited extent. With the exception of capital/energy and energy/capital, which
were complements, the pairs of labor/capital, labor/energy, capital/labor,
capital/material, energy/labor, and material/capital were substitutes.

Effects of Technological Change-Bias: Over the study period, the Canadian
sawmilling industry’s production technology was characterized as capital-using,
labor- and raw material-saving, and Hicks neutral for energy. This means that
there was increasing demand for capital, holding prices of other inputs and
output constant. In contrast, management might have minimized demands for
labor and raw material as their respective prices increased, ceteris paribus.
Hicks-neutrality for energy implied that technological change did not affect
demand for it.

Input Substitution Elasticities: The input pairs of labor/capital, labor/energy,
capital/ material, and energy/ material were substitutes to each other. On the
other hand, the pairs of labor/ material and capital/energy were complements.
Only the labor/energy substitution elasticity was positive and greater than unity,
suggesting that it was easy for the industry to substitute labor for energy.

With the exception of the significant substitutability between labor and
energy as well as significant complementarity between capital and energy, all
other elasticities were less than unity, implying that it was not that easy for the
industry to substitute one input for another.

Three key conclusions are worth reiterating. Firstly, the nonparametric and
parametric results showed that technical efficiency improvements and

technological progress contributed to the growth of the industry’s productivity.

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Secondly, it was observed that the industry had gained economies of scale over
the study period. Thirdly, it was verified that tax incentives do indeed spur capital
formation and consequently enhance TFP.

However, the multilateral index model revealed annual irregularities in
TFP over the study period. That is, the Canadian sawmilling industry’s annual
TFP performance fluctuated rapidly and tended to decline in the later years (i.e.,
the 19903) of the forty-year study period.

It is difficult to pin point specific causes of the instability and the tendency
to decline, because several factors influence TFP growth. In fact, effects of most
of the presumed factors, such as international trade disputes, the globalization of
markets, taxation, industrial policy measures, stumpage fee charges, and
restrictive environmental regulations, are beyond the control of the industry and
the scope of this study.

But, it is recommended that the industry look into the factors over which it
has some control and makes necessary adjustments. For example, the following
and similar actions will lead to enhanced TFP and thereby an improved
competitiveness: increasing investments in R&D; improving quality of human
capital through skill upgrading on site and formal training; diversifying output mix;
ensuring harmonious relationship between management and labor unions;
improving plant level efficiency; and reviewing overall efficiency of the

management system.

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8.1.3 Some Features of Strength

This study’s strength and its contributions to the body of knowledge are
summarized here. Several features make it different from any of the previous
studies:
Structure of Data: To conduct credible analysis, the statistical adequacy of the
data sets, assessed in terms of parsimony, sample size, consistency, and
predictive power, is imperative. As detailed in sections 1.3 and 6.4, this aspect is
one of the features that established credibility of this study. Compared to the
previous studies (Section 6.4) that did not cover more than 20 years, this study
has covered 40 years. Thus, historical trends in the data and dynamics of
multiple technological attributes were analyzed for a much longer period than
was done previously.
Rental Price of Capital: Unlike the previous studies that used various implicit
derivation techniques, the perpetual inventory method, which accounts for
opportunity cost of a given capital asset, was used in this study. For each of the
three assets of capital, the rental price of using a given asset was calculated with
the application of the perpetual inventory method (Section 4.2). This rental price
reflects the effects of corporate income tax rates, investment tax credits, and
property taxes on the true cost of capital investments. It includes the interest cost
of the funds in physical assets, economic depreciation, and capital gains or
losses due to changing asset prices.
Completeness of Database: A complete database structure that details the

multi-output and multi-input nature of the industry was used. Many of the

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previous studies did not specify the industry’s production technology as it was
done in this study.

Joint Implementation of Two Major Empirical Methods: This is the main
feature that establishes uniqueness of this study. As argued in Chapter 2, there
is a need for joint implementation of the nonparametric and parametric methods.

The key scientific merit of the joint implementation is that it enables the
researcher to explain the dichotomy between the vertical shift in the production
frontier, which is analyzed with the application of the nonparametric method, and
the input driven moment along the frontier, which is analyzed with the application
of the parametric method.

The following important features make the nonparametric method
particularly attractive and credible: it displays input, output, and productivity
measures in index form by data point; reveals data anomalies that prompt the
researcher to take remedial measures; allows multiregional and international
comparisons; enables measurement of productivity levels and growth rates; is
easily understood by nonspecialists, such as policy makers and business
executives; avoids the usual problems of model specification and estimation
associated with parametric models; and explains the degree of vertical shift in the
production frontier. In addition, results of this method serve as benchmarks for
parametric empirical work due to their simplicity and transparency.

The main drawback of the nonparametric method is that it does not
provide parametric measures, such as price elasticities of derived demand for

inputs, elasticity of production cost with respect to output, and economies of

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scale that characterize a given production technology. This can only be achieved
”by using an econometric method. Thus, the joint implementation of the two
methods has strengthened this empirical work.

