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MARKET IMPACTS AND POLICY IMPLICATIONS OF US.
RESTRICTIONS ON SOFTWOOD LUMBER IMPORTED
FROM CANADA

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MARKET IMPACTS AND POLICY IMPLICATIONS OF US. RESTRICTIONS
ON SOFT WOOD LUMBER IMPORTED FROM CANADA

By

J ungho Back

A DISSERTATION

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

DOCTOR OF PHILOSOPHY
Department of Forestry

2004

ABSTRACT

MARKET IMPACTS AND POLICY IMPLICATIONS OF US. RESTRICTIONS
ON SOFTWOOD LUMBER IMPORTED FROM CANADA

By
Jungho Back

The softwood lumber trade dispute is the largest and most contentious dispute
between the United States and Canada. The core issue of the dispute is Canada’s
subsidies to its lumber producers in the form of low stumpage fees and restrictions on
log exports in British Columbia (BC). The US. government has imposed restrictions —
the Memorandum of Understanding (MOU) during 198624-199123, the Softwood
Lumber Agreement (SLA) during l996:2-2001:1, and the current 27.2% tariff to
regulated lumber flows from Canada.

With an expanded list of variables for the period of 198021-200124, this study
developed a structural simultaneous system of equations (SSE) and a nonstructural
vector auto-regression (VAR) model to analyze the US. lumber market structure and to
assess the impacts of the US. trade restrictions.

The SSE and VAR models show that the MOU caused Canada’s exports to
decrease by 8-9% during 198624-199lz3, which in turn pushed up the domestic
production by 3.0%, but it did not lead to higher lumber prices. However, the SLA did
not have any significant impacts on Canadian exports, domestic production, and lumber
prices during 1996:2-2001:1. In addition, the results show that, the price elasticities of
domestic and export supply are smaller than those commonly used in evaluating the
gains and losses of the US. restrictions, while such market factors as housing starts, log

prices, and exchange rates have played major roles in shaping the lumber market.

Combining the modest market impacts of the restrictions and smaller price elasticities,
therefore, leads to moderate welfare consequences of the trade restrictions. In addition,
the simulated results under an export/import tax and a quota scheme show that from the
US. perspective, a quota scheme is preferred to an export/import tax for restricting
softwood lumber imported from Canada, as long as all Canadian provinces and all
lumber products are included in the regime. In combination, these findings indicate the
need not only for a broader and more dynamic perspective but also for a comprehensive
approach to understanding the U.S.-Canada lumber trade and designing effective trade

policies.

The assistance, support, and prayer of two
people made this dissertation possible.
I dedicate this work to them with all my love:

my wife, Eunji and my daughter, Jiyeon

ACKNOWLEDGEMENTS

This study would not have been possible without the guidance and assistance of
numerous individuals.

I first express my deep gratitude to my advisor, Dr. Runsheng Yin. His expertise,
questions, and kind critiques gave me direction and the will to “keep on keeping on.”

I am indebted to the members of my committee, Dr. Karen Potter-Witter, Dr.
Larry Leefers, and Dr. James Oehmke. I thank them for their encouragement and
suggestions to this work and the time they shared from busy schedules.

Thanks also to Dr. Joseph Buongiomo at University of Wisconsin, and Dr. Jeffrey
Wooldridge in the Department of Economics for their valuable comments on econometric
analyses.

Finally, I would like to thank my wife, Eunji, my daughter, Jiyeon (Jiya), and my
parents, Donghak, Back and Songja, Shin. Particularly, I would like to express my deep
gratitude to my parents-in-law, Seunghan, Lee and Gunja, Song for their love, support,
and prayers. I love you very much indeed.

Financial support for this project was provided by Dr. Runsheng Yin, Canadian
Studies Program, Department of Foreign Affairs, Canada, Walker Hill Scholarship,
International Studies & Programs, MSU, and Dissertation Completion Fellowship,

College of Agricultural Economics and Natural Resources.

TABLE OF CONTENTS

 

 

 

 

LIST OF TABLES IX
LIST OF FIGURES XII
CHAPTER 1. INTRODUCTION 1
1.1. Statement of Problem ............................................................................................... 2
1.2. Objectives ................................................................................................................. 8
1.3. Hypothesis to Be Tested ........................................................................................... 8
1.4. Dissertation Outline ................................................................................................. 9
CHAPTER 2. U.S.-CANADA SOFTWOOD LUMBER TRADE 11
2.1. North American Softwood Lumber Market ........................................................... 11
2.1.1. U.S. Softwood Lumber Market ....................................................................... 12
2.1.2. Canadian Softwood Lumber Market ............................................................... 16
2.1.3. North American Lumber Industry and Macroeconomic Variables ................. 18

2.2. U.S.-Canada Softwood Lumber Trade Dispute ..................................................... 24
2.2.1. Core Issues of the Trade Dispute .................................................................... 24
2.2.2. History of the Trade Dispute ........................................................................... 26
2.2.2.1. The First Countervailing Duty Investigation ........................................... 26
2.2.2.2. The Second Countervailing Duty Investigation ....................................... 27
2.2.2.3. The Third Countervailing Duty Investigation .......................................... 28
2.2.2.4. The U.S.-Canada Softwood Lumber Agreement ..................................... 30
2.2.2.5. The Fourth Countervailing Duty Investigation ........................................ 32

2.3. Summary and Conclusions ..................................................................................... 36
CHAPTER 3. DATA DESCRIPTION AND TESTING FOR UNIT ROOTS .......... 37
3.1. Data Description ..................................................................................................... 37
3.2. Testing for Unit Roots ............................................................................................ 42
3.2.1. Tests for Structural Change ............................................................................. 43
3.2.1.1. Tests with Known Break Point ................................................................. 44
3.2.1.2. Tests with Unknown Break Point ............................................................. 45

3.2.2. Test Results for Structural Change .................................................................. 47
3.2.2.1. Test Results with Known Break Point ..................................................... 47
3.2.2.2. Test Results with Unknown Break Point ................................................. 51

3.3. Summary and Conclusions ..................................................................................... 53

CHAPTER 4. A STRUCTURAL MODEL FOR US. SOFTWOOD LUMBER

 

MARKET 55
4.1. Theoretical Framework .......................................................................................... 55
4.1.1. Demand for Softwood Lumber ....................................................................... 57
4.1.2. Supply of Softwood Lumber ........................................................................... 58
4.1.3. Canadian Export Supply of Softwood Lumber ............................................... 59

vi

4.2. Econometric Models and Estimation Methods ...................................................... 60

 

4.2.1. A Simultaneous System of Equations (SSE) Model ....................................... 60
4.2.2. A Reduced-Form Equation (RFE) Model ....................................................... 63
4.3. Empirical Results ................................................................................................... 65
4.3.1. SSE Model ....................................................................................................... 65
4.3.1.1. Results of Dataset I .................................................................................. 66
4.3.1.2. Results of Dataset II ................................................................................. 67
4.3.2. The RFE Model ............................................................................................... 70
4.3.2.1. Results of Lumber Price Model ............................................................... 73
4.3.2.2. Results of Canadian Export Supply Model .............................................. 74
4.3.2.3. Robustness of RFE Model in Previous Studies ............................................ 74
4.4. Summary and Conclusions ..................................................................................... 77
CHAPTER 5. A NONSTRUCTURAL MODEL FOR US. SOFTWOOD LUMBER
MARKET 79
5.1. Theoretical Framework .......................................................................................... 80
5.1.1. Johansen Co-integration Test .......................................................................... 80
5.1.2. Vector Error-Correction (VEC) Model ........................................................... 82
5.2. Johansen Co-integration Test ................................................................................. 84
5.2.1. Dataset I ........................................................................................................... 85
5.2.2. Dataset II ......................................................................................................... 91
5.2.3. Testing for Unique Co-integration Vectors ..................................................... 93
5.3. Vector Error-Correction Model .............................................................................. 96
5.3.1. Dataset I ........................................................................................................... 96
5.3.1.1. Basic VEC Model ..................................................................................... 96
5.2.2.2. Parsimonious VEC Model ........................................................................ 98
5.2.2.3. Structural VEC Model ............................................................................ 100
5.3.2. Dataset II ....................................................................................................... 107
5.3.2.1. Basic VEC Model ................................................................................... 107
5.3.2.2. Parsimonious VEC Model ...................................................................... 108
5.3.2.3. Structural VEC Model ............................................................................ 109
5.4. Summary and Conclusions ................................................................................... 114
CHAPTER 6. WELFARE ESTIMATION OF US. RESTRICTIONS ................... 116
6.1. Theoretical Framework ........................................................................................ 1 17
6.1.1. Export Tax ..................................................................................................... 117
6.1.2. Tariff-Regulated Quota ................................................................................. 120
6.2. Welfare Impacts of Trade Restrictions ................................................................ 122
6.2.1. Welfare Impacts of the MOU ........................................................................ 122
6.2.1.1. Case I: an 8% Reduction in Exports ....................................................... 123
6.2.1.2. Case H: a 9% Reduction in Exports and a 3% Increase in Production .. 126
6.2.2. Welfare Impacts of the SLA .......................................................................... 129
6.3. Simulation for Trade Policies ............................................................................... 134
6.3.1. Scenarios ....................................................................................................... 134
6.3.2. Simulation Results ......................................................................................... 135
6.4. Summary and Conclusions ................................................................................... 140

vii

CHAPTER 7. CONCLUSIONS AND POLICY IMPLICATIONS - 143

 

 

 

7.1. Summary of Results ............................................................................................. 143
7.2. Conclusions and Policy Implications ................................................................... 145
LITERATURE CITED 151
APPENDIX A: TABLES 158
APPENDIX B: FIGURES 168

 

viii

Table 2.1.

Table 2.2.

Table 3.1.

Table 3.2.

Table 3.3.

Table 3.4.

Table 3.5.

Table 3.6.

Table 3.7.

Table 4.1.

Table 4.2.

Table 4.3.

Table 4.4.

Table 4.5.

Table 5.1.

Table 5.2.

Table 5.3.

Table 5.4.

Table 5.5.

Table 5.6.

Table 5.7.

LIST OF TABLES

Ownership of forestlands in the US. and Canada (%) .................................... 25
Canadian Lumber Exports to the US. under the SLA ..................................... 32
Data Description ............................................................................................... 40
Summary Statistics ........................................................................................... 41
Results of ADF unit-root tests .......................................................................... 47
Results of ADF unit-root tests with split samples ............................................ 50
Results of ADF unit-root tests with known break point .................................. 51
Results of recursive and rolling unit-root tests ................................................ 52
Results of sequential unit-root tests ................................................................. 52
Results of the SSE model for the US. lumber market ..................................... 69
Elasticities for the US. softwood lumber market ............................................ 70
Results of reduced-form equations for lumber price ........................................ 71
Results of reduced-form equations for Canadian export supply ...................... 72
Sources of price elasticities for softwood lumber used in previous studies ..... 78
Results of lag order selection criteria (dataset I) .............................................. 85
Results of residual tests (dataset I) ................................................................... 86
Results of Johansen co-integration test (dataset I) ........................................... 87
Results of weak exogeneity tests (dataset I) .................................................... 87
Results of lag order selection criteria for endogenous variables (dataset I) 89
Results of residual tests for endogenous variables (dataset I) .......................... 89
Results of Johansen co-integration test for endogenous variables (dataset I).. 89

ix

Table 5.8. Results of Johansen co-integration test (dataset II) .......................................... 91

Table 5.9. Results of Johansen co-integration test for endogenous variables (dataset H) 92

Table 5.10. Results of testing for unique co-integration vectors ...................................... 95
Table 5.11. Results of the basic VEC model (dataset I) ................................................... 98
Table 5.12. Results of the conditional PVEC model (dataset I) ..................................... 100
Table 5.13. Results of the structural PVEC model (dataset I) ........................................ 104
Table 5.14. Results of the basic VEC model (dataset II) ................................................ 108
Table 5.15. Results of the structural PVEC model (dataset II) ....................................... 111

Table 6.1. Results of market and welfare impacts for l986:4-1987:3 under MOU (case I)
................................................................................................................................. 124

Table 6.2. Results of market and welfare impacts for 1986:4-1991:3 under MOU (case I)
................................................................................................................................. 125

Table 6.3. Results of market and welfare impacts for 1986:4-1987:3 under MOU (case II)
................................................................................................................................. 127

Table 6.4. Results of market and welfare impacts for 1986:4-1991:3 under MOU (case H)
................................................................................................................................. 128

Table 6.6. Results of market and welfare impacts for 1996:2-2001:1 under SLA ......... 132

Table 6.7. Results of market and welfare impacts under various trade policies ............. 137
Table 6.8. Estimated economic impacts of import and export tax .................................. 139
Table 7.1. Summary of impacts of the trade restrictions and log market dynamics ....... 144
Table A-1. Results of lag order selection criteria (dataset II) ......................................... 159
Table A-2. Results of residual tests (dataset II) .............................................................. 159
Table A-3. Results of weak exogeneity tests (dataset II) ................................................ 160

Table A-4. Results of lag order selection criteria for endogenous variables (dataset H) 160
Table A-5. Results of residual tests for endogenous variables (dataset II) ..................... 160

Table A-6. Results of residual tests for basic VEC model (dataset I) ............................. 161

Table A-7. Results of F-tests for the basic VEC model (dataset I) ................................. 161

Table A-8. Results of the parsimonious VEC model (dataset I) ..................................... 162
Table A-9. Results of residual tests for basic VEC model (dataset II) ........................... 163
Table A-10. Results of F—tests for the basic VEC model (dataset H) .............................. 163
Table A-11. Results of the parsimonious VEC model (dataset II) .................................. 164
Table A-12. Results of market and welfare impacts under MOU (case I) ...................... 165
Table A-13. Results of market and welfare impacts under MOU (case H) .................... 166
Table A—14. Results of market and welfare impacts under SLA (dataset II) .................. 167

xi

LIST OF FIGURES

Figure 2.1. US. softwood lumber consumption, production, and imports (1980-2001) .. 12

Figure 2.2. US. softwood lumber consumption (2001) .................................................... 13
Figure 2.3. U.S. softwood lumber production by regions (1980-2001) ............................ 14
Figure 2.4. US. imports for softwood lumber (1980-2001) ............................................. 15
Figure 2.5. Canada’s lumber consumption, production, and exports (1980-2001) ........... 17
Figure 2.6. Canada’s lumber exports and market share in the US. (1980-2001) ............. 18
Figure 2.7 Softwood lumber consumption and housing starts (1980: 1-2001:4) ............... 19
Figure 2.8. US. softwood lumber production and log prices (1980:1-2001z4) ................ 20
Figure 2.9. A plot of US. softwood lumber price and log prices in the PNW ................. 21

Figure 2.10. US. lumber imports from Canada and exchange rates (1980: l-2001:4) ..... 22

Figure 3.1 A plot of lumber price series ............................................................................ 48
Figure 3.2. A plot of lumber production series ................................................................. 49
Figure 4.1. Structure of the US. softwood lumber market. .............................................. 57

Figure 5.1. Co—integration vectors and recursive estimates of the eigenvalues (dataset I)90

Figure 5.2. Impulse responses for SPVEC model (dataset I) .......................................... 105
Figure 5.3. One-step and dynamic model-based forecasts for SPVEC model (dataset I)
................................................................................................................................. 105
Figure 5.3. One~step and dynamic model-based forecasts for SPVEC model (dataset I)
................................................................................................................................. 106
Figure 5.4. Impulse responses for SPVEC model (dataset II) ........................................ 112
Figure 6.1. Structure of the US. lumber market under an export tax ............................. 117
Figure 6.2. Structure of the US. lumber market under a tariff-regulated quota ............. 120

xii

Figure B-l. Co-integration vectors and recursive estimates of the eigenvalues (dataset H)
................................................................................................................................. 169

Figure B-2. Fitted and actual values and diagnostics for basic VEC model (dataset I).. 170
Figure B-3. One-step residuals and Chow test of basic VEC model (dataset I) ............. 171
Figure B—4. Fitted and actual values and diagnostic for SPVEC model (dataset I) ........ 172
Figure B-5. One-step residuals and Chow tests of SPVEC model (dataset I) ................ 173
Figure B-6. Fitted and actual values and diagnostics for basic VEC model (dataset H) 174
Figure B-7. One-step residuals and Chow tests for basic VEC model (dataset H) ......... 175
Figure B-8. Fitted and actual values and diagnostics for SPVEC model (dataset II) ..... 176

Figure B-9. One-step residuals and Chow tests for SPVEC model (dataset II) .............. 177

xiii

CHAPTER 1

INTRODUCTION

The softwood lumber trade dispute is the largest and most contentious dispute
between the United States and Canada. The US. is the world’s largest importer of
softwood lumber, with more than 90% of its lumber imports coming from Canada.
Canada is highly dependent on the US. lumber market, with more than 60% of its lumber
production exported to the United States (Howard 2000). For decades the trade volume
between the two countries has risen substantially, with Canada’s share of the US. market
having reached more than 30% in 2000, up significantly from about 15% in 1965. The
core issues of the dispute are the US. claim that Canadian producers have expanded their
US. market share with subsidized stumpage rates — fees paid by forest products
companies to the provinces for the rights to cut trees — and restrictions on log exports in
British Columbia.1 As a result, over the last two decades the US. government has
imposed trade restrictions to regulate lumber flows from Canada. The Memorandum of
Understanding (MOU) required Canada to impose a 15% export tax on its lumber
exported to the US. for the period between the fourth quarter of 1986 and the third
quarter of 1991 (198624-199lz3). The Softwood Lumber Agreement (SLA) mandated
Canada to charge at least $50 per thousand board feet (MBF) for its lumber exports in
excess of 14.7 billion board feet (BBF) per year for the period between the second quarter

Of 1996 and the first quarter of 2001 (1996:2-200121). Currently, the US. government

imposes tariffs of averaging 27.2% on imported Canadian lumber — 18.79% for
countervailing duty (CVD) and 8.43% for anti-dumping duty (ADD), to protect the

domestic lumber market.

1.1. Statement of Problem

Many scholars have studied the impacts of the trade restrictions on softwood
lumber imported from Canada. Myneni et al. (1994) used a simultaneous system of
equations (SSE) to estimate the welfare effect of the MOU (1986-1990). With the
estimated price elasticities of demand (-0.10), supply (0.27), and Canadian export supply
(0.19) they found that US. consumer lost $147.4 million/year (in 1982 dollars), whereas
U.S. producer gained $109.5 million/year for the first 4 years under the MOU. As a
result, the net U.S. loss was about $38.3 million/year. Other studies simply adopted a
reduced-form equation (RFE) in their analyses. Wear and Lee (1993) used an RFE to
investigate the market and welfare impacts of the MOU (1986-1990). They showed that
the MOU reduced Canadian exports by 2.6 BBF/year — a 5% decline in Canadian
market share, which in turn pushed up US. production by 1.83 BBF/year. Coupled with a
price increase of $20/MBF annually, this resulted in a reduction in US. consumption of
0.76 BBF/year. As a result, US. consumers lost about $947.4 million/year (in 1982
dollars), whereas U.S. producers gained about $658.1 million/year, resulting in a net U.S.

loss of $289.3 million/year for the first 4 years under the MOU.

 

1 British Columbia (BC) precludes exports of unprocessed logs to foreign countries. The US. producers
insist that the restriction on log exports prevent non-BC producers from accessing logs harvested in BC. In
addition, the log ban helps keep BC producers’ wood costs artificially low (Ragosta and Clark 2000).

In contrast to the above moderate estimates, more recent RFE studies indicate
substantial impacts from the US. trade restrictions. Lindsey et al. (2000) used the RFE
for lumber prices to estimate the impacts of the MOU and the SLA. They found that the
price effect of the trade restrictions was in the range of $50 to $80/MBF, which in turn
pushed up the cost of new home prices by $800 to $1,300. Also, Zhang (2001) used an
RFE to assess the price impact of the SLA. He found that under the SLA, the estimated
annual change in lumber price was about $59.1/MBF, or 16%, on average, for the period
1996-2000. As a result, US. consumer lost about $12.5 billion (in 1997 dollars), whereas
U.S. producers gained about $7.7 billion, resulting in a net U.S. loss of $4.8 billion for
the first 4 years under the SLA.

In addition, some studies employed a vector auto—regression (VAR) model to
investigate the impacts of macroeconomic variables on Canadian lumber exported to the
US. Jennings et al. (1991) showed that macroeconomic variables, especially housing
starts in North America have a significant effect on the Canadian lumber industry. Sarker
(1996) showed that demand side factors, such as housing starts, disposable income, and
wage rates have played key roles in affecting the lumber trade.

While previous studies have advanced our understanding of the market and
welfare ramifications of the trade restrictions, they have some critical weaknesses. First,
certain methodological weaknesses exist. Previous studies mostly employed an RFE to
assess the impacts of the trade restrictions, which are vulnerable to problems of
endogeneity, simultaneity, and collinearity (Wooldridge 2000). Endogeneity describes
the presence of an endogenous explanatory variable, a variable that is correlated with the

error term, either because of an omitted variable, measurement error, or simultaneity.

Simultaneity means that at least one explanatory variable in a multiple linear regression
model is determined jointly with the dependent variable. Collinearity refers to the
existence of correlation between explanatory variables. In addition, most of these studies
employed small sample sizes, covering 20 to 30 annual observations (Wear and Lee
1993, Myneni et al. 1994, Lindsey et al. 2000). Coupled with the use of OLS estimation,
these problems could cause coefficients of the RFE to be sensitive to its specification and
even inconsistent (Wooldridge 2000).

Moreover, many studies have taken price elasticities from other sources for the
welfare evaluations since the RFE model does not generate the relevant price elasticities.
Considering the crucial role that the price elasticities play in generating the welfare gains
and losses, it is not appropriate to take them from other sources. As noted by Boyd and
Krutilla (1987), gains and losses to US. consumers and producers as well as to Canadian
producers would be significantly altered by changes in the price elasticity of Canadian
export supply alone. In fact, the price elasticity of Canadian export supply in Adams and
Haynes (1986, 0.917) markedly differs from that of Myneni et al. (1994, 0.19). As such,
the measured welfare changes and the recommended policy options may suffer from a
lack of precision and pertinence.

Second, certain data deficiencies exist. In demand side, it is more appropriate to
include personal disposable income, instead of GDP or GNP (Wear and Lee 1993,
Lindsey et a1. 2000). One major reason is that demand for lumber is mainly attributed to
demand for new housing and repair & remodeling. The former is stimulated by housing
starts, while the latter is driven by disposable income (USDA Forest Service 2001).

These two variables are thus convenient measures of the likely impact of a stronger

economy on lumber consumption (Yin and Back 2004). Further, unlike disposable
income, the effect of GDP or GNP on lumber price and/or consumption in previous
studies is questionable. For example, such studies that used GDP or GNP, as an
alternative to disposable income found that the estimated coefficients were consistently
insignificant (Wear and Lee 1993, Lindsey et al. 2000). In contrast, the studies that
employed disposable income found that the estimated coefficients were significant
(Myneni et al. 1994, Sarker 1996). This implies that econometrically, disposable income
is a more relevant variable for explaining the demand function (Wooldridge 2000). In
addition, lumber demand is mainly attributed to housing demand, which is in turn
strongly affected by financing trends, especially mortgage rates, instead of the 3-month
T-bill interest rate (Jennings et al. 1994).

In supply side, previous studies paid little attention to log prices/markets. Logs are
a key input in lumber production, accounting for about 70% of variable lumber
production costs (Ragosta and Clark 2000). Excluding log prices in the supply function
thus may cause the problem of biased estimates in assessing the impacts of the trade
restrictions. This is called the omitted variable bias (Wooldridge 2000). In addition, log
and lumber prices tend to track each other closely over time (Yin 2001). Moreover, since
the 19908, the federal harvest reductions in the Pacific Northwest (PNW) and the Asian
financial crisis have contributed to a period of more volatile log and lumber prices.
Without accounting for the log market dynamics, therefore, previous estimates of the
trade restriction impacts might have not been robust (Yin and Back 2004).

In addition, it is necessary to include lumber processing capacity and sawrnilling

wage rates in the supply function. First, given its high correlation coefficient with lumber

production (0.7), lumber processing capacity can be represented as a proxy for capital
costs in the supply function (Zhang 2001). Second, since lumber is a direct and primary
output of sawmill industry, it is more reasonable to adopt sawrnilling wage rates, instead
of construction wage rates (Sarker 1996), as labor costs in the supply function.

In sum, there have been a number of studies on the impacts of the restrictions on
imported Canadian lumber. However, due to their weaknesses in modeling approaches
and variable uses, appropriately constructed and complete analyses are few. As such,
with the intensified dispute and search for solutions, there remains a strong need for
improved and up-to-date analysis of the lumber trade and quantification of the market
and welfare effects of the US. trade restrictions.

For a more careful and comprehensive analysis, it is crucial to analyze the
softwood lumber market structure appropriately and then to assess the effects of the trade
restrictions and other market factors on lumber prices, domestic production and imported
volume accurately. It is because all of the welfare measurements depend on these prices
and volume effects from the trade restrictions. The estimated welfare consequences in
turn indicate the effectiveness of a specific trade restriction (Yin and Back 2004).

Therefore, this study assesses the impacts of the trade restrictions with improved
variables and models. First, this study expands the list of variables, including variables
from the log markets in the US. and Canada. Given that the central argument of the trade
dispute has revolved around Canadian stumpage subsidies, it is essential to incorporate
log prices when examining the price, volume, and welfare effects of the trade restrictions.
In so doing, this study can properly decompose the effects of the trade restrictions and

other market variables on the domestic lumber market.

Second, this study uses both the structural SSE model and the nonstructural VAR
model in the assessment. This approach allows us not only to assess the market and
welfare impacts of the trade restrictions in a corroborative way, but also to take
advantage of both systems. Specifically, the VAR model enables us to explore the
dynamic linkages of economic variables associated with the U.S.-Canada lumber trade
without imposing a priori theoretical structure. Also, this model can capture short run
and long run responses of an endogenous variable to other variables endogenous to the
system, and reveal the potential effects of a trade restriction on every endogenous
variable. It should be noted that so far, few studies have used a VAR model to assess the
trade restriction effects and the dynamic interactions of the related market variables at the
same time. On the other hand, a structural SSE model allows us to obtain the price
elasticities, so that the welfare effects of the trade restrictions can be directly calculated.
Moreover, with an expanded list of variables, these models will make it possible to
contrast our estimates with those of previous studies. These complementary features
should allow us to draw more balanced and robust conclusions.

Finally, this study discusses the potential effects of different restriction regimes.
The main focus will be on what the most feasible and effective policy options are, how
the gross as well as distributional welfare effects vary under different regulating regimes,
and what strategies the US. government and industry should adopt in negotiating with
their Canadian counterparts. In so doing, this study not only provide some estimates of
what gains or losses to both countries are under different trade restrictions, but also

examine the practicality of the restriction options.

1.2. Objectives

The objectives of this study are:

(1) To analyze the US. softwood lumber market structure;

(2) To assess the impacts of the MOU and the SLA;

(3) To examine the welfare and policy implications of different U.S. restriction
regimes.

The specific questions that this study will answer are:

(1) How have the trade restrictions and market factors affected lumber prices,
domestic production and imported volume?

(2) What are the welfare implications of these prices and volume effects?

(3) What are the most feasible and effective policy options for the US. to deal

with the lumber trade?

1.3. Hypothesis to Be Tested

The hypothesis to be tested is: the US. trade restrictions have caused the US.
lumber prices to increase, imported volume to decrease, and the US. lumber production
to increase more than would have occurred without the trade restrictions. This study will
test this hypothesis using both the structural SSE model and the nonstructural VAR

model with an expanded list of variables.

1.4. Dissertation Outline

To accomplish the objectives and answer the specific questions, my dissertation
consists of six chapters in addition to the introduction.

Chapter 2 provides an overview of the North American lumber market and the
trade dispute between the US. and Canada over the last two decades. The overview
includes historic trends of consumption, production, and trade in the US. and Canada,
and their causal relationships with other market factors such as housing starts and
exchange rates. A description of the core issues and the history of the trade dispute are
then presented.

Chapter 3 presents data description and testing for unit roots. Particularly, this
chapter provides extensive discussion on unit root tests. One of the major reasons is that
it is prerequisite to test for the existence of unit roots in time-series data for estimating an
appropriately specified VAR model adopted in chapter 5. Moreover, it is necessary to
include tests for structural change since standard tests of unit roots, including the
augmented Dickey-Fuller (ADF) test have lower power and are unable to detect a
structural break in the series. After a description of the data, tests for structural change
with known and unknown break points are performed, and then the stationarity of the
time-series data are discussed.

Chapter 4 provides empirical analyses of the structural models — a simultaneous
system of equations (SSE) and a reduced form equation (RFE) — for the US. softwood
lumber market. The main tasks of the SSE model are to assess the price and volume
impacts of a restrictive regime and to obtain the price elasticities used for welfare

analysis in chapter 6. The RFE model is adopted to estimate the price and Canadian

export impacts of the restrictions and to detect the potential variations between this and
other studies. The theoretical framework and economic models as well as the estimation
procedures for the structural model are discussed. A discussion of the empirical results
and comparisons with other studies are also presented.

Chapter 5 provides empirical analyses of the nonstructural models — a vector
auto-regression (VAR) and an error-correction (VEC) model. The main tasks of the
VAR/VEC models are to not only discern the dynamic linkages among related market
variables but also assess the impacts of the US. restrictions in a corroborative way. The
theoretical framework for the J ohansen co-integration test and the VAR/VEC models are
discussed. The empirical results as well as the estimation procedures for the two models
are discussed, followed with a summary and conclusions.

Chapter 6 includes the welfare impacts of the trade restrictions and simulation for
different future policy options. The theoretical framework and the welfare consequences
for the MOU and the SLA are presented. The simulated results for various policy options
are then discussed, followed with a summary and conclusions.

Chapter 7 is a conclusive chapter that summarizes the major findings from the
previous chapters. The implications of the results are also discussed and areas of future

research are identified.

10

CHAPTER 2

U.S.-CANADA SOFTWOOD LUMBER TRADE

This chapter provides an overview of the North American softwood lumber
market and the trade dispute between the US. and Canada over the last two decades. The
overview includes historic trends of consumption, production, and trade in the US. and
Canada, and their causal relationships with market factors such as housing starts and
exchange rates. A description of the core issues and the history of the trade dispute are

then presented, followed with a summary and conclusions.

2.1. North American Softwood Lumber Market

The trade of softwood lumber between the US. and Canada is one of the major
trade flows of forest products in the world. These two countries are not only the world’s
largest producers of softwood lumber, but also the world’s largest importer and exporter,
respectively (Fukuda 2001). In 2000, the US. shared 45% of world imports for softwood
lumber, while Canada provided 48% of world lumber exports (FAO 2001). More
importantly, these two countries are highly interdependent on each other’s lumber
markets. That is, more than 90% of US. softwood lumber imports comes from Canada.
Canada exports more than 60% of its softwood lumber production to the US. As a result,
U.S. imports of softwood lumber have a strong influence on the North American lumber

market.

11

2.1.1. U.S. Softwood Lumber Market

Figure 2.1 shows the levels of US. softwood lumber consumption, production,
and imports for the period of 1980 to 2001. It can be seen that while US. consumption
for softwood lumber has increased, the domestic production has not been consistent with
the consumption. As a result, imports for softwood lumber have increased and thus

provided a large percentage of the US. total consumption.

 

50-

30«

Billlon Board Feet

20]

10<

 

 

 

1 980 1 982 1 984 1 986 1 988 1 990 1 992 1 994 1 996 1 998 2000

 

+Consurrption —I—-— Production + Irports '

 

Data source: Statistics for the Wood Product Industry (various years)

Figure 2.1. US. softwood lumber consumption, production, and imports (1980-2001)

12

During the last two decades, consumption of softwood lumber in the US. has
consistently risen. Growing lumber consumption in the US. has mainly been attributed to
an increase in housing demand, which consists of new houses and repair & remodeling
(AF&PA 2001). As shown in Figure 2.2, in 2000 the share of these two sectors
represented about 70% of the US. total consumption. In particular, with a strong housing
market stimulated by unprecedented economic expansions, average annual lumber
consumption in the US. rose to 52.2 BBF for the period of 1996 to 2000, which far

exceeded the record high of 50.5 BBF in 1987.

