a ,
«my ‘

t

:1 gig;

4%.;

any“? .
. immmfiu

I:
.-

 

 

lulu. I}: .
z}.
I. .

 

 

 

 

THESOS

2664

p .l‘ .’ / 7 x" "
¢.. r ~ ’ ’
(Pg-J J ‘T ’9‘”

LIBRARY
Michigan State
University

This is to certify that the
dissertation entitled

PRODUCTION STRUCTURE OF THE SAWMILLING
INDUSTRY OF THE LAKE STATES

presented by

JAMES ROBERT GEORGE MCQUEEN

has been accepted towards fulfillment
of the requirements for the

Ph.D. degree in Forestry

 

 

Major Professor’s Signature

W2? X603

Date

 

MSU is an Affirmative Action/Equal Opportunity Institution

PLACE IN RETURN BOX to remove this checkout from your record.
To AVOID FINES return on or before date due.
MAY BE RECALLED with earlier due date if requested.

 

DATE DUE DATE DUE DATE DUE

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

6/01 c:/ClFlC/DateDue.p6&p.15

 

PRODUCTION STRUCTURE OF THE SAWMILLING INDUSTRY
OF THE LAKE STATES
By

James Robert George McQueen

A DISSERTATION
Submitted to
Michigan State University

in partial fulfillment of the requirements
for the degree of

DOCTOR OF PHILOSOPHY
Department of Forestry

2003

ABSTRACT

PRODUCTION STRUCTURE OF THE
SAWMILLING INDUSTRY OF THE LAKE STATES

By

James Robert George McQueen

This study examined the production structure of the sawmilling industry of the
Lake States (Michigan, Minnesota and Wisconsin) in order to determine elasticities of
substitution, elasticities of demand, technological change, the bias of technological
change and returns to scale. A homogeneous translog cost function was estimated using
pooled time—series data for the period 1963-1996.

Results for the Allen Partial Elasticity of Substitution (AES) indicate that labor
and materials were inelastic substitutes while labor and capital were elastic complements.
Materials and capital were also inelastic substitutes. Materials and capital have the
greatest substitutability but only slightly more so than labor and materials.

The Morishima Elasticity of Substitution (MES) results indicate that all three
inputs were inelastic substitutes with the greatest substitutability between
capital/material. The results for the substitutability of labor/material and material/labor
were similar to the AES results. The labor/capital and material/capital rates of
substitution were much less than the capital/labor and capital/material rates.

The own-price elasticities of demand were all inelastic and negative indicating
downward sloping demand curves. All other elasticities were inelastic and indicate that
materials was a substitute for labor and capital but labor and capital were complements.

Changes in the price of materials had a relatively large, but inelastic, effect on the

demand for capital with a cross-price elasticity of 0.56. Changes in the price of labor also
had a relatively large effect on the demand for capital, but in a complementary fashion,
with an elasticity of -0.46. Changes in the price of materials had a greater effect on the
demand for labor than the other way around with cross—price elasticities of 0.55 and 0.30,
respectively.

Variable costs increased by 0.8% per year over the study period ceteris paribus.
The results for bias of technical change showed that it was materials and capital-using
and labor-saving. The labor savings were not as high as other lumber producing regions
of North America with an average value of -0.62%/year. The bias of technical change for
materials was 0.31%lyear and for capital, it was 0.30%lyear. These figures are important
in that they may limit the competitiveness of the industry in the Lake States with respect
to other regions because labor productivity was not increasing as fast as it was elsewhere.

The hypothesis of constant returns to scale could not be rejected at the 1% level.
This was common for studies of the sawmill industry but seems particularly common to
regions where the industry was made up primarily of small mills. Constant returns to
scale in a mature sawmill industry would lead to the outcome of many mills of similar
size as all economies of scale have been exhausted and the industry has settled into an
equilibrium firm size near the minimum of the long run cost function. Nevertheless, this
does not explain why the average mill size in the Lake States is small compared to the

Pacific Northwest and Southeastern U.S.

To my wife Lorie Srivastava and my parents, George and Janet McQueen.

iv

ACKNOWLEDGEMENTS

There are many people that deserve acknowledgement for their support and
efforts in helping me complete my degree.