Factor Cost Shares in Total Cost and Productivity Performance: Factor
cost shares provide useful information on resource allocation by revealing the
inputs that account the greatest proportion of the total cost of production. With
this information, decision makers can target the inputs whose costs need to be
minimized so that productivity is improved. The nonparametric method involved
calculation of factor shares in total cost that served as weights of the aggregate
input quantity and output shares in total revenue that served as weights of the
aggregate output in calculating TFP (Section 5.1).

Ten-year interval average annual growth rates revealed that in the 19603
capital, labor, energy, and sawlogs accounted for 9%, 46%, 2%, and 43% of the
total cost of production. In the 19903, however, each factor accounted for 8%,
20%, 2%, and 69%. The shares of capital and energy remained almost constant,
while that of labor declined, suggesting declining demand for labor input. The
substantial increases in the share of sawlogs implied rising demand for these
inputs over the study period, signaling growth in production operations over the
years.

Consequently, sawlogs accounted for the least partial factor productivity. This
result indicated that sawlogs contributed to the rapidly fluctuating trends in gross
TFP. Hence, targeting sawlogs for cost minimization would have been advisable

for the industry.

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Completeness of the Parametric Measures: The extensive nature of the
empirical results adds to the strength and scope of this study. It has used more
parametric measures than the previous studies discussed earlier to characterize
the Canadian sawmilling industry’s production technology.

Taxation Policy Instruments: Taxation policy affects the way in which scarce
economic resources are allocated. In this study, the nonparametric method was
used to analyze effects of investment tax incentives that involved increasing the
capital cost allowance and the income tax credit as well as reducing the
corporate income tax on capital formation and TFP growth. It was observed that
the tax incentives indeed stimulated capital formation that led to TFP growth.

In short, this study characterizes the Canadian sawmilling industry’s
production technology more fully than was done previously. The theoretical
dichotomy of the vertical shift in the production frontier due to technological
progress, inferred through the growth rates of TFP, and the input driven
movements along the frontier due to technical efficiency improvements, gauged
with several parametric measures, was fully explored with the joint
implementation of the two empirical methods. In addition, the effects of
investment tax incentives on capital formation and TFP growth were explained.
8.2 INDUSTRIAL POLICY IMPLICATIONS
A. Some Perspectives on Canada’s Industrial Forest Policy

Because markets alone cannot achieve required technical efficiency
improvements and technological progress, industrial forest policy is necessary.

That is, notwithstanding the debate about the degree of a govemment’s

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intervention to correct market failure and to participate in the workings of the
economy, the market mechanism left on its own leads to sub-optimal outcomes
in many cases. Thus, a range of industrial policy instmments is needed to foster
productivity and thereby economic growth.

At the federal level, Canada’s industrial policy instruments aim at
improving macroeconomic performance; maintaining competitive positions of
industries in the global marketplace; assisting the provincial and territorial
governments in managing natural resources in a sustainable manner; diversifying
and developing community-based economies; and enhancing R&D investments.

Specific policy instruments that focus on forest resource-based industries
are crucial in Canada, not only because Canadians demand for sustainable
supply of the multiple benefits from their forest resources, but also because
forest products’ export earnings account a larger share of trade balance, varying
by province. For example, in 2005, the Canadian Forest Service reported that the
total value of Canadian forest-products’ export earnings was $41.9 billion, which
was regionally distributed as British Columbia, $13.7 billion (33%); Quebec,
$11.6 billion (28%); Ontario, $8.4 billion (20%); and other provinces, $8.2 billion
(20%).

The Canadian forestland tenure system also plays important role in
sustainable forest ecosystem management. The 10 provinces and three
territories have jurisdictional authority over 77% of Canada’s forest resources
(Canadian Forest Service 2006a). They develop and enforce policy instruments;

allocate timber-harvesting licences; set and collect stumpage fees; and collect

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data. The federal government is steward of 16% of the national forest resources,
while 7% is owned privately. The federal government is responsible for matters
related to the national economy (e.g., fiscal and monetary policies), international
trade and investments, federal lands and parks, and forest resource development
issues that deal with Aboriginal peoples.

Moreover, the rising trends in globalization and Canada’s commitment to
the rules of several international trade organizations (e.g., GATT and WTO) and
to the Kyoto Protocol on climate change have implications on the economic
performance and competitiveness of forest products industries.

Thus, the multidimensionality of the federal govemment’s industrial forest
policy has implications for technical efficiency improvements and technological
progress in the sawmilling industry. This study implemented two major empirical
methods jointly to examine the effects of an array of issues on the productivity
performance of the Canadian sawmilling industry. Several nonparametric and
parametric measures were used to analyze dynamics of multiple technological
attributes over a forty-year period.

B. Implications of the Key Empirical Findings

Because of the extensive nature of the nonparametric and parametric
findings, policy implications of the key ones are summarized here.

Total Factor Productivity: Total factor productivity (TFP) growth is considered
as one of the engines of economic growth. Its importance is manifested through
the facts that it has become a workhorse of empirical economic growth analysis

and that it is a closely watched government statistic.