All others
Shipping Container 8%
9%
New Fbuse
Non- Residential 39%
1 5%

    

Repair & Rermdeling

29%

Data source: AF&PA (2001)

Figure 2.2. US. softwood lumber consumption (2000)

 

25<

20<

154

Blllion Board Feet

10-

W

 

 

 

f r

1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000

 

[+Somh +West—t—North]

 

Data source: Statistics for the Wood Product Industry (various years)

Figure 2.3. US. softwood lumber production by regions2 (1980-2001)

On the other hand, over the last two decades, softwood lumber production in the
US. has not been consistent with growing lumber consumption. Specifically, in the
I980S U.S. lumber production had generally taken an upward trend, with all-time high
levels of 38 BBF for the period of 1987 to 1989. In the early 19903, however, the lumber
production began to decline, due mainly to the timber harvest reductions from federal

lands in the Pacific Northwest (PNW) region. As a result, the West, as the largest lumber

 

2 The South includes Alabama, Arkansas, Florida, Georgia, Kentucky, Louisiana, Maryland, Mississippi,
North Carolina, Oklahoma, South Carolina, Tennessee, Texas, and Virginia. The West includes Alaska,
Arizona, California, Idaho, Montana, Oregon, and Washington. The North includes Illinois, Indiana, Iowa,
Maine, Michigan, Missouri, New York, Ohio, Pennsylvania. and Wisconsin.

14

producing region in the U.S., has reduced its lumber production from 23.9 BBF in 1987
to 15.8 BBF in 1995, its share of U.S. production from more than 60% to about 50%
(Figure 2.3). Consequently, the U.S. total production declined from 38.2 BBF in 1987 to
33.2 BBF in 1995. During the 1996-2001 period, due mainly to the increasing timber
production in the South,3 the lumber production has recovered up to about 34 BBF

annually, close to that of the early 1990s.

25

 

2077 777.77

Bllllon Board Feet

 

1980 1982 1984 1 986 1988 1990 1992 1994 1996 1998 2000

 

{I Lurrber 'rrports from Canada I Total lunber 'rrportsJ

 

Data source: Statistics for the Wood Product Industry (various years)

Figure 2.4. U.S. imports for softwood lumber (1980-2001)

 

3 The South has increased its production from 12.5 BBF in 1987 to 14.7 BBF in 1995. increasing its share
of U.S. production from 32.6% to 45.6% during the period. Currently, the South and the West region
produce nearly equal amounts of softwood lumber (Howard 2000 and AF&PA 2001).

 

Coupled with the expanded domestic consumption and constrained domestic
supply, the U.S. would not be able to satisfy its demand for softwood lumber without
imports. As a result, during the last two decades, average annual imports of softwood
lumber in the U.S. have risen from 12.4 BBF during the 1980-1990 period to 17.1 BBF
during the 1991-2001 period (Figure 2.4). In particular, since 1992, import demand for
lumber has increased substantially because of the timber harvest reductions in the PNW
and the strong growth of the U.S. economy. In 2001, the total volume of softwood lumber
imports reached a record high of 19.9 BBF.

Canada has remained the principal source of the U.S. softwood lumber imports,
providing about 94% of total imports in 2000. Specifically, U.S. softwood lumber
imports from Canada have grown fairly steadily in the 19908. An average annual lumber
import by the U.S. has risen to 16.5 BBF during the 1991-2000 period, up significantly
from 12.3 BBF in the 19808. Moreover, with the unprecedented expansion of the U.S.
economy during the 1996-2001 period, U.S. lumber imports from Canada has reached a
record high of more than 18 BBF annually, about 34% of total U.S. consumption for the

period.

2.1.2. Canadian Softwood Lumber Market

Figure 2.5 shows the levels of Canadian softwood lumber consumption,
production, and exports for the period of 1980 to 2001. In general, due to relatively small
population in Canada, domestic consumption for softwood lumber has maintained
steadily low over the last two decades. In contrast, Canada’s production of softwood

lumber has taken an upward trend. An average annual production of softwood lumber in

16

Canada has risen from 21.2 BBF during the 1980-1990 period to 26.0 BBF during the
1991-2001 period. Accordingly, an average annual export for softwood lumber in Canada
has increased from 15.2 BBF during the 1980-1990 period to 19.5 BBF during the 1991-

2001 period.

35000

 

30000 <

25000 4

M
O
O
8

15000 4

Million Board Feet

10000 «

WWW.

 

 

 

1 980 1 982 1 984 1 986 1 988 1 990 1 992 1 994 1 996 1998 2000

 

[—0— Consumption ——l—— Production + Exports ]

 

Data source: Statistics for the Wood Product Industry (various years)
Figure 2.5. Canada’s lumber consumption, production, and exports (1980-2001)

A large percentage of Canadian production of softwood lumber has been exported
to the U.S. over the last two decades. Particularly, about 63% of total production in
Canada has exported to the U.S. during the 1991-2001 period, up from 58% in the 19808.

As a result, the Canadian share of U.S. market has reached from 29% in the 19808 to

17

about 33% in the 19908. Figure 2.6 shows the trends of Canadian exports of softwood

lumber and market share in the U.S.

 

 

 

20000 40%
17500 W 35%
15000 »30%

.. 12500 I 25%

3 . 1

IL

‘2

8 10000 20%

In

C

2

5

7500 1 5%

10%

uz'urllllllfll I I II:

1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000

5000

 

 

 

 

 

 

2500

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

[- Lun'ber exports to the U.S. Lurrber exports to Japan —'- Market share in the U.S. l

 

Data source: Statistics for the Wood Product Industry (various years)

Figure 2.6. Canada’s lumber exports and market share in the U.S. (1980-2001)

2.1.3. North American Lumber Industry and Macroeconomic Variables

Figure 2.7 shows U.S. softwood lumber consumption and housing starts for the
Period of 1980 to 2001. The movements of the two series over the period are quite similar
and thus show a strongly positive correlation (0.87). For instance, housing starts declined
for the period of 1981 to 1982 and 1990 to 1991, respectively, due mainly to the

economic recessions. In response, lumber consumption went down for those periods.

18

Since 1992, however, the U.S. economic boom has led to the consistent increase of
housing starts, which in turn resulted in a steady increase of lumber consumption. In
addition, lumber consumption is strongly correlated with personal disposable income
(0.78) and mortgage rates (0.84). However, lumber consumption is only weakly

correlated with the 3-month T-bill interest rate (-0.26).

 

 

 

14000» t
12000“ t ‘
‘ ’
I

§ 10000~ ‘
1! I .g
3n 8 I' 3003

000 I! ' p
c - §

.5

.9 P
-
-

6000
E ‘ I

4000”

“100
2000”
0 ILA‘IJJAIIIJLL‘Alll‘AllllllllllllA‘IAIILAA‘JJIAILI A IL lllllllllllllllllllllllllllllllll O
"Y'YY‘YTerY'"V'YYY'YV"YYYYYYY'Y'YVVYVVVYVVVYYYVYYYfi ''''''''''''''''''''''''''''

 

 

 

198021 198223 198521 198723 199021 199223 199521 199723 200021

 

+ Lunber consumption —0— Housing starts ]

 

Data source: Statistics for the Wood Product Industry (various years)

Figure 2.7 Softwood lumber consumption and housing starts (1980:1-200124)

Figure 2.8 shows U.S. softwood lumber production for the period of 1980 to 2001
and the price for Douglas-fir sawlogs (#2) in the PNW for the period of 1989 to 2001.

The U.S. production has been strongly correlated with the log price (-0.78) over the last

19

decade. As an example, in the early 19908, due to the federal harvest reductions,
production in the PNW, the largest timber production region, has been reduced
significantly. As a result, the U.S. total production declined and the log price increased
considerably. On the other hand, in the late 19908, due mainly to the increased capacity in
the South, lumber production has recovered nearly to the volume of the early 19908.

Consequently, the log price has drifted down over the period.

 

 

12000 900
800
10000
1 700
I' l
8000 ~- 600
E 500 8
8 6000 9:
in l I
g 5
4000 300
i 200
2000,
l 100
o r j. 111111 ELL 0

 

 

198021 198223 198521 198723 199021

 

1+ Lurrber production + Log price I

 

Data source: Statistics for the Wood Product Industry (various years)

Figure 2.8. U.S. softwood lumber production and log prices (198021-200124)

20

900

 

800 1

700 1

§

SIMBF (1996 US)
01
8

§

200 <

100 1

 

 

0 ......-
1989A

 

f Y I ‘V

199123 199421 199623 199921 200123

 

to— Lurrber price -I-- Log price I

 

Data source: Random Lengths (2002) & Log Line (2002)

Figure 2.9. U.S. softwood lumber price and log prices in the PNW

Figure 2.9 shows U.S. softwood lumber prices and log prices in the PNW for the
period of 1989 to 2001. The two price series tend to track each other closely over time
and thus show a strongly positive correlation (0.83). For example, due to the federal
harvest reductions in the PNW, the average log price went up from $380/MBF in 1989 to
$580/MBF for the period of 1991 to 1994. During the same period, the average lumber
price increased to $332/MBF, up from $240/MBF in 1989. In contrast, since late 1997,
the Asian financial crisis has sharply reduced U.S. log exports to Asian countries,
particularly Japan, which thus brought the average log price down to $490/MBF for the

period of 1997 to 1998. Consequently, the average lumber price has dropped to

21

$295/MBF for the same period. Strong linkages thus exist between the lumber and timber

markets in the U.S.

 

 

6000 175
4000 _ ' , 1“ '1
,‘I I 1.25

Million Board Feet
01
§
‘
----—_-;v
I
r
”F
‘1.
GAS/USS

20001

11 0.75
1000 1-

 

 

o 11111111111111111111111111111111111111111111111111111111111111111111111111111111111111 0.5
198021 198223 198521 198723 199021 199223 199521 199723 200021

 

 

+ Lurrber inports from Canada + Exchange rates I

 

Data source: IMF & Statistics for the Wood Product Industry (various years)

Figure 2.10. U.S. lumber imports from Canada and exchange rates (198021-200124)

Figure 2.10 shows the U.S. softwood lumber imports from Canada and the real
exchange rate between the U.S. and Canada for the period of 1980 to 2001. Softwood
lumber imports from Canada have a strongly positive correlation (0.9) with the exchange
rate. This indicates that exchange rate is one of the most significant factors in explaining
the increased quantity of U.S. lumber imports from Canada over the last two decades. For

instance, the U.S. dollar has strengthened against the Canadian dollar by nearly 30% for

22

the period of 1992 to 2001. If all other factors were held constant, such an appreciation of
the U.S. dollar against the Canadian dollar could represent a considerable improvement in
the competitive advantage of Canadian lumber producers in the U.S. market. Indeed,
Canadian lumber exported to the U.S. has increased to about 40% in close parallel with

rising exchange rates over the period.

23

2.2. U.S.-Canada Softwood Lumber Trade Dispute

2.2.1. Core Issues of the Trade Dispute

The softwood lumber trade dispute between the U.S. and Canada extends back
over the last 20 years. At the core of the dispute is the U.S. claim that Canada subsidizes
its softwood lumber industry with low stumpage rates — fees paid by forest products
companies to the provinces for the rights to cut trees. This allegation is based on the
different systems of forestland ownership and different methods of stumpage pricing in
the two countries.

In Canada, the provinces are mainly responsible for forest management. As
shown in Table 2.1, most of Canada’s forests (94%) are publicly owned (known as
Crown lands), with 71% managed by provinces and 23% managed by the federal
government. Specifically, British Columbia is the province holding the most valuable
timberland, where about 96% of timberland is publicly owned. In addition, about 90% of
forestlands is publicly managed in Quebec, Ontario, and Alberta. Notice that most of the
6% private forestlands is found in Manitoba and Nova Scotia (Statistics of Canada 2001).

Public forest policy in Canada has been designed to make timber available in
ways that would support the development of increased processing capacity, and thus
contribute to regional economic development (Irland 1986). To this end, provincial
governments sell the stumpage on Crown lands to private forest companies under long-
term leasing or licensing arrangements, known as the tenure system. In exchange, forest
companies are required under these arrangements to create jobs and maintain community
economic bases (Cashore 1998). In this circumstance, the provincial governments have

determined stumpage fees administratively, rather than on the basis of market forces.

24

In contrast, only 42% of forestlands in the U.S. is publicly owned, with 23%
managed by states and 19% managed by the federal government, whereas 58% of
timberlands is privately owned. In particular, the South is dominated by private
forestlands, where about 90% of timberland is privately owned. In addition, about 75% of
timberland in the North is privately owned. Public ownership is predominant in the West,
where about 70% of timberland is publicly owned.

Public forest policy in the U.S. has mainly evolved to reflect multiple interests
including timber harvests, environmental preservation, and recreational use. Hence,
regional economic development is generally in a secondary position behind other values
(Irland 1986). Moreover, much of the timber in the U.S. sold by public and private
landowners are based on competitive bidding systems. Therefore, the U.S. lumber
industry argues that Canadian timber from Crown lands is sold at a lower stumpage rate
administratively set by provincial governments. As a result, these lower stumpage rates

include a subsidy to the Canadian lumber industry.

Table 2.1. Ownership of forestlands in the U.S. and Canada (%)

 

 

 

 

 

 

U.S. (1997) Canada (2001)
Ownership
North South West Total BC Quebec Ontario Alberta Maritimes Total
Private 75 88 31 58 4 ll 11 4 58 6
State 18 6 35 23 95 89 88 87 40 71
Federal 7 6 34 19 l 0 l 9 2 23

 

 

 

 

 

 

 

 

 

 

 

Data Source: USDA Forest Service (1997) and Statistics of Canada (2001)
Note:

1. See footnote 1 for the definitions of North, South and West in the U.S.
2. State in the U.S. corresponds to province in Canada.

3. BC represents British Columbia.

25

 

2.2.2. History of the Trade Dispute
2.2.2.1. The First Countervailing Duty Investigation

In 1981, the Northwest Independent Forest Manufacturers (NIFM) first alleged
that Canadian subsidized softwood lumber resulted in increased unemployment in the
Pacific Northwest (PNW) forest industry. The Senate Finance Committee asked the
International Trade Commission (ITC) to investigate this complaint. In April 1982, the
ITC found that Canadian lumber producers gained market share with their low timber
costs. However, the IT C report made no recommendation, and did not constitute a finding
of injury (Cashore 1998).

In July 1982, NIFM enlisted the support of companies outside of PNW and
formed the nationwide Coalition for Fair Canadian Lumber Imports (CFCLI, now the
Coalition for Fair Lumber Imports, CFLI). In October 1982, the CFCLI formally
launched its first countervailing duty (CVD) petition against Canadian softwood lumber
imports, known as Lumber I.4 The CFCLI alleged that Canadian stumpage rates provided
a subsidy and materially injured U.S. lumber producers. Investigation by the Department
of Commerce (DOC) and the ITC focused on the stumpage programs in British Columbia
(BC), Alberta, Ontario, and Quebec. In November 1982, the ITC ruled that there is a

“reasonable indication” that the U.S. was being injured by Canadian lumber imports. In

 

4 A countervailing duty (CVD) is a special duty imposed to protect domestic industry from injury caused by
imports that have benefited from subsidies provided by a foreign government. A CVD can only be applied
if it has been established in an investigation that imported goods have been subsidized and that such
subsidized imports are causing material injury, or threatening to cause injury to the domestic industry.
According to the U.S. trade law, the ITA in the DOC must determine whether a foreign government is
directly or indirectly providing a countervailing subsidy for the manufacture, production or exportation of
merchandise imported or sold into the United States. On the other hand, the International Trade
Commission must determine whether the U.S. industry producing the like goods has been materially
injured, or threatened with material injury, by reason of subsidized imports. If these two conditions are met,
a CVD equal to the amount of the subsidy is imposed upon the imports of the subsidized merchandise
(Department of Foreign Affairs and International Trade 2001).

26

May 1983, however, the International Trade Administration (IT A) in the DOC concluded
that stumpage practices did not automatically restrict timber “specially” to the lumber
industry and stumpage prices did not discriminate in an unfair manner by providing

timber to exporters at preferential rates (Hoberg and Howe 1999).

2.2.2.2. The Second Countervailing Duty Investigation

In May 1986, the U.S. producers again petitioned for another CVD investigation
with the DOC and the ITC. This is referred to as Lumber H. The U.S. lumber industry
requested a tariff of 27% on imports of softwood lumber from Canada. The ITC again
found preliminary evidence of injury to the U.S. lumber industry. In October 1986, the
IT A reversed its 1983 determination and ruled that Canadian producers received a
subsidy of 15% ad valorem (i.e., 15% of lumber prices). The IT A explained that court
rulings, legislative changes and the correction of errors it made in 1983 were the causes
of this reversal (Cashore 1998).5 On December 30, 1986, the day before the final ITA
determination, the U.S. and Canada negotiated an agreement (the Memorandum of
Understanding, MOU), with a 15% tax imposed on Canadian lumber exported to the U.S.
That export tax went into effect on January 8, 1987.

Subsequent amendments to the MOU allowed provincial governments to reduce
or eliminate the 15% export charge by implementing so called “replacement measures”,
defined as increased stumpage or other provincial charges on softwood lumber

production. British Columbia changed their stumpage pricing system in 1987 and the

 

5 In 1984, the U.S. Congress amended the Tariff Act of 1930 to include “upstream” or “input product”
subsidies as countervailable where “the input product bestows a competitive benefit on those goods by
affecting significantly the cost of production” (Tougas 1988-89, p.144).

27

U.S. government agreed to the elimination of the 15% export tax. In addition, Quebec
also changed their stumpage prices, allowing the province to reduce the export tax to

3.1%.

2.2.2.3. The Third Countervailing Duty Investigation

In October 1991, the Canadian government unilaterally declared the termination
of the MOU, stating that it had sufficiently increased stumpage fees to eliminate the
export tax. In response, the US Trade Representative (USTR) immediately imposed
provisional duties on Canadian lumber. Specifically, a 6.2% duty was set on Quebec,
while a 15% duty is placed on softwood lumber from Ontario, Alberta, Manitoba, and
Saskatchewan. Softwood lumber from British Columbia was exempted since higher
stumpage fees imposed as a result of the MOU remained in effect. Meanwhile, the DOC
self—initiated a new CVD investigation without a petition from lumber industry and
imposed a temporary bonding requirement on lumber imports. This was termed Lumber
III —— the first CVD case after the signing of the U.S.-Canada Free Trade Agreement
(FTA).

In March 1992, the ITA issued a preliminary finding of 14.48% ad valerom
subsidies. With a final determination, in May 1992, the ITA established a 6.51% ad
valerom subsidy — 2.91% for stumpage and 3.6% for log export restraints in British
Columbia. A8 a result, a CVD of 6.51% was imposed on lumber imports from the major
four provinces (British Columbia, Ontario, Quebec and Alberta), Saskatchewan,
Manitoba, the Yukon Territory and the Northwest Territories. Notice that in addition to

investigating the traditionally alleged subsidies of Canadian stumpage fee, the U.S.

28

government targeted another Canadian forestry practice, which is log export restrictions
in British Columbia.6 The claim was that these restraints served to lower domestic log
prices in British Columbia, which provided a subsidy to its lumber producers and other
firms using unprocessed logs as an input to their manufacturing processes (Ragosta and
Clark 2000).

In August 1992, Canada immediately responded to these rulings by appealing to
the General Agreement on Tariff and Trade (GATT) and to binational panels established
under Chapter 19 of the U.S.-Canada FTA. The GATI‘ panel ruled that the U.S. acted
properly when it self-initiated the CVD investigation. However, the bilateral panel found
that the US acted improperly when it imposed interim import bonds on Canadian
shipment to the US. In May 1993, the panel remanded the ITA finding for further
analysis. In September 1993, the ITA revised its findings from 6.51% to 11.54% ad
valerom subsidies. In December 1993, the panel again remanded the IT A finding and
ordered the ITA to find no subsidies. In January 1994, the IT A announced that, in
accordance with the panel’s instructions, it determined that Canada’s stumpage and log
export policies were not countervailable.

In April 1994, the U.S. Trade Representative (USTR) requested the establishment
of an Extraordinary Challenge Committee (ECC) under the Chapter 19 of the FT A to
review the binational panel decisions. However, the ECC was dismissed for failing to
meet FT A standards. In August 1994, the DOC published a notice in the Federal Register
confirming termination of the CVD order and declared liquidation of all entries. All

countervailing duties tentatively paid by Canadian exporters (approximately $800

 

6 The U.S. government made a conclusion that log export restrictions in Quebec, Alberta and Ontario had
no practical effect (Cashore 1998).

29

million) were refunded. In December 1994, the U.S. Congress passed legislation that
specifically changed/clarified those parts of U.S. trade law that the binational panels used
in their rulings, trying to ensure that future binational panels would no longer misinterpret
U.S. trade law.7 This legislation threatened the Canadian government and industry with
the possibility of another CVD action. Accordingly, Canada sought a compromise with
the U.S., holding a number of formal and informal meetings. Finally, in May 1996, the
U.S. and Canada signed the “Softwood Lumber Agreement between the Government of

Canada and the Government of the United States of America (SLA).”

2.2.2.4. The U.S.-Canada Softwood Lumber Agreement

The Softwood Lumber Agreement (SLA) was signed on May 29, 1996 and went
into effect retroactively from April 1, 1996, to March 31, 2001. The SLA is a voluntary
export restraint (a tariff-regulated quota system) agreed upon by the Canadian
government, so that only Canada imposed a governmental regulation on softwood lumber
exports. In addition, the SLA had no limitation imposed on the volume of softwood
lumber exported from Canada. Canadian producers could export as much softwood
lumber as they liked into the U.S., as long as they were willing to pay the export fees for
the quantity exceeding the base volume (Fukuda 2001).

The SLA imposed export regulation on softwood lumber exported from the four
major softwood lumber producing provinces in Canada: British Columbia, Alberta,

Ontario, and Quebec. Softwood lumber producers operating in the four provinces were

 

9 ‘6

7 In December 8, 1994, the Uruguay Round Agreements Act explicitly approved the President 8 statement
of administrative action (SAA)”, which stated because of Canadian practices, lumber imports from Canada
could be subject to a CVD (Gorte and Grimmett 2002).

30

permitted to ship 14.7 BBF of lumber a year to the U.S. duty-free, referred to as the
“established base.” The next 650 million board feet (MBF) — export volumes between
14.7 BBF and 15.35 BBF — were subject to a fee of $50/MBF, referred to as the “lower
fee base.” All greater quantities, in excess of 15.35 BBF, were subject to a charge of
$100/MBF, referred to as the “upper fee base.” The fee levels could be adjusted for
inflation annually based on an average of Consumer Price Indices (CPI) in the two
countries. The trigger price was defined as the average for a complete calendar quarter of
the price reported by Random Lengths for Spruce-Pine-Fir, Eastern, Kiln Dried, 2x4,
Standard & Better, delivered to the Great Lakes. If the trigger price met or exceeded
$405/MBF in any quarter during the first two years or $ 410/MBF thereafter, 92 million
board feet of additional tax-free exports would be allocated in the subsequent quarters
within one year of issuance. According to the SLA, Canada allocated the export quota to
the four provinces based on historical shipments to the U.S.: British Columbia (8.673
BBF, 59%), Alberta (1.132 BBF, 7.7%), Ontario (1.514 BBF, 10.3%), and Quebec (3.381
BBF, 23%). The volume of softwood lumber exported from the four provinces into the
U.S. over the past five year (1996-2001) is summarized in Table 2.2.

On the other hand, as a part of the agreement, the U.S. government agreed not to
pursue trade remedy actions under CVD or other trade laws for five years. However,
several additional disputes (such as reclassification of pre-drilled studs, rougher-header

lumber, and notched studsg, and stumpage fee reduction in British Columbia) arose

 

8 In 1999, the U.S. Customs proposed to reclassify pre-drilled studs, notched lumber and rougher—headed
lumber from a classification in the Harmonized Tariff Schedule of the United States (HTSUS) not covered
by the SLA into a category that was covered. Canada responded by petitioning the reclassification of drilled
studs to the World Customs Organization (WCO). The WCO ruled in Canada’s favor, but the ruling was
non-binding. Finally, just before the expiration of the SLA, an arbitration panel ruled that the U.S. violated
the SLA by reclassifying drilled studs and notched lumber (BC STATS 2001 May).

31

during the SLA period.9 The SLA expired in March 31, 2001 without either an extension

01' a new agreement.

Table 2.2. Canadian Lumber Exports to the U.S. under the SLA

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Cglrdiirsblia Alberta Ontario Quebec Total
April 1996- Export (MBF) 8,858,275 1,209,841 1,821,716 4,019,866 15,909,700
March 1997 Share (%) 55.6 7.6 11.5 25.3 100.0
April 1997- Export (MBF) 8,738,284 1,218,272 1,665,270 3,935,347 15,557,174
March 1998 Share (%) 56.2 7.8 10.7 25.3 100.0
April 1998- Export (MBF) 8,579,010 1,203,022 1,719,746 3,921,669 15,423,448
March 1999 Share (%) 55.6 7.8 11.2 25.4 100.0
April 1999- Export (MBF) 8,681,546 1,324,227 1,728,025 3,945,664 15,679,465
March 2000 Share (%) 55.4 8.4 11.0 25.2 100.0
April 2000- Export (MBF) 8,480,384 1,208,800 1,669,817 3,835,869 15,194,871
March 2001 Share (%) 56.0 7.7 11.0 25.3 100.0
Data source: Department of Foreign Affairs and International Trade (2001)
Note:

1. A calendar quarter for the SLA starts from April between 1996 and 2001.
2. MBF represents thousand board feet.

2.2.2.5. The Fourth Countervailing Duty Investigation

When the SLA expired in March 31, 2001, the U.S. softwood lumber industry
immediately petitioned for a new CVD investigation. In addition to the allegation of
subsidies to Canadian lumber producers, the U.S. industry, for the first time, also accused
the Canadian industry of dumping — selling below costs — softwood lumber into the

U.S. market. The U.S. producers required the imposition of 39.9% CVD and 28%-38%

 

9 In May 1998, the BC government announced that it would lower stumpage fees in the province, effective
June 1. Fees to Coast mills thus dropped an average of CA$8.10/m3 and fees to Interior mills dropped an
average of CA$3.50/m3. The main reason of the reduction was that the Coastal forest industry suffered
from a serious economic downturn, due to the Asian financial crisis. Specifically, Japanese markets
plummeted while the SLA made it impossible for companies, especially along the Coast, to redirect
shipments to the U.S. market without exceeding their individual quotas. The CFLI countered with a
challenge under the SLA dispute settlement procedures. In July 1999, a settlement between the two
countries was announced, which called for BC’s upper- and lower-fee base shipments during the fourth and
fifth years of the SLA to be set at their average for the first and second years. This resulted in the
province’s share of the 650 million board feet (lower-fee base) being lowered by 90 million board feet per
year. The agreement also set an upper-fee base limit of 110 million feet. Accordingly, shipments exceeding
that amount would carry a “super fee” of $146.25/MBF in the fourth year and $148.47/MBF in the fifth
year (Department of Foreign Affairs and International Trade 2001).

32

 

anti-dumping duty (ADD) on imported Canadian lumber.10 This episode is referred to as
Lumber IV.

In April 2001, the DOC announced that it was initiating CVD and ADD
investigation. The DOC decided to investigate first whether provincial and federal forest
management regimes (including stumpage and log export bans) confer a countervailing
duty. In August 2001, the DOC issued its preliminary determination with finding of
19.31% ad valorem subsidies. The DOC also made the affirmative critical circumstances
determination, concluding that there had been a surge of softwood lumber exports from
Canada since April 1, 2001. As a result of these two decisions, the DOC could apply
retroactive measures, in the form of bonds or cash deposits in the amount of 19.31% to
shipments made on or after May 17, 2001. Later, in October 2001, the DOC issued its
preliminary dumping determination and found that producers/exporters of softwood
lumber from Canada sold their product below market value. In contrast to the CVD case,
the DOC preliminarily found that critical circumstances did not exist on the anti-dumping
case. In March 2002, the DOC announced its final determinations of CVD and anti-
dumping cases. In May 2002, with the final material injury determination ruled by the

ITC, the DOC applied CVD (18.79%) and ADD (average 8.43%) on Canadian softwood

 

1° Dumping is the sale of goods in foreign markets at prices that are below those charged for comparable
sales in the home market or that are below the cost of producing the goods. Unlike a CVD that examines
the subsidy practices of governments, anti-dumping investigation concern the pricing practices of
individual firms. Under an anti-dumping investigation, only select companies would be investigated to
determine an “all others” rate. According to the U.S. trade law, the ITA in the DOC must determine
dumping margins by comparing the price at which the subject goods are sold in the U.S. with the “normal
value” of the goods. Normal value is the price at which comparable sales of the subject goods are made in
the home market. If the volume of home market sales is insufficient or if such sales are not made in the
ordinary course of trade, normal value can be determined on the basis of sales to a third country, or on the
cost of producing the goods, including a reasonable amount for profit. On the other hand, the ITC must
determine whether the U.S. domestic industry producing like products is materially injured, threatened with
material injury or, the establishment of an industry in the U.S. is materially retarded by reason of the
subject imports (Department of Foreign Affairs and International Trade 2001).

33

lumber. In responses, Canada has filed the CVD and ADD cases to the North American
Free Trade Agreement (NAFTA) and World Trade Organization (WTO).

In January 2003, the DOC released a policy bulletin, “Proposed Analytical
Framework, Softwood Lumber from Canada”, known as Aldonas Proposal, which
provided the procedure to bring to an end the CVD. That is, the DOC reviews the
elimination of the 18.79% CVD on a province-specific basis, if a province in Canada
changes its stumpage system to a market-based system sufficiently. Since then, with
exchanging proposals, a number of negotiation sessions between the U.S. and Canada
have been held to resolve the softwood lumber dispute. However, these have not resulted
in a resolution of the dispute until the end of 2003.

In December 2003, the U.S. and Canada finally reached a tentative agreement to
end the recent dispute. The proposed agreement eliminates the 27% U.S. tariff on
Canadian lumber, but reduces the amount of softwood lumber that Canadian companies
can export to the U.S. without penalty. That is, Canadian producers should drop their
exports to 31.5% of U.S. total lumber consumption, and pay a tariff of $200 for each
additional thousand board feet, which is referred to as “quota allocation principles.” This
deal also includes the 52% return of the $1.6 billion U.S. duties that Canadian companies
have paid, with U.S. companies keeping the rest.

In the meantime, the WTO and the NAFTA released their decisions on Canada’s
challenge of the CVD and the ADD cases. In July 2002, the WTO panel released the
preliminary ruling that the U.S. should abolish or change the Byrd Amendment, which
stipulates the distribution of duties collected from the anti-dumping and countervailing

duties to U.S. petitioners. In addition, the panel ruled that Canadian stumpage prices can

34

represent a subsidy, although the U.S. government cannot use cross-border comparisons
to determine the level of subsidy. In July 2003, after reviewing the ADD determination,
the NAFTA remanded it back to the DOC to recalculate the 8.4% duty, which lowered to
8.1% on October. In August 2003, the NAFTA panel ruled on Canada’s challenge of the
CVD case, concluding that the DOC may not calculate the countervailing duties by
comparing Canadian stumpage rates to U.S. stumpage rates. In January 2004, the WTO
Appellate Body reversed the decision of July 2002, ruling that the DOC may use a
benchmark other than private prices within Canada in “very limited circumstance” for
estimating the magnitude of timber subsidies conferred to Canadian lumber industry. In
addition, in April 2004, the WTO panel released its final decision on the ADD case,
which found that the U.S. could impose anti-dumping duties on lumber imported from
Canada. However, the WTO rejected the use of zeroing as a method for calculating anti-

dumping rates and remanded the case back to the DOC to recalculate the duties.ll

 

” Zeroing means the practice of assigning a margin of zero to goods for which the export price exceeds the
home market price. Zeroing prevents the negative margin for one category of goods from offsetting a
margin of dumping for another category of goods, thus inflating the overall dumping margin (Department
of Foreign Affairs and International Trade 2001).

35

2.3. Summary and Conclusions

Over the last two decades U.S. consumption for softwood lumber increased, while
the domestic production has not been consistent with the consumption, resulting in a
consistent increase of lumber imports from Canada. As a result, with an increase of
Canada’s share of the U.S. lumber market, the two countries have involved in the
softwood lumber trade dispute. The core issue of the dispute is the U.S. claim that
Canada subsidizes its lumber industry with low stumpage rates. This is mainly attributed
to the different systems of forestland ownership and thus different methods of stumpage
pricing in the two countries. This allegation has led to four rounds of CVD cases. In
1982, U.S. producers filed their first CVD case against imported Canadian lumber, but no
subsidies were found (Lumber I). In 1986, however, preliminary subsidy findings led to
the MOU (Lumber 11). With the unilateral termination of the MOU by the Canadian
government in 1991, the U.S. imposed a 6.51% CVD on Canadian lumber (Lumber III).
In 1996, the U.S. and Canada agreed to enter into the SLA. With the expiration of the
SLA in 2001, U.S. producers filed CVD and anti-dumping cases against Canadian
softwood lumber (Lumber IV). In December 2003, the U.S. and Canada reached a
tentative agreement to end the recent dispute. This agreement would allow shipping to the
U.S. fee free until it reached 31.5% of U.S. total consumption, and pay a fee of $200 for

each thousand board feet.