Dr. Karen Potter-Witter served as my major professor for most of my stay at
Michigan State and she was very patient and encouraging of my efforts and provided
valuable guidance as well as giving me the opportunity to interact with students in the lab
and in the classroom. She was also responsible for securing the funding for this project.

Drs. Leefers, Swinton, Yin and Vasievich provided almost all of the rest of the
assistance with regards to the content of the dissertation and helped steer me clear of
some blind alleys, quicksand, and tiger traps.

Funding for this research was provided by the USDA Eastern Hardwood
Utilization Research Program and the Michigan Agricultural Experiment Station. I am
grateful to the administrators of those organizations that they saw fit to support this
research.

Dr. James Stevens was my first adviser at Michigan State and coauthor of my first
refereed journal article. I look forward to meeting up with him out West.

My wife Lorie Srivastava was also instrumental in maintaining my good humour
and making our time at the university very much fun.

My parents also always provided encouragement and never doubted my ability to
finish, despite the fact that no phone conversation was complete without the polite query:
“Are you done yet?". Parents!

Lastly, I’d like to thank DB, SY and XTC for keeping me awake during many a

long night in the final stretch.

TABLE OF CONTENTS

 

 

 

 

 

 

 

TABLE OF CONTENTS vi
LIST OF TABLES viii
LIST OF FIGURES i!
LIST OF FIGURES ii
1.0 INTRODUCTION 1
1.1 THE INDUSTRY ........................................................................................................................ 2

1.2 THE FOREST RESOURCE .......................................................................................................... 7

1.3 TIMBER PRICING ...................................................................................................................... 9

1.4 TIMBER SUPPLY .................................................................................................................... 13

1.5 PRODUCTIVITY IN THE SAWMILL INDUSTRY .......................................................................... 14

1.6 RESEARCH QUESTIONS .......................................................................................................... 16

1.7 OBJECI'W ES ........................................................................................................................... 17

1.8 DISSERTATION OUTLINE ........................................................................................................ 18

2.0 THEORETICAL BACKGROUND, METHODS AND DATA 20
2.1 BEHAVIORAL AND THEORETICAL FRAMEWORK .................................................................... 20

2.1.1 Producer Behavior ........................................................................................................ 20

2.1.2 Production Function ..................................................................................................... 21

2.1.3 Duality ...................... - .................................................................... 22

2.1.4 Transcendental Logarithmic Functional Form ............................................................. 22

2.2 APPLICATIONS OF THE THEORY ............................................................................................. 25

2.3 EMPIRICAL METHODS ............................................................................................................ 28

2. 3.1 Translog Cost Function Model ..................................................................................... 29

2.3.2 Demand Equations ........................................................................................................ 31

2.3.3 Elasticities .................................................................................................................... 31

2.3.3.1 Allen-Uzawa versus Morishima Elasticity of Substitution .................................................. 32

2.3.3.2 Elasticity Calculations ......................................................................................................... 34

2.3.4 Technological Change .................................................................................................. 34

2.3.5 Returns to Scale ............................................................................................................ 36

2.4 DATA ..................................................................................................................................... 38

2.4.1 Labor Quantity ............................................................................................................. 40

vi

2.4.2 Labor Price ................................................................................................................... 40

 

 

 

 

2.4.3 Sawlog Price ................................................................................................................. 40

2.4.4 Capital Stock ................................................................................................................. 41

2.4.5 Lumber Output .............................................................................................................. 46

2.4.6 Variable Cost and Input Cost Shares ............................................................................ 46

3.0 MODEL RESULTS AND DISCUSSION 50
3.1 MAINTAINED HYPO'I'HESES ................................................................................................... 50

3.2 MODEL SELECTION PROCEDURE ........................................................................................... 51

3.2.1 Other Cost Function Properties ................................................................................... 55

3.3 DATA POOLING ..................................................................................................................... 56

3.4 ELASTICITIES OF SUBSTITUTION ............................................................................................ 56

3.4.1 Labor-Material Substitution ......................................................................................... 58

3.4.2 Labor-Capital Substitution ........................................................................................... 59

3.4.3 Materials-Capital Substitution ..................................................................................... 60