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TFP is a consequence of the dynamics of several forces, such as
technological progress attained mainly through enhanced investments in R&D,
the quality of human and physical capital, institutional arrangements, and
efficiency of the management system. It is the best available yardstick to
measure and analyze performance of a given economic entity, such as a firm
and an industry.

For the purpose of this study, TFP growth is considered as an indicator of
output growth realized through the combined effects of scale of production and
technological progress, revealed through the rate of cost diminution. The two
mutually reinforcing effects cause vertical shift in the frontier of the production
technology.

Annual growth results revealed that the Canadian sawmilling industry’s
TFP fluctuated rapidly over the study period. In addition, it was observed that the
industry’s TFP performance was better in the earlier periods (19603 and 19803)
than in the later years of the 19903, when it was sluggish. Thus, it is
recommended that the industry take immediate policy measures to improve its
TFP performance. The measures can involve overall restructuring and
rationalization as well as enhanced investments in R&D and in human capital
quality improvement through formal and informal (on site) training.

Input Substitution Elasticities: One of the implications of the cost minimization
assumption in studies such as this is that a rise in one input’s cost increases total

cost, calling for substituting one input, whose price is lower for another, whose

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price is higher. For this to be realized, however, the degree of substitutability, i.e.,
the elasticity of input substitution, must be greater than unity.

In this study, less than unity elasticities of substitution between pairs of
most of the inputs revealed that the industry experienced limited input
substitution opportunities over the study period. Hence, it can be inferred that the
lack of flexibility in input substitution might have contributed to the fluctuation of
TFP over the study period.

However, the nature of substitutability by itself has some merits. For
example, because sawlogs accounted for nearly 70% of the total cost of
production, the limited degree of substitutability between capital and sawlogs (the
sole raw material) suggested that introducing technology (e.g., modernizing
equipment and machinery) that would have enhanced efficiency in harvesting
timber and in processing sawlogs would have been an important policy action to
minimize cost.

According to the AES results, the input pairs of labor/material and
capital/energy were complements. Complementarity has important implications
on cost of production. For example, if rental price of capital rose, the price of
energy also would rise. This would lead to significant rise in total cost. Thus,
targeting the pairs of inputs for cost minimization would be advisable for the
Canadian sawmilling industry.

Own- and Cross-Price Elasticities of Derived Demand for Inputs: Only
capital and energy were found to be complements in production, while the other

inputs were substitutes. The highly inelastic nature of the price elasticities

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indicated that each input was treated as a “basic” good; and, hence, there was
input price “rigidity”. This condition is believed to be one of the sources of
inefficiency along the production line, because cross-price effects, substitution
effects, and output effects are mutually reinforcing factors that influence the
demand for an input and thereby productivity.

Impacts of Biased Technological Change: The production technology of the
Canadian sawmilling industry was characterized as capital-using, energy-saving,
and Hicks-neutral for labor and material. That is, technological change resulted in
rising demand for capital; declining demand for energy; and no effect on the
individual demand functions for labor and material, ceteris paribus.

Biased technological change has important economic implications that call
for a continual research on the dynamics of factor supply and demand. For
example, the capital-using result suggests need for investments in machinery,
equipment, and computer hardware and software in order to improve efficiency.
On the other hand, the Hicks-neutrality on labor and material implies that
technological change in the Canadian sawmilling industry might have led to the
use of labor and material proportionately to produce an optimal output, 0',
leaving the marginal rate of technical substitution of martial for labor or vise versa
as well as the price ratio of the two inputs fixed. That is, the isoquant moved
inward (toward the origin) along the expansion path in the production process of
Q. at a least-cost combination of the two inputs. Moreover, the declining demand

for energy might be attributed to the rising trends in its price.

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8.3 LIMITATIONS AND FUTURE RESEARCH DIRECTIONS
8.3.1 Limitations

Strength and value of this study were highlighted in Subsection 8.1.3.

However, like any other empirical work, this study has limitations.
Industry Level Data: In this study, like in all previous studies, using industry
level data was based on a strong assumption that perfectly competitive firms in
the Canadian sawmilling industry were homogeneous in organizational behavior.
That is, all decision making units (DMUs), reacted equally and similarly to shocks
from market and non-market forces. This is very unlikely, because each DMU
has its own unique goals, objectives, resource constraints, and organizational
structure.

However, using national level, aggregated, industrial data was the only
way to obtain data on capital in order to specify the long-run production function
and subsequently the dual long-run cost function that provided full information on
the industry’s production technology. In fact, this is the main reason why all
previous studies used industry level data. In Canada, secondary capital data are
not available at the firm or provincial levels.

Supply Side Focus: This study examined only the dynamics of technological
attributes of the industry. Thus, focus on the supply side only does not explain
fully the competitive position of the industry in the marketplace.