36

CHAPTER 3

DATA DESCRIPTION AND TESTING FOR UNIT ROOTS

This chapter describes data used in this study and conducts diagnostic tests,
especially unit roots. One major reason is that testing for the presence of unit roots in
time-series data is a prerequisite for estimating an appropriate vector auto-regression
(VAR) model adopted in chapter 5. In other words, the procedures to construct an
appropriate VAR system are closely related to between the time-series and stationarity.
For example, if all the variables are stationary or non-stationary in the general VAR
system with n variables, it is appropriate to use unrestricted VAR system in level or first
difference forms (Harris 1995). Moreover, since standard tests of unit roots, including the
augmented Dickey-Fuller (ADF) test, have lower power and are unable to detect
structural breaks in the series, it is thus necessary to include tests for structural changes of
the series. After a description of the data, therefore, this chapter performs tests for
structural changes with known and unknown break points to examine whether there is
any evidence of structural breaks in the series under consideration (Perron 1989 and
Banerjee et al. 1992). Unit root tests of the time-series data are then discussed in the last

section.

3.1. Data Description

Data used in this study are quarterly observations for the period of 1980-2001.
The data sources are as follows. U.S. lumber consumption, production and imports from

Canada (in million board feet, MMBF) were collected from the Statistics for the Wood

37

Product Industry published by the American Forest and Paper Association (AF&PA).
Lumber prices ($/thousand board feet, MBF) — framing lumber composite price (a
weighted average of 15 key framing lumber prices) — were from Random Lengths. Log
prices ($/MBF) in the PNW — Douglas fir (#2 sawmill logs) in Washington and Oregon
— were taken from Log Lines. Housing starts (in thousand units) came from the U.S.
Census Bureau. Personal disposable income (U.S.$) was from the Bureau of Economic
Analysis, Department of Commerce. The 30-year fixed mortgage rate was taken from the
U.S. Federal Reserve Bulletin. U.S. lumber processing capacity (in MMBF) came from
the USDA Forest Service. Wage rates ($ per hour) in U.S. sawmill industry (Standard
Industrial Classification, SIC, 242) were taken from the U.S. Bureau of Labor Statistics.

Canadian log prices (CA$/m3, an average rate for BC coast) were from the
Revenue Branch of the BC Ministry of Finance. Canadian sawrnilling wage rates (CA$
per hour) and lumber processing capacity (in MMBF) were taken from the Canadian
Forest Service. The exchange rate (expressed as Canadian $ per U.S. $) was obtained
from International Financial Statistics published by the International Monetary Fund
(IMF). Finally, CPI and PPI for the U.S. were from the Bureau of Labor Statistics and the
Survey of Current Business, respectively. CCI and PPI for Canada were obtained from
Statistics Canada and the Bank of Canada.

The dummy for the MOU was set to one for the period of 1986:4—1991:3, and
zero otherwise. Likewise, the dummy for the SLA was set to one for the period of
1996:2-2001:1, and zero otherwise. Producer Price Indices (PPI) were used to derive real

wage, and log and lumber prices for the two countries, and the U.S. Consumer Price

38

Index (CPI) was used to deflate personal disposable income. Tables 3.1 and 3.2
summarize the data descriptions and preliminary statistics.

U.S. log prices in the PNW could only be traced back to the first quarter of 1989
(Arbor-Pacific Forestry Service 2001). This study thus compiled two datasets for the
analysis. Dataset I contained every variable but the PNW log prices for 1980:1-2001:4.
To capture shocks from log markets in the U.S., therefore, two dummy variables were
introduced in dataset I. The first dummy (DUMI) represented the federal harvest
reductions in the PNW for the period of 1991:1-1993z4. The second dummy (DUMZ)
covered the Asian financial crisis for the period of 1997:3—1998z4. Dataset H covered all
the variables for 198921-200114. Also, because all series are available in original form,

seasonally unadjusted, this study will consider seasonality explicitly in the model.

39

Table 3.1. Data Description

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Data Abbreviation Measurement Source
Lumber Demand DEM MMBF‘ AF&PA}
Lumber Production SUP MMBF‘ AF&PA]
Canadian Lumber Export EXP MMBFr AF&PA3
Lumber Prices P U.S.$/MBF2 Random Lengths
Housing Starts HS 1,000 units Census Bureau
Disposable Income DI U.S.$ per capita Bureau of Economic Analysis
Mortgage Rates MR % U.S. Federal Reserve Bulletin
Log Prices LP U.S.$/MBF: Log Lines
Processing Capacity PC MMBFT U.S. Forest Service
Wage Rates W U.S.$ per hour U.S. Bureau of Labor Statistics
Canadian Log Prices CLP CA$/cubic meter British Columbia Forest Service
Canadian Processing Capacity CPC MMBFI Canadian Forest Service
Canadian Wage Rates CW CA$ per hour Canadian Forest Service
Exchange Rates EX CA$/U.S.$ International Monetary Fund
Time Trend T Integer 1980:1=1, 1980:2=2, etc
Memorandum of Understanding MOU 1 or 0 Dummy (=1 for 1986:4-1991 :3)
Softwood Lumber Agreement SLA 1 or 0 Dummy (=1 for l996:2-200121)
Federal Harvest Reduction DUM, 1 or 0 Dummy (=1 for 1991:1-1993z4)
Asian Financial Crisis DUMZ 1 or 0 Dummy (=1 for 1997:3-1998:4)
U.S. Consumer Price Index CPI 1996:100 U.S. Bureau of Labor Statistics
U.S. Producer Price Index PPI 1996:100 Survey of Current Business
Canadian Consumer Price Index CPI 19962100 Statistics Canada
Canadian Producer Price Index PPI 1996:100 Bank of Canada

 

 

 

 

Note:
1. Million board feet.
2. Thousand board feet.

3. American Forest & Paper Association.

 

Table 3.2. Summary Statistics

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Variable Observations Mean Standard Minimum Maximum
Deviation

DEM 88 11,3913 1,871.7 5,846.0 14,723.0
SUP 88 8,224.1 1,185.7 4,593.0 9,984.0
EXP 88 3,598.9 791.4 1,840.0 5,124.8
P 88 282.7 85.1 163.0 475.0
HS 88 361.5 78.2 176.7 558.4
D1 88 5,124.8 1,889.7 2,248.1 8,706.2
MR 88 10.2 2.9 6.8 17.7
LP 52 579.4 119.8 328.0 793.0
PC 88 10,5485 749.1 9,110.6 11,843.5
W 88 9.5 1.5 6.4 12.3
CLPI 88 77.9 28.9 43.2 138.9
CPC 88 6,561.5 592.8 5,122.5 7,159.5
CW 88 15.2 2.8 9.1 19.1
EX 88 1.3 0.1 1.1 1.6
T 88 - - 1 88
MOU - - - 0 1
SLA - - - 0 1
DUM, - - - 0 1
DUMz - - - 0 1
Note:

1. Factor for converting cubic meter (m3) to thousand board feet (MBF) is 2.36. Thus, CA$ 77.9/m3 is

equivalent of CA$ 183.9/MBF.

41

 

3.2. Testing for Unit Roots

When dealing with time-series data, it is necessary to test for the presence of unit
roots not only to avoid the problem of spurious regression but also to set up an
appropriate vector auto-regression (VAR) system. First, if a series has a unit-root, then it
is non-stationary. Unless this non-stationary series combines with other non-stationary
series to form a stationary co-integration relationship, the estimation can falsely represent
the existence of a meaningful economic relationship, which is known as spurious
regression problem (Wooldridge 2000). Note that if two time-series data are co-
integrated, they will move closely together over time and the difference between them
will be stable or stationary. Second, the procedures to construct an appropriate VAR
system are linked closely to between the time-series and stationarity. For instance, if all
the variables are stationary in the general VAR system with 72 variables, it is appropriate
to use unrestricted VAR system in level forms. Or, if all the variables are non-stationary,
say integrated of order one, or I (1),12 but show no co-integration relationships, then it is
necessary to estimate unrestricted VAR system in first difference forrrrs. However, if all
variables are non-stationary and co-integrated, it is appropriate to treat the system as a
vector error—correction (VEC) model (Harris 1995).

Even though there are several tests for the presence of unit roots, the (augmented)
Dickey-Fuller (ADF) test (Dickey and Fuller 1979) has been more popular due to its
simplicity (Harris 1995). However, since the early 19908, many studies have pointed out

that the ADF test has critical shortcomings (Perron 1989, Banerjee et al. 1992, Blough

 

'2 Integrated of order zero, or I (0) is defined as a stationary, weakly dependent time-series process. On the
other hand, integrated of order one, or I (l) is defined as a time—series process that needs to be first-
differenced in order to produce an I (0) process (Wooldridge 2000).

42

1992, Maddala and Kim 1998). First, the ADF method has a problem of test power
(Blough 1992). That is, because the correct form of the ADF model is unknown, different
lag lengths cause different results with respect to rejecting the null hypothesis of non-
stationarity. Second, the ADF test is unable to detect a structural break in the series,
because the implicit assumption of the test is that the deterministic trend is correctly
specified (Maddala and Kim 1998). As such, if there is a break in the deterministic trend,
then ADF test could lead to a false conclusion that there is a unit root, when in fact there
is not (Perron 1989). As a result, to overcome the shortcomings of the usual ADF
procedure, this study performs tests for unit roots under structural changes with a known

and an unknown break point.

3.2.1. Tests for Structural Change

Before adopting tests for structural changes, this study also introduced the usual
ADF procedure to compare between the results without and with structural change. The
ADF approach is to test the null hypothesis that a series contains a unit root, or is non-
stationary, against the alternative of stationarity (Dickey and Fuller 1979). To illustrate

the ADF test, assume that y, follows AP( p) process,

:1: p-l
yt =<P yr-1+ Z (PrAYr—i+0‘+l3’+ur (3.1)
' 1

l:
where u, is assumed to be white noise. If (p* = 0, then y, contains a unit root. As shown

in (3.1), the ADF test involves adding an unknown number of lagged first differences of

the dependent variable to capture auto-correlated omitted variables, which otherwise

43

enter the error term a, . Hence, it is very important to select the appropriate lag-length for

the ADF test (Wooldridge 2000).

3.2.1.1. Tests with Known Break Point
Perron (1989) pointed out that if a time-series is stationary around a deterministic
time trend due to a permanent shift sometime during the period under consideration,
standard tests of unit roots, including ADF, have very low power since they do not
consider this change in the slope. In addition, there is a similar loss of power if there has
been a shift in the intercept and/or trend. As an alternative approach, therefore, Perron
(1989) has suggested a modified ADF test for a unit root with three different models to
take into account structural changes. Specifically, if a structural break in time-series is
known, then it is relatively simple to adjust the ADF test by including dummy variables
that allow a one-time change in the structure occurring at a time TB , which refers to the
time of break. The three different models are parameterized as:
Model (A): y, = no + 8: + ulDU, + u,
where DUl =1 if t > TB , and 0 otherwise.
Model (B): y, = II + 501‘ + 51DT, + u,
where DTt = 1 if t = TB +1, and 0 otherwise.
Model (C): y, = no + ulDU, + 801 + 8,DT,”‘ + u,
where DTt = t if t > TB , and 0 otherwise.

Model (A) considers a one-time change in the intercept of the trend function,

which is referred to as the crash model. Model (B) is referred to as the changing growth

model to allow a one-time change in the slope of the trend function. Model (C) allows

for both changes (slope and intercept) to take place simultaneously. Because the three
different models include different dummy variables (DU ,,DT,,DT,* ), the null

hypothesis of a unit root is different. The null hypothesis is a broken-trend stationary.

3.2.1.2. Tests with Unknown Break Point

Perron’s method has been criticized because his procedure is based on a
conditional test given a known break point. First, it is implausible that the break points
are treated as known a priori (Banerjee et al. 1992). Second, because a known break is
treated as an exogenous event using a dummy variable, the assumption raises the problem
of pre-testing and data-mining with respect to the choice of the break point (Maddala and
Kim 1998). As a result, Banerjee et a1. (1992) has developed a method that treats the date
of the break as unknown a priori (BLS test). For this purpose, they employed recursive,
rolling and sequential procedures to formulate the asymptotic distributions for the test
statistics and tabulate the critical values for these statistics.

Recursive statistics are obtained using sub-samples t=1,...,k for k =k0,...,T,
where k0 is a start-up value and Tis the size of the full sample. That is, the recursive

statistics are computed for sub-samples that start with the first sub-sample ranging from 1

to k0 with k0 = 0.25T, and sequentially increase to cover the full sample. The usual ADF

model (equation 3.1) is estimated for each sub-sample, and then the minimum and
maximum statistics are chosen and compared to the critical values provided in Table 1 of

Banerjee et al. (1992) to test the null of a unit root.

45

Similarly, rolling statistics are computed using sub-samples that are a constant

fraction 50 of the full sample, rolling through the sample. The first sub-sample covers 1

to k with k =0.3T , the second sub-sample covers 2 to k =0.3T+I , and so on. Again,
the estimated statistics are compared to the critical values in Table 1 of Banerjee et al.
(1992).

The sequential statistics are computed using the full sample and the following
adaptation of the ADF model.

p-l
Yr = (9* Yr—l 1' 2 (Pi AYt—i +YDr '1'“: (3.2)

i:
where D, captures the possibility of a shift or jump in the trend at period t. Banerjee et

al. (1992) considered two cases — shift in trend (slope change) and shift in mean value

(intercept change):

t if t > k
Case A: shift in trend D, =

0 iftSk

1 if t > k
Case B: shift in mean D, =

0 if tSk

The unknown date of the break or shift is assumed to occur at k, which is
searched out between 0.15T and T—0.15T. Minimum statistics for the trend and/or
mean-shift models are then compared to the critical values in Table 2 of Banerjee et al.
(1992). In addition, F -8tati8tics is used to test the null H 0 :(p' = y = 0 in the trend-shift

and mean-shift models, and then the maximum values of F -statistics are compared to the

critical values in Table 2 of Banerjee et al. (1992).

46

3.2.2. Test Results for Structural Change

The findings of the ADF test are first reported to compare them with the test
results of structural change (Table 3.3). The tests included intercepts and trends, and lag-
length was selected based on the Akaike information criteria. The results indicate that for
the null hypothesis of a unit root all the data series but U.S. and Canadian processing

capacity (PC and CPC ) cannot be rejected at the 5% and even 10% significant level.

Table 3.3. Results of ADP unit-root tests

 

 

 

Series Level First Difference La 8 ‘
SUP -2.27 -10.49** 2
EXP -1.90 -7.17** 2

P —2.06 —4.83** 2
EX -0.88 -4.36** 2
HS -2.24 -6.95** 5
D1 -1.05 -3.49** 4
MR 015 -6.96** 2
W -2.08 -3.06** 3

CW -1.26 -3.97** 6
PC ~2.95* -1.80 5
CPC -3. 19* -2.28 4
LP -1.61 -3.96** 4
CLP -2.20 -3.05** 5

 

 

 

 

 

Note:

1. ** and * denote rejection of null hypothesis of a unit root at 5% and 10% significant level.

2. The 5% and 10% critical values for the ADF including a constant and a trend are -2.89 and -2.58.
3. The lag lengths were chosen on the basis of the Akaike information criteria.

3.2.2.1. Test Results with Known Break Point

For Perron’s test, descriptive analyses for time-series data were first done to select
an appropriate model for each series. Figure 3.1 shows a plot of the logarithm of lumber
price series (P), which behaves in correspondence to Model (A). A characteristic of this
graph is the conspicuous increase of lumber price series between 199121 and 19912.
Except for this change, the trend appears consistently stable (same slope) over the entire

period. The fitted trend (solid line) was estimated from a regression on a constant, a trend

47

and a dummy variable taking a value of 0 prior and at 1991:1, and value 1 afterwards. It
is found that four variables have followed the pattern similar to that of Model (A) with
different break points. These variables are lumber price (P), U.S. and Canadian

processing capacity (PC and CPC ), and Canadian log price (CLP ).

625

_ L—— P — Firrecfl
W A A

5.75— W u
lewd WWI] IN \A

1980 1985 1990 1995 2000

 

 

 

 

 

 

Figure 3.1. A plot of lumber price series

Figure 3.2 shows a plot of the logarithm of U.S. lumber production (SUP), which
behaves depicted by Model (C). The break point is in 1991:1, but in this case there
appears to be both a sudden change in the intercept of the series in 1991:1 and the slope
afterwards. The fitted line is the estimated trend with an intercept dummy (0 prior and at
1991:1, 1 after 1991:1) and a slope dummy (0 prior and at 1991:1 and t after 1991:1).
Eight variables follow the pattern depicted by Model (C) with different break points.
Among those variables are U.S. lumber production (SUP), housing starts (HS ),
Canadian lumber export (EXP), exchange rate (EX ), disposable income (DI ),
mortgage rate (MR), wage rate (W), Canadian wage rate (CW), and log price (LP).

Note that no variables follow the pattern depicted by Model (B ).

48

 

9.25

 

 

9.00

8.50

 

 

 

I I I I I I L I I 1 I 1 I I 1 4L 1 I 1 1 I I
1980 1985 1990 1995 2000

 

Figure 3.2. A plot of lumber production series

Based on descriptive analyses two unit root tests have been performed. First, the
ADF unit root test for split samples was employed in accordance to the break point. The
results are summarized in Table 3.4, which indicate that as seen in the ADF test with full
samples (Table 3.3), all the data series except for U.S. and Canadian processing capacity
(PC and CPC ) cannot be rejected with the null hypothesis for a unit root at 5% and
10% significant level.

Then, Perron’s test for unit roots was performed with two different models. The
results in Table 3.5 are quite consistent with findings without a break point. That is, the
unit root hypothesis cannot be rejected for all but two series, or PC and CPC , which
behave in correspondence to Model (A). The test statistic was —3.86 for PC , where the
critical value at 5% with /1 =0.45 (/l is the ratio of pre—break sample size to total sample
size) was —3.72~-3.76. While the test statistic of CPC was —3.48, the critical value of
10% with /l =0.45 was —3.44~-3.46. As a result, the null hypothesis of a unit root for both

series is rejected at 5% and 10% significance level, respectively.

49

Table 3.4. Results of ADF unit-root tests with split samples

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Series Period Observation Lags Test statistic
SUP l980:l-l991:1 45 4 -2.15
l991:2-2001:4 43 2 -2.22
198021-1991:1 45 3 -0.35
EXP 199122-2001 :4 43 3 -2.35
P 1980: l- 1991:1 45 3 -2.24
199112-200124 43 2 -2.26
EX 1980:1-1991:1 45 3 -l.98
1991 :2-2001 :4 43 2 -2.39
HS 1980:1-1991:1 45 4 -2.52
199122-2001:4 43 4 -1.83
DI 198021-1991:1 45 l -0.74
1991:2-2001:4 43 2 -1.90
MR l980:l-1987:1 29 1 -2.19
1987:2-2001 :4 54 6 -0.72
W 1980: l- 1991 :1 45 l -0.25
1991 22-2001 :4 43 2 -2.36
CW l980:l-l995:1 61 2 -1.46
1995 22-2001 :4 27 2 -1.28
PC l980:l-l989:4 4O 4 -3.16**
1990: 1-2001 :4 48 1 -2.66*
CPC 1980:1-1989:4 4O 4 -4.47**
1990: 1-2001 :4 48 4 -2.95**
LP l989:l-l99l:4 4 j - -
1991:2-2001 :4 48 I 2 -2.46
CLP 1980:1-1984:4 20 | 1 -094
1985:1-2001:4 68 | 1 -l.86

 

 

 

 

Note:

1. See Table 3.1 for definitions of the variables.

2. ** and * denote rejection of null hypothesis of a unit root at 5% and 10% significant level.

3. The 5% and 10% critical values (71 = 50) for the ADF tests including a constant and a trend are -2.93
and —2.60.

4. LP for the period of 1989: 1-1991 :4 was not tested due to small observation.

5. The lag lengths were chosen on the basis of the Akaike information criteria.

50

 

Table 3.5. Results of ADF unit-root tests with known break point

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Series Break point Observation Model ,1 Lags Test statistic
SUP 199 1 :1 88 C 0.51 4 -3.20
EXP 199 l :1 88 C 0.51 3 -0.45

P 1991:1 88 A 0.51 2 -2.22
EX 1991:1 88 C 0.51 2 -2.16
HS 1991:1 88 C 0.51 2 283
D1 1991:1 88 C 0.51 4 -2.38
MR 198721 88 C 0.33 6 -1.89
W 1991:1 88 C 0.51 4 -2.72
CW 1995:l 88 C 0.69 4 -2.32
PC 198924 88 A 0.45 1 -3.86**

CPC l989:4 88 A 0.45 4 -3.48*
LP 1991:1 52 C 0.17 2 -2.65
CLP 198424 88 A 0.22 1 -2.70

Note:

1. See Table 3.1 for definitions of the variables.

2. xi is the ratio of pre-break sample size to total sample size.

3. ** and * denote rejection of null hypothesis of a unit root at 5% and 10% significant level.

4 The 5% and 10% critical value for Model (A) are -3.77 and -3.47 if A =0.2, -3.76 and -3.46 if A=0.5.
The 5% and 10% critical value for Model (C) are -3.99 and —3.66 if A=0.2, —4.17 and -3.87 if 21:03,
-4.24 and -3.96 if A=0.5, -4.18, and —-3.86 if A :07. Critical values are obtained from Table 48, SB,
and 6B in Perron (1989).

5. According to Perron’s procedure, the lag lengths were chosen by a test on the significance of the

estimated coefficients for lagged variables in each model.

3.2.2.2. Test Results with Unknown Break Point

The BLS tests were implemented with two lags, and the results are reported in

Table 3.6 and 3.7. The recursive and rolling tests in Table 3.6 indicate that all the data

series cannot be rejected the unit root null at 5% and 10% significant level. On the other

hand, the sequential test in Table 3.7 shows that there is little evidence for rejecting the

null hypothesis of a unit root even with allowing the possibility of a break in the series.

Only the lumber price series shows weak evidence of a break under a trend-shift regime

at the 10% significant level; and by examining the maximum values of F -statistics, it

appears that if there was a breakpoint, then it occurred in the first quarter of 1991 (see

Figure 3.1).

51

 

Table 3.6. Results of recursive and rolling unit-root tests

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Series Observation ADF statistic Recursive Rollifl
Max I DF Min tDF Max I DF MID tDF
SUP 88 -l.90 -0.70 -2.14 -1.33 -2.46
EXP 88 -2.27 -l.94 -4.29 -0.80 -4.96
P 88 -2.06 -1. 18 -2.45 -0.05 -2.36
EX 88 -1.26 0.02 -0.41 -l.48 -2.l3
HS 88 -2.08 -1.93 -3.30 -l.85 -3.76
D1 88 -0.88 1.02 -2.49 -1.15 -2.84
MR 88 -2.24 -l.l9 -3.87 -l.32 -3.03
W 88 -l.05 -l.64 -3.29 -l.46 -2.68
CW 88 -O. 15 072 -2.95 - l .01 -2.87
PC 88 -2.95 0.30 -2.80 -l.26 -2.95
CPC 88 -3.19 -0.04 -2.70 -0.65 -3.61
LP 52 - l .61 052 -2.65 -l.07 -3.60
CLP 88 -2.20 -0.57 -2.18 -1.30 -3.03
Note:

1.

 

** and * denote rejection of null hypothesis of a unit root at 5% and 10% significant level; The 5% and
10% critical values for the ADF including a constant and a trend are -2.89 and -2.58 if n =88, -2.93
and —2.60 if :1 =52; The lag lengths (k =2) was chosen on the basis of the Akaike information criteria.
The 5% and 10% critical values for Min tDF (sample size T=100) are 4.33 and —4.00 if recursive
tests, -5.01 and —4.71 if rolling tests. The 5% and 10% critical values for Max t or (sample size
T =100) are -1.99 and —1.73 if recursive tests, -1.49 and —1.31 if rolling tests. Critical values are from
Table 1 in Banerjee et al. (1992).

Table 3.7. Results of sequential unit-root tests

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Series Observation Mean-shift statistic Trend-shift statistic
Min tor: Max F Min tDp Max F
SUP 88 -3.16 12.33 -3.65 11.43
EXP 88 -3.76 13.81 -3.58 13.33
P 88 -3.44 13.64 -4.21* 1430*
EX 88 -2.01 6.52 -2.91 7.46
HS 88 -2.52 5.21 -2.57 5.30
D1 88 -l.82 5.24 -1.72 5.57
MR 88 -3. 12 7.46 -1.99 6.99
W 88 -1.74 8.80 -2.17 8.40
CW 88 -1.06 8.09 -l.70 9.72
PC 88 -2. 12 7.39 -1.78 8.29
CPC 88 -3. 17 5.07 -2.25 4.61
LP 52 -1.18 0.74 -1.36 3.93
CLP 88 -2.81 4.38 -3.43 5.90
Note:
1. ** and * denote rejection of null hypothesis of a unit root at 5% and 10% significant level; The 5% and

10% critical values for the ADF including a constant and a trend are -2.89 and —2.58 if 7: =88, -2.93
and -2.60 if n =52; The lag lengths (k =2) was chosen on the basis of the Akaike information criteria.
The 5% and 10% critical values for Min top (sample size T =100) are -4.48 and —4.20 if trend-shift
tests, -4.80 and -4.54 if mean-shift tests. The 5% and 10% critical values for Max F (sample size
7’ =100) are 16.30 and 13.64 if trend-shift tests, 18.62 and 16.20 if mean-shift tests. Critical values are
from Table 2 in Banerjee et al. (1992).

52

 

3.3. Summary and Conclusions

This study collected quarterly data for 1980-2001. For the U.S., the data include
lumber production and prices, log prices, housing starts, disposable income, lumber
processing capacity, sawrnilling wage rates, and mortgage rates. For Canada, the data
include lumber exports, log prices, bilateral exchange rates, lumber processing capacity,
and sawrnilling wage rates. Because U.S. log prices in the PNW can only be traced back
to the first quarter of 1989, this study compiled two datasets, with dataset I containing
every variables but PNW log prices for 1980:1-2001:4 and dataset H all the variables for
l989:l-2001:4.

This study employed the usual ADF and structural change procedures to test for
the existence of unit roots in the time-series. The usual ADF test shows that there is no
evidence for rejecting the unit root null hypothesis for all the series but CP and CPC
series. The Perron’s tests with known break points confirm the findings of the usual ADF
test. Furthermore, the BLS tests with unknown break points show little evidence of a
break except for lumber price series. Based on these results, therefore, it is safe to
conclude that CP and CPC series cannot be treated as non-stationary for further time-
series analyses.13

In contrast, this study found that the lumber price series to be non-stationary in
view of the following facts. First, Perron’s test for the price series indicates that there is
little evidence of a structural change around the first quarter of 1991. In addition, with the

BLS tests, the unit root null was rejected on the borderline of the 10% significant level.

 

‘3 Note that this study employed interpolation of the annual data for processing capacities for the U.S. and
Canada to obtain quarterly observations. In conjunction with a strong trend in the capacity series, this
treatment may influence the results of unit root tests and their usefulness in the estimation.

53

Second, the structural change tends to under-reject the null of no co-integration (Gregory
et al. 1996). In other words, the structural change could change in the number of co-
integrating vector (Quintos 1995, Maddala and Kim 1998). However, the co-integration
rank test in this study is shown to be sustainable regardless of whether or not a structural
break exists in the series. For example, with the first quarter of 1991 as the break point
the full sample (1980:1-2001:4) was separated into two different periods — Sample I
(1980:1-1990:4) and Sample H (1991:1-2001z4). The Johansen co-integration test was
then applied three endogenous variables, including EXP, SUP, and P, in order to find a
change in the rank of co-integration space.14 As shown in Table 3.8, this study found that
with all three cases there is only one co-integration equation at 5% significant level, or
rank one (r =1). This implies that the structural change in the lumber price series does
not change the number of co-integration rank. In combination, therefore, it is acceptable
that the lumber price series can be treated as non-stationary and thus included in further

analysis.

Table 3.8. Results of J ohansen co-integration test with structural change

 

 

 

 

 

 

 

 

 

 

 

 

Sample Full sample Sample 1 Sample 11
(1980:1-2001:4) (1980:1-199024) (1991:1-2001:4) 5% Critical

Null E-Value Trace E-Value Trace E-Value Trace value
hypothesis statistics statistics statistics

R=0 0.370 4234* 0.560 40.33* 0.426 36.41 * 29.68

RSI 0.031 3.54 0.145 7.48 0.222 11.96 15.41

1L<2 0.01 l 0.91 0.029 1.22 0.020 0.87 3.76
Note:

1. * denotes rejection of the null hypothesis at the 5% level.
2. With four lags, the tests indicate 1 co-integration equation at 5% level ( r = 1).

 

‘4 Given small observations for sample I and II ( n = 44for each), the Johansen co-integration test with
structural change was only applied to the three endogenous variables (see Chapter 5.2 for detailed co-
integration tests).

54

 

CHAPTER 4

A STRUCTURAL MODEL FOR U.S. SOFTWOOD LUMBER MARKET

This chapter provides empirical analyses for the structural models, a simultaneous
system of equations (SSE) and a reduced-form equation (RFE), for the U.S. softwood
lumber market. First, an SSE model is used to characterize the relationships among all the
variables associated with the lumber market. The main tasks of the SSE model are to
assess the price and volume impacts of a restrictive regime and to derive the price
elasticities used for welfare analysis later. Second, several previous studies have used an
RFE to assess the effects of the U.S. trade restrictions on lumber prices and Canadian
share in the U.S. market. Given that, estimating an RFE for lumber prices and Canadian
export supply in this study makes it possible to detect causes and effects of the potential
variations between this and other studies. This step also helps discover how and why
results derived may differ from those obtained from the SSE and VAR models in this
study. This chapter is organized as follows. First, the theoretical framework for the
structural models is discussed. Next, economic models as well as the estimation
procedures for both the SSE and RFE models are presented. Then, the empirical results
are discussed. Finally, this chapter ends with summary and comparison of the results with

other studies.

4.1. Theoretical Framework

Assuming that softwood lumber is a homogenous commodity, this study develops

models for the U.S. softwood lumber market in aggregation. This aggregate analysis

55

serves as a useful approach to assessing the overall impacts of the U.S. trade restrictions
— the 1986 MOU and the 1996 SLA (Wear and Lee 1993). However, this approach does
not take into account the spatial structure of regional markets and transportation costs.
Hence, consumers are assumed to be indifferent to lumber sources, and U.S. import
demand and Canadian export supply can be seen as a function of a single representative
price.

Figure 4.1 illustrates the approach for estimating market impacts of a trade
restriction. Specifically, Figure 4.1 shows demand and supply in the U.S.-Canada
softwood lumber trade with U.S. import demand and Canadian export supply. In this
model, the action of a trade restriction, such as an export tax and a quota, on softwood
lumber imported from Canada can be envisioned as an upward shift in Canadian export
supply. As a result, the new equilibrium is achieved at a reduction in imported lumber

quantity from Canada (QO ——>Q'), an increase in U.S. prices of both imported and
domestic lumber (P0 —>P'US), and a decrease in the price received by Canadian
producers (PC —> P'm ).

The extent of those changes in the U.S. and Canada mainly depends on the price
elasticities of Canadian export supply and U.S. import demand. For example, if Canadian
export supply is elastic (sensitive to price changes), price changes by a trade restriction
will have a great effect on the quantity of lumber imported. In other words, if market
price were to change even slightly, the quantity imported would change significantly.
Similarly, if U.S. import demand is elastic, a restriction will cause smaller price changes

and larger import quantity changes in the U.S. The price elasticity of U.S. import demand

56

depends on the price responsiveness of U.S. demand and of U.S. production for lumber

 

 

 

 

 

 

 

(Adams 2003).
Price
Canadian export supply with a restriction
Canadian export supply
Plus \\
P0 I / '
P1ca /
‘ .S. Import Demand
Q’ Q0 Volume traded

Figure 4.1. Structure of the U.S. softwood lumber market.

4.1.1. Demand for Softwood Lumber

The derived demand for softwood lumber can be obtained from the total cost
function of the primary end uses, which is known as the duality between production and
cost function (Mas-Colell et al. 1995). Specifically, according to economic theory, the
determinants of the cost of end uses for softwood lumber are price, the level of end
outputs, and the costs of all other factors. As a result, the total cost function (TC ) can be

specified in the following;

TC = f(P,Y,C)

57

where P is lumber price, Y is the level of end outputs, and C is the costs of all other
factors such as the costs of labor and capital, and all other materials. The derived demand
for lumber (DEM ) then can be obtained directly from the total cost function by using

Shephard’s Lemma (Mas-Colell et al. 1995).