3.4.4 Elasticity of Substitution Discussion Summary ............................................................. 61

3.5 PRICE ELASTICl'I'IES .............................................................................................................. 63

3.5.1 Own-Price Elasticities .................................................................................................. 63

3.5.2 Cross-Price Elasticities ................................................................................................ 66

3.5.3 Elasticity of Demand Discussion Summary .................................................................. 69

3.6 PRODUCTlVlTY GROWTH ....................................................................................................... 72

3.6.1 Total Factor Productivity ............................................................................................. 73

3.6.2 Technical Change Bias ................................................................................................. 74

3.7 RETURNS TO SCALE ............................................................................................................... 77

4.0 CONCLUSIONS AND POLICY IMPLICATIONS 82
4.1 SUMMARY OF RESULTS ......................................................................................................... 82

4.2 CONCLUSIONS AND POLICY IMPLICATIONS ........................................................................... 83

4.3 FURTHER RESEARCH ............................................................................................................. 86

LITERATURE CITED 88
APPENDIX A: Model Data 95
APPENDIX B: Model Output 102

 

vii

LIST OF TABLES

Table 1-1. Volume of Standing Timber 1996 (million cubic feet) ................................................ 7
Table 2-1a. Summary of Sawmill Production Structure Studies ................................................. 27
Table 2-1b. Summary of Sawmill Production Structure Studies ................................................. 28
Table 3-1. Estimates of the Cost Function Parameters (1963-1996) ........................................... 53

Table 3-2. The Allen-Uzawa Partial Elasticity of Substitution and Morishima Elasticity of
Substitution based on FIML estimates of Model (2) (at mean level of Observations) 1963—1996. 57

Table 3-3 Allen Elasticity of Substitution Results of Selected Studies ....................................... 62
Table 3-4. Own and Cross-Price Elasticities (at mean level of observations) 1963-1996. .......... 63
Table 3-5 Own-Price Elasticity of Demand Results of Selected Studies ..................................... 71
Table 3-6 Cross-Price Elasticity of Demand Results of Selected Studies ................................... 72
Table 3-7. Technical Change 1963-1996 ..................................................................................... 75
Table A-1. Summary of Data Calculations .................................................................................. 96
Table A-2. Model data for Michigan (27 observations) All figures are in 1996 dollars. ............ 97
Table A-3. Model data for Minnesota (17 observations) All figures are in 1996 dollars. ........... 99
Table A—4. Model data for Wisconsin (22 observations) All figures are in 1996 dollars. ......... 100
Table A-5. Sawlog Receipts by Sawmills in the Lake States (million cubic feet) .................... 101
Table B-1. Model (1)Homogeneous of degree one in input prices ............................................ 103

Table B-2. Model (2) Homogeneous of degree one in input prices; Constant returns to scale . 105

Table B-3. Model (3) Homogeneous of degree one in input prices; Constant elasticity of
substitution ................................................................................................................................. 107

Table B-4. Model (4) Homogenous of degree one in input prices; Constant returns to scale;
Constant elasticity of substitution .............................................................................................. 109

Table B-5. Model (2) with State dummy variables; Homogenous of degree one in input prices;
Constant returns to scale ............................................................................................................ 111

viii

LIST OF FIGURES

Figure 1-1. Number of Employees by State 1963-1996, SIC 242 .............................. 4
Figure 1-2. Number of Establishments by State 1992, SIC 242 ................................ 5
Figure 1-3. Lumber Production by State, 1963-1996, (MMBF) ................................ 6
Figure 1—4. Forestland Area by State and Ownership 1996, (thousands of acres) ............ 8
Figure 1-5. Timber Removals by State and Ownership 1996, (million cubic feet) .......... 9
Figure 2-1. Input Factor Cost Shares for Michigan (1963-1996) ............................. 47
Figure 2-2. Input Factor Cost Shares for Minnesota (1963-1996) ............................ 48
Figure 2-3. Input Factor Cost Shares for Wisconsin (1963-1996) ............................ 48
Figure 3-1. Number of Establishments, SIC 242 (1963-1992) ................................ 78
Figure 3-2. Lumber Output per mill. MI, MN and W1, 1963-1992. (MBF/mill) ........... 79

ix

1.0 INTRODUCTION

This is a study of the production structure of the sawmill industry of the Lake
States (Michigan, Minnesota, and Wisconsin). Productivity and the demand for inputs are
important aspects of the competitiveness of the industry as resource constraints increase.