The Role of Time Trend Variable: Using time trend variable as a proxy
measure of technological progress is not reliable, because it is used under a

strong assumption that technological progress is smooth and steady. If the

177

objective is to obtain an exact measure of technological progress, this problem is
quite serious. But, if the objective is to test for the existence of technological
change and statistical significance of its impact on production cost, this approach
is valid. Hence, like all previous studies (Section 3.1), this study used time as an
indicator of presence of technological progress over the forty-year study period.
8.3.2 Future Research Directions

To rectify the above identified limitations, the following long-term research
projects are warranted:
Firm Level Studies: Although by far more effective than economy wide
(macroeconomic) studies, industrial studies are less effective than firm specific
studies. That is, decision-making unit (DMU) level cost and/or production function
models are statistically more effective in generating credible parametric results
than those specified at industry level. This is because the models are not
affected by the usual data aggregation problems associated with industry and
macroeconomic data. Particularly, parameters such as economies of scale and
returns to scale are more meaningful at the firm level than at an industry level. In
addition, DMU level studies conducted at provincial levels will have highly
relevant industrial policy implications. But, it should be realized that there would
be challenges in acquiring correct annual flow and stock of capital data.
North American Inter-regional Comparative Studies: There are at least three
regions between Canada and the United Sates where there are distinctively
different links of trade. The rates and types of the flow of goods and services

between the Canadian Maritime Provinces and the state of Maine are different

178

from those between the central Canada provinces of Ontario and Quebec, which
are closely linked to the Lake States. The same situation applies between the
Prairie Provinces and British Columbia, which have close trade ties with the
western states of the United States. In short, there are opportunities for
conducting interregional comparative analyses of productivity performance of
production technologies of the Canadian and American sawmilling industries.
The same projects can be initiated for the pulp and paper industries and other
forest products’ industries.

To sum up, despite the limitations, several features have established the
strength and uniqueness of this study. Unlike other previous studies, the
statistical adequacy of the empirical work has been validated. The joint
implementation of the nonparametric method and the parametric method made it
possible to use dynamics of multiple technological attributes to fully explore the
dichotomy between the vertical shift in the production technology frontier,
realized through technological progress, and the input driven movements along
the frontier, realized through technical efficiency improvements. Important policy

implications of the empirical findings were also highlighted.

179

APPENDICES

180

Appendix A. Primary variables and their sources, and derived variables

Table A.1. Industrial output data

 

VARIABLES

SOURCES

 

Total lumber output

The Canadian Forest Service (2006a). Selected
Forestry Statistics Canada, Table l-4, complete time
series from

http://www.nrcan.qc.calselfor/1 com prod ship/newli-
4 tot e.htm (accessed June 2006).

 

Quantity and value of
lumber shipments for
deriving implicit price
senes

1) The Canadian Forest Service (2001). Selected
Forestry Statistics Canada Special Edition — Historical
Series, Table I-6 for the 1970-96 period

2) Statistics Canada Catalogue No. 35—204 and 35-250
for 1961-69 and 1997, while the three data points
(1998-00) were estimated based on the historical
sefies.

 

Value added in
production of shakes and
shingles

1)The Canadian Forest Service, Selected Forestry
Statistics Canada, Information Reports: E-X-34 (1984)
Table lV-4 for 1970-82 and E-X-48 (1995) Table III-17
for 1983-1993; and for 1994-00 from

http://www2.nrcan.qc.ca/cfs-scf/selfor/defauIt.html, (accessed
June 2006)

2) Statistics Canada Catalogue No. 35-204, 35-250,
and 31-203 for 1961-69

 

 

Industrial product price
index (IPPI) (1992 = 100)
for shakes and shingles
for deriving implicit
quantity series

 

The Canadian Forest Service (2001). Selected Forestry
Statistics Canada Special Edition - Historical Series,
Table V-1 complete series for 1961-99; and Statistics
Canada Catalogue No. 62-011 for year 2000

 

181

 

 

Aggregate quantities and
prices of wood residues
sold to pulp mills

 

 

1) Quantities and prices: Manning, G.H. 1972. The
utilization of wood residue in Canada. Info. Rep. E-
X-13, Forest Economics and Research Institute,

Environment Canada, Forestry Service, for 1961-68

2) Quantities and prices: (a) The Canadian Forest
Service (2001). Selected Forestry Statistics Canada
Special Edition — Historical Series, Tab/e l-3 for the
1970-99 and (b) for 1969 Statistics Canada Cat. No.
25-001; 35-204, and 35-003, while the single data point
for 2000 was estimated, based on the historical data.
3) IPPI (1992 = 100) for wood industries from The
Canadian Forest Service (2001), Selected Forestry
Statistics Canada Special Edition — Historical Series,
Table V-1 for 1961-99 and Statistics Canada Catalogue
No. 62-011 for year 2000

 

Table A. 2. Industrial input data

 

VARIABLES

SOURCES

 

Capital: (a) current and real
dollar expenditures and (b)
price indices and rates of
depreciation for each of the
three components

Special request from Capital Stock Division, Statistics
Canada (details in Section 4.2).