DEM = 91C- : f(Y,P,C)
3p

The demand for end outputs is mainly derived from the demand for housing,
including residential construction and repair & remodeling. The demand for housing is a
function of housing starts (HS), disposable income (DI), and mortgage rates (MR).
Housing demand will rise with an increase in housing starts and disposable income.
Additionally, the demand for housing will rise with a decrease in mortgage rates.
Therefore, by substituting housing starts, disposable income, and mortgage rate for the

end outputs, the derived demand for lumber in the U.S. can be specified in the following;

DEM = f(HS,DI,MR,P)

4.1.2. Supply of Softwood Lumber
The supply of softwood lumber can be derived from the profit function, which is
known as Hotelling’s lemma (Mas-Colell et al. 1995). Specifically, individual sawmills

can be viewed as possessing a profit function (P, X) , where P is lumber price and X is

the price (cost) of all other factors. Then, the supply of lumber can be obtained directly

from the profit function by using Hotelling’s lemma (Mas-Colell et al. 1995).

an
SUP=—= P,X
3P f( )

58

The cost of all other factors is a function of the prices of input factors such as
labor (W), capital (V), logs (LP), and the price of all other materials (M ). The supply
of softwood lumber will fall with a rise in prices of input factors. Note that this study
used lumber processing capacity (PC) as a proxy for capital input (V) in order to reflect
embodied technical change in lumber production. Hence, the supply of lumber will rise
with an increase in lumber processing capacity. Therefore, by substituting wage, lumber
capacity and log prices for the price of all other factors, the supply of lumber in the U.S.
can be specified in the following;

SUP = f(W,PC, LP, P)

4.1.3. Canadian Export Supply of Softwood Lumber

Canadian export supply of softwood lumber also can be derived from the profit
function by using Hotelling’s lemma (Mas-Colell et al. 1995). As such, Canadian export
supply of lumber can be specified as a function of the prices of input factors such as labor
(CW) and log (CLP ), lumber processing capital (CPC ), and exchange rates (EX ).
Note that Canada’s export supply of lumber should rise with a depreciation of Canadian
dollar against U.S. dollar via decreasing Canadian real costs relative to those in the U.S.
Hence, exchange rate is an important factor determining the relative cost competitiveness
between the U.S. and Canada. As a result, Canadian export supply of lumber can be

specified in the following;

EXP = f(CW,CPC,CLP, EX, P)

59

4.2. Econometric Models and Estimation Methods

4.2.1. A Simultaneous System of Equations (SSE) Model

In order to develop and estimate an SSE model for the U.S. softwood lumber
market, a four-equation system is postulated based on the discussion in the previous
section. Specifically, the U.S. demand (DEM ) is specified as a function of lumber prices
(P), housing starts (HS ), personal disposable income ( DI ), and mortgage rates (MR).
Similarly, the U.S. supply (SUP) is specified as a function of lumber prices (P), log
prices (LP), processing capacity (PC), sawrnilling wage rates (W), trend (T), and
shocks from the log market —— DUM , for the federal harvest reductions in the PNW and

DUM2 for the Asian financial crisis. Notice that these two dummies are only added

when estimating with dataset I, which does not have the data for U.S. log prices.15
Canadian export supply of softwood lumber (EXP) is specified as a function of lumber
price (P), Canadian log prices (CLP ), Canadian processing capacity (CPC ),
sawrnilling wage rates (CW), exchange rates (EX), and dummies for the trade
restrictions ( MOU and SLA ). These three equations include seasonality (for quarters 2-
4). Finally, as an identity in quantities, the domestic demand for lumber is defined as the
sum of domestic supply and Canadian export supply less U.S. exports (LGEX ).

Therefore, the SSE model is expressed as the following:

 

'5 Recent studies show that the log market dynamics have influenced the lumber market. Yin (2001) found
that at least 70% of the log price changes could have been caused by the federal harvest reductions, which
in turn contributed to higher and more volatile prices for lumber in the early 19908. In addition, Yin and Xu
(2002) found that export log prices lead the formation of log prices in the PNW, which in turn affects the
domestic lumber prices. Thus, it is essential to incorporate the dummy variables to capture effects of the
federal harvest reductions and Asian financial crisis.

60

DEM, =al +a2P, +a3HS, +a4DI, +a5MR, +SEA +u,

SUP, =8, +B,P, +fl3PC, +fl4W, +fl_.,LPt +fl6T +,8,DUM, +fl,,DUM2 +SEA +u,
EXP, = y, + sz, +y 3CPC, +y 4CWt +y 5CLPt +y 6EXt +y 7MOU +32 8SLA +SEA + u,
DEM = SUP + EXP — LGEX

where 0t' 8, 6'8, and y' s are coefficients to be estimated, I denotes the time period of the

observation, and 68 are i.i.d error terms. With an identity to close the system, this study
has four equations in four endogenous variables (DEM ,SUP,EXP and P), which is
similar to the approach of Myneni et al. (1994). Unlike that work, however, this study has
not only a full coverage of the two major episodes of the trade restrictions, but also a
substantially expanded list of variables.16 Furthermore, the use of quarterly instead of
annual data results in more observations for analysis.

The trend variable in the domestic equation is taken to reflect disembodied
technical change in lumber production. The processing capacity is a proxy for capital
input (including embodied technical change), but only annual data are available (Howard
2000). Hence, the annual data is interpolated to obtain quarterly observations in a way
similar to Zhang (2001). Compared to Sarker (1996) that only considered demand factors,
Canadian log prices, lumber processing capacity, and sawrnilling wage rates are included
in the Canadian export equation. The two dummy variables (MOU and SLA) are used to
allow for an intercept shift in Canadian export supply during the periods of the trade
restrictions. As in Myneni et al. (1994), the SSE model assumes that a significant drop in
Canadian export supply due to a trade restriction will lead to a significant price increase

and thus domestic production increase.

 

'6 Previous studies on the impacts of the trade restrictions have incompletely covered the 1986 MOU and
the 1996 SLA.

61

Notice that the SSE model satisfies the order condition for identification, which
requires that the number of exogenous variables excluded from any equation must be as
least as large as the number of endogenous variables in that equation (W ooldridge 2000).
In the demand equation (DEM ), there are two endogenous variables (DEM and P) and
more than two excluded exogenous variables such as LP , PC, and W. Similarly, the
condition is satisfied for the supply and Canadian export supply equation. It should be
noted, however, that the requirement is the only necessary condition for identification.
Hence, this study assumes that an equation that satisfies the order condition is identified
for consistent estimation (Wooldridge 2000).

The procedure of three-stage least squares (3SLS) is employed to estimate the
SSE model. This method constitutes both a seemingly unrelated regression (SUR)
approach and an instrumental variable (IV) approach (Wooldridge 2000). Specifically, an
SUR approach is employed to use the information from the full system of equations to
obtain efficiency. An IV approach is used to generate consistent estimators. This study
uses all the exogenous variables in the three equations as instrumental variables (IV). As
a result, a 3SLS is called a full information system method. For that reason, 3SLS
produces more efficient estimators than those of limited information methods, such as
two-stage least squares (ZSLS) and limited information maximum likelihood, which
estimate one equation’s parameters only using information in that equation (Darnell

1994).

62

4.2.2. A Reduced-Form Equation (RFE) Model

An RFE is a reduced version of an SSE model. It is defined as a linear equation in
which an endogenous variable is a function of exogenous variables and unobserved errors
(Wooldridge 2000). To understand this concept, consider a two-equation structural model

as follows:

yl :(X,y2 +B,Z, '1'“, (41)
yZ :a2y1+BZZZ +u2

where zl and 22 are exogenous variables, so that they are not correlated with error terms,
a, and u,. Assuming that we focus on estimating the first equation, it is possible to
express the two equations as the reduced form for y,. That is, if we solve the two

equations for y2 ,

yz :H21Z1+H22z2 +1), (42)
where 11,, = A, “,2 = ——Bz—-, and v2 = (git-'1’). Equation (4.2) can be
(l—oc,or,) (l—a,a,) (1—01201l

estimated by ordinary least squares (OLS) regression of y2 on z .

Given the nature of an RFE, exogenous variables contained in the SSE model can
be expressed as the determinants of endogenous variables such as lumber prices (P) and
Canadian export supply (EXP). The determinants of the lumber demand include housing
starts (HS ), disposable income (DI), and mortgage rates (MR). The determinants of
lumber supply include log prices (LP), lumber processing capacity (PC), sawrnilling

wage rates (W), and shocks from the log market (DUM , and DUM 2 ). The determinants

of Canadian export supply include Canadian log prices (CLP ), Canadian lumber

processing capacity (CPC ), Canadian sawmilling wage rates (CW), exchange rates

63

(EX ), and dummies for the trade restrictions (MOU and SLA ). The RFE model can be
specified as:

P: f(HS, DI, MR, LP, PC, W, CLP, CPC, CW, EX, DUM,, DUMZ, MOU, SLA)
0r,

EXP= f(HS, DI, MR, LP, PC, W, CLP, CPC, CW, EX, DUM,, DUMz, MOU, SLA)
Note that DUMl and DUM 2 are only used when estimating dataset I, where U.S.

log prices are unavailable. In addition, dummy variables for trade restrictions are used in
different ways. As in the SSE, a single dummy was first introduced to cover all the years
under a specific policy — MOU during 1986419913 and SLA during 1996:2-2001:1.
Another way was to use multiple dummies for the individual years under the SLA (Zhang
2001) ‘to look into the potential ramifications of these alternative specifications. Finally,
whether or not each of the variables in the above specification is included in the final
model will be determined by model performance.

For comparison, among studies of the lumber price impact of the trade
restrictions, Lindsey et al. (2000) included housing starts growth rates for the current and
previous year, previous year’s price for lumber, Japanese GDP. The effects of the trade
restrictions were estimated in two ways. One way was to use a single dummy including
both the MOU and the SLA between 1986-1998. The other way was to make distinction
between the SLA during 1996-1998 and the earlier forms of restriction during 1986-
1995. Zhang’s (2001) final model had previous year’s price for lumber, housing starts,
lumber production capacity, sawrnilling wage rates, lumber productivity, and exchange
rates. He also included multiple dummies for the individual years of the SLA during
1996:2-2000:1 and a single dummy for the MOU during 1986:4-1991:3 to estimate the

trade restriction effects. On the other hand, Wear and Lee (1993) included housing starts,

64

GNP, time trend, U.S. lumber and log exports, Canadian lumber consumption, exchange
rates, and a single dummy for the MOU (1986-1990) in assessing the impact of the trade
restrictions on Canadian market share

For estimating the RFE, data series were detrended because of better model
performance in terms of goodness-of-fit and coefficient significance. Detrending data
were obtained from the residuals derived from the regression of each of dependent and

independent variables on a constant, and time trend (Wooldridge 2000).

4.3. Empirical Results

4.3.1. SSE Model

This study adopted both logarithmic and linear functional forms to estimate the
SSE model with dataset I (198021-200124) and dataset H (1989:1-2001:4). Linear
function forms showed better model performance, in terms of a better fit and the number
of significant variables. This presentation thus focuses on the results derived from the
linear regression, which are reported in Table 4.1. Overall, the SSE model fits the data
well. The R2 is quite high, above 0.8. In addition, the Durbin-Watson (DW) indicates that
the hypothesis of no serial correlation cannot be rejected at the 1% level. More
importantly, the coefficients have the expected/acceptable signs, and most of them are
significant. To mitigate the influence of collinearity, the demand equation was estimated
with either mortgage rates or personal disposable income for the two datasets, depending

on which alternative would give rise to a better fit.'7

 

'7 This study detected a high correlation between mortgage rates and personal disposable income (—0.93).

65

4.3.1.1. Results of Dataset I

All the coefficients of lumber demand are significant at the 5% level and have the
expected signs. Specifically, demand for softwood lumber is negatively related to lumber
prices and mortgage rates, but positively related to housing starts. All coefficients but

DUM2 in supply equation are statistically significant and have expected signs. That is,

domestic supply of softwood lumber is positively related to lumber prices, production
capacity, and wage rates. Further, domestic supply of softwood lumber is negatively

related to time trend and DUM , . The negative time trend indicates that the slow down of

the disembodied technical change during the 1980-2001 period, but the coefficients imply
only a very small effect (less than 1%). In addition, the coefficient of the dummy for the
log market shock, resulting from the spotted owl debate and federal harvest reductions,
indicates a significant negative effect on U.S. production, -5.4%. However, the dummy

for the Asian financial crisis (DUMZ) is insignificant.

Most coefficients in Canadian export equation are statistically significant and
have the expected signs. In particular, Canadian export supply is positively related to
lumber prices, exchange rates, and Canadian production capacity. On the other hand,
Canadian export supply is negatively related to the dummy variable for the MOU. On a
percentage basis, the MOU depressed Canadian exports by about 8%. However, the
dummy for the SLA is insignificant, implying that it had little impact on Canadian
exports.

To better gauge the influences of explanatory variables on demand, and domestic
and export supply, this study calculated the elasticities (Table 4.2) corresponding to

coefficient estimates in Table 4.1 and mean values of the variables in Table 3.2. Overall,

66

the prices elasticities are very low. Specifically, the price elasticity of lumber demand is
relatively very low (-0.13), compared to other market variables. For example, when
lumber prices increase by 1%, demand for softwood lumber falls by 0.13%, holding other
factors fixed. On the other hand, when housing starts increase by 1%, demand for lumber
increases by 0.33%. In addition, demand for lumber decreases by approximately 0.20%,
as mortgage rates go up by 1%. Additionally, the impact of lumber prices on domestic
production is smaller than the influences of other variables. For instance, the elasticity of
lumber price is 0.26, but the elasticities of wage rates and production capacity are 1.08
and 1.88, respectively. Finally, the price elasticity of Canadian export supply is extremely
low (0.13). In other words, when lumber price increases by 1%, Canadian lumber
exported to the U.S. only increases by 0.13%, holding other factors fixed. In contrast, the
high price elasticity of exchange rates shows that when the U.S. dollar depreciates against
the Canadian dollar by 1%, softwood lumber imports from Canada increase by almost the

same proportion (0.91).

4.3.1.2. Results of Dataset 11

Despite a small sample size (71:52), the SSE model with dataset H provides useful
information on the U.S. lumber market in the 19908. Because of the high correlation
between mortgage rate and personal disposable income (-0.93) with dataset H, lumber
demand is specified as a function of lumber price, housing starts, personal disposable
income, and seasonality (for quarters 2-4), which gives a better goodness-of-fit. The
results showed quite high R2 (about 0.88), and all the coefficients are significant at the 5%

level and have the expected signs. Demand for softwood lumber is negatively related to

67

lumber prices, but positively related to housing starts and disposable income. Notice that
the elasticity of lumber price (-0.08) with dataset H is lower than that from dataset I (-
0.13, Table 4.2). It implies that the price elasticity for lumber demand has become lower
in the 19908. The results show that housing starts (0.34) and disposable income (0.46)
have significant impacts on demand for softwood lumber in the 19908.

Note that, instead of the dummies for log market shocks, log prices were directly
used with dataset H. All coefficients but production capacity in supply equation are
significant at the 5% level and have the expected signs. Domestic supply of softwood
lumber is positively associated with lumber prices and wage rates, but negatively related
to log prices. It is now proven that log prices have a significant negative effect on lumber
supply. In addition, the elasticity of lumber prices (0.15) is slightly lower than that from
dataset I (0.26, Table 4.2).

Canadian export supply equation has only two significant variables — lumber
price and exchange rate, with the expected signs. Canadian export supply is positively
related to lumber prices and exchange rates. The elasticity of lumber prices is lower
(0.15). The elasticity of exchange rates is relatively high (0.62), but lower than those
from dataset I (0.91~0.92, Table 4.2). However, the dummy variables for the 1986 MOU
and the 1996 SLA are not statistically significant. Notice that the small sample size for
the 1986 MOU (1 l-quarter period) with dataset 11 may influence the significance of the

dummy.

68

Table 4.1.

Results of the SSE model for the U.S. lumber market

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

. . Dataset I (198011-2001 :4) Dataset II (1989: 1-2001 :4)
Equation Explanatory variables . _ .
Coefficrent t-statistic Coefficient t-statrstrc

Intercept 12658.35 19.49* 3983.06 5.40*
Lumbeflrice -5.07 -3.67* -2.74 -2. 15 *
Housing starts 10.94 10.92* 11.91 4.35*
Mortgage rate -238.94 -17.96*
Disposable income 0.86 4.33*

DEM Seasonal (2“:I quarter) -628.93 -3.11* -479.83 -l.6l
Seasonal (3rd quarter) -680. 19 -3.56* -604.57 -2.18*
Seasonal (4lh quarter) -781.51 -4.61* -650.12 -3.57*
R2 0.89 0.87
DW 2.05 1.72
Intercept -53194.37 - 17.24* - 12233.04 -4.90*
Lumber price 7.09 7.52* 3.88 3.23*
Wage rate 941.24 6.44 * 1940.87 8.70*
U.S. Capacity 1.40 1927* 1.10 1.15
Log price -2.01 -2.94*
Trend -l70.48 -16.93* 13.58 4.06*

SUP DUM. (I99lzl-I993:4) -465.18 2.51*
DUM2(I997:3-1998:4) 259.38 1.19
Seasonal (2“d quarter) 471.82 4.31* 459.41 4.55*
Seasonal (3rd quarter) -147.53 -1 .08 192.51 1.86
Seasonal (4'h quarter) -308.71 -2.58* -27.96 -0.27
R2 0.89 0.80
DW 1.86 1.60
Intercept -5547.64 -l 1.37* -l3382.70 -3.11*
Lumber price 1.64 237* 1.76 305*
Exchange rate 2490.34 7.05* 1845.23 3.65*
Canadian Capacity 0.20 929* 0.09 0.66
Canadian Log price -0.43 -0.18 10.84 1.22
Canadian Wage rate -6.64 -0.15 8.32 0.25

EXP MOU (1986:4-199lz3) -288.56 -3.55* -l30.24 -l.47
SLA (199622-2001: I) -139. 12 -l .50 -98.52 -0.76
Seasonal (2ml quarter) 523.22 656* 410.30 5.45*
Seasonal (3” quarter) 444.47 5.46* 241.63 266*
Seasonal (4‘h quarter) -21.46 -O.28 -2.59 -0.03
R2 0.88 0.93
DW 1.41 2.00

Note:

1. Numbers in parentheses are t-values; * indicates significance at the 5% level.

2. The Durbin-Watson test indicates that the hypothesis of no serial correlation cannot be rejected at the
1% level in all but one case. Even for the Canadian export equation with dataset I and for the supply

equation with dataset II, the statistics are well within the 5% fail-to-reject region.

69

 

Table 4.2. Elasticities for the U.S. softwood lumber market

Variables Dataset I Dataset II
Lumber ‘ -0. 13 -0.08
Housin starts 0.33 0.34
rates -0.2 1
income 0.46
Lumber ' 0.26 0.15

W rates 1.08 2.41
' ' 1.88

—0. l4

Trend -0.93 0.04

Lumber ' 0.13 0.15

EXP Exchan rates 0.91 0.62
' CA 0.37 0.16

 

Note:
1. Data means from Table 3.2 and coefficient estimates from Table 4.1 are used to derive the elasticites.

4.3.2. The RFE Model

The OLS was used to estimate the RFE models for lumber price and Canadian
export supply with dataset I (1980:1-2001:4) and dataset II (1989:1-200124). A
logarithmic functional form was adopted with detrended data series. Results of the RFE
estimation are reported in Tables 4.3 and 4.4. Overall, the RFE models fit the data well

(R2 is above 0.7). In addition, AR(q) serial correlation test (F test) and Breusch-

Godfrey test (LM test) indicate that the hypothesis of no serial correlation cannot be
rejected at the 5% level. Breusch-Pagan (B - P) test indicates that the hypothesis of no

heteroskedasticity cannot be rejected at the 5% level.

70

Table 4.3. Results of reduced-form equations for lumber price

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Variables Dataset I (1980:1-2001:4) Dataset II (1989:1-2001:4)
Housing starts 0.45 0.47 0.49 0.66
(3.56)* (3.64)* (1.97)* (2.71)*
Mortgage rate —0.1 1 0.13 0.01 0.11
(-0.44) (0.50) (0.01) (0.40)
Wage rate 0.29 2.18 —0.89 -1.05
(0.30) (2.32)* (-l.45) (-l.69)
Capacity -3.52 -4.29 -3.39 -4.58
(-l.9l) (~2.31)* (-0.77) (-1.34)
Log price 0.47 0.60
(2.66)* (3.86)*
Canadian log price 0.67 0.84
(3.87)* (5.74)*
Canadian wage rate -0.03 0.26
(-O. 10) (0.79)
Exchange rate -0.06 -0.74 0.37 -0.12
(-0.14) (-2.12)* (0.53) (-0.18)
MOU87-9l 0.1 l 0.13 -0.04 0.003
(1986:4-199123) (1.99)* (2.15)* (-0.76) (0.07)
SLAM,” 0.07 0.09
(199622-199721) (1.18) (1.43)
SLA97.93 0.1 1 0.04
(1997:2-1998: 1) (1.27) (0.64)
SLA98_99 0.08 -0.03
(1998:2- 1999: 1) (0.91) (-0-43)
SLA99_00 0.19 0.09
(1999240001) (3.35)* (1.28)
SLAoom -O.1 1 -0. l 3
(2000200011) (-1.77) (-l.95)
SLA96.01 0.05 0.02
(1996:2-2001:1) (1.47) (0.47)
DUM, 0.15 0.13
(1991:1-199324) (2.17)* (1.85)
DUM; -0.11 -0.08
(1997:3-199824) (-l.23) (-l.44)
SEA! -0. 14 —0. 15 -0. 18 -0.24
(2"1 quarter) (-2.70)* (-2.70)* (-2.17)* (~2.84)*
SEA; -0. 17 -O. 18 -0. 19 -0.24
(3rd quarter) (-3.67)* (-3.29)* (-2.72)* (-3.29)*
SEA; -0. 12 -0. ll -0. l4 -0. 14
(4th quarter) (-3.39)* (-2.87)* (-2.95)* (-3.05)*
Intercept 0.05 0.07 0.13 0.15
(1.55) (1.83) (2.30)* (2.48)*
R2 0.71 0.67 0.82 0.76
Note:

1. Numbers in parentheses are t-values, and * indicates significance at the 5% levels.

2. The hypothesis of no serial correlation cannot be rejected at the 5% level.

3. Variables are in logarithmic terms with detrending. To mitigate collinearity between U.S. and
Canadian capacity in both datasets (0.94), the equations were estimated with either U.S. or Canadian
capacity, and the estimation that gives a better fit is reported. To mitigate collinearity between U.S. and
Canadian wage rates in dataset II (-0.74), the equations were estimated with either U.S. or Canadian
wage rates and reported the estimation that gives a better fit.

71

 

Table 4.4. Results of reduced-form equations for Canadian export supply

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Variables Dataset 1 (1980:1-2001:4) Dataset II (1989:1-200124)
Housing starts 0.62 0.63 0.45 0.49
(8.09)"‘ (8.39)* (4.08)* (4.78)*
Mortgage rate 0.04 0.06 -0.09 ~0.12
(0.36) (0.54) (0.81) (-1.04)
Wage rate -1.42 -l.45 -0.51 -0.51
(-3.37)* (-3.73)* (-1.92) (-1.88)
Capacity 2.90 2.59
(1.53) (1.57)
Canadian capacity 1.62 1.60
(4.68)* (4.75)*
Log price 0.14 0.14
(1.98)* (2.28)*
Canadian log price 0.07 0.09
(0.68) (0.98)
Canadian wage rate 0.35 0.39
(1.77) (2.18)*
Exchange rate 0.62 0.59 0.17 0.05
(2.79)* (2.68)* (0.54) (0.17)
MOU37-91 ~0.13 -0. 13 -0.06 -0.02
(1986:4-199123) (-3.31)* (-3.42)* (-2.53)* (-0.93)
SLA9697 -0.02 0.04
(1996:2-1997: 1) (-0.46) (1.40)
SLAM.” -006 0.01
(1997:2-1998zl) (-1.21) (0.18)
SLAgg,” -0. 10 -0.04
(199822-1999zl) (~1.89) (-1.23)
SLA99-00 -0.01 -0.04
(1999:2-2000:1) (-0.13) (-1.31)
SLAOO-Ol -0.05 -0.03
(200022-200121) (-1.37) (-1.08)
SLA96_01 -0.03 -0.01
(l996:2-2001: 1) (- 1.63) (-0.59)
DUM, -0.01 -0.02
(1991:1-199324) (-0.33) (-0.46)
DUM; 0.06 0.01
(1997:3-199824) (1.12) (0.30)
SEA1 -0.10 -O. 10 -0.05 -0.06
(2ml quarter) (-2.99)* (-3.15)* (-134) (-1.68)
SEA; -0.09 -0.09 -0.04 -0.05
(3311mm) (.3.27)* (—3.31)* (1.12) (4.49)
SEA3 -0. 10 -0. 10 -0.03 -0.04
(4‘h quarter) (-4.59)* (-4.60)* (-147) (-1.73)
Intercept 0.1 l 0.1 l 0.03 0.04
(5.16)* (5.36)* (1.41) (1.70)
R2 0.82 0.82 0.84 0.81
Note:

 

1. Numbers in parentheses are t-values, and * indicates significance at the 5% levels.

2. The hypothesis of no serial correlation cannot be rejected at the 5% level; Variables are in logarithmic
terms with detrending.

3. To mitigate collinearity between U.S. and Canadian capacity in both datasets (0.94), the equations
were estimated with either U.S. or Canadian capacity and reported the estimation that gives a better fit.
Similarly, disposal income and wage rates were dropped.

72

4.3.2.1. Results of Lumber Price Model

With dataset I, the final model for lumber prices is a function of housing starts,
mortgage rates, U.S. and Canadian wage rates, U.S. production capacity, Canadian log
prices, exchange rates, seasonality, and dummies for the trade restrictions and log market
shocks. Note that to mitigate collinearity between U.S. and Canadian capacity (0.94) in
both datasets, the RFE models were estimated with either U.S. or Canadian capacity, and
the estimation that gives a better fit was selected. The same procedure was applied to
between disposable income and mortgage rates (correlation:-0.93). Housing starts, U.S.
wage rates and production capacity, Canadian log prices, and exchange rates are
statistically significant at the 5% level. For dummy variables, the MOU is statistically
significant, pushing up the lumber price by 13% for the period 1986:4-1991:3. However,
a single and multiple dummies for the SLA had little impact on lumber prices. Finally,

DUM1 for log market shock is statistically significant, suggesting that the federal harvest

reductions pushed up lumber prices by 15%.

With dataset II, the final model for lumber prices was a function of housing starts,
mortgage rates, U.S. wage rates, log prices, U.S. production capacity, exchange rates,
seasonality, and dummies for the trade restrictions. Note that to mitigate collinearity
between U.S. and Canadian wage rates (-0.74) in both datasets, the RFE models were
estimated with either U.S. or Canadian wage rates, and the estimation that gives a better
fit was selected. The same procedure was applied to between U.S. and Canadian log
prices (correlation:-0.83). Housing starts and log prices are statistically significant at the
5% level. In addition, a single and multiple dummies for the SLA are not statistically

significant. It is thus proven that the SLA had little impact on lumber prices.

73

4.3.2.2. Results of Canadian Export Supply Model

With dataset I, the final model for Canadian export supply was a function of
housing starts, mortgage rates, U.S. and Canadian wage rates, Canadian production
capacity, Canadian log prices, exchange rates, seasonality, and dummies for the trade
restrictions and log market shocks. Housing starts, U.S. wage rates and Canadian
production capacity, Canadian wage rates, and exchange rates are statistically significant
at the 5% level. For dummy variables, the MOU is statistically significant, and it pushed
down Canadian exports by 13% for the period 1986:4-199123. However, as in the RFE
model for lumber prices, a single and multiple dummies for the SLA had little impact on
Canadian exports. In addition, unlike the RFE model for lumber prices, dummies for log
market shock are not statistically significant.

With dataset II, the final model for lumber prices was a function of housing starts,
mortgage rates, U.S. wage rates, log prices, U.S. production capacity, exchange rates,
seasonality, and dummies for the trade restrictions. Like the RFE model for lumber
prices, only housing starts and log prices are statistically significant at the 5% level.
However, a single and multiple dummies for the SLA are not statistically significant.

Interestingly, the MOU is significant, and it depressed Canadian exports by 6 %.

4.3.2.3. Robustness of RFE Model in Previous Studies

The RFE model estimated by OLS is the best linear unbiased estimator if the
Gauss-Markov (G-M) assumptions are all met. However, if any one of the assumptions
fails, then OLS estimators are not unbiased (Wooldridge 2000). As such, robust

estimation involves construction of alternative estimators, which are less sensitive to

74

violations of the assumption than is the OLS estimator (Darnell 1994). Although robust
estimator could, in principle, be constructed for any violation of the G-M assumptions,
the focus of robust estimation generally involves violations of the assumed condition for
zero mean and zero correlation. Zero mean condition involves the error (u) has an

expected value of zero, or E (u) = 0, given any values of the independent variables. Zero
correlation condition means that correlation between the error term (u) and independent

variables are zero, or C0v(x,- ,u) = 0, for i = 1,2,.., k, where x,- are independent variables.

Thus, correlation between u and any of independent variables generally causes all of the
OLS estimators to be inconsistent (Wooldridge 2000).

The inconsistency in OLS estimators is closely related to the problem of
excluding a relevant variable (omitted variable bias) caused by the attribute of an RFE.
That is, since an RFE is expressed as an endogenous variable in terms of exogenous
variables in a single equation, multicollinearity problem usually arises. For example, in
his RFE model, Zhang (2001) considered many exogenous variables as determinants of
lumber prices, and then dropped several variables from the final model to avoid
multicollinearity. In fact, when we meet multicollinearity problem in empirical analysis,
it is reasonable to drop some independent variables from the model in an effort to reduce
multicollinearity. In addition, high (but not perfect) correlation between independent
variables is not a violation of the GM Theorem. However, dropping a variable that
belongs in the population model may cause the problem of omitted variable bias. As
such, the OLS estimators can be inconsistent (Wooldridge 2000).

For example, this study can prove that excluding log prices in the RFE model

could cause omitted variable bias, resulting in the inconsistency in the OLS estimators.

75

Specifically, first, this study regressed log prices on other independent variables as

follows.

LP = f(HS, DI, MR, PC, W, CLP, CPC, CW, EX, MOU, SLA)
Then, let 7 denote residual from this regression. Second, using the property of
probability limits, correlation between V and u— residual from the RFE model for
lumber prices — can be obtained.18 As a result of the estimation, if y and u are not

correlated, then the OLS estimators without including log prices in the model are

consistent. If y and u are positively correlated, the OLS estimators without including log
prices are then overestimated. Or, if y and u are negatively correlated, the OLS
estimators without including log prices are then underestimated.

From these two steps, this study found that y and u are positively correlated —

around 0.3 and 0.2 for lumber price and Canadian export models, respectively. It implies
that excluding log prices in the RFE model cause the omitted variable bias, which in turn
tend to overestimate the effects of the trade restrictions. As a result, it is essential to
incorporate log prices in determining lumber price/volume changes due to the trade
restrictions, or at least introduced dummy variables to capture effects of the market
shocks in the early 19908. However, previous studies that estimated the impacts of the
trade restriction, particularly the SLA (Zhang 2001), have never included log prices in
their RFE models, which must have caused their OLS estimators to be inconsistent and

biased.

 

‘8 The property of probability limits can be defined as follows.

P lim B,- = B,- + Cov(x,- , u) / Var(x,-) , where Bi is estimated coefficients of independent variables ( x,- ). If

the estimators are consistent, Cov(xi , u) = 0 (Wooldridge 2000).

76

4.4. Summary and Conclusions

With two datasets, this study used the procedure of the 3SLS to estimate the SSE
model in linear functional forms. The results show that the price effects of U.S. demand
for and supply of lumber, and Canadian export supply are generally smaller than those
commonly used by previous studies. Specifically, the price elasticities are -0.08~-0.13 for
domestic demand, 0.15~0.26 for domestic supply, and 0.13~0.15 for Canadian exports,
respectively. In contrast, other market factors, such as housing starts, log prices, and
exchange rates, have significant impacts on U.S. demand and supply for lumber, and
Canadian export supply. For instance, the price elasticity of demand is the smallest
among all of the factors affecting lumber demand: housing starts, lumber prices,
mortgage rates, and disposable income. Similarly, the price elasticity of domestic supply
is smaller than that of wage rates and production capacity, and the price elasticity of
Canadian exports is smaller than that of exchange rates and Canadian production
capacity. As a result, other market factors such as housing starts, log prices, and exchange
rates, have played key roles in shaping the U.S. lumber market. Particularly, the
dynamics of log market have affected domestic and export supply significantly. For
example, the federal harvest reductions in the PNW caused the domestic production to
decrease by 5.4%, resulting in lumber prices and volume changes. Finally, the SSE model
found that while the MOU depressed Canadian exports by 8%, the SLA had little impact
on Canadian exports.