 

Miscellaneous rates for
computing capital rental
prices: (1) investment tax
credit, (ii) corporate income
tax, (iii) capital cost
allowance, and (iv) Scotia
McLeod bond yield

Obtained from the database of Ghebremichael and
Nanang (2004)

 

Labor: Two sets: (a) total
number of employees and
salaries and wages in
production activities and (b)
total number of employees
and salaries and wages in
management and admin.
Activities

Selected Forestry Statistics Canada, Table III-11A.
Principal Statistics for 1961-97 in
http://www2.nrcan.qc.ca/cfs-scf/selfor/defauIt.html.
(accessed June 2006)

Three data points (1998-00) were estimated based on
the historical series.

 

 

Energy: (a) total cost of fuels
and electricity and (b)
industrial energy
consumption price indices for

(a) Cost of fuels and electricity from Selected Forestry
Statistics Canada, Table III-11A. Principal Statistics
from 1961-97 in httpzllwww2.nrcan.qc.ca/cfs-
scf/selfor/default.html, (accessed June 2006)

 

 

 

 

 

182

 

deriving implicit quantity
senes

Three data points (1998—00) were estimated based on
the historical series

(b) Department of Finance Canada, Economic
Reference Tables (old title) and Fiscal Reference Tables
(new title)

 

 

Sawlogs: (i) quantities and
(ii) prices

 

(i) Complete annual series from Selected Forestry
Statistics Canada, Table H in
http://www2.nrcan.qc.ca/cfs-scf/selfor/default.html.
(accessed June 2006)

(ii) Implicit price series were derived from quantities and
values of shipments from Statistics Canada Catalogue
No.25-201

 

Appendix B. Time series of Selected Empirical Results: Summary

Results summarized in Tables 8.1, B2, and B3 (Appendix B) and in

Tables C1 and C2 (Appendix C) were obtained without changes in CCA, ITC,

and CIT. Summarized in Tables D1, D2, D3, and D4 (Appendix D) are results

with the changes.

183

 

 

Table 3.1. Factor shares in total cost without the changes in taxation for the
Canadian sawmilling industry: 1961-2000

 

 

Year Capital Labor Energy Material
1961 8.4 57.9 1.3 32.5
1962 8.4 52.5 1.5 37.6
1963 7.5 52.6 1.4 38.5
1964 7.7 47.9 1.6 42.8
1965 7.8 46.3 1.5 44.4
1966 8.6 44.3 1.6 45.5
1967 9.1 42.1 1.7 47.1
1968 9.3 40.8 1.6 48.3
1969 9.2 37.5 1.5 51.8
1970 10.5 40.6 1.4 47.5
1971 9.6 42.3 1.5 46.6
1972 8.9 44.1 1.6 45.4
1973 7.0 41.2 1.5 50.4
1974 7.3 42.7 2.0 48.3
1975 8.8 41.8 2.0 47.5
1976 7.1 39.0 2.0 52.0
1977 6.1 39.2 2.1 52.7
1978 6.1 39.9 2.1 51.9
1979 6.6 36.7 2.0 54.7
1980 7.9 36.6 2.2 53.3
1981 10.1 37.9 2.8 49.2
1982 10.7 35.1 3.2 51.1
1983 8.6 33.8 3.2 54.3
1984 9.1 33.1 3.3 54.5
1985 9.1 33.4 3.3 54.3
1986 9.7 30.7 2.9 56.6
1987 9.3 32.1 2.5 56.2
1988 9.3 27.5 2.4 60.8
1989 9.7 27.1 2.4 60.8
1990 11.6 27.6 2.6 58.1
1991 11.3 24.5 2.5 61.8
1992 9.8 23.5 2.5 64.2
1993 8.2 22.1 2.3 67.5
1994 8.1 21.3 2.2 68.5
1995 7.6 19.3 2.0 71.1
1996 7.5 19.9 2.1 70.5
1997 7.8 20.0 2.1 70.1
1998 8.4 20.5 2.2 68.8
1999 7.6 18.3 2.1 71.9
2000 8.1 18.0 2.1 71.8

 

 

184

 

Table 8.2. Trends in input quantities without the changes in taxation for the
Canadian sawmilling industry: 1961-2000

 

 

 