Now, this study can compare the price elasticities obtained from the SSE model
with those of previous studies. Price elasticities used in previous studies are summarized

in Table 4.5. In Wear and Lee ( 1993) and Zhang (2001), the price elasticity of demand

77

for softwood lumber (—0. 174) came from Adams et al. (1986), Spelter (1992), and Adams
and Haynes (1996). Similarly, the elasticity of supply (0.4) was used as an average of the
three regional counterparts for the Pacific, Interior, and South (0.239, 0.460, and 0.510),
as documented in Adams et al. (1986). For the price elasticity of Canadian export supply,
Zhange’s (2001) 0.9 was an average of the estimates reported by Adams et al. (1986,
0.917), and Boyd and Krutilla (1987, 0.89), while Wear and Lee (1993) assumed unity
for analytic convenience. The price elasticities obtained in this study are similar to those
of Myneni et al. (1994). They estimated price elasticities derived from their SSE model
for demand, supply and Canadian export supply for the U.S. market are —0.10, 0.27, and
0.19, respectively.

Based on the RFE models for lumber prices and Canadian export supply, the
MOU might have pushed up the lumber price by 11-13%, and caused the Canadian
export supply to drop by as much as 13%. These significant REF effects of the MOU are
far greater than that obtained from the SSE model. As to the SLA, unlike the result of
Zhang (2001), however, it had little impact on lumber prices or Canadian export supply.
It implies that Zhang must have overestimated his SLA effect on lumber prices, due

mainly to the omitted variable bias.

Table 4.5. Sources of price elasticities for softwood lumber used in previous studies

 

 

 

 

 

 

 

 

 

 

Source DEM SUP EXP
Adams et al. (1986) 0.239 0’), 0.460 (I). 0.510 (S) 0.917
Boyd and Krutilla (1987) 0.890
Spelter (1992) -0. 174
Myneni et al. (1994) -0. 10 0.27 0.19
Adams and Haynes (1996) 0174 0.572 (P), 0.574(1), 0.950 (S) 0.625

 

Note:
1. P, I, and S represent Pacific, Interior and South, respectively.

78

 

CHAPTER 5

A NONSTRUCTURAL MODEL FOR U.S. SOFTWOOD LUMBER MARKET

This chapter provides empirical analyses for the nonstructural models, including
the J ohansen co-integration test and the vector error-correction (VEC) model, for the U.S.
softwood lumber market. The main tasks of the nonstructural modeling are not only to
discern the dynamic linkages among related market variables in the short run and long
run, but also to assess the impacts of the U.S. restrictions in a corroborative way. For this
purpose, the Johansen multivariate co—integration test was first introduced to estimate a
long run nonstructural model on time-series. Long run is defined as a state of equilibrium
in which economic forces such as demand and supply are in balance and thus there is no
tendency to change. When it comes to dealing with non-stationary data series in an
econometric model, therefore, the long-run equilibrium is identical to the concept of co-
integration (Harris 1995). Non-stationary time-series data can be said co-integrated, if a
linear combination of them is stationary, which thus tends to move closely together over
time (Wooldridge 2000). Second, the VEC model was employed to estimate the short run
dynamics in the relationship among time-series variables. Short run is defined as a state
of disequilibrium in which adjustment to the equilibrium is occurring. The short run
model is closely associated with the VEC model, which provides the useful information
on the short-run adjustment behavior of economic variables (Wooldridge 2000). The two
models are closely linked since the co-integration relationships are explicitly included in
the VEC model. This chapter is organized as follows. First, the theoretical framework for

the Johansen co-integration test and the VEC model is presented. Next, the empirical

79

results as well as the estimation procedures for the two models are discussed. Finally, this

chapter ends with a summary and conclusions.

5.1. Theoretical Framework

5.1.1. Johansen Co-integration Test
If a series is differenced d times before it becomes stationary, then it is integrated

of order d , denoted as I (d)(Harris 1995). Consider two time-series, y, and x, , which
are both I (d ). In general, any linear combination of the two series will be I (d ). In other
words, the residual obtained from regressing y, on x,, say u, = y, —Bx,, will be I ((1).
However, if it is possible that for some B¢0, u, = y, -—Bx, is of a lower order of
integration, 1 (d —b) , where b > 0 , the two time-series, y, and x, , can be said to be co-
integrated of order (d —b) (Engle and Granger 1987). If y, and x, are co—integrated, a
regression of y, on x, indicates that there is a long-run equilibrium relationship between
y, and x, (Wooldridge 2000). In other words, the two time-series will move closely

together over time and the difference between them will be stable, or stationary. Thus, the
concept of co-integration indicates the existence of a long-run equilibrium to which an
economic system converges over time (Harris 1995).

The Johansen co-integration test procedure is a multivariate method with
simultaneous maximum likelihood estimation (Johansen and Juselius 1990, Johansen

1995). Given a vector y, of n potentially endogenous variables, it is possible to model

y, as an unrestricted vector auto-regression (VAR) involving up to k lags:

80

y, = A,y,_l +...+ AkyH +14, (5.1)
where Ak is an (nxn) matrix of parameters, and u, is a vector of normally and

independently distributed error terms, or white noise. Sims (1980) has advocated this type
of VAR-model as a way to estimate dynamic relationships among jointly endogenous
variables without imposing a priori restrictions. In other words, unlike the structural
econometric model discussed in the previous chapter, a VAR system does not require
particular structural relationships and/or the exogeneity of some variables in the system.

The system is in reduced form with each variable y, regressed on only lagged variables

of both itself and all the other variables in the system. Therefore, ordinary least squares
(OLS) is efficient to estimate each equation because the right-hand side of each equation
in the system consists of a common set of regressors including lagged and predetermined
variables (Harris 1995 and Wooldridge 2000).

The equation (5.1) can be reformulated as follows:

AYI = I“1Ay1—1 +-~+Fk—1A)’z—k+i +HYI—k +141 (5-2)
where 1‘,- = —(I -A, —...- Ai),(i = l,...,k-1) and TI = —(I — A1-...—Ak). The system

specified this way contains information on both short run and long run adjustments to

changes in y, , via the estimates of I“,- and 1'], respectively. That is, II = 043', where 01
represents the speed of adjustment to equilibrium and B’ is a matrix of long-run
coefficients such that the term B'y,_k represents up to (n—l) co-integration relationships
in the system (Johansen 1995).

Assume that y, is a vector of non-stationary I (1) variables. Then, while all the

terms involving Ay,_k in (5.2) are [(0), l‘ly,_k also should be stationary, or I (0) , for

81

u, ~ [(0) to be white noise (Hamilton 1995). There are three cases when the requirement
of l'ly,_k ~ [(0) is satisfied. First, when all the variables in y, are stationary (H has a
full rank), then the variables in y, are I (0). Second, when there is no co-integration at
all (Fl has a zero rank), implying that there are no linear combinations of the y, , which
are [(0) , and consequently II is a (n x n) matrix of zeros. However, neither of these two
cases is particularly interesting. Third, when there exists up to (n—l) co-integration
relationships (H has reduced rank), l'ly,_k is [(0). In this case, r S (n -1) co-
integration vectors exist in 13. That is, r columns of B consist of r linearly independent
combinations of the variables in y, along with (n-r) non-stationary vectors. As a

result, testing for co-integration is identical to a consideration of the rank of 11. In other
words, co-integration tests are to identify the number of r linearly independent columns

in 11 (Harris 1995, p.79).

5.1.2. Vector Error-Correction (VEC) Model

Even though it is possible to estimate a long run nonstructural model on time-
series using the J ohansen co-integration test, it is also of interest to consider the short run
dynamics in the relationship among the variables under consideration. Particularly,
because a state of equilibrium may rarely be observed, the short run structure of the
model provides the useful information that can be obtained from the short—run adjustment
behavior of economic variables (Wooldridge 2000). A state of disequilibrium is mainly
attributed to the inability of economic agents to adjust to new information

instantaneously, due mainly to substantial adjustment costs. As a result, in an

82

econometric model, adjustment costs cause the current value of the dependent variable,
say Y , to be determined not only by the current value of explanatory variables, say X ,
but also by past values of explanatory variables. In addition, when Y changes over time in
response to current and previous values of X , lagged values of Y also enter the short run
dynamic model. This inclusion of lagged values of Y on the right-hand of the equation is
a means of simplifying the form of the dynamic model (Harris 1995).

If all variables in a vector stochastic process y, are I (1) and co-integrated, it is
possible to formulate a short run dynamic model, which is known as a vector error-
correction (VEC) model (Engle and Granger 1987).

Ay, = FlAy,_l + + Fk_lAy,_k+1+ (1([3' y,_1) + u, (5.3)
where B'y,_l is a measure of the error or deviation from the equilibrium, which is

stationary since the series are co-integrated.

A comparison between equations (5.2) and (5.3) shows that the VEC model is
closely linked to the concept of co-integration. Indeed, Engle and Granger (1987) show
that if y, and x, are co-integrated, then there must exist a VEC model. Conversely, they
show that a VEC model generates co-integrated series. In addition, because variables are

co-integrated, the VEC model incorporates both short-run and long-run effects, which is

known as a restricted VAR model (Doomik and Hendry 1994). That is, if at any time the

equilibrium holds, B' y,_] = 0. During periods of disequilibrium, this term is non-zero and

measures the distance the system is away from equilibrium during time t. Hence, an
estimate of 01 provides information on the speed of adjustment, which implies how the

variable y, changes in response to disequilibrium.

83

5.2. Johansen Co-integration Test

The main task of the Johansen co—integration test is to find a correctly specified
VAR model to identify structural economic relationships underlying the long run model.
For this purpose, with all non-stationary variables,19 the Johansen co-integration test was
implemented twice. The first co-integration test was applied to find how the all the non-
stationary series are correlated and which of them can be treated as weakly exogenous
(Johansen 1995). This is called an unrestricted VAR model. Then, another Johansen co-
integration test was employed to the endogenous variables to identify the long run
relationships among them.

Before implementing the Johansen co-integration test, the appropriate lag-lengths
were first determined to define a correctly specified VAR model. For this purpose, a
number of VAR lag selection criteria and diagnostic tests were adopted. The VAR lag
selection criteria include Log Likelihood Ratio (LR), Final Prediction Error (FPE),
Akaike Information Criterion (AIC), Schwarz Information Criterion (SC), and Hannan-
Quinn Information Criterion (HQ, Quantitative Micro Software 1998). In addition, the
diagnostic tests include the tests of the normality, serial correlation, and homoskedasticity
for the estimated residuals. Note that even though the main task of the procedure is to
find a correctly specified VAR model, this is not always possible. For this reason, the
minimum requirement set for an appropriate VAR model is that the model selected by the
lag selection criteria is free of serial correlation in diagnostic tests (Doomik and Hendry

1994).

 

'9 Stationary series such as U.S. and Canadian lumber capacity were excluded from the analysis since they
are not suited to the Johansen co-integration test.

84

5.2.1. Dataset I

The order of the VAR specification was first chosen on the basis of the five lag
selection criteria. VAR of order 1 through 5 were investigated in logarithmic forms.20 As
shown in Table 5.1, the results are mixed. For example, while the FPE, AIC and HQ tests

indicate 5 lags, LR and SC tests indicate 4 lags and l lag, respectively.

Table 5.1. Results of lag order selection criteria (dataset I)

 

 

 

 

 

 

 

 

 

 

Lag LR FPE AIC SC HQ
0 NA 3305-20 -16.48 -l6.19 -16.36
1 1416.08 1.07E-27 -33.74 -30.53* -32.45
2 202.12 5.05E-28 -34.59 -28.47 -32. 13
3 162.90 3.20E-28 -35.31 -26.28 -3 1.68
4 183.28* 7.99E-29 -37.26 -25.32 -32.46
5 124.27 5.42E-29* -38.74* -23.88 -32.77*
Note:

1. * indicates lag order selected by criterion at 5% level.
2. LR, FPE, AIC, SC, and HQ represent log likelihood ratio, final prediction error, Akaike information
criterion, Schwarz information criterion, and Hannan-Quinn information criterion, respectively.

The diagnostic tests were then examined with 1, 4, and 5 lags to find the most
appropriate approximation of the data generating process (DGP). The 5th order VAR
specification was chosen because the VAR satisfied the minimum requirement for the
correctly specified model, which is free of serial correlation. Table 5.2 summarizes the
results of diagnostic tests. In the residual serial correlation test for individual equations
and in the whole system, the null hypothesis of no serial correlation was accepted at the
5% significant level. In addition, the null hypothesis of no heteroskedasticity was
accepted at the 5% significant level for all the equations. However, normality is rejected

in two equations (EXP and CLP) and in the system.

 

2° With the sample size (n = 88 ), the software (EViews) allowed up to 5 lags for the tests.

85

Table 5.2. Results of residual tests (dataset I)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Equation Serial Correlation Heteroskedasticity Normality
FAR (2.27) FARCH (421) Z (2)

AEXP 0.65 [0.53] 0.10 [0.98] 26.24 [0.00]*
ASUP 0.76 [0.47] 1.42 [0.25] 0.95 [0.62]
AP 0.95 [0.39] 0.63 [0.65] 2.53 [0.28]
AHS 1.12 [0.34] 0.98 [0.43] 1.01 [0.60]
ADI 1.98 [0.15] 0.51 [0.73] 1.69 [0.43]
AMR 0.01 [0.99] 1.47 [0.23] 1.01 [0.60]
AW 2.02 [0.14] 1.19 [0.33] 0.95 [0.62]
ACW 0.65 [0.53] 0.46 [0.77] 0.41 [0.82]
AEX 0.52 [0.10] 0.47 [0.76] 1.91 [0.39]
ACLP 0.32 [0.73] 3.58 [0.17] 26.69 [0.00]*
System 0.041099] - 65.67 [0001*
Note:

1. Values in brackets are p-value; * indicates that the null hypothesis is rejected at 5% level.

2. Serial correlation of the residuals of individual equations and a whole system was examined using the
F-form of the Lagrange-Multiplier (LM) test, which is valid for systems with lagged independent
variables; Heteroskedasticity was tested using the F-form of the LM test; Normality of the residuals
was tested with the Doomik-Hansen test (Doomik and Hansen 1994).

The 5‘h order VAR model was tested by using the Johansen co-integration
procedure. If the series were co-integrated, then it would be possible to obtain some
indication of the weak exogeneity of the variables (Johansen 1995). Note that because
one problem with the VAR model is its high dimension, or many variables, weak
exogeneity with respect to the long-run parameters allows the co-integrated relations to
be estimated from systems of smaller dimension than the whole model (Hetemaki et al.
2001). The results of the Johansen co-integration test are reported in Table 5.3, which
indicates that there are two co-integration equations at the 5% significant level, or rank

two (r = 2). With this knowledge, this study tested the weak exogeneity and found seven

weakly exogenous variables, which are HS , DI , MR, W, CW , EX , and CLP (Table
5.4). As a result, the VAR model for dataset I is defined as three endogenous variables

(EXP , SUP , and P) and seven exogenous variables.

86

Table 5.3. Results of Johansen co-integration test (dataset I)

 

 

 

 

 

 

 

Null hypothesis Eigenvalue Trace Statistic 5% Critical Value
R=0 0.692 360.05 233.13*
RSI 0.615 261.09 192.89*
R52 0.489 150.15 156.00
RS3 0.423 121.10 124.24
RS4 0.242 74.90 94.15
R35 0.223 51.65 68.52
R56 0.177 30.45 47.21
R57 0.086 14.05 29.68
R58 0.070 6.46 15.41
R59 0.004 0.37 3.76

Note

1. * denotes rejection of the null hypothesis at the 5% level.
2. With 5 lags, the test indicates 2 co-integration equations at 5% level (r = 2 ).

Table 5.4. Results of weak exogeneity tests (dataset I)

 

 

 

_ Weak exogeneity
Equations H0 : at = 0
EXP 21.07 [0.00]*
SUP 11.33 [0.00]*
P 7.53 [0001*
HS 3.03 [0.08]
DI 2.64 [0.11]
MR 0.29 [0.59]
W 0.99 [0.32]
CW 0.74 [0.39]
EX 0.83 [0.37]
CLP 0.63 [0.42]

 

 

Note:
1. * denotes rejection of the hypothesis at the 5% level.

2. Weak exogeneity under r = 2 follows 12 (2).

Another Johansen procedure was applied to identify the long-run co-integration
relationships among the endogenous variables. That is, with the three endogenous
variables (EXP, SUP, and P), five lag selection criteria and diagnostic tests were
adopted to construct the correctly specified VAR model. VAR of order 1 through 5 were
examined in logarithmic forms. As shown in Table 5.5, the results are mixed. For

example, LR and the FPE tests indicate 4 lags. While AIC tests indicate 5 lags, SC and

87

 

 

HQ tests show 1 lag. The diagnostic tests were then examined with 1, 4, and 5 lags to
find the most appropriate approximation of the data generating process (DGP). As a
result, the 4th order VAR specification was chosen due to no serial correlation (Table
5.6).

With the 4th order restricted VAR model, the Johansen co-integration procedure
was implemented to identify possible long run relationships among the three endogenous
variables (EXP, SUP, and P). As shown in Table 5.7, the Johansen co-integration test
indicates that there is only one co-integration equation at 5% significant level, or rank

one (r = I ).2] Figure 5.1 shows the time-series of co-integration vectors and recursive
estimates of the three non-zero eigenvalues. The first three graphs show the normalized

,B-matrix to see if any of the 13' y, are stationary. The next three graphs show long run

fitted and actual values. The first co-integration vector looks fairly stationary, with fitted
and actual values tracking each other reasonably closely. The last two vectors seem less
non-stationary (upward trending), with not much relation between fitted and actual
values. In addition, the last three graphs indicate that the eigenvalues are relatively
constant, the first one at non-zero value, and the last two at close to zero throughout. As a
result, these plots satisfy there is one co-integrated relationship among the three

endogenous variables.

 

2' The Johansen co-integration test included seven exogenous variables and seasonal dummy variables.
However, the system specification tests indicated that trend was unnecessary.

88

Table 5.5. Results of lag order selection criteria for endogenous variables (dataset I)

 

 

 

Lag LR FPE AIC sc HQ
0 NA 1.971305 .2.32 -197 -2.18
1 349.18 2.471507 -6.70 -6.09* -6.46*
2 21.58 2.29507 -6.78 -591 -6.43
3 8.14 2.541307 -6.68 5.54 -6.22
4 2271* 2.26E-07* -6.80 -540 -6.24
5 14.72 2.24507 -6.82* -5.15 -6.15

 

 

 

 

 

 

Note:

1. * indicates lag order selected by criterion at 5% level.

2. LR, FPE, AIC, SC, and HQ represent log likelihood ratio, final prediction error, Akaike information
criterion, Schwarz information criterion, and Hannan-Quinn information criterion, respectively.

Table 5.6. Results of residual tests for endogenous variables (dataset I)

 

 

 

 

 

 

 

 

 

 

Equation Serial Correlation Heteroskedasticity Normality
FAR (5 .59) FARCH (4.56) 12 (2)
AEXP 2.24 [0.07] 0.40 [0.81] 29.83 [0.00]*
ASUP 1.01 [0.42] 2.14 [0.09] 7.15 [0.03]*
AP 1.48 [0.21] 0.25 [0.91] 5.38 [0.07]
System 1.19 [0.22] - 54.85 [0.00]*
Note:

1. Values in brackets are p-value; * indicates that the null hypothesis is rejected at 5% level.

2. Serial correlation of the residuals of individual equations and a whole system was examined using the
F-form of the Lagrange-Multiplier (LM) test, which is valid for systems with lagged independent
variables; Heteroskedasticity was tested using the F-form of the LS test; Normality of the residuals was
tested with the Doornik-Hansen test (Doomik and Hansen 1994).

Table 5.7. Results of Johansen co-integration test for endogenous variables (dataset I)

 

 

 

 

 

 

 

Null hypothesis Eigenvalue Trace Statistic 5% Critical Value
=0 0.370 42.34 2968*
R51 0.031 3.54 15.41
R52 0.011 0.91 3.76
Note:

1. * denotes rejection of the null hypothesis at the 5% level.
2. With 4 lags, the test indicates 1 co-integration equations at 5% level (r = I ).

89

 

 

 

Figure 5.1. Co-integration vectors and recursive estimates of the eigenvalues (dataset I)

vector3

 

vector] — vector2

 

 

425

          

 

 

 

1 iLiliirilig JLlllLIIIIIJ

1980 19807 1990 2000 1980 1990 2000

 

 

 

 

 

 

 

 

 

 

 

 

 

 

f-"fitted—EXP F-——fitted-—P
6.5
925
900
61)
875
5.5
850
1980 1980
0.4 0.4 — —Eval3
02" 02" 053*
1— p [-
.— ). ,.
[: L 1 L I I 1 r 1 1 WA J Mr J
1995 2000 1995 2000 1995 2000

90

5.2.2. Dataset 1122

VAR of order 1 through 4 were considered in logarithmic forms (Table A-l). The
results of dataset II are also mixed. That is, the LR, FPE, and AIC tests indicate 3 lags,
whereas SC and HQ tests indicate 4 lags. The diagnostic tests were then examined with 3
and 4 lags to find the most appropriate VAR model and thus the 3rd order VAR
specification was chosen due to no serial correlation. All the diagnostic tests for
individual equations and in the whole system were accepted at the 5% significant level
(Table A-2).

The Johansen co-integration test was implemented to examine the 3rd order VAR
model (Table 5.8). The results indicate that there are two co-integration equations at 5%
significant level, or rank two (r: 2). In addition, the weak exogeneity test in the co-

integration vector found six weakly exogenous variables, which are HS , DI , MR, W,

EX , and LP (Table A-3).

Table 5.8. Results of J ohansen co-integration test (dataset II)

 

 

 

 

 

 

 

Null hypothesis Eigenvalue Trace Statistic 5% Critical Value
R=0 0.757 240.61 192.89*
RSI 0.596 168.27 156.00*
R52 0.521 122.09 124.24
RS3 0.455 84.51 94.15
RS4 0.352 53.56 68.52
R55 0.300 31.47 47.21
RS6 0.161 13.25 29.68
RS7 0.072 4.32 15 .41
R58 0.010 0.51 3.76
Note:

1. * denotes rejection of the null hypothesis at the 5% level;
2. With 3 lags, the test indicates 2 co-integration equations at 5% level (r = 2 ).

 

22 Due to the small sample size (n = 52), the nonstructural modeling with dataset II confined to the U.S.
market variables. Hence, among non-stationary variables, Canadian wage rates (CW ) and Canadian log
prices (CLP) were excluded from both the co-integration test and VEC modeling.

91

 

Another Johansen method was applied to identify the long-run co-integration
relationships for the three endogenous variables. VAR of order 1 through 4 were
examined in logarithmic forms (Table A-4). The results show that while the LR, AIC and
SC tests indicate 2 lags, the FPE and HQ tests indicate 3 lags. The diagnostic tests were
then examined with 2 and 3 lags to find the most appropriate VAR model, and thus the
2nd order VAR specification was chosen due to no serial correlation. All the diagnostic
tests for individual equations and in the whole system were accepted at the 5% significant
level (Table A-5).

With the 2"d order restricted VAR model, the Johansen co-integration procedure
was implemented to identify possible long run relationships among the three endogenous
variables (EXP, SUP, and P). The Johansen co-integration test (Table 5.9) indicates
that there is only one co-integration equation at the 5% significant level, or rank one

(r=1)23.

Table 5.9. Results of Johansen co-integration test for endogenous variables (dataset II)

 

 

 

 

 

 

 

Null hypothesis Eigenvalue Trace Statistic 5% Critical Value
R=0 0.366 33.66 2968*
R51 0.174 11.81 15.41
R52 0.053 2.61 3.76
Note:

1. * denotes rejection of the null hypothesis at the 5% level.
2. With 2 lags, the test indicates 1 co-integration equations at 5% level ( r =1).

As seen in dataset 1, plots of the co-integration vectors and recursive estimates of

eigenvalues are presented in Table B-1. These indicate that while the first two vectors are

 

23 The Johansen co-integration test included six exogenous variables and seasonal dummy variables.
However, the system specification tests indicated that trend was unnecessary.

92

 

non-stationary, the third looks stationary. In addition, the eigenvalues are relatively stable
over time, the first one at non-zero value, and the last two at close to zero throughout.
Thus, these plots satisfy there is one co-integrated relationship among the three

endogenous variables.

5.2.3. Testing for Unique Co-integration Vectors

After having determined how many co-integration vectors are in the VAR models,
it is now necessary to consider whether these are unique and thus whether they tell us
anything about the structural economic relationships underlying the long run model
(Harris 1995). In general, because the Johansen co-integration procedure only determines
how many unique co-integration vectors span the co-integration space, the estimates

produced for any particular column in the co-integration vectors, ,6 , are not necessarily

unique. As a result, it is necessary to impose linear restrictions on the co-integration
vectors to obtain unique vectors lying within the co-integration space, and then test
whether the co-integration vectors are identified. This is called testing for identification
(Doomik and Hendry 2001).

To obtain unique co-integration vectors for the VAR models, the implementation
of the restriction tests proceeded as follows. First, with three endogenous variables
(EXP, SUP, andP) in the VAR models, two coefficients were restricted at a time to

equal 1 and —l and the third to equal an unrestricted value (denotes (p) in B vector such
as B = [1, - 1, (0] to see if particular relationships span the co-integration space. Then, joint
tests of restriction on both the co-integration vectors (B) and speed-of-adjustment

parameters (0t) were implemented to consider weakly exogenous to the long run

93

parameters in the restrictive models. Notice that this study found that there is only one
co-integration vector in the VAR models. In general, when rank is one (r =1), the co-
integration space is uniquely defined by a single vector. However, the testing for unique
co-integration vectors still requires because it may not be possible to identify unique
vectors, and this does not invalidate the long run stationary relationships between the
variables in the co-integration space (Harris 1995).

For the VAR model with dataset I, only the restriction of the coefficients for
Canadian export supply (EXP) and domestic supply (SUP) at a time to equal 1 and —1,

and lumber price (P) to equal an unrestricted value (B = 0.27) was not rejected since the
LR test statistic is not significant (x20) = 0.14). Then, with the test of the restrictions

being 12(2) = 5.36, the linear restriction and the feedback to zero for P related to long

run weak exogeneity were only accepted. Similarly, with dataset II, the restriction of the

coefficient for EXP and SUP at a time to equal 1 and —1, and P to equal an unrestricted

value (B = 0.31) was only accepted (760) = 1.95 ). Then, the linear restriction and the

weak exogeneity test for P was only accepted (x2 (2) = 3.60 ). The results are reported in

Table 5.10.

The results of testing for unique co-integration vectors in the VAR models
indicate that there exist long run relationships between Canadian export supply and
domestic supply. In addition, the joint tests show that U.S. lumber price is weakly
exogenous to the long run parameters in the U.S. softwood lumber market. However,
weak exogeneity for Canadian export supply and domestic supply was rejected. These
findings will be used for the VEC modeling in the following section. Notice that the long

run responses of Canadian export supply and/or domestic production to U.S. lumber

94

prices are relatively small, which are 0.27-0.31. That is, when U.S. lumber prices increase
by 1%, Canadian lumber exports to the U.S. only increases by 0.27-0.31% in the long

run.

Table 5.10. Results of testing for unique co-integration vectors

 

 

 

 

 

 

 

 

 

 

 

 

Hypothesis LR test statistic

Dataset 1 Dataset II
131 =1. 132 =-l.133 =9 0.14 [0.71] 1.95 [0.16]
B. =1. B: =9. 3 = -1 12.2710.00]* 10.9010.00]*
l3. =9. 2 =1. 3 =-1 34.40 [0.00]* 11.0510.00]*
6. =1. B: =-l.133 =9. a. =1 23.67 [0.00]* 13.18 [0.00]*
B. =1. B; =-1.B3 =9. 01; =1 19.26 [0.00]* 11.23 [0.00]*
Br =1. B; =-l. B3 =9. a. =1 5.36 [0.07] 3.60 [0.17]
Note

1. Bl , B2, and B3 represent the coefficients of the co-integration vectors for EXP, SUP and P ,
respectively. In addition, 011, (12, and 01;, represent the coefficients of the speed—of-adjustment
parameters for EXP , SUP and P , respectively.

2. LR test statistic is based on the x2 distribution and parenthesis is p-value.

3. (0 represents an unrestricted value and * denotes significance at the 5% level.

95

 

5.3. Vector Error-Correction Model

The main task of the VEC model is to find the information on the short-run
adjustment behavior of time-series variables. For this purpose, this study explicitly
included the co-integration relationships that were already obtained, and estimated the
VEC models. The VEC modeling employed the Hendry approach of a general-to-specific
procedure (Doomik and Hendry 1994, and Hendry 1995). First, this study constructed the
basic VEC model by differencing and the co-integration relationships. Second, the
parsimonious VEC (PVEC) model was estimated based on tests of the significance of the
variables in the basic VEC model. In addition, the conditional PVEC (CPVEC) model
was estimated by conditioning on any weakly exogenous variables in the system. Finally,
the structural model was constructed to consider any simultaneous effects among the
variables in the PVEC model, and test to ensure that the resulting restricted model

parsimoniously encompasses the PVEC model.

5.3.1. Dataset I
5.3.1.1. Basic VEC Model

Having obtained the long run co-integration relations using the Johansen
procedure, the basic VEC model was estimated with explicit inclusion of the error-

correction terms. For this purpose, equation (5.3) is reformulated as:

A
Ayt = FlAyt—l + + rk—lAYt—k +1 + (10391—1) + u: (5.4)

96

A
where B' y,_, is the error-correction term that consists of the co-integration relationship

obtained from the Johansen approach. Based on equation (5.4), the basic VEC model was

defined as follows:

— —

 

 

HS,

DI, ’MOU ‘
SUP, SUP,_1 SUP,_4 MR, SLA A
EXP, =A1 EXP,_1 +...+/l4 EXP,_4 +B W, +1“ DUM, +0t(By,_1)+8,
P. PM 0-4 CW. DUM2

CLP, _Seasonalityd

_EX, -

 

 

To be clear, this study has separated the normal exogenous variables from the dummies
for trade restrictions, log market shocks, and seasonality. The lag length of endogenous
variables (k = 4) is determined by the Johansen co-integration test. In addition, there is
no restriction placed on the speed of adjustment (01) to encompass weakly exogenous.
The results from estimating the basic VEC model are reported in Table 5.11. Notice that
the error correction term for lumber prices was not significant in the basic VEC model.
To check whether the basic VEC model is consistent with the data evidence, the
various diagnostic tests of the residuals for endogenous variables were implemented. The
model fits the data quite well and has approximately white noise, normally distributed
errors (Table B-2). Additionally, the first three graphs in Table B-3 show that the model
has generally constant coefficients because the one-step residuals are placed within their
approximate 95% confidence bands with constant standard errors. The next four graphs
in Table B-3 then indicate that no break point Chow test is anywhere significant within
the 1% line. As a result, no major specification problems were identified in the system

(Table A-6).

97

Table 5.11. Results of the basic VEC model (dataset I)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

. EXP SUP P
Varrable
Coefficient t-value Coefficient t-value Coefficient t-value

EXPt-I -075 -4.86* -029 -3.89* -003 -029
EXP.-2 -0.57 -3.55* -020 298* 0.07 0.36
Exp,_3 -0.48 -3.21* -020 212* -0.01 -097
EXP“, -032 266* -0.17 -0.84 0.09 0.59
Pt-I -0.11 -094 0.01 1.01 -0.15 -102
P,-2 -0.26 -1.13 -0.05 -059 -031 206*
p,_3 0.01 0.02 0.23 278* 0.22 1.46

Endogenous P14 -005 -1.65 0.03 0.30 -014 -093
SUPt-l -032 230* -032 203* 0.41 1.45
sum 0.17 0.89 -034 239* 0.04 1.36
SUP1-3 0.04 0.19 -024 265* -005 on
sun... -020 -l.08 , -0.04 -0.32 -0.03 -014
HS 0.27 240* 0.25 306* 0.16 0.46
MR -001 210* -001 -0.96 -001 074
D1 0.21 1.40 -023 -132 -0.36 -094
w -147 207* 0.16 0.31 -022 -0.26
cw 0.10 0.36 —0.15 -042 -0.36 -0.88
CLP -009 -0.76 -0.19 -172 -004 -033
EX 0.26 200* -0.01 -1.06 0.24 1.56
MOU ,, ,,
(198614499123) -0.08 251 0.04 2.30 0.04 0.91
SLA

Exogenous (1996240011,) -003 -0.63 0.04 1.42 0.02 0.56
DUM, ..
(199,:,_1993:4) 0.01 0.24 -0.06 225* 0.11 1.99
DUM2
(1997:} I99“) 0.01 0.17 0.01 0.31 -002 -0.48
SEA, * * ,,
(2..., quarter) 0.12 3.16 0.11 4.20 0.13 2.79
SE.“ 0.08 1.33 0.15 400* 0.06 0.88
(3 quarter)
3123,53 0.03 0.57 0.06 1.98* 0.01 0.25
(4 quarter)

Error-correction term -0.74 -4. 17* -0.49 -6.27 * -0.29 - l .85

 

 

 

 

 

 

 

Note:
1. * indicates significance at the 5% level.
2. Based on the co-integration test, four lags were identified.