Year Capital Labor Enggy Material
1961 1.00 1.00 1.00 1.00
1962 1.00 1.01 1.14 1.06
1963 1.01 1.03 1.22 1.11
196 1.02 1.04 1.24 1.12
196 1.04 1.04 1.28 1.13
196-1.06 1.03 1.33 1.14
196 1.06 1.01 1.30 1.14
196.108 1.02 1.31 1.17
196° 1.14 1.04 1.34 1.22
1970 1.19 1.02 1.31 1.24
1971 1.23 1.05 1.43 1.26
197 1.28 1.11 1.57 1.29
197 1.35 1.16 1.56 1.41
197 1.40 1.12 1.60 1.32
197 1.43 1.03 1.81 1.23
197. 1.45 1.10 1.94 1.41
197 1.46 1.14 1.91 1.45
197 1.48 1.20 1.90 1.51
197° 1.52 1.21 2.16 1.53
19801.55 1.19 2.22 1.50
1981 1.57 1.16 2.22 1.40
198 1.55 1.07 2.17 1.35
198 1.53 1.11 2.17 1.51
198 1.52 1.12 2.15 1.55
198 1.50 1.13 2.30 1.56
198 1.51 1.11 2.26 1.60
198 1.55 1.15 2.36 1.70
198 1.61 1.15 2.20 1.68
198° 1.63 1.12 2.20 1.68
19901.63 1.07 2.23 1.56
1991 1.60 1.02 2.12 1.57
199 1.58 1.06 2.25 1.64
199 1.59 1.10 2.23 1.68
199 1.64 1.16 2.34 1.71
199 1.69 1.16 2.37 1.75
1991.71 1.17 2.43 1.73
199 1.75 1.19 2.27 1.75
199 1.76 1.19 2.04 1.70
199° 1.75 1.19 2.09 1.84
20001.76 1.19 2.04 1.84

 

185

 

 

Table 8.3. Output shares in total revenue without the changes in taxation for the
Canadian sawmilling industry: 1961-2000

 

 

 

Outputs and their respective shares (%)
Year Lumber Shakes & Shingles Wood Residues
1961 89.18 1.34 9.47
1962 90.74 1.37 7.89
1963 89.94 1.81 8.26
1964 88.79 1.30 9.92
1965 85.82 1.14 13.04
1966 86.93 1.03 12.04
1967 82.22 1.34 16.44
1968 82.99 1.70 15.31
1969 80.27 1.30 18.43
1970 74.38 1.08 24.53
1971 88.23 1.66 10.11
1972 90.08 1.61 8.31
1973 91.20 1.20 7.59
1974 85.98 1.02 13.00
1975 82.22 1.80 15.98
1976 83.14 1.62 15.24
1977 86.95 1.46 11.59
1978 89.09 1.47 9.44
1979 89.51 1.06 9.43
1980 84.97 1.26 13.77
1981 80.97 1.18 17.85
1982 80.84 0.95 18.21
1983 86.06 0.79 13.15
1984 84.46 0.99 14.55
1985 82.89 1.11 16.00
1986 83.39 1.15 15.47
1987 81.33 0.98 17.69
1988 80.21 0.94 18.84
1989 77.05 0.92 22.03
1990 73.68 1.10 25.22
1991 74.74 0.96 24.30
1992 79.88 1.03 19.08
1993 84.26 0.74 15.00
1994 82.23 0.56 17.21
1995 69.81 0.55 29.63
1996 82.50 0.66 16.84
1997 84.71 0.74 14.55
1998 83.38 0.66 15.96
1999 84.82 0.43 14.74
2000 80.99 0.77 18.23

 

 

186

 

Appendix C. Partial and Total Factor Productivities and Aggregate Output
and Input Quantities

Table C.1. Partial factor productivity indices without the changes in taxation for
the Canadian sawmilling industry: 1961-2000

 

 

Year Capital Labor EnergL Material
1961 1.00 1.00 1.00 1.00
1962 1.08 1.08 0.95 1.03
1963 1.20 1.17 0.99 1.09
1964 1.24 1.22 1.02 1.13
1965 1.28 1.28 1.05 1.18
1966 1.28 1.32 1.01 1.19
1967 1.26 1.33 1.04 1.18
1968 1.38 1.46 1.13 1.27
1969 1.37 1.51 1.16 1.27
1970 1.33 1.55 1.21 1.28
1971 1.47 1.72 1.26 1.43
1972 1.56 1.80 1.27 1.55
1973 1.64 1.92 1.43 1.58
1974 1.44 1.81 1.26 1.53
1975 1.19 1.65 0.94 1.39
1976 1.60 2.10 1.19 1.64
1977 1.75 2.24 1.33 1.75
1978 1.85 2.29 1.44 1.82
1979 1.88 2.36 1.33 1.87
1980 1.80 2.34 1.26 1.86
1981 1.61 2.19 1.14 1.81
1982 1.50 2.18 1.08 1.73
1983 1.94 2.66 1.36 1.97
1984 1.98 2.68 1.40 1.94
1985 2.23 2.97 1.46 2.15
1986 2.24 3.05 1.50 2.12
1987 2.49 3.34 1.63 2.28
1988 2.36 3.31 1.73 2.26
1989 2.30 3.33 1.70 2.23
1990 2.16 3.28 1.58 2.26
1991 2.11 3.33 1.60 2.16
1992 2.28 3.40 1.60 2.20
1993 2.40 3.47 1.71 2.27
1994 2.46 3.50 1.73 2.36
1995 2.47 3.60 1.76 2.38
1996 2.41 3.52 1.70 2.39
1997 2.41 3.55 1.85 2.40
1998 2.36 3.50 2.03 2.44
1999 2.69 3.96 2.25 2.56
2000 2.77 4.13 2.40 2.65

 

 

187

 

Table C.2. Trends in aggregate input and output quantities and TFP without the
changes in taxation for the Canadian sawmilling industry: 1961-2000

 

 

Year Output Input TFP
1961 1.00 1.00 1.00
1962 1.08 1.05 1.03
1963 1.21 1.12 1.08
1964 1.27 1.14 1.12
1965 1.34 1.15 1.16
1966 1.35 1.15 1.18
1967 1.34 1.12 1.20
1968 1.49 1.17 1.27
1969 1.56 1.25 1.25
1970 1.59 1.27 1.25
1971 1.81 1.32 1.36
1972 1.99 1.43 1.39
1973 2.22 1.63 1.36
1974 2.02 1.49 1.35
1975 1.70 1.31 1.30
1976 2.31 1.60 1.44
1977 2.54 1.70 1.50
1978 2.74 1.83 1.49
1979 2.86 1.89 1.51
1980 2.79 1.84 1.52
1981 2.53 1.69 1.50
1982 2.33 1.53 1.53
1983 2.97 1.76 1.68
1984 3.01 1.82 1.65
1985 3.36 1.85 1.81
1986 3.39 1.88 1.80
1987 3.86 2.07 1.86
1988 3.80 2.07 1.84
1989 3.74 2.04 1.84
1990 3.52 1.82 1.94
1991 3.39 1.77 1.91
1992 3.60 1.91 1.88
1993 3.81 2.02 1.89
1994 4.04 2.15 1.88
1995 4.17 2.23 1.87
1996 4.14 2.22 1.86
1997 4.20 2.26 1.86
1998 4.15 2.18 1.91
1999 4.70 2.40 1.96
2000 4.89 2.41 2.03

 

 

188

 

Appendix D. Selected Empirical Results with the Changes in Taxation

Table D.1. Share of each input in total cost with the changes in taxation for the
Canadian sawmilling industry: 1961-2000

 

 

 

Year Capital Labor Energy Material
1961 11.7 55.8 1.2 31.3
1962 11.6 50.6 1.4 36.3
1963 10.5 50.9 1.4 37.2
1964 10.8 46.3 1.5 41.3
1965 11.1 44.6 1.5 42.8
1966 12.1 42.6 1.6 43.8
1967 12.7 40.5 1.6 45.2
1968 12.3 39.4 1.6 46.6
1969 12.3 36.2 1.4 50.0
1970 13.9 39.0 1.4 45.7
1971 13.7 40.4 1.5 44.4
1972 13.0 42.2 1.5 43.4
1973 11.0 39.4 1.4 48.2
1974 11.7 40.7 1.6 46.0
1975 14.7 39.1 1.8 44.4
1976 12.1 36.9 1.8 49.2
1977 11.0 37.1 2.0 49.9
1978 10.6 38.0 2.0 49.4
1979 10.2 35.3 1.9 52.6
1980 11.5 35.2 2.1 51.2
1981 14.1 36.2 2.6 47.0
1982 15.2 33.3 3.1 48.5
1983 12.5 32.4 3.1 52.0
1984 12.7 31.8 3.1 52.4
1985 12.6 32.1 3.1 52.2
. 1986 13.1 29.6 2.8 54.5
1987 12.4 30.9 2.4 54.3
1988 13.2 26.3 2.3 58.2
1989 13.6 25.9 2.3 58.2
1990 15.8 26.3 2.5 55.4
1991 15.1 23.4 2.4 59.1
1992 13.2 22.6 2.4 61.8
1993 11.4 21.4 2.2 65.1
1994 11.2 20.5 2.1 66.1
1995 10.8 18.6 1.9 68.7
1996 10.7 19.2 2.0 68.1
1997 11.0 19.3 2.1 67.6
1998 11.7 19.8 2.2 66.4
1999 10.6 17.7 2.1 69.6
2000 11.0 17.4 2.0 69.6

 

189

 

Table 0.2. Shares of capital in total cost, without and with changes in taxation for
the Canadian sawmilling industry: 1961-2000

 

 

 

 

Shares (%)
Without Change =
Year (Sck1 ) With (Sck2) (Sck2-Sk1)
1961 8.4 11.7 3.3
1962 8.4 11.6 3.2
1963 7.5 10.5 3.0
1964 7.7 10.8 3.2
1965 7.8 11.1 3.3
1966 8.6 12.1 3.5
1967 9.1 12.7 3.6
1968 9.3 12.3 3.1
1969 9.2 12.3 3.1
1970 10.5 13.9 3.4
1971 9.6 13.7 4.1
1972 8.9 13.0 4.1
1973 7.0 11.0 4.0
1974 7.3 11.7 4.4
1975 8.8 14.7 5.9
1976 7.1 12.1 5.0
1977 6.1 11.0 4.9
1978 6.1 10.6 4.5
1979 6.6 10.2 3.6
1980 7.9 11.5 3.6
1981 10.1 14.1 4.1
1982 10.6 15.2 4.5
1983 8.6 12.5 3.9
1984 9.1 12.7 3.5
1985 9.1 12.6 3.5
1986 9.7 13.1 3.3
1987 9.3 12.4 3.1
1988 9.3 13.2 3.9
1989 9.6 13.6 4.0
1990 11.6 15.8 4.2
1991 11.3 15.1 3.8
1992 9.8 13.2 3.5
1993 8.2 11.4 3.2
1994 8.0 11.2 3.2
1995 7.6 10.8 3.2
1996 7.5 10.7 3.2
1997 7.8 11.0 3.2
1998 8.4 11.7 3.3
1999 7.6 10.6 3.0
2000 8.1 11.0 2.9