5.2.2.2. Parsimonious VEC Model
To estimated the parsimonious VEC model, all the insignificant lagged and

exogenous variables in the basic VEC model were eliminated using an F - test (Table A-

98

 

7).24 The null hypothesis that the omitted explanatory variables are zero was not rejected

by the overall F - test (F (21,161) = 1.07, p - value = 0.37 ). The results from estimating

the PVEC model are reported in Table A-8. Notice that the error-correction term for
lumber prices still were not significant at the 5% level.

From the Johansen co-integration tests and the significance of the error correction
term in the PVEC model, it is now possible to restrict any weakly exogenous in the
system, known as a conditional PVEC (CPVEC) model (Harris 1995). In other words,
from the co-integration tests, lumber prices were identified as a weakly exogenous
variable in the system. In addition, the error correction term in the PVEC model was not

significant. As a result, lumber price can be conditioned in the system as follows:

"HS,
EX,

MOU

SUP’ AOP A SUP” +A SUP” +A [EXP ]+B SLA +(X(B )+e
= + _ _

EXP, t l EXPt-l 2 EXP,_2 3 t 3 DUM Yr 1 t

1

DUM2

_Seasonality_

 

 

Notice that as a conditioned variable, lumber prices are located in the right-hand side
without lagged variables. At this stage, Ct is restricted as 0t3 = 0, where a3 is the speed
of adjustment for lumber prices. The resulting reduction to the CPVEC model was

supported by the overall F-tests. That is, the null that the omitted explanatory variables

are zero was not rejected (F (36,157) = 1.30, p - value = 0.25 ). Finally, the results from

estimating the CPVEC model are presented in Table 5.12. Notice that estimates of the

 

2‘ Insignificant variables must be dropped from the system altogether since all equations have the same
formulation by construction (Doomik and Hendry 2001).

99

coefficients for the error-correction terms verify that the speed of adjustment to long run

changes in the Canadian exports and U.S. production is relatively slow but significant.

Table 5.12. Results of the conditional PVEC model (dataset I)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Variable EXP SUP
Coefficient r-value Coefficient t-value
EXPt-l -0.60 -4.63* -0.10 -2.27*
EXP” -0.38 -3.01* -0.08 -2.l6*
-0.28 -2.62* 0.06 0.96
Endogenous EXP”
SUPH -0. 17 -2.39* -0.33 -2.97*
SUP,-2 —0. 10 -0.97 -0.30 -2.63*
P 0.27 1.54 0.20 2.91*
HS 0.14 214* 0.09 203*
EX 0.17 208* -0.14 -1.43
MOU
(198624-1991:3) ’0'09 '3-67* 0.03 227*
SLA
“99614001,” -0.04 -1.38 0.01 0.45
DUM.
E (1991:,49914) 0.01 1.02 -0.04 -2.43*
xogenous DUM;
(1997:3_1998:4) 0.03 0.88 0.01 0.36
SEA, 1..
(an quarter) 0.03 0.96 0.09 4.14
SEAZ a: :11
(3rd quarter) 0.09 2.11 0.11 3.90
SEA; 1..
(4th quarter) 0.06 1.70 0.05 2.18
Error-correction term 056 -2.55* -0.23 -2.91*
Multivariate tests Far( 12,122) = 1.24 ; Fher(36,157) = 1.17; x2 (4) = 4.90

 

Note:

1. * indicates significance at the 5% level.

2. Based on the co-integration test, two lags were identified.

3. Multivariate tests for serial correlation, heteroskedasticity, and normality were not rejected at the 5%
significant level.

5.2.2.3. Structural VEC Model
The main task for estimating the structural VEC model is to reduce simultaneous
effects between endogenous variables in the (conditional) PVEC model (Doomik and

Hendry 2001). For example, this study found that in the conditional PVEC model with

100

 

dataset I, the residual of Canadian exports is strongly correlated with that of U.S.
production (-0.42). This implies that the two equations may be simultaneously
determined in the system, and thus OLS estimation for the model is no longer consistent.
As such, the structural VEC model was estimated by imposing some restrictions on the
CPVEC model. That is, according to economic theory, this study assumes that Canadian
exports contemporaneously depend on the level of U.S. production in the lumber market.
Thus, the structural VEC model included the endogenous variable for U.S. production as
additional explanatory variables in Canadian export supply equation. In addition, from
the CPVEC model, this study deleted all the lagged variables and exogenous variables
with a t-statistic less than one (Doomik and Hendry 2001). The structural VEC model is

now redefined as:

 

 

"HS, _
EX,
SUPz—i SUB—2 A
SUP, =(DOP, +A1 +A2 +B MOU +a(By,_l)+€,
EXP...1 EXP.-2
DUM,
_Seas0nality_
'HS, _
s EX,
EXP, = HOP, + HOSUP, + P,[ "‘ J + P, [EX19,_2 ]+ P,[EXP,_, ]+ T MOU + 61(8 y,_, ) + e,
"‘ DUM,
_Seasonality_

 

 

Notice that the endogenous variable for U.S. production (SUP,) is included in the

Canadian exports equation. As seen in the conditional PVEC model, the speed of
adjustment (or) for lumber prices was restricted. The structural VEC model was

estimated by full-information maximum likelihood (FIML) and reported in Table 5.13.

101

The resulting structural model was supported by the system reduction test. That is, the

null hypothesis that the deleted explanatory variables are zero was not rejected

(x2 statistic is 2.83, p - value = 0.59). More importantly, the LR test of over-identifying

restrictions was not rejected (76(4) = 2.52 , p - value = 0.64).25 Thus, the structural VEC

model can be said to parsimoniously encompass the conditional PVEC model.

The impulse responses for the SVEC are plotted in Figure 5.2. Impulse responses
trace out the effect of a one-time shock to one standard deviation of the residual on
current and future values of the endogenous variables —SUP and EXP (Doomik and
Hendry 2001). The first column shows the effects of an unexpected one-time shock in
domestic supply on all two endogenous variables. The second column shows the effect of
an unexpected increase in Canadian exports on the endogenous variables. These
estimated impulse responses show patterns of persistent common variation between
domestic supply and Canadian exports. For example, an unexpected shock in Canadian
exports on domestic supply slowly fades away over 5 quarters.

Finally, diagnostic tests of whether the model is congruent with the data evidence
are provided in Tables B-4 and B-5. The structural VEC model appears to fit the data

quite well, there is no evidence of within-equation residual serial correlation and the

 

25 The structural model requires to be identified. The order condition for identification involves the number
of unrestricted coefficients. Specifically, it specifies that no more than I = (nx(k -1)) + r explanatory

variables can enter any equation and no more than n xl unknowns can enter the model (n = number of
variables, k = lag lengths, and r = number of co-integration). In other words, the order condition ensures a
sufficient number of equations, which can be identified by just counting the number of unrestricted
coefficients. On the other hand, the rank condition requires that equations are linearly independent. Thus,
the actual location of the restrictions placed on an unrestricted structural VEC model is an important
element in identifying unique short run equations. As a general guide, each equation in the model requires
at least one unique predetermined variables (entering with a non-zero coefficient) to identify it (Harris 1995
and Doomik and Hendry 2001). In this study, EXP,_3 only enters Canadian export equation, whereas

SUP,-2 only enters U.S. production equation.

102

densities and distributions are close to normality (Table B-4). The model has generally
constant coefficients and no break points in the individual equations and in the system as
a whole (Table B-5). Moreover, the residual correlation between Canadian exports and
U.S. production obtained from the FIML model is -0.07, which indicates some success in
constructing the structural model. Figures 5.3 shows one-step static (ex-post) and
dynamic forecast for the last four years of the data. None of the forecasts lie outside their

individual confidence bars, and therefore constancy of the model is readily accepted. This
is confirmed by the final graph, which shows the Chow test of stability, with all x2-

values lying below 1% significance line. Finally, estimates of the coefficient of the error
correction terms confirm that the speed of adjustment to long run changes in the variables

is slow but significant.

103

Table 5.13. Results of the structural PVEC model (dataset I)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Variable EXP SUP
Coefficient t-value Coefficient t-value
EXPt—l -0.61 -5.36* -0.16 -2.89*
EXP,-2 033 -2.98* -0.15 -2.19*
EXPV; -0.29 -3.15*
Endogenous SUP -0.06 229*
SUPt-l -0-18 -2-98* -O.26 -3.20*
SUP(-2 ‘024 -2.94*
P 0.28 1.83 0.18 294*
HS 0.20 3.16* 0.09 222*
EX 0.25 257* -0.15 -1.57
MOU
(1986:4-1991:3) -0.09 -3.83* 0.03 297*
SLA
(1996:2-200111) "0'04 '1'39
Exogenous 39515-19934) 0.03 1.03 -004 253*
SEA. *
(20d quarter) 0.04 1.16 0.10 5.40
SEA; * *
(3,.) quarter) 0.09 2.37 0.10 5.35
SEA; *
(4,), quarter) 0.06 1.74 0.04 2.01
Error-correction term -0.50 -2.97* -0.23 -3.92*
Multivariate tests F...(12,124)=1.44 ; Fhe:(36,160)=1.28 ; x2(4)=l.84
LR test of over-identification x2 (4) = 2.52

 

 

Note:

1. * indicates significance at the 5% level.

2. Multivariate tests for serial correlation, heteroskedasticity, and normality were not rejected at the 5%
significant level.

3. LR test of over-identification restriction was not rejected at the 5% significant level.

104

 

Figure 5.2. Impulse responses for SPVEC model (dataset I)

 

 

 

 

 

f -—- DSLP (DSUPeqn) 0.050
F—
002 .._ 0.025
” 0.000
0.00 /\r =—
7 \/ -0.025
'— 1 I 1 1 1 1 g 1 1 1 L 1
O 5 10
F———- DSUP (DBG’ eqn) 0050
0.002
FM 0.025
0 000 —
0.000
F
F -0025
-0. 002
1 1 1 1 4 L J
0 5 10

105

 

 

 

 

 

 

_ —DEXP(DSUPeqn)
A A Av
\/ v V
1 L 1 1 1 L
0 5 10
———DEXP(DEXPeqn)
/\ /\ Aw
\/ v
P 1 l 1 1 L
0 10

Figure 5.3. One-step and dynamic model-based forecasts for SPVEC model (dataset I)

— l-step Foretasts - - -

0.50~ —1~step Forecasts = - = DEX?

      

 

 

. l

 

 

 

 

 

 

 

 

106

5.3.2. Dataset II
5.3.2.1. Basic VEC Model

Based on equation (5.4), the basic VEC model for dataset H is defined as:

VHS, ‘

DI,
SUP, SUP,__l SUP,_2 MR MOU A
EXP, = A, EXP,_l +42 EXP,_2 +3 Wt ’ +1“ SLA +01(B y,_1)+8,
P, P,_, P,_2 LP, Seasonalzty

_EX,d

 

 

The lag length of endogenous variables (k =2) is determined by the Johansen co-
integration test. In addition, there is no restriction placed on the speed of adjustment (01)
to consider weakly exogenous. Note that instead of the dummies for log market shocks,
log prices is directly included in this system. The results from estimating the basic VEC
model are reported in Table 5.14. Notice that unlike in dataset I, the error correction
terms for the three endogenous variables were significant at the 5% significant level.

The diagnostic tests of the residuals for endogenous variables show that the model
fits the data quite well and has approximately white noise, normally distributed errors
(Table B-6). In addition, the model has generally constant parameters (Table B-7). As a

result, no major specification problems were identified in the model (Table A-9).

107

Table 5.14. Results of the basic VEC model (dataset II)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

. EXP SUP P
Variable
Coefficient t-value Coefficient t-value Coefficient t—value
EXPH -0.80 -5.15* -0.50 -3.45* -0.90 -3.85*
EXP,_2 -0.47 -2.51* -0.43 -3.08* -0.23 -1.24
PM -0.07 -0.79 0.05 0.83 -0.07 -0.41
Endogenous p,_2 -015 -l.46 0.04 1.20 -0.69 -3.41*
SUP” -0.43 -3.90* 0.18 1.23 0.55 1.46*
SUP,-2 0.18 -1.03 0.10 1.14 0.76 1.60
HS 0.28 209* 0.23 269* 1.19 1.27
MR 001 -0. 13 0.02 1.68 -0.06 -1.38
DI 0.26 0.64 -0.45 -l.50 -1.04 -1.30
W -0. 19 -0.32 -0.40 -3.55* 0.87 1.28
LP 0.14 246* 0.06 1.04 -0. 12 - l .49
EX 0.56 1.98* -0.50 -0.70 -0.86 -2.91*
MOU
E “98624499, :3) -0.03 -0.70 -0.04 -1.45 -0.09 -l.18
xogenous SL A
(l996:2-2001:l) -0.04 -l.33 0.04 1.03 -0.04 -0.96
SEA, ...
(2nd quarter) 0.09 2.02 0.12 1.08 -0.04 -1.11
SEAZ * a:
(3rd quarter) 0.14 3.03 -0.05 -1.25 -0.09 -2.01
SEA3 *
(4.), quarter) 0.09 2.40 -0.01 -l.28 -0.09 -1.44
Error-correction term 045 -4.44* -0.42 -7.55* -0.62 -2.52*

 

 

 

 

 

 

 

Note:

1. * indicates significance at the 5% level.
2. Based on the co-integration test, two lags were identified.

5.3.2.2. Parsimonious VEC Model

As in dataset I, this study deleted all the insignificant exogenous variables and

lagged variables using an F -test (Table A-10). The null that the omitted variables are

zero was not rejected by the overall F-test (F (6,56) = 0.96, p - value = 0.46). Thus, the

PVEC model was reformulated based on the above procedures.

SUP,

EXP A SUP” A EXP”
= +
’ ‘ 5X04 2 13.2

P:

108

HS,

EX,

MOU
+3 LP, +1“ SLA

A

+ OMB yr-l ) + 8:

Seasonality

 

The PVEC model were estimated and presented in Table A-ll. Note that with
dataset II, it was not appropriate to condition on lumber prices to construct the
conditional PVEC model in view of the following facts. First, lumber prices in dataset II
were also identified as a weakly exogenous from the co-integration involving the long
run model. However, unlike dataset I, the error correction term in the equation was
significant at the 5% level. Second, the resulting reduction to the conditional PVEC
model was not supported by the overall F -test. That is, the null that the omitted

explanatory variables are zero was rejected (F (18,79)= 1.97 , p -value = 0.02). Thus,

with dataset II, this study only estimated the PVEC model. Finally, the diagnostic tests
indicate that there is no evidence against the specification (multivariate tests in Table A-

11).

5.3.2.3. Structural VEC Model

Note that with dataset H, the residuals of the endogenous variables show little
simultaneous effects. That is, the correlation coefficients between the three endogenous
variables are less than 0.10. This study thus constructed the structural VEC model for
dataset H by only imposing the restriction of weak exogeneity on the PVEC model. In
addition, insignificant lagged variables were dropped from the PVEC model. Thus, the
structural VEC model is estimated by full-information maximum likelihood (FIML) and
reported in Table 5.15. The resulting structural VEC model was supported by the system
reduction test. The null that deleted explanatory variables are zero was not rejected

(xzstatistic is 1.26, p- value = 0.26). In addition, the LR test of over-identifying

109

restrictions was not rejected (752(6) = 6.33, p - value = 0.27). As a result, as in dataset I,

the structural VEC model can be said to parsimoniously encompass the PVEC model.

The impulse responses for the SVEC are plotted in Figure 5.4. The first column
shows the effects of an unexpected one-time shock in domestic supply on all three
endogenous variables. The second column shows the effect of an unexpected increase in
Canadian exports on the endogenous variables. The last column shows the effect of a
one-time shock in lumber prices on all three endogenous variables. As seen in dataset I,
the estimated impulse responses between domestic supply and Canadian exports indicate
patterns of persistent common variation. However, an unexpected rise in lumber prices on
Canadian exports does not show patterns of persistent common variation in the short run
(over two quarters).

The various diagnostic tests of the residuals for endogenous variables were
implemented and provided in Tables B-8 and B9. The tests show that the model fits the
data well and has approximately white noise, normally distributed errors. The model has
generally constant parameters. Additionally, Figure 5.5 show one-step static forecast for
the last two years of the data. None of the forecast (except one time in U.S. production)
lies outside their individual confidence bars, and thus constancy of the model can be
accepted, which is confirmed by the Chow test of stability. Finally, the coefficients of the

error correction terms are significant.

110

Table 5.15. Results of the structural PVEC model (dataset II)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Variable EXP SUP P
Coefficient t-value Coefficient t-value Coefficient t-value
EXPH -0.81 -4.69* -0.34 -3.08* -0.96 -2.94*
-0.34 -2.95*
Endogenous EXP”
P.-2 -0.75 -2.59*
SUPH 0.40 236*
HS 0.17 214* 0.26 322* 0.22 273*
LP 0.12 3.00* -0.01 -1.24 -0.03 - l .26
EX 0.28 3.02* -0.41 -3.49* -1.00 -3.19*
MOU
(I 98624-1991 :4) -0.02 -0.41 0.06 0.53 -0.03 -0.91
SLA
Exogenous ( 1 99634001,” -0.05 -1.41 -0.01 -0.63 -0.03 -0.81
SEA, ...
(20d quarter) 0.01 1.09 0.06 2.72 0.03 1.52
SEA; :1:
(3rd quarter) 0.07 1.58 -0.01 -0.36 -0.10 -2.03
SEA3 a:
(4,}, quarter) 0.09 2.68 -0.01 -0.17 -0.08 -1.19
Error-correction term -0.56 -3.64* -O.46 -2.70* -0.43 -2.33*

 

 

 

 

Multivariate tests

Far(18,76)= 0.97 ; F1...(60.104) = 0.53; x2(6) = 11.46

 

 

LR test of over-identification

 

x2(6) = 6.33

 

Note:

1. * indicates significance at the 5% level.
2. Multivariate tests for serial correlation, heteroskedasticity, and normality were not rejected at the 5%
significant level.

111

 

Figure 5.4. Impulse responses for SPVEC model (dataset II)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

0.06F — DSUP (DSUP eqn) 0,0025 - — DEXP (DSUP eqn) 0,03 _ — Dp (DSUP eqn)
0.04 (1m '-
0.0025 ~ ~
0.02: . /\
1 0.0050 VAV,
0.... _.-- \/
0 5 10 0 5 10 0 5 10
0,010 r — DSUP (DEX? eqn) 010 - — DEXP (DEXP eqn) 0.015 - — DP (EXP eqn)
0.005 r
0.000 . /\
0.000 VA
.0... . \/
0 A 5 10 0 A A 5 A 10 0 5 10
0.0, __ DSUP(DP eqn) —DEXP (DP eqn) . — DP(DP eqn)
0'00] A /\\/l- 0.05 -
0.01 . \/ . /\
.0. _ » \/
F

 

 

 

 

 

 

0 5 10 0 5 10 0 5 10

112

Figure 5.5. One-step model-based forecasts and Chow tests for SPVEC model (dataset H)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

— l-step Forecasts — - — DSUP . — l-step Forecasts - - - DEXPQ15 _— l-step Foremsts - — — DP
0.1 *
* 11 l
i 0.00 b ' ‘T TT
0 0 L——— - m .
l ’- \ \ /
l- _
i 1—
-0.1 ' -025 t—
F 1
'1 1 P 1 1 1 1 1
2(X)2 1998 2000 2002
1.0r— ———————— 1.0— -------- 1.00— ---------
F—NanSUP--- 1% ,—NanEXP--- 1% —NanP--- 1%
0.75 r
0.5, 0.5 = 0.50 —
F » .
F— >-
_ 0.25 —
F 1 1 1 1 _1 L 1 1 1 1 1 1 1 1 1
1998 1999 1998 1999 1998 1999

—- Ndn CHOWS - - - 1%

1998 1999

113

5.4. Summary and Conclusions

With two datasets, this study employed the Johansen co-integration test and the
VEC model to analyze the U.S. lumber market structure and to estimate the impacts of
U.S. restrictions. Although these multiple procedures for the nonstructural modeling were
time and effort consuming, they have generated some interesting and consistent results
with the structural models. The derived results are thus very helpful for us to understand
the U.S.-Canada softwood lumber trade.

The results show that the MOU caused Canada’s exports to drop by about 9% and
thus pushed up domestic production by about 3%. These results were very close to the
findings of the SSE model in which the impact of the MOU was an 8% reduction of
Canadian exports. As in the SSE model, however, the SLA had little impact on the
lumber market. On the other hand, as a log market shock, the federal harvest reductions
in the PNW caused the domestic production to decrease by 4%, which is 1.4% lower than
that derived from the SSE model. However, the Asian financial crisis had little effects.

This study also found that lumber prices have little effect on Canadian exports in
the short-run. In contrast, other market factors, such as housing starts, exchange rates, and
log prices, have significant impacts on Canadian export supply. These results confirm the
findings of previous studies (Jennings et al. 1991 and Sarker 1996) that housing starts
have a significant effect on the level of Canadian exports. Unlike these two studies,
however, this study found that the exchange rate is one of the most significant factors on
softwood lumber imported from Canada. Additionally, U.S. log prices affect Canadian
supply significantly, which in turn indicates that U.S. producers are sensitive to log prices

in their lumber manufacturing. It should be noted that the insignificant impact of lumber

114

prices on Canadian export supply in the short-run does not mean that prices are not an
important determinant of export supply in the long run. That is, the results from the co-
integration procedure show that the long run response of Canadian exports to prices is
significant, which is 0.27 to 0.31. If we interpret the long run response as the upper bound
of the price elasticity (Quantitative Micro Software 1998), the price elasticity of
Canadian export supply cannot be larger than 0.31 at best. In other words, when lumber
price increases by 1%, Canadian export increases by 0.31% at maximum, holding other
factors fixed. The price elasticity is larger than that obtained from the SSE model (0.13-

0. 15), but still much smaller than that derived from previous studies.

115

CHAPTER 6

WELFARE ESTIMATION OF U.S. RESTRICTIONS

This chapter provides the ex post welfare evaluations of the trade restrictions and
simulation for the potential effects of the past and proposed future restriction regimes.
First, using the price elasticities and the impacts of the trade restrictions estimated from
our models, this study evaluates the welfare effects of the MOU and the SLA. Note that
this study consistently found that the SLA did not have any significant effects on the
lumber market during 1996:2-200121. To compare with the results of the previous study
(Zhang 2001), however, this study assumes that the SLA significantly reduced Canadian
exports by 4%, which is derived from the estimated coefficients in our models. Second,
this study simulates the potential impacts of the past and proposed future restriction
regimes. The main task of the simulation is to explore more feasible and effective policy
options to restrict Canadian lumber exported to the U.S. If the dispute and restrictions are
likely to continue in the future, then it is necessary to find which type of restriction — an
import tariff, an export tax, or a quota — would be the most effective to regulate lumber
imported from Canadian. In so doing, this study will not only provide some estimates of
what gains or losses to both countries are under different trade restrictions, but also
examine the practicality of the restriction options. This chapter is organized as follows.
First, the theoretical framework for the welfare analysis of the trade restrictions is
discussed. Next, the market and welfare impacts of the MOU and the SLA are presented.
Then, the simulated results for various policy options are discussed. Finally, this chapter

ends with summary and conclusions.

116

6.1. Theoretical Framework

 

 

6.1.1. Export Tax
Price Sf SS
\ S...

Sf
'\ 5‘1

P1

130 it-F.-,-:::::::::::::-15:':1---'

SF Sg ' $33.81;“ Q1‘ Q0. Volume

Figure 6.1. Structure of the U.S. lumber market under an export tax

Figure 6.1 illustrates the approach to estimating the market and welfare impacts of
an export tax, such as the MOU. Figure 6.1 describes the structure of the U.S. softwood

lumber market with a demand function for lumber (D) and a two-part lumber supply
with total supply (S T) equal to the sum of Canadian supply (S ‘) and domestic supply
(S “5 ). In this model, an ad valorem export tax on Canadian lumber results in an inward
shift in Canadian export supply (AS ‘ ), and a consequent shift in total U.S. supply (AST ).

The difference, AS T —AS‘, is then described by movement along the domestic supply

117

curve (AS “5 ). An export tax raises the import price at any volume by the tax fraction

(AP= P, —P,,). Hence, the result at the new market equilibrium is a reduction in the

imported volume, an increase in U.S. production, an increase in lumber prices, and a
reduction in the price received by Canadian producers. Note that the effectiveness of an
export tax mainly depends on the price elasticities of demand, domestic supply, and
Canadian export supply. For example, if Canadian export supply is sensitive to price
changes (elastic), an export tax will produce larger volume reductions and larger price
increases in the U.S. than if it were less sensitive to price (inelastic).

The market impacts under an export tax can be calculated once the price
elasticities and the estimated impact of an export tax on Canadian lumber are provided.
That is, from the definition of elasticity, the changes in total demand, domestic supply,

and Canadian export can be calculated as:

P.
SJ.“
AS = S—AP (6.2)
r' (‘ SS
AS =5 PAP (6.3)

0
where n, 8 and 5" are the own-price elasticities of demand, domestic supply and
Canadian export, respectively. The subscript 0 refers to base year observations. The

identity in volume can be defined as AQ = AS T = AS ““ + AS ‘.

118

The welfare impacts can be directly estimated from the market impacts and
Canadian and domestic supply equations as well as the demand equations.26 Consumer
surplus is defined as the area under the demand curve and above the price line. Change in

consumer surplus is defined by the total quantity and price changes shown in Figure 6.1:

AC5 = —1<P. - P.>Q. + gm). - 0.111: — 12.)] (6.4)

Producer surplus is defined as the area above the supply curve and under the price

line. Change in domestic producer surplus also follows directly from Figure 6.1:
(If us" 1 US “5
APS‘ =(P. -P.)S.‘ +509. -50 )(P. -P,)] (6.5)

The change in producer surplus for Canada under an export tax is based on
treating the shifted Canadian export curve as the effective supply. Accordingly, change in

producer surplus is defined as follows:

APS’ = (1 — 60135; — g Pfo - £1005; (6.6)
p: = E
1 Sir

where or is the export tax rate and P,‘ is the price defined by the pre-policy supply curve

at S f . The export tax revenue is defined as R = 01P,S,‘ .

 

2" These equations are obtained from the price elasticities and base year observations.

P
(l)Demand:P=a—01Q, Ot=—0—, a=P0 +01Q0
o

 

 

' “S P US
(2) Domestic supply: P = b + BS , B = (:3 , b = P0 - BS
. r: c c r‘ P0 6 c c
(3)Canad1an export supply: P =b +B S ,B = 50$, , b = P0 -B S

119

6.1.2. Tariff-Regulated Quota

 

 

 

 

Price SC
P2+50
P2 ----------- : -------------------------------------
Pl """""" """"""""
P0+50 .......... 5
Po __________ .................
Sf S5 56 Sf," S,“ Q, Q0 Volume

Figure 6.2. Structure of the U.S. lumber market under a tariff-regulated quota

Figure 6.2 demonstrates the method to estimating the market and welfare impacts
of a tariff-regulated quota, such as the SLA. As shown in Figure 6.1, the structure of the
U.S. lumber market consists of a demand function for lumber (D) and a two-part lumber
supply with total supply (S T) equal to the sum of Canadian export supply (S " )27 and
domestic supply (S "’ ). Notice that under the SLA, an export fee of $50/MBF is placed

when the total export from the four provinces exceeds 14.7 BBF (Sf) until the additional

 

27 The SLA imposes an export quota on shipments of softwood lumber from British Columbia, Alberta,
Ontario, and Quebec to the U.S. Hence, Canadian export supply in Figure 6.2 includes these four Canadian
provinces. In addition. supply from other Canadian provinces is included in domestic supply.

120

650 MMBF annual limit (A5,” ) is reached. Any additional export beyond S;
(= S,‘ +AS,“) is subject to a fee of $100/MBF. Hence, the Canadian export supply (Sf )

and total U.S. supply (S T) under the SLA become kinked curves.

As seen in an export tax, the market and welfare impacts of the SLA also can be
calculated using equation (6.1)—(6.6) once the price elasticities and the estimated quantity
impact are provided. Note that there are two differences between the MOU and the SLA

to estimating the welfare impacts. First, the price (P0) when Canadian export supply

equal S ," can be calculated as:

 

S ‘ — S ‘ P
APO=P2-(° ')2 (67)
85,;
where 5C is the price elasticity of Canadian export supply.

Second, change in Canadian producer surplus under the SLA is calculate as:

(P2 — P0 -50)(Sf + SE) _ (P1 — Po)(5f + 53)
2 2

 

 

APS" = 505; + (6.8)

The first two components are the portion of the producer surplus where price is above P0
under the SLA. The third component is the portion of the producer surplus where price is
above P0 under the no-SLA. Note that Canadian producers as a whole paid a $50/MBF
fee for export volume exceeding S,r in four years (1997:2-200121) and that their total

exporting volume was just about equal to or slightly greater than S;. As a result, like
Zhang (2001), this study only considered the scenario when Canadian producers paid a

$50 fee and when they collectively exported S; amount of softwood lumber to the U.S.

121

6.2. Welfare Impacts of Trade Restrictions

6.2.1. Welfare Impacts of the MOU

This study calculated the market and welfare impacts of the MOU using the
equations 6.1-6.6 and the price elasticities estimated from the models.28 Specifically, this
study found that the MOU reduced Canadian exports by 8-9% during 1986:4-199lz3.
Considering levels of lumber consumption during the same period, an 8-9% reduction in
Canadian exports would amount to a reduction of approximately 1.1 BBF annually.
However, this does not mean that domestic production would have increased by the same
amount during 198624-199lz3. Domestic production is influenced by the changes in
lumber prices and consumption simultaneously (Figure 6.1). As a result, as long as the
demand for lumber is downward sloping, 1.1 BBF is the upper bound on any increase in
domestic production caused by the MOU. To estimate these changes in production and
consumption, the price elasticities estimated from my models were used to equations 6.1-
6.3. Additionally, to estimate the impacts of the MOU, these equations were applied to
actual production, consumption, and price data during 1986:4-199lz3. In so doing, this
study simulated what the market results would have been if the MOU had not been in
place. Note that this study simulated two estimated impacts of the MOU. That is, ( 1) an
8% reduction in Canadian exports estimated from the SSE model (case I) and (2) a 9%
reduction in Canadian exports and a 3% increase of domestic supply obtained from the

VAR model (case 11).

 

28 Demand elasticities (n) = —0.08~-0.13; Domestic supply elasticities (8) = 0.15~0.26; Canadian export
supply (SC ) = 0.l3~0.15.

122

6.2.1.1. Case I: an 8% Reduction in Exports29

This study presents detailed estimates of impacts for the first year (1986:4-1987z3,
Table 6.1) and then summarizes total impacts for the period of 1986:4-1991:3 (Table
6.2). The results for the first year showed that Canadian exports declined by 1.1 BBF
from the otherwise open market solution, and domestic production increased by 642.2
MMBF. The consequent change in lumber consumption showed a 443.3 MMBF
reduction with a price increase of $14.2/MBF. With these market impacts, detailed
welfare impacts of the 8% decline in Canadian exports were calculated for the first year.
U.S. lumber producers gained $502.5 million, whereas U.S. consumers lost $703.1
million. As a result, estimate net loss to the U.S. was $200.6 million. On the other hand,
while Canadian producers lost $269.5 million, the provincial governments gained $417.8
million in export tax revenue. Together, net gains to Canada are $148.3 million. The
overall impact of the MOU for the first year was a net loss of $52.3 million, due to U.S.
consumer costs exceeding gains to U.S. producers and Canada.

The total and the average annual impacts showed that due to the MOU, Canadian
lumber exports reduced by 5.2 BBF during 1986:4-1991:3, whereas U.S. production
increased by 3.1 BBF (Table 6.2). As a result, with an annual price increase of
$12.9/MBF, U.S. consumption reduced by 2.1 BBF during the same period. With these
market impacts, detailed welfare impacts of the 8% decline in Canadian exports were
calculated for the full course of the MOU. U.S. lumber producers gained $2.2 billion,

whereas U.S. consumers lost $3.1 billion. Together, net loss to the U.S. was $884.1

 

29 Case I assumes that a significant drop in Canadian export supply due to the MOU leads to a significant
price and thus domestic production increase. In addition, to compare our results with Wear and Lee (1993),
estimates of the price and welfare impacts were converted into 1982 U.S. dollars.

123

million. On the other hand, while Canadian producers lost $1.2 billion, the province
governments gained $1.8 billion in export tax revenue. Accordingly, net gains to Canada
were $616.5 million. As a result, this analysis placed the deadweight loss at about $267.6
million over the five years, because U.S. producer profits and net gains to Canada were

more than offset by larger U.S. consumer costs.

Table 6.1. Results of market and welfare impacts for l986:4-1987:3 under MOU (case I)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

With MOU Without MOU Policy impact
Consumption -151.1
(MMBF) 49,237.0 49,388.1 “0.3)
Production +1,070.l
Market (MMBF) 35’668'6 34'598'5 (+3.0)
impact Canadian exports -l,085.5
(MMBF) 13,5684 14.7896 (80)
Price +14.2
(U.S.$/MBF) 205'3 191" (+6.9)
U.S. consumer surplus 38,877.9 39,581.0 1038;
U.S. producer surplus +5025
6,370.7 5,868.2 (+8.56)
U.S. net 1mpact 45,2486 45,4492 -200.6
(-0.4)
Welfare Canadian producer surplus ~269.5
impact 2,367.6 2,637.1 (40.2)
EXPO" tax revenue 417.8 0.0 +417.8
Canadian net 1mpact 2,785.5 2, 637.1 +148.3
(+5.6)
Deadweight loss _52 3
(U.S.+ Canadian net impact) '
Note:

1. All values for welfare impact are in million 1982 U.S. $; Values in parentheses are percentages.

 

2. Price elasticities estimated from dataset I are adopted (demand: -0.l3, domestic supply: 0.26, and
Canadian exports: 0.13); Welfare results calculated by price elasticities estimated from dataset II are
reported in Table A-12.

124

Table 6.2. Results of market and welfare impacts for 1986:4-1991:3 under MOU (case I)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Total change Annual change % chanL
Shirfizgflggtion 2129.4 -4259 -0.9
Market 1311401311321)" 6,077.8 +6156 +1.8
impact $711332? exports -5,207.2 - 1,041 _4 -8.0
[Sis/MBF) ‘ +129 +7.0
U.S. consumer surplus -3,076.4 -615.3 -1,8
U.S. producer surplus 44,1923 +4385 +8.6
U.S. net impact -884.1 -l76.8 -0.4
$331: Canadian producer surplus - 1,208.5 _241,7 -105
Export tax revenue +1,825.0 +3650 -
Canadian net impact +6 , 6.5 +1233 +5.3
36.118936288113533“ net impact) .2676 -535 -
Note:

 

 

 

 

1. All values for welfare impact are in million 1982 U.S. $.

2. Price elasticities estimated from dataset I are adopted (demand: —0.l3, domestic supply: 0.26, and
Canadian exports: 0.13); Welfare results calculated by price elasticities estimated from dataset II are
reported in Table A-12.

Compared with the results of Wear and Lee (1993), these results indicate that the
MOU had a smaller welfare impact on the U.S. lumber market. Specifically, Wear and
Lee (1993) found that the MOU led to a 5% reduction of Canadian share in the U.S.
market. Given this impact, they estimated market and welfare impacts using the

following price elasticities: demand elasticities (n) = —0.17, domestic supply elasticities

(5) = 0.40, and Canadian export supply (8") = 1.0. Notice that they assumed 5‘ equal to
unity for analytical convenience. They found that the MOU reduced Canadian lumber

exports by 10.4 BBF and pushed up U.S. production by 7.3 BBF during 1986-1990. The

125

consequent change in lumber consumption was a 3.1 BBF reduction with an annual price
increase of $20/MBF. With these market impacts, U.S. lumber producers gained $2.6
billion for the first four years of the MOU, whereas U.S. consumers lost $3.8 billion,
resulting in net U.S. loss of $1.2 billion. These higher market and welfare impacts of the

MOU may be due to their higher price elasticities, particularly Canadian export supply.

6.2.1.2. Case 11: a 9% Reduction in Exports and a 3% Increase in Production

To estimate the market and welfare impacts of a 9% reduction in Canadian
exports and a 3% increase of domestic supply under the MOU, the same procedure used
above was adopted. Note that the assumption in case I is no longer valid since the MOU
had little effect on lumber price. Hence, the following assumptions were introduced for
case 11. First, the price is fixed for each year of the MOU. For this reason, the MOU
results in an inward shift in Canadian export, and consequent shifts in demand and total
supply, including domestic supply. As a result, the new equilibrium is only related to
changes in market lumber volume. Second, a change in consumption ( ADEM ) due to the
MOU is equal to the subtraction of change in domestic supply (ASUP) and change in
Canadian export (AEXP ).

Table 6.3 presents detailed estimates of impacts for the first year (1986:4-1987z3)
under the MOU. Canadian exports reduced by 1.2 BBF from the otherwise open market
solution, and domestic production increased by 1.1 BBF. The consequent change in
lumber consumption shows a 151.1 MMBF reduction with no price effect. With these
market impacts, detailed welfare impacts of case H were calculated for the first year. U.S.

lumber producers gained $191.1 million, whereas U.S. consumers lost $119.3 million. As

126

a result, the net gain to the U.S. was $71.8 million. On the other hand, while Canadian
producers lost $491.9 million, the provincial governments gained $417.8 million in
export tax revenue. Together, the net loss to Canada was $74.1 million. Compared to
case I, the deadweight loss for the first year shrunk to $2.3 million, with smaller U.S.

consumer COSIS.

Table 6.3. Results of market and welfare impacts for l986:4-1987:3 under MOU (case H)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

With MOU Without MOU Policy impact
Consumption -151.1
(MMBF) 49,237.0 49,388.] (-03)
Production +1,070.1
Market (MMBF) 35,668.6 34,598.5 (+3.0)
impact Canadian exports -l,221.2
(MMBF) 13,5684 14.7896 (-90)
Price
(U.S.$/MBF) 205.3 205.3 0.0
U.S. consumer surplus 3 8,877.9 3 8,997.2 - (1.1) 932;
U.S. producer surplus 6,370.7 6,179.6 +191.l
(+3.1)
U.S. net 1mpact 45,248.6 45,176.8 +7l.8
(+0.2)
Welfare Canadian producer surplus -491.9
impact 2,367.6 2,859.6 (-172)
EXPO“ tax revenue 417.8 0.0 +417.8
Canadian net 1mpact 2,785.5 2,859.6 -74.1
(-2.6)
Deadweight loss _ _ _2 3
(U.S. + Canadian net impact) '
Note:

1. All values for welfare impact are in million 1982 U.S. S; Values in parentheses are percentages.

2. Price elasticities estimated from dataset I are adopted (demand: -0.13, domestic supply: 0.26, and
Canadian exports: 0.13); Welfare results calculated by price elasticities estimated from dataset II are
reported in Table A-13.

Table 6.4 summarizes the total and the average annual impacts of the MOU. The
results show that due to the MOU, Canadian lumber exports reduced by 5.9 BBF during

1986:4-199lz3, whereas U.S. production increased by 5.1 BBF. As a result, U.S.

127

 

consumption reduced by 753.8 MMBF without a price increase. With these market

impacts, detailed welfare impacts of case H were calculated for the full years of the

MOU. U.S. lumber producers received gains anticipated from such policy; profit

increased by $829.0 million. However, the costs to U.S. consumers were much smaller,

with $546.7 million. Hence, the net gain to the U.S. was $282.4 million. On the other

hand, while Canadian producers lost $2.2 billion, the provincial governments gained $1.8

billion in export tax revenue. Accordingly, the net loss to Canada was $366.1 million.

The deadweight loss of the MOU for the five years was a net loss of $83.8 million, which

was much smaller than that in case I.

Table 6.4. Results of market and welfare impacts for 1986:4-1991:3 under MOU (case H)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Total change Annual change % change__
Consumption
(MMBF) -753.8 -150.8 -0-3
Production
Market (MMBF) +110“ “’020'8 +30
impact Canadian exports
(MMBF) -5,858.1 -1,171.6 -9-0
Price
(U.S.$/MBF) ' 0'0 0'0
U.S. consumer surplus _5 46.7 409.3 .03
U.S. producer surplus +8290 +165.8 +3.1
U.S. net 1mpact +2824 +56.5 +0.1
Welfare Canadian producer surplus _2’ ,9, .2 438.2 -175
1mpact
Export tax revenue +1,825.0 +365.0 _
Canadian net 1mpact -366.1 -732 -29
Deadweight loss
(U.S. + Canadian net impact) .838 46.8 -
Note:

1. All values for welfare impact are in million 1982 U.S. $.
2. Price elasticities estimated from dataset I are adopted (demand: -0.13, domestic supply: 0.26, and
Canadian exports: 0.13); Welfare results calculated by price elasticities estimated from dataset II are
reported in Table A-l3.

128

Compared to case I, the results of case 11 showed different size and distribution of
welfare gains and losses. Under case I, the MOU placed the maximum burden on U.S.
consumers with Canadian producers incurring the second largest loss. Additionally, with
consumer costs exceeding producer gains, net impact on the U.S. was negative. In
contrast, the Canadian net impact was positive, with export tax revenue exceeding
Canadian producer losses. Under case 11, however, the ordering of the losses changes:
due to little price effects, Canadian producers were the largest losers, with U.S. consumer
bearing the second largest burden. In addition, with higher increase in domestic
production, U.S. producer gains exceeded consumer losses, which resulted in positive net
impact on the U.S. In contrast, Canada suffered a loss in economic surplus, with much
larger producer costs exceeding tax revenue.

Furthermore, the results of case H imply that even the SSE model (case I) may be
exaggerated the market and welfare impacts of the MOU, due to its assumption that a
significant impact in Canadian exports due to the MOU leads to .a significant price and
thus domestic production increase. However, as seen in case H, the assumption was not
valid. That is, the MOU led to the reduction in Canadian exports and thus increase in
domestic production, but it did not increase lumber prices. As a result, the deadweight

loss under case H was much smaller than that obtained from case 1.

6.2.2. Welfare Impacts of the SLA30
This study calculated the market and welfare impacts of the SLA using the

equations 6.1-6.8 (except 6.6) and the price elasticities estimated from our models. Note

 

3° To compare my results with Zhang (2001), estimates of the price and welfare impacts were converted
into 1997 U.S. dollars.

129

that this study consistently found that the SLA did not have any significant effect on the
lumber market during 1996:2-2001:1. However, in order to compare with the results of
Zhang (2001), this study estimated the market and welfare impacts of the SLA, assuming
that the restriction significantly reduced Canadian exports by 4%, which is derived from
the estimated coefficients in the models.

This study presents detailed estimates of impacts for the first year (1996:2-199721,
Table 6.5) and then summarizes total impacts for the period of 1996:2-2001:1 (Table
6.6). The results for the first year showed that Canadian lumber exports reduced by 628.8
MMBF from the otherwise open market solution, and domestic production increased by
354.9 MMBF. The consequent change in lumber consumption showed a 273.9 MMBF
reduction with a price increase of $18.3/MBF. With these market impacts, detailed
welfare impacts of the 4% decline in Canadian exports were calculated for the first year.
U.S. lumber producers gained $585.9 million, whereas U.S. consumers lost $912.1
million. As a result, estimated net loss to the U.S. was $326.1 million. On the other hand,
Canadian producers in four provinces gained $237.1 million. It means that even though
Canadian producers should reduce their export volume due to the SLA, they gained even
more with an increase of lumber price. Additionally, Canadian producers in non-quota
constrained provinces gained $39.4 million due to increased exports of lumber to the U.S.
Thus, the net gains to Canada were about $327.8 million. However, the overall impact of
the SLA for the first year was a net loss of $75.7 million, due to larger U.S. consumer

COSIS.

130

Table 6.5. Results of market and welfare impacts for l996:2-l997:1 under SLA

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

With SLA Without SLA Policy impact
Consumption -273.9
(MMBF) 49651.0 49924.9 (-0- 6)
Production +354.9
(MMBF) 32,165.2 31,810.3 (+1.1)
Market Canadian exports ~6288
impact (MMBF) 15,7190 16.3478 (40)
Other exports +112.5
(MMBF) 1,766.8 1,654.3 (+6.4)
Price +183
(U.S.$/MBF) 431 ‘7 413 '4 (+4.2)
U.S. consumer surplus 82,442.0 83,354.1 2112,;
U.S. producer surplus 12,0809 11,4949 +585.9
(+5.1)
U.S. net 1mpact 94,5229 94,8490 -326.1
(-0.3)
Welfare Canadian producer surplus +237.l
impact 1,563.4 1,326.4 (+179)
Other producer surplus 381.4 3419 +394
(11.5)
Canadian net impact +327.8
2,017.4 1,689.6 (+194)
Deadweight loss _ _ _75 7
(U.S. + Canadian net impact) '
Note:

1. All values for welfare impact are in million 1997 U.S. $; Values in parentheses are percentages.

2. Price elasticities estimated from dataset I are adopted (demand: -0.13, domestic supply: 0.26, and
Canadian exports: 0.13); Welfare results calculated by price elasticities estimated from dataset II are
reported in Table A-l4.

3. Other exports (producer surplus) are the volume (gain) of Canadian exporters in non-quota constrained
provinces, such as New Brunswick and Nova Scotia.

The total and the average annual impacts showed that due to the SLA, Canadian
lumber exports reduced by 3.1 BBF during 1996:2-2001:1, whereas U.S. production
increased by 1.8 BBF (Table 6.6). As a result, with an annual price increase of
$14.1/MBF, U.S. consumption reduced by 1.3 BBF during the same period. With these
market impacts, detailed welfare impacts of the 4% decline in Canadian exports were
calculated for the full course of the SLA. U.S. lumber producers gained $2.5 billion,
whereas U.S. consumers lost $3.7 billion. Together, net loss to the U.S. was $1.2 billion.

On the other hand, Canadian producers in four provinces and other producers gained

131

 

$791.4 million and $200.9 million, respectively. Accordingly, net gains to Canada were

$922.3 million. Overall, this analysis places the deadweight loss at about $160.6 million

over the five years, because U.S. producer profits and net gains to Canada were more

than offset by much larger U.S. consumer losses.

Table 6.6. Results of market and welfare impacts for l996:2-2001:1 under SLA

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Total changL Annual change % chanL
Market Canadian exports
impact (MMBF) 1103.0 -6206 4.0
8511;336ng“ +681 .5 +1363 +5.7
Price
(U.S.$/MBF) ' ”4'1 +18
U.S. consumer surplus -3,689.5 _737.9 -1.0
U.S. producer surplus +2,536.6 +5073 +4.6
U.S. net 1mpact _,’,52.9 -230.6 .03
W .
i 5,1)?ch Canadian producer surplus +7914 +1583 +7.3
Other producer surplus +2009 +402 +2.3
Canadian net 1mpact +9223 +1985 +7.3
Deadweight loss
(U.S. + Canadian net impact) .1606 .321 -75",
Note:

1. All values for welfare impact are in million 1997 U.S. $.
2. Price elasticities estimated from dataset I are adopted (demand: -0.13, domestic supply: 0.26, and
Canadian exports: 0.13); Welfare results calculated by price elasticities estimated from dataset H are
reported in Table A-l4.
3. Other exports (producer surplus) are the volume (gain) of Canadian exporters in non-quota constrained
provinces, such as New Brunswick and Nova Scotia.

Compared with the results of Zhang (2001), these results indicate that even if the

SLA had a significant effect, it would have had much smaller welfare impact on the U.S.

lumber market. Specifically, Zhang (2001) found that under the SLA, the estimated

132

annual change in lumber price was approximately $59.1/MBF, or 16%, on average, for
the period 1996-2000. Given this price impact, he estimated market and welfare impacts

using the following price elasticities: demand elasticities (n) = —0.17, domestic supply

elasticities (8) = 0.40, and Canadian export supply (5‘) = 0.9. He found that Canadian
lumber exports reduced by 12.8 BBF for the first four years under the SLA, whereas U.S.
production increased by 7.4 BBF, which in turn decreased lumber consumption of 4.8
BBF. With these market impacts, U.S. lumber producers gained $7.7 billion for the first
four years of the SLA, whereas U.S. consumers lost $12.5 billion, resulting in net U.S.
loss of $4.7 billion.

These higher welfare impacts of the SLA may be due to the weaknesses of
modeling approach (i.e. RFE) and variable use for estimating the restriction effects as
well as the adoption of high price elasticities (i.e. Canadian export supply). Particularly,
compared to the SSE and VAR findings, the RFE models tend to result in greater
restriction effects. In addition, with the problem of excluding a relevant variable (omitted
variable bias), Zhang (2001) has overestimated the effect of the SLA (see section
4.3.2.3). Further, even the RFE models could not detect that the SLA had caused the
lumber prices to increase by $60/MBF. In addition, even with such a substantial price
increase, the welfare gains and losses could not reach billions of dollars a year, because
the SSE model showed that the price elasticities in general and that of Canadian export

supply in particular are very small.

133

6.3. Simulation for Trade Policies

The main task of the simulation is to find the more feasible and effective policy
options to regulate Canadian lumber exported to the U.S. For instance, if the dispute is
likely to continue in the future, then it is necessary to find which type of restriction —
tariff, export tax, or quota — would be more effective to restrict Canadian lumber. In so
doing, this study can provide some estimates of gains or losses under trade policies to the
both countries, and look into the practicality of the options. Like van Kooten (2002),
therefore, this study used a partial equilibrium model to analyze the impacts of various
trade policy options. For this purpose, this study continues to employ the method of
comparing the results of a simulation with no trade restriction (free trade) with a second

simulation with a restrictibn in place.

6.3.1. Scenarios

To analyze the effects of various restriction regimes, realistic free trade volume
and price were first determined as the baseline. As noted above, this study simulated what
the market results would have been if the SLA had not been in place. In this context, the
derived volume and price with no SLA in place can be interpreted as the market
condition of unrestricted free trade during the recent periods. Using the average levels of
price, demand, and supply including Canadian exports during 1996-2001, the free trade

equilibrium volume and price were calibrated as follows: (a) U.S. consumption: 56 BBF,

134

(b) domestic production: 37 BBF, (c) Canadian exports: 19 BBF, and (d) lumber prices:
$400/MBF.3'

Then, the results of free trade were compared with the simulation of the following
three scenarios. That is, (a) an ad valorem countervailing duty (CVD) or import tariff
with 6.5% and 27.2%, (b) an ad valorem export tax with 15% and 20%, and (c) an export
quota with the restriction of Canadian exports to 31.5% of U.S. total consumption. This
scenario consists of two cases. Quota (1) assumes that Canadian exports only come from
four major provinces, whereas quota (H) includes the lumber exports from non-quota
constrained provinces. Note that specific tax rates and a quota regulation were chosen
based on the past and current trade policies. Chronologically, a 15% export tax was
levied by the MOU during 1986:4-1991:3. A 6.5% CVD was then implemented by the
U.S. following the termination of the MOU. The U.S. government imposed a 27.2%
CVD on Canadian lumber imports with an expiration of the SLA in the early 2001. Most
recently, the U.S. and Canada reached a tentative agreement to restrict Canadian exports
to 31.5% of U.S. total consumption. Note that a 20% export tax was chosen to compare

the results with a 27.2% CVD.

6.3.2. Simulation Results
The estimated results of alternative scenarios indicate that an import tariff has a
similar impact on U.S. consumers and producers as an export tax (Table 6.7). That is,

with an import tax or export tax, U.S. consumers and Canadian producers are worse off

 

3‘ van Kooten (2002) calculated the free trade volume and price as follows: (a) U.S. consumption: 59 BBF,

(b) domestic production: 39 BBF, (c) Canadian exports: 20 BBF, (d) lumber prices: $453/MBF. He
calibrated the free-trade equilibrium using the assumed autarkic prices and volume in the U.S. and Canada.

135

than under free trade, whereas U.S. producers are better off. The difference between the
two policies is associated with the distribution of tax revenue. For example, under a
27.2% import tax, the U.S. gain in tariff revenue is $2.1 billion/year, which more than
offsets the price impact of the import tax — the excess of consumer loss over producer
gain. As a result, the net U.S. welfare gain is $1.9 billion/year. This result occurs from the
monopsony position of the U.S. in the lumber market and capacity to leverage the terms
of trade (Boyd 1988). On the other hand, under a 20% export tax, the tax revenue is
sufficient to offset the net Canadian producer loss. As a result, the net gain in Canada
from its monopoly position in the lumber market is about $511.2 million/year. Notice that
a 27.2% has a similar impact as a 20% export tax.

A quota scheme basically has a similar impact on U.S. consumers and producers
as an import tariff and an export tax; while U.S. consumers are worse off than under free
trade, U.S. producers are better off. However, under an export quota, Canadian producers
could gain compared to free trade. For example, with the quota scheme, lumber producers
in four Canadian provinces could gain $318 million/year compared to what they would
earn under free trade. Additionally, for this simulation, U.S. producers would gain
substantially from the quota scheme (about $600 million/year), which is larger than under
a tariff system. Notice that despite the larger size of deadweight loss, the quota scheme is
more effective on regulating Canadian exports than other schemes. That is, the quota

leads to about a 9% (about 1.7 BBF) average annual reduction in imports from Canada.

136

Table 6.7. Results of market and welfare impacts under various trade policies

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

6.5 % 27.2% 15% 20% Quota Quota
Free trade . .
import tax import tax export tax export tax (I) (II)

ffjstfiggon 56 000 -57.2 204.1 -1420 -1913 -287.8 -993
(MMBF) (~0.l) (-0.4) (~02) (-0.3) (-05) (-0.2)
Erlznuiiig‘n 37 000 +756 +2697 +187.6 +2528 +3872 +1312
(MMBF) (+0.2) (+0.7) (+0.5) (0.7) (+1.1) (+0.4)
Change in

. -l32.8 -473.7 -329.6 -444.1 -1 675.0 -230.5
Canadian exports 19,000 ’
(MMBF) (-0-7) (-2.5) (-1.7) (24) (88) (-12)
Change in price 400 +3.1 +11.2 +7.8 +11.0 +16.1 +5.5
($/MBF) (+0.8) (+2.8) (+2.0) (+2.7) (+4.0) (+1.4)
:fifimmer +86 153 -175.9 -626.8 -436.3 -587.6 -883.2 -3052
(3 million) (-0.2) (—O.7) (-0.5) (-0.6) (-l.l) (-0.4)
333:0duce‘ +12 876 +116.4 +416.4 +2893 +3903 +5988 +2022
(3 million) (+0.9) (+3.2) (+2.3) (+3.0) (+4.7) (+1.6)
Government
revenue - +4952 +2,072.2 - - - -
($ million)
Net U.S. impact -59.5 -210.4 .
($ million) +99,029 (+4208) (+1,861.8) -147.0 -197.4 -284.4 -103.0
giggitildzgurplus +3 800 229.4 -805.4 -634.5 -818.4 +3183 +1016
(8 million) (-6-1) (-21.2) (-16.7) (21.5) (+8.4) (+1.4)
Government
revenue - - - +l,142.1 +1,529.6
($ million)
Net Canadian
impact +3.800 -229.4 -805.4 +507.6 +511.2 +3183 +101.6
($ million)
Note:

1. Quota (I) restricts lumber export from four Canadian provinces to 31.5% of U.S. total consumption,
while quota 11 includes exports to the U.S. by non-quota constrained provinces.
2. Values in parentheses are percentage changes, which is relative to free trade; net U.S. impact values in
parentheses are total U.S. gains with tariff revenue.
3. Price elasticities estimated from dataset I are adopted (demand: -0.l3, domestic supply: 0.26, and
Canadian exports.

However, as van Kooten (2002) pointed out, the effectiveness of a quota on

restricting Canadian lumber depends on whether or not all Canadian provinces are

included in the system. For example, while the quota scheme I restricts Canadian exports

from four Canadian provinces, lumber exports from non-quota constrained provinces

137

 

undermine the effectiveness of a quota. The quota II shows that if other Canadian
provinces other than the four provinces are excluded under a quota scheme, the policy
leads to only a 1.2% (about 230.5 MMBF) average annual reduction in Canadian exports.
Therefore, it is crucial to include all Canadian provinces under a quota scheme to restrict
Canadian exports effectively.

In addition, the effectiveness of a restrictive regime depends on the assumption
about the price elasticities of demand, domestic supply, and Canadian export supply.
Particularly, changes in the price elasticity of Canadian export supply alone significantly
alter the effectiveness of a restrictive regime (Boyd and Krutilla 1987). Hence, this study

simulated impacts of an import tariff and an export tax using different price elasticities of
Canadian export supply (8r ). Note that while 5‘: 0.31 is estimated from our models,

8‘ = 0.9 is obtained from previous studies (i.e. Zhang 2001). The effects of changes in the
price elasticity of Canadian export are summarized in Table 6.8. The results indicate that

higher price elasticity of Canadian export leads to a significant reduction of lumber

imported from Canada. For example, with 5‘=0.9, a 27.2 % import tariff pushes
Canadian exports down by 10.7% (about 2.0 BBF) annually, which is much higher than
under a quota scheme. The same holds true under a 20% export tax. Therefore, the results
imply that the price elasticities play crucial role in deciding the effectiveness of a

restrictive regime.

138

Table 6.8. Estimated economic impacts of import and export tax

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Elasticity 27.2% import tax 20% export tax 15% export tax
Chafle % Change % Change %
Canadian ex orts 0.13 -437.7 -2.5 -444.1 -2.4 -329.6 -l.7
p 0.31 -988.6 -52 -9251 49 -681.6 -3.6
(MMBF)
0.90 -2,036.6 -10.7 -l,898.5 -10.0 -l,379.0 -7.3
Price 0.13 +11.2 +2.8 +11.0 +2.7 +7.8 +2.0
0.31 +23.4 +5.9 +21.9 +5.5 +16.l +4.0
(S/MBF)
0.90 +482 +12.1 +44.9 +11.2 +326 +8.2
0.13 -626.8 -0.7 -587.6 -0.6 -436.3 -0.5
U.S. consumer surplus
- - 0.31 -l,305.4 -1.5 -l,221.7 -l.4 -901.0 -l.1
($ million)
0.90 -2,678.2 -3.1 -2,497.9 -2.9 -l,818.l -2.1
U S producer surplus 0.13 +416.4 +3.2 +390.3 +3.0 +2893 +2.3
(5' million) 0.31 +8724 +6.8 +815.9 +6.3 +600.0 +4.7
0.90 +1,811.5 +14.l +1,686.8 +13.l +1,220.4 +9.5
Government revenue 3 i: +3ng3§ - - ' - -
($ million) ' + ’ ' ' ‘ ' ' ‘
0.90 +2,068.0 - - - - -
Net U S im act 0.13 +1,86l.8 +1.9 -197.4 -146.9 -O.2
. '. ' p 0.31 +1.6413 +1.7 -4059 -04 -3000 -03
($ million)
0.90 +1,201.3 +1.2 ~81 1.1 -0.8 ~597.6 -0.6

 

 

 

 

 

 

 

 

 

139

6.4. Summary and Conclusions

This study evaluated the ex post welfare consequences of the trade restrictions and
simulated the potential effects of the past and proposed future restriction regimes. The
results of the welfare analyses reflect effective rent seeking by domestic producers and/or
Canadian producers. For example, the MOU caused Canadian exports to drop by 8-9%
during 1986:4-199lz3, which in turn led to considerable improvement in the competitive
position of U.S. producers in the domestic market. As a result, under the MOU, U.S.
producers increased domestic production by 1.8-3.0% and gained more than $615
million/year (in 1982 dollars). In addition, under the SLA, despite a 4% reduction of their
exports, Canadian producers and the Canadian provincial government gained about $350
million/year (in 1997 dollars) in the U.S. market. In contrast, U.S. consumers lost about
$110-$615 million/year (in 1982 dollars) under the MOU and about $740 million/year (in
1997 dollars) under the SLA, respectively. As a result, the trade restrictions can be seen
as effective measures of welfare transfer from U.S. consumers to U.S. producers and/or
Canadian producers.

However, this study showed that compared with the results of Wear and Lee
(1993) and Zhang (2001), the MOU and the SLA had moderate welfare impacts on the
U.S. lumber market. It is because in addition to little price effect estimated by the VAR
model, the SSE model found that the price elasticities in general and that of Canadian
export supply in particular are very small. The results of this study thus showed that the
net loss to the U.S. under the MOU was at maximum $884 million with an estimated
price increase of $12.9/MBF (in 1982 dollars) during 1986:4-199lz3. Additionally, the

net loss to the U.S. under the SLA was about $1.2 billion with an estimated price impact

140

of $14.1/MBF (in 1997 dollars) during 1996:2-2001zl. In contrast, the results of Wear
and Lee ( 1993) showed that an estimated price increase of $20/MBF (in 1982 dollars)
resulted in about $1.2 billion of the net U.S. loss. Furthermore, Zhang found that the SLA
caused lumber prices to go up by approximately $60/MBF (in 1997 dollars), which in
turn resulted in $4.7 billion of the net U.S. loss for the first 4 years under the SLA (1996-
2000). Hence, the results of the welfare consequences confirmed the two findings in
previous chapters. First, compared to the SSE and VAR findings, the RFE models tend to
overestimate the effects of the trade restrictions. Second, considering the crucial role that
price elasticities play in generating welfare gains and losses, the higher price elasticities
used in previous studies may result in significant welfare consequences of the
restrictions.

The simulation results demonstrated that from the U.S. perspective, the best
strategy for a restrictive regime is the quota scheme that includes lumber producers in all
Canadian provinces since it provides the greatest reduction of Canadian exports to the
U.S. For example, the quota scheme leads to about a 9% (about 1.7 BBF) average annual
reduction of Canadian lumber. Furthermore, U.S. producer benefits could be about $600
million/year, which is larger than under a tariff system. The results also suggested that as
a second best alternative, the U.S. could employ an import tariff and directly collect the
tax revenue by the trade restriction. As van Kooten (2002) suggested, on the other hand,
the best strategy for Canada is also the quota system that includes all Canadian provinces.
This scheme provides the greatest benefits (about $320 million/year) to Canadian
producers. As a second best alternative, Canada could employ an export tax and directly

collect the tax revenue by the trade restriction. Therefore, the quota scheme including all

141

Canadian provinces could be a mutually acceptable strategy for a restrictive regime
because it provides not only the efficient restriction of Canadian exports but also the
greatest benefits to both U.S. and Canadian producers, all at the expense of U.S.

consumers.

142

CHAPT ER 7

CONCLUSIONS AND POLICY IMPLICATIONS

7.1. Summary of Results

With an expanded list of variables for the period 198021-2001z4, this study has
developed both the structural SSE and the nonstructural VAR models to analyze the U.S.
softwood lumber market structure and to assess the market and welfare impacts of the
U.S. restrictions. In addition, this study employed the RFE to detect the potential
variations between this and previous studies, and to discover the differences between the
RFE results and those obtained from the SSE and VAR models.

The SSE and VAR models showed that the MOU caused Canadian exports to
drop by 89% during 1986:4-199123, which in turn pushed up domestic production by
3.0%. But it did not lead to a significant increase of lumber prices. However, the SLA did
not have any significant impact on Canadian exports, domestic production, and lumber
prices during 1996:2-200121. On the other hand, the RFE models for lumber prices and
Canadian export supply resulted in greater MOU impacts. That is, the MOU pushed up
lumber prices by 11-13%, and caused the Canadian export supply to drop by as much as
13%. However, even with the RFE models, this study could not detect that the SLA had a
significant impact on lumber prices or Canadian export supply (Table 7.1).

The SSE model showed that the price elasticities of demand for and supply of
lumber and Canadian export supply are generally very low. Particularly, the price
elasticity of Canadian export supply (0.13—0.15) is much smaller than that used by

previous studies (0.6-0.9) for welfare analysis. The VAR model corroborates this finding;

143

lumber prices do not have a significant effect on Canadian exports in the short run, while
even in the long run the price response of Canadian exports is cannot be larger than 0.31
at maximum. In contrast, market factors such as housing starts, log prices, and exchange
rates, have played key roles in shaping the U.S. lumber market. Particularly, the
dynamics of log market have affected domestic and Canadian export supply significantly.
For example, the federal harvest reductions in the PNW caused the domestic production
to decrease by 405.4%, which in turn resulted in lumber prices and volume changes

(Table 7.1).

Table 7.1. Summary of impacts of the trade restrictions and log market dynamics

 

 

 

 

 

 

SSE model VAR model RFE model
- Significant - Significant - Significant
MOU * EXP: -8% * EXP: -9% * EXP: -l3%
(1986:4-199lz3) * SUP: +3% * P: +11-l3%
* P: insignificant
SLA - Insi nificant - Insi nificant - Insi nificant
(199622-2001zl) g g g
- Significant - Significant - Significant
Harvest reductions * SUP: -5.4% * SUP: -4% * P: +15%
(l991:l-l993:4)
Asian financial crisis - Insi nificant - Insi nificant - Insi nificant
(1997:3-199824) g g g

 

 

 

 

Note:

1. EXP, SUP, and P represent Canadian export supply, domestic production, and lumber prices,

respectively.

This study found that compared with the results of previous studies, the MOU and

 

the SLA had moderate welfare consequences on the U.S. lumber market. For example,
the net loss to the U.S. under the MOU was about $884 million/year (in 1982 dollars) at

maximum, with an annual price increase of $129/MBF. Wear and Lee (1993) estimated

144

that the MOU caused lumber prices to increase by $20/MBF annually, resulting in about
$1.2 billion/year of the net U.S. loss. In addition, even if the SLA is assumed to be
effective, the restriction caused lumber prices to go up by $14.1/MBF (in 1997 dollars)
annually, which in turn resulted in about $1.2 billion/year of the net U.S. loss. Zhang
(2001) estimated that the net loss to the U.S. under the SLA was about $4.7 billion/year
(in 1997 dollars), with an annual price increase of about $60/MBF.