 

 

190

 

Table D.3. Capital intensity without and with changes in taxation for the
Canadian sawmilling industry: 1961-2000

 

 

 

Year Without With Growth (%)
1961 1801.14 2603.62 44.55
1962 1857.55 2662.85 43.35
1963 1840.51 2647.15 43.83
1964 1857.61 2717.38 46.28
1965 1945.04 2876.68 47.90
1966 2186.75 3197.39 46.22
1967 2349.64 3410.07 45.13
1968 2614.60 3602.41 37.78
1969 2978.81 4138.85 38.94
1970 3540.78 4894.60 38.24
1971 3458.61 5185.78 49.94
1972 3400.45 5201.61 52.97
1973 3282.02 5393.84 64.34
1974 3701.26 6215.85 67.94
1975 4773.00 8536.50 78.85
1976 4506.90 8151.51 80.87
1977 4251.60 8070.12 89.81
1978 4598.97 8429.42 83.29
1979 5994.18 9571.75 59.68
1980 7605.27 11496.72 51.17
1981 9548.51 14035.42 46.99
1982 11371.90 17070.21 50.11
1983 10288.68 15625.12 51.87
1984 11435.83 16501.15 44.29
1985 11708.45 16883.66 44.20
1986 13493.56 18816.34 39.45
1987 15094.84 20945.74 38.76
1988 15422.61 22821.86 47.98
1989 16591 .57 24547.00 47.95
1990 20425.74 29189.33 42.90
1991 22649.82 31667.53 39.81
1992 20184.37 28401.46 40.71
1993 18535.52 26798.29 44.58
1994 19487.47 28207.27 44.75
1995 20866.33 30695.27 47.10
1996 20321 .47 29924.69 47.26
1997 21092.15 30931.07 46.65
1998 22279.52 32016.95 43.71
1999 22543.67 32332.54 43.42
2000 24229.84 34133.15 40.87

 

191

 

_ ..-_._ - .wm
.'. 211‘

 

Table 0.4. TFP1, TFP2, and rates of their marginal differences for the Canadian
sawmilling industry: 1961-2000

 

 

Marginal difference
Year TF P1 (without) TFP2 (with) (%)= (TFP2-TFP1)x100
1961 1 .0000 1 .0000 0.0000
1962 1 .0330 1 .0331 0.0095
1963 1.0788 1.0790 0.0143
1964 1.1163 1.1161 -0.0181
1965 1.1615 1.1603 -0.1204
1966 1.1796 1.1772 -0.2415
1967 1.1956 1.1924 -0.3145
1968 1.2719 1.2676 -0.4335
1969 1.2510 1.2436 -0.7459
1970 1.2532 1.2429 -1.0272
1971 1.3649 1.3518 -1.3087
1972 1.3943 1.3796 -1.4614
1973 1.3630 1.3467 -1.6336
1974 1 .3502 1 .3277 -2.2487
1975 1.2972 1.2670 -3.0169
1976 1.4449 1.4190 -2.5844
1977 1 .4998 1 .4744 -2.5351
1978 1 .4948 1 .4703 -2.4428
1979 1.5132 1.4866 -2.6545
1980 1.5170 1.4873 -2.9750
1981 1 .4977 1 .4641 -3.3600
1982 1.5273 1.4904 -3.6916
1983 1 .6822 1 .6499 -3.2340
1984 1 .6518 1 .6220 -2.9798
1985 1.8140 1.7827 -3.1283
1986 1.7985 1.7673 -3.1160
1987 1.8638 1.8317 -3.2120
1988 1.8394 1.8031 -3.6251
1989 1 .8362 1.7980 -3.8106
1990 1.9351 1.8895 ~4.5633
1991 1.9139 1.8710 -4.2902
1992 1.8814 1.8445 -3.6886
1993 1 .8864 1 .8508 -3.5577
1994 1.8830 1 .8450 -3.7946
1995 1.8736 1.8341 -3.9511
1996 1.8619 1.8204 -4.1410
1997 1.8616 1.8185 -4.3121
1998 1 .9070 1 .8605 -4.6445
1999 1.9579 1.9148 -4.3081
2000 2.0274 1 .9818 -4.5546

 

 

192

 

 

References

193

 

T. .'. - 3 1°. nuts. :3... _
v. 9

 

 

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