Finally, the simulation results demonstrated that from the U.S. perspective, the
best strategy for a restrictive regime is the quota scheme covering all Canadian lumber
producers, as long as the U.S. ignores the well being of its consumers. This provides the
greatest reduction of lumber imported from Canada as well as the greatest benefits to
U.S. producers. Alternatively, the US. could make use of an import tariff to regulate
Canadian exports as well as to collect the tax revenue by the restriction. However, the
results suggest that the most worrisome regime would be an export tax. That is, an export
tax results in large Canadian government revenues and less benefits to U.S. producers

than under a quota or an import tax.

7.2. Conclusions and Policy Implications

This study advances a methodological as well as a policy contribution. The SSE
and VAR models provide a substantial contribution for analyzing the U.S. lumber market
structure as well as assessing the impacts of the trade restrictions. The SSE model
mitigated the RFE’s vulnerability to problems of endogeneity, simultaneity, and
collinearity, and used all the information from the full system of equations to obtain

efficient estimates of the trade restriction effects. Further, the SSE model derived the

145

price elasticities, so that this study was able to contrast the estimates with those of
previous studies and to calculate the welfare effects directly. Nonetheless, the SSE model
has its shortcomings, mainly because of the absence of a true structure to capture the
underlying market and the lack of dynamic interaction of the relevant variables (Hamilton
1994). Moreover, considering the way the SSE model is constructed, it cannot directly
capture all the effects of a trade restriction, particularly those on lumber prices, Canadian
exports, and U.S. production. Instead, the effects of the restriction on U.S. production and
lumber prices are normally inferred by solving the SSE. For example, the SSE model
estimated the impact of the MOU with the presence of a dummy variable in the Canadian
export supply. For the welfare analysis, this study then solved the SSE simultaneously for
the equilibrium values of other endogenous variables — lumber prices and U.S.
production. To this end, the SSE procedure assumed that a significant drop in Canadian
exports due to the MOU leads to significant price and thus U.S. production increase.

The VAR model was well suited to explore the dynamic linkages of related
variables without imposing a priori theoretical structure. Moreover, the VAR model
demonstrated the ability to capture both the short run and long run responses of an
endogenous variable to other variables endogenous to the system, and its revelation of the
potential effects of a trade restriction on every endogenous variable. For example, the
VAR showed that the MOU caused changes in two endogenous variables — a reduction
in Canadian exports and thus an increase in U.S. production, but had little impact on the
other endogenous variable — lumber prices. In addition, the VAR found that the impact
of lumber prices on Canadian exports is little in the short run and is quite small even in

the long run. This implies that even the SSE may exaggerate the market and welfare

146

impacts of the trade restrictions, as long as it assumes that a significant impact in one
endogenous variable translates into significant impacts in others. In fact, two welfare
analyses of the MOU confirmed this speculation. That is, with little price effect (case H),
the market and welfare impacts of the MOU are quite smaller those derived from the SSE
(case I). From this perspective, therefore, the nonstructural VAR analysis was well served
to identify the relationships of the U.S. lumber market.

However, it should be noted that employing both the SSE and the VAR models
have helped this study to draw more balanced and consistent conclusions. First, this
approach helped estimate the impacts of the trade restrictions in a corroborative way. For
example, the SSE and VAR models generated quite consistent results of the MOU effect
— an 8% or a 9% reduction in Canadian exports. This finding thus leads to compare the
estimates with those from previous studies and conclude that the RFE tends to
overestimate the effects of the trade restrictions. Second, this approach allowed taking
advantages of both systems — deriving the price elasticities from the SSE and identifying
the market dynamics from the VAR. Thus, these complementary features have greatly
enhanced the knowledge of various aspects of the lumber trade and the quality of this
study in the hotly contested area.

On the other hand, the results showed that market factors other than lumber prices
have significant impacts on consumption, production, and Canadian exports. In other
words, it is crucial to understand the influences of other market factors and their dynamic
interactions (i.e. log markets) other than the trade restrictions in order to resolve the
dispute. In addition, while U.S. log prices affect domestic production and Canadian

export supply significantly, Canadian log prices have no significant impact on its exports.

147

These results might have to do with the different stumpage pricing systems and limited
extent of the log market. It might also imply that, unlike their U.S. counterparts,
Canadian producers are insensitive of log prices in their lumber manufacturing, due
mainly to lower log prices caused by restrictions on log exports. The results further
suggest that it is true to a large extent; Canadian exports are driven by U.S. demand-side
factors, such as housing starts and mortgage rates. However, Canadian exports have also
to do with U.S. supply side factors such as manufacturing capacity and log prices. This
study, therefore, concludes that demand as well as supply factors have influenced on
shaping the U.S. softwood lumber market.

The welfare analyses showed that the trade restrictions had moderate welfare
consequences on the U.S. lumber market, compared with the results of previous studies
estimated by the FRE. It is because, other than modest impacts of the restrictions, the
SSE shows that the price elasticities in general and that of Canadian export supply in
particular are very small. As a result, the welfare analyses confirm that an RFE model
must have exaggerated the welfare consequences with the combined use of the
overestimated market effects of the restrictions and higher price elasticities, borrowed or
assumed.

This study also found that the best strategy for a restrictive regime to regulate
Canadian exports is the quota scheme covering all Canadian lumber producers. However,
It should be emphasized that, while a quota scheme is the best strategy for a restrictive
regime, it should overcome the following potential shortcomings to regulating Canadian
lumber effectively. First, in addition to including all Canadian provinces, a quota scheme

also should encompass all softwood lumber products. For example, any supplies of non-

148

covered Canadian lumber, such as roughers and predrilled studs under the SLA, could
undermine the effectiveness of the scheme by decreasing lumber prices in the market.
Second, a quota scheme needs to abandon a trigger-price mechanism, which simply
constitute another means by which some Canadian producers can get around the system

(van Kooten 2002).

7.3. Future Research

This study has taken macroeconomic approach to analyze the U.S. lumber market
structure and thus to assess the market and welfare impacts of the trade restrictions.
Given the overall picture of the North American lumber market, future research on the
following issues could be conducted. First, after the expiration of the SLA, the Canadian
provincial governments, particularly British Columbia (BC) proposed its forest policy
change measures to seek a durable solution of the dispute. To this end, BC’s proposal
provided a framework of stumpage pricing system determined by competitive auctions.
Thus, it would be an interesting research area to assess the progress for the policy
changes and thus to contrast this with U.S. stumpage pricing system.

Second, this study found that exchange rates have a substantial effect on the level
of Canadian lumber exported to the U.S. However, this result puts at odds with other
studies that Canadian exports might have had little to do with the exchange rate (Jennings
et a1. 1991, Sarker 1996). Thus, it would be worthwhile to revisit this issue by assessing
the pass-through from exchange rates to import prices. Finally, a study on production

efficiency of lumber industry in the U.S. and Canada could provide useful information on

149

the Canadian producers’ claim that they have extended their market share in the U.S.

through competitive advantage of production efficiency.

150

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157

 

APPENDIX A: Tables

158

 

E...

Table A-1. Results of lag order selection criteria (dataset H)

 

 

 

 

 

 

 

 

 

Lag LR FPE AIC SC HQ
0 NA 7.7lE-21 -20.77 -20.42 -20.64
1 509.23 3.60E-25 -30.80 -27.29 -29.47
2 146.96 9.47E-26 -32.49 -25.83 -29.97
3 169.92* l.57E-30* -36.72* -25.71 -32.50
4 128.52 1.35E-26 -35.54 -34.63* -3 l .83*
Note:

1. * indicates lag order selected by criterion at 5% level.
2. LR, FPE, AIC, SC, and HQ represent log likelihood ratio, final prediction error, Akaike information

criterion, Schwarz information criterion, and Hannan-Quinn information criterion, respectively.
3. Given the sample size (n = 52), the software (EViews) only allowed up to 4 lags for the tests.

Table A-2 Results of residual tests (dataset II)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Equation Serial Correlation Heteroskedasticity Normality

FAR (3.26) Fm. (4.21) 12 (2)
AEXP 0.44 [0.65] 0.06 [0.99] 1.92 [0.38]
ASUP 0.37 [0.29] 0.77 [0.56] 0.01 [0.99]
AP 0.29 [0.84] 0.27 [0.89] 2.21 [0.33]
AHS 0.08 [0.97] 0.32 [0.86] 1.99 [0.37]
ADI 1.36 [0.28] 0.25 [0.91] 4.39 [0.11]
AMR 0.79 [0.51] 2.06 [0.12] 1.96 [0.37]
ALP 2.19 [0.10] 0.33 [0.85] 2.61 [0.27]
AEX 2.82 [0.08] 0.62 [0.65] 2.62 [0.27]
AW 1.34 [0.29] 0.65 [0.64] 0.17 [0.92]
S stem 0.13 [0.99] - 17.90 [0.46]
Note:

1. Values in brackets are p-value; * indicates that the null hypothesis is rejected at 5% level.

 

 

2. Serial correlation of the residuals of individual equations and a whole system was examined using the
F-form of the Lagrange-Multiplier (LM) test, which is valid for systems with lagged independent
variables; Heteroskedasticity was tested using the F-form of the LS test; Normality of the residuals was
tested with the Doornik-Hansen test (Doomik and Hansen 1994).

159

Table A-3. Results of weak exogeneity tests (dataset II)

 

 

 

Weak exogeneity

 

Equations ”0 : at = 0
EXP 11.82 [0.00]**
SUP 14.62 [0.00]**

P 20.65 [0.00]**
HS 5.51[0.14]
DI 2.89 [0.41]
MR 7.39 [0.06]
LP 1.97 [0.58]
EX 5.25 [0.15]
W 7.14 [0.07]

 

 

 

Note:

1. * denotes rejection of the hypothesis at the 5% significant level.

2. Weak exogeneity and variable exclusion under r = 2 follow x2 (2).

Table A-4. Results of lag order selection criteria for endogenous variables (dataset H)

 

 

 

 

 

 

 

Lag LR FPE AIC SC HQ
0 NA 2.02E—06 -4.60 -4.25 4.47
1 1 19.89 1.70E-07 -7.08 -6.38 -6.82
2 36.10* 1.35E-07 -7.95* -6.54* —6.92
3 23.90 7.34E-08* -7.93 -6.27 -7.42*
4 11.83 7.71E-08 -7.32 -6.17 -7.27

 

 

Note:

“ff-y

 

1F _..-.-

 

l. * indicates lag order selected by criterion at 5% level.
2. LR, FPE, AIC, SC, and HQ represent log likelihood ratio, final prediction error, Akaike information
criterion. Schwarz information criterion, and Hannan-Quinn information criterion, respectively.

Table A-5. Results of residual tests for endogenous variables (dataset H)

 

 

 

 

 

 

 

 

 

Equation Serial Correlation Heteroskedasticity Normality
FAR (2:36) FARCH (430) 12 (2)
AEXP 1.35 [0.27] 0.18 [0.95] 2.26 [0.32]
ASUP 0.36 [0.71] 0.73 [0.58] 0.26 [0.88]
AP 1.29 [0.29] 0.74 [0.58] 2.84 [0.24]
System 0.70 [0.81] - 11.85 [0.07]
Note:

1. Values in brackets are p-value; * indicates that the null hypothesis is rejected at 5% level.

2. Serial correlation of the residuals of individual equations and a whole system was examined using the
F-form of the Lagrange-Multiplier (LM) test, which is valid for systems with lagged independent
variables; Heteroskedasticity was tested using the F-form of the LS test; Normality of the residuals was
tested with the Doomik-Hansen test (Doomik and Hansen 1994).

160

 

Table A-6. Results of residual tests for basic VEC model (dataset I)

 

 

 

 

 

 

 

 

. Serial Correlation Heteroskedasticity Normality
Equation FAR (7.47) FARCH (4.46) 2’2 (2)
AD(EXP) 1.77 [0.17] 0.44 [0.78] 25.54 [0.00]*
AD(SUP) 2.00 [0.07] 0.32 [0.87] 4.85 [0.09]
AD(P) 1.20 [0.32] 0.12 [0.97] 1.26 [0.53]
System 1.12 [0.30] - 4.39 [0.35]

 

 

Note:

1. Values in brackets are p-value;* indicates that the null hypothesis is rejected at 5% level.

2. Serial correlation of the residuals of individual equations and a whole system was examined using the
F-form of the Lagrange-Multiplier (LM) test, which is valid for systems with lagged independent
variables; Heteroskedasticity was tested using the F-form of the LS test; Normality of the residuals was
tested with the Doomik-Hansen test (Doornik and Hansen 1994).

Table A-7. Results of F-tests for the basic VEC model (dataset I)

 

 

 

 

 

 

 

 

 

 

 

Variable F-statistic p-value
EXPt-I 8.80 0.00**
EXP“ 4.97 0.00**
Exp,_3 3.95 0.01"
EXPM 2.13 0.11
Pt-I 1.36 0.27
Pt-Z 3.03 0.04**
Endogenous Pt-3 3.57 0.02“
Pt-4 1.57 0.21
SUPt-I 4.71 0.00**
SUP” 2.20 0.09*
SUP,-3 1.22 0.31
SUP,-4 0.35 0.79
HS 6.42 0.00**
MR 1.58 0.21
DI 1.61 0.65
Exogenous W 1 . 19 0.32
CW 0.48 0.70
CLP 0.94 0.43
EX 2.90 0.05**
Overall F-test: F (21, 161) 1.07 0.37

 

Note:
1. ** and * indicate significance at the 5% and 10% level.
2. The null hypothesis of the overall F-test is the omitted explanatory variables are zero.

161

 

Table A-8. Results of the parsimonious VEC model (dataset I)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Variable EXP SUP P
Coefficient t-value Coefficient t-value Coefficient t-value
EXPt-I -0.68 -5.15* 018 202* -031 -131
EXP 1-2 -O.39 -293* -0. 14 -246* -0.11 -0.78
EXP,-3 -0.29 -260* 0.12 0.20 -0. 13 —1.15
EXPr-4
Pt-l
P,-2 -0. 12 -1 .17 0.01 0.19 -0.23 -2.23*
Endogenous 1),-3 0.01 0.03 0.16 246* 0.29 279*
Pt-4
SUPt-l -0.20 -298* -0.34 -2.32* -0.60 -2.94*
SUP,-2 -0. 1 1 -0.95 -0.33 -224* -0.08 -1.28
SUPt-3
SUPt-4
HS 0.17 244* 0.26 283* 0.09 1.17
MR
DI
W
LP
CLP
EX 0.30 1.97* -0.17 -1.38 -0.31 -1.58
MOU
(1986449913) 009 -3.24* 0.05 273* 0.01 0.31
SLA
Exogenous ”9962400,,” -0.04 -1.23 0.01 0.22 -0.01 -0.04
DUM,
( 199, 21499324) 0.02 0.05 -0.03 -2.20* 0.11 253*
DUM; _ -
(19973349984) 0.02 0.58 0.02 0.58 0.01 0.26
SEA] * II:
(2nd quarter) 0.05 1.60 0.12 5.73 0.13 3.79
SEA; .1
( 3m qu a rter) 0.09 1.78 0.13 4.24 0.03 0.51
SEA3 *
(4th quarter) 0.05 1.45 0.05 2.11 -0.01 -0.31
Error-correction term -055 245* -024 -3.54* -041 -1.58

 

 

 

 

 

 

 

Note:

1. * indicates significance at the 5% level.

162

 

Table A-9. Results of residual tests for basic VEC model (dataset II)

 

 

 

 

 

 

Serial Correlation Heteroskedasticity Normality
Equation FAR (2.28) FARCH (4.22) 2
X (2)
AD( EXP) 0.86 [0.43] 0.32 [0.86] 5.87 [0.06]
AD(SUP) 0.08 [0.92] 1.12 [0.37] 0.75 [0.69]
AD( P) 0.31 [0.74] 0.18 [0.94] 7.59 [0021*
System 1.52 [0.11] - 11.47 [0.08]

 

 

 

 

 

Note:

1. Values in brackets are p-value; * indicates that the null hypothesis is rejected at 5% level.

2. Serial correlation of the residuals of individual equations and a whole system was examined using the
F-form of the Lagrange-Multiplier (LM) test, which is valid for systems with lagged independent
variables; Heteroskedasticity was tested using the F-form of the LM test; Normality of the residuals
was tested with the Doornik-Hansen test (Doomik and Hansen 1994).

Table A-10. Results of F-tests for the basic VEC model (dataset H)

 

 

 

 

 

 

 

 

 

 

Variable F-statistic p-value

EXPH 10.71 0.00*

EXP,-2 5.45 000*

PM 0.71 0.56

Endogenous P12 324 0.04,,
SUPH 4.32 0.01*

sup,2 1.67 0.20
HS 3.14 004*

MR 2.30 0.11

E DI 1.73 0.18
xogenous w 2.31 0.11
LP 3.52 003*

EX 4.80 0.00*

Overall F-test: F (6, 56) 0.96 0.46

 

 

 

Note:
1. * indicates significance at the 5% level.

2. The null hypothesis of the overall F—test is the omitted variables are zero coefficient.

163

L “uranium

Table A-1 1. Results of the parsimonious VEC model (dataset H)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Variable EXP SUP P
Coefficient t-value Coefficient t-value Coefficient t-value
EXPH -0.85 -4.7 l * -0.39 -3.10* -1.02 -2.94*
Expt_2 -0.29 - l .63 -0.37 -2.98* -0. 18 -0.94
Endogenous PM

pp2 -0.1 l -0.69 0.03 1.60 -0.73 -2. 14*

SUPH 0.39 200* 0.15 0.86 0.52 1.23

SUPt-Z

HS 0.16 212* 0.25 2.94* 0.20 268*

MR

D1

W

LP 0.11 298* —0.01 -l.l3 -0.02 -1.19

EX 0.29 1.98* -0.41 -3.54* -0.99 -3.17*

MOU

(I989:l_1991:3) 001 -0. 12 0.05 0.20 -0.02 -0.88

Exogenous SL A

(l996:2-2001:1) 0.05 -1.05 -0.01 -l.23 -0.03 -1.01

SEA,

(2nd quarter) 0.01 2.04* 0.06 2.60* -0.05 -l.48

SEA; *

(3rd Quarter) 0.07 1.44 -0.02 -1.59 -0.09 -2.08

SEA3 *

(4m quarter) 0.09 2.48 -0.01 -1.40 -0.09 -l.25
Error-correction term -O.50 -2.47* -0.43 -3.41* -0.46 -2.42*

 

 

Multivariate tests

 

Far(18,76)= 0.97 ; Fher(60,104) = 0.53; 12(6) = 11.46

 

 

Note:

1. * indicates significance at the 5% level.
2. Multivariate tests for serial correlation, heteroskedasticity, and normality were not rejected at the 5%
significant level.

164

 

’11

Table A-12. Results of market and welfare impacts under MOU (case I)

 

1986:4-198723

1986:4-199lz3

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

With Without Policy Total Annual %
MOU MOU impact change change change_
Consumption -460.3
(MMBF) 49,2370 49.6973 (-09) -2.21 1.1 -442.2 -0-9
Production +6252
Market (MMBF) 35,668 .6 35,043 .4 (+1.8) +2.996.1 +5992 +1.8
impact Canadian exports 4.0855
(MMBF) 13,568.4 14,653.9 (-8.0) -5,207.2 -l.041.4 -8.0
Price +242
(U.S. $/MBF) 205'3 181'3 (+1 1.7) ' +219 +1 1'8
U.S. consumer 63,1765 64,3632 '1'186'7 -5,l9l.8 -1,038.4 -1.9
surplus (-l.8)
U'S' pmducer surplus 6,773.5 5,925.3 33:2?) +3,700.1 +7400 +14.4
U.S. net impact 69,9500 70,2886 i383) -l,491.8 -298.4 -0.5
Welfare CA producer surplus 2’3 67. 6 2,522.9 -155.2 _ 697.2 _139. 4 -6.4
1mpact (-6.2)
EXPO“ “1" revenue 417.8 0.0 +417.8 +1,825.0 +3650 -
CA net 1mpact 2,735.5 2,522.9 ””2616 +1,127.9 +2256 +102
(+10.4)
Deadweight loss _ _ _759 -363.9 -72.8 _
Note:

1. All values for welfare impact are in million 1982 U.S. 5; Values in parentheses are percentages.

2. Price elasticities estimated from dataset II are adopted (demand: -0.08, domestic supply: 0.15, and
Canadian exports: 0.15).
3. Deadweight loss is the sum of U.S. and Canadian net impacts.

165

Table A-13. Results of market and welfare impacts under MOU (case H)

 

1986:4-1987:3

l986:4-l99l:3

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

With Without Policy Total Annual %
MOU MOU impact change change change—
Consumption -151.1
(MMBF) 49,2370 49.3881 (_03) -753.8 -150.8 .03
Production +1 ,070.l
Market (MMBF) 35,668.6 34,598.5 (+3.0) +5,104.2 +1,020.8 +3.0
impact Canadian exports -1,221.2
(MMBF) 13.5684 14.7896 (_90) -5,858.l -l,171.6 -9.0
Price
(US. SIMBF) 205.3 205.3 0.0 - 0.0 0.0
”'3' consumer 63,1765 63,3724 ’193'9 -888.3 -177.7 .0.3
surplus (-0.3)
”'5' pmducer 6,773.5 6,570.3 +2032 +88l.4 +176.3 +3.1
smilus (+3.1)
U'S' "6‘ "“1”“ 69,9500 69,940.7 +93 +6.9 +1.4 +0.1
(+0.1)
Welfare CA pmduce’ 2,367.6 2,883.1 ““73 -2,288.4 -4577 -18.1
1mpact surplus (—l7.9)
EXPO“ ”X 417.8 0.0 +417.8 +1,825.0 +3650 -
revenue
CA “Ct "“9““ 2,785.5 2,883.1 193747) -463.4 +927 .37
Deadwe‘g'“ 1°55 - - -88.3 -470.3 -94.1 -
Note:

1. All values for welfare impact are in million 1982 U.S. $: Values in parentheses are percentages.

2. Price elasticities estimated from dataset II are adopted (demand: -0.08, domestic supply: 0.15, and
Canadian exports: 0.15).
3. Deadweight loss is the sum of U.S. and Canadian net impacts.

166

 

3H1

Table A-14. Results of market and welfare impacts under SLA (dataset II)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

l996:2-1997:l l996:2-2001.1
With Without Policy Total Annual %
SLA SLA impact change change change
Consumption -289.9
(MMBF) 49.6510 49.9349 (_ O. 6) - 1,347.1 -268.4 -0.5
Production +3449
(MMBF) 32.1652 31.8203 (+1.1) +1,755.8 +3512 +1.0
Market Canadian exports -6283
impact (MMBF) 15.7190 16.3478 (_4'0) +3.103.0 -620.6 -4.0
Other exports +189.4
(MMBF) 1,766.8 1,577.4 (+107) +1,l49.3 +2299 +9.7
Price +309
(U. S. $/MBF) 431.7 400.9 (+7.2) - +238 +6.5
”'5' consumer 133.9682 135.5047 '1’536'4 -6,221.8 -1,244.4 -10
surplus (-l.1)
U'S' pmduce' 12,8446 1 1,857.4 +9872 +4,277.9 +8556 +7.5
surplus (+8.3)
”'5' "6‘ “Pa“ 146.8129 147.3621 153.3 -l,943.8 -388.8 -03
Welfare CA pmduce’ 3,274.5 2,877.2 +3973 +1,504.4 +3009 +124
1mpact surplus (+13.8)
Other pmduc‘" 381.4 316.2 +652 +3333 +66.7 +4.1
surplus (+206)
CA "Ct ‘mpac‘ 3,655.8 3,193.4 +4625 +1,837.7 +3675 +132
(+145)
Deadweight loss _ _ -86.8 -106.2 -212 _
Note:

1. All values for welfare impact are in million 1997 U.S. $; Values in parentheses are percentages.

2. Price elasticities estimated from dataset II are adopted (demand: -0.08, domestic supply: 0.15, and
Canadian exports: 0.15).

3. Deadweight loss is the sum of U.S. and Canadian net impacts.

4. Other exports (producer surplus) are the volume (gain) of Canadian exporters in non-quota constrained
provinces, such as New Brunswick and Nova Scotia.

167

APPENDIX B: Figures

168

Figure B-l. Co-integration vectors and recursive estimates of the eigenvalues (dataset II)

 

 

 

 

 

 

 

 

1 vector] -205 r vectorz — — vector3
9 ’ _55 _
1L8*— ~2L0" -
r ..
+ -21 5 r- -6 o +—
11.6 F“ _ ..
- ~22.0 — b
1111111111111111111111111111 11111111111111
1990 1995 2000 1990 1995 2000 1990 1995 2000
---fitted—SUP 9.0~---fitted —EXP — -——fitted—P

   

 

 

 

1 1 1 1 1 1 1 1 1 1 1 l 1

 

 

 

 

 

 

 

 

 

 

1990 1995 2000
0.4 4 m 0.4 f Evalz 0.4 '—_ Eva13
r F b
0 2 H 0.2 " 0 2 ”-
L L L J A L l L l J A W 1 J
2000 2000 2000

169

 

Figure B-2. Fitted and actual values and diagnostics for basic VEC model (dataset I)

— DSUP — - - Fitted . —DEXP “ ‘ ’ Filled — DP — — - Fitted

0.25

,-
r
.-
.—

0.00

  
 

1 I 1 1 I l l T l

 
 

0.0
-0.25

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

t E“
* ’ _t
,. ._ f
0 ‘3 ’— -0.50 C
- .b 1 1 1 1 1 1 1 1 1 1 L J 4 1 L 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1980 1990 2000 1980 1990 2000 1980 1990 2000
r—r:DSUP “‘N(0,1) — —rZDEXP "‘N(0.1) c—T3DP ""‘N(0.1)
1- F— .. 1- g .—
04 — \ 04 — d 0.4 ~ _.
: 1 ’ 1 * *0
1- » t. ’/
I
0.2 *— 0 2 "‘ 0.2 *‘
\
1- 1' f
1 - _ ‘ L 1 _1' 1 - - 1 - _ 7 1 1 1 7 . 1. 1
0.0 2.5 -5.0 -2.5 0.0 2.5 5.0 -2.5 0.0 2.5
1 — l [— 1 —
_ — ACF-IZDSUP 1 — ACF-IIDEXP 1— ACF-I'ZDP

 

 

 

 

 

170

Figure B-3. One—step residuals and Chow test of basic VEC model (dataset I)

0.1”-

VA 00 1 /\w\

_ 1 .vv 1
* -0.lr-
* ~01 _

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

01— r
1 1 1 1 1 1 1 1 1 1 _1_ 1 1 1 1 1 1 1 1 1 1
2000 2000 2000
10— --------------- 100— --------------- 10+ ———————————————
P—Ndn DSUP - - - 1% —Ndn DEXP - - - 1% _—Ndn DP ~ -*- 1%
“ 075+ *
(15'— r 0.5'-
+- .—
. 050+ . K
L 1 1 1 J 1 4 1 1 1 1 l 1 J 41 1 1 1 1L 1 4
2000 2000 2000
Hm— ———————————————
-—NdnCHOWs --- 1%
1-
1-
075*
(150'—
1 1
2000

171

Figure B-4. Fitted and actual values and diagnostic for SPVEC model (dataset I)

0.0

0.75

0.50

0.25

—D&JP - - -Fitted

T l 1 1 I I l l

   

 

 

 

 

 

 

 

 

172

—r:DSUP - - — N(0.1)

 

 

 

 

 

 

 

 

 

 

 

1 l 1 1 1 1 1 1 1 1 l 1 L 1 J1 1 1 1 1 l 1

1985 1990 1995 2000

_ — AGorzDEXP

 

 

 

 

 

Figure B-S. One-step residuals and Chow tests of SPVEC model (dataset 1)

01

0.0 -

0.5

0.5

 

 

 

 

 

 

_ —— r DSUP
L.
1 1 1 1 1 1 1 1 1 1 1 1 1 J
1990 1995 2000
— Ndn DSUP - - - 1%
1—
1.
1 1 1 1 1 1 1 1 1 1. 1 1 1 J
1990 1995 2000
— Nch CHOWs - ' ' 1%
L.
1‘
1—
1990 1995 2000

173

0.0

0.5

 

 

 

 

+ —rDEXP
.- 1"H-L 1 J 1 1 l 1 J 1 1 1 1 1
1990 1995 2000
_ — th DEXP - - - 1%
1—
L 1 1 l 1 L 1 1 1 1 1
1990 1995 2000

Figure B-6. Fitted and actual values and diagnostics for basic VEC model (dataset II)

1 - - - DSUP — Fitted . —r:DSUP __- - N(0.l) 1 _. — ACF-rzDSUP
0.1 *- » c

1 2
1' I
0.0 I

11111111111111 '1‘1'11

1990 1995 2000 -2.5
_ - - - DEXP — Fitted ' —r:DEXP -_- - N(0.1)

T

T

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1
:/

 

\

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1 v 1 1 1 1 1_1_1‘ 1 1 1 1 1 1 1 1 1 1 1
1990 1995 2000 0.0 2.5 0 5 10
[_ _ _ DP _FM - —r:DP —_--N(0.l) 1 C—ACF-rzDP
1 r _
: 0.4~ 1
a 1 ~ I
0-5? * If
*- I
0.00 ,A V
1—1 VJ
1
#11111111111111
1990 1995 2000

   

174

Figure B-7. One-step residuals and Chow tests for basic VEC model (dataset II)

0.05

0.00

-0.05

1.00

0.75

0.50

 

1.25 —

1.00

0.75

0.25

 

 

—rDSllP 0.10r —rDEXP 0.2{ -—rDP'
T /\ 0.05 0.1+ i i '
\v \ 0.00 h \\/\ 0.0 b
-005 ~ -0.1 —

 

 

 

 

 

 

 

1.00

0.50

 

2001

 

 

 

 

 

175

2001 2002
—— Ndn DEXP - - - 1%
1 1 1 1 1 1
2001 2002

 

Figure B-8. Fitted and actual values and diagnostics for SPVEC model (dataset II)

— DSUP - - - Fitted ——r:DSUP - - — N(O,l) 1 — ACF-r:DSUP
0-1 0.4 — E —
r h ’ \
, x A

 

7 v

l l
\ \I I 0.2 b--
l- H ’-
I | ’ ’ ‘
I
v- ‘ ’- ,_
. l/ ’
V _ L
-0J _
b >-
J 1 1 1 1 1 1+ 1 1 1 1 J l 1 1 l 1 I l 1‘ 7 I J 1 1 1 1 l 1 J 1_ 1

I —u
i ‘ ~ /
0.0 . ,A' ML ‘- ~ ‘/

/]
Cl

 

0-11-1"

 

 

—~..."‘_,

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1990 1995 2000 -25 0.0 2.5 o 5 10
_ — DEXP - — — Fitted l —nDExg — - - MD.” 1 — — ACF-rzDEXP
0.2 ~ _
: 0.50 r ”
. l ~

 

 

0.0"1 \ w 1111 l1
:H' W W

1, t
l

 

 

r
.0
I»)
~Ii
Y T r I T Y

 

 

 

 

 

 

1 1 1 1 1 1 1 1 1 1 1 1 1 1

l 990 1995 2000

 

 

—- DP ~ - * Fitted

0.50 —

Y I 3' I T I T 1

 

3 I I K' ‘ 0
0.00 11 21' -l .V 1‘ 0.25—

 

 

 

 

 

 

 

 

 

 

 

 

WW 11'” "1

i— 1 P
P 1

F1. . , r l . . l

1990 1995 2000

 

176

Figure B-9. One-step residuals and Chow tests for SPVEC model (dataset II)

0.10 *—rDSUP 1 —rDEXP
* 01 ~ _ "
(105 - [
(100 01) /\
V 1/ v \jV \
4105 - ”
-01 — 1
4 1 1 1 1 h 1 1 1 1
1998 2000 2002 1993 2000 2002
1.0 ———————————————— 1.00 ~ ———————————————
L—Ndn DSUP 1% —NanEXP --- 1%
_ (175 —
015~
_ (150 —
_ 025 ”/ff/
1 1 1 1 1 1 1 1 1 1
1998 2000 2002 1998 2000 2002
100 ----------------
——NdnCHOWs —-- 1%
075-
050»—
O.25 ”m
1 1 l
1998 2000 2002

 

 

 

 

 

 

 

 

 

177

0.01 r/_\’\ -A/

 

 

 

 

-0.2»— .
1 1 1 1
1998 2000 2002
1.0 ----------------
_—NanP--— 1%
+—
0.51-
1 1 1 1
1998 2000 2002

  

1111111111111111111111

11111293