At the root of economics is the concept of opportunity cost and the tradeoffs
implied by that. Along those lines, the concept of suStainable forestry raises the question
of the tradeoffs made in forest management in an environment of increasing scarcity. One
of those tradeoffs is between harvesting timber or not. Forest managers and private
landowners are making that decision all the time although not necessarily in the context
of sustainable forest management. Nevertheless, if the decision is not to harvest, or to
harvest later, the timber supply is constrained and that could have an effect on the mix of
inputs used in the sawmill industry.

The purpose of the study is to provide an understanding of the relationships
among the inputs to the sawmill sector, how those relationships changed over the study
period, the effect of input price changes on input demand and the effect of output levels
on industry costs. A translog cost function was estimated to determine the elasticities of
substitution and the own and cross-price elasticities of demand for the major inputs
(labor, materials and capital). In addition, total factor productivity, the bias of
technological change and economies of scale were measured.

This chapter provides background on the sawmill industry in the Lake States from
1963-1996 with regards to input supply and demand, major changes in milling

technology, and a comparison to other regions in the US. It also includes background on

the research questions, motivation and objectives of the research and an outline for the

dissertation.

1.1 The Industry

The sawmill industry of the Lake States has been an important part of the regional
economy since the first European settlers arrived in the 19‘h century. Today, it is not as
important as other manufacturing industries, but still employs a large number of people.
In 1996 there were almost 11,000 production workers employed in the sawmill industry
in the Lake States as compared to 9,200 in Washington and 13,000 in Oregon. The value
of shipments was $1.5 billion in 1996 while they were $2.8 billion in Washington and
$3.3 billion in Oregon (ASM 1996).

The Standard Industrial Classification (SIC) system classifies industries in
increasingly specific categories with increasing number of classifying digits. SIC 242
(Sawmills and Planing Mills) represents a three-digit industry, and is a subset of SIC 24
(Lumber and Wood Products). Thus, all of SIC 242 is contained in SIC 24. Other three
digit industries within SIC 24 include Logging (SIC 241), Millwork, Plywood and
Structural Members (SIC 243), Wood Containers (SIC 244), Wood Buildings and Mobile
Homes (SIC 245), and Miscellaneous Wood Products (SIC 249). The hierarchy continues
with four-di git industries as well.

This study is restricted to SIC 242 which encompasses sawmills and planing mills
producing lumber, both hardwood and softwood. A sawmill takes sawlogs as its primary
material input and using a variety of saws removes the unwanted wood to produce lumber
for use in building construction, furniture building, flooring and so on. Sawmills do not

include operations that peel logs for use as veneer nor do they produce structural panels

such as plywood or engineered wood products such as oriented strand board (OSB).
While sawmills and planing mills produce the manufactured wood product input for the
furniture industry, the furniture industry is not part of SIC 24; it is part of SIC 25
(Furniture and fixtures).

In the early to mid-19th century, the states conducted surveying of land for
assigning legal title and logging of white pine in particular began in earnest in the region.
This continued until about the turn of the century when stocks of white pine were
virtually exhausted. The production process at the time involved logging camps scattered
throughout the forest with logging taking place primarily in winter. Logs were stored next
to streams and rivers and floated downstream during spring runoff. Mills were typically
located along large rivers or at the mouth of large rivers flowing into the Great Lakes
(Steams 1997).

During the mid-19‘h century, milling and sawing technology also changed. Mills
switched from water power to steam power with the waste wood from milling providing
the fuel. Later, the muley saw and the circular saw replaced the sash saw. The circular
saw had a very wide kerf and wasted a lot of wood. It was eventually replaced with the
band saw (Steams 1997).

In the late 19703 and early 19808 there was a large change in the technology of
modern sawmills in North America, primarily in the softwood lumber producing regions.
The advent of computers drastically reduced labor requirements in many mills.
Computerized cutting control allowed more lumber to be sawn from fewer logs and from
logs that were previously unmerchantable. These changes, combined with the North

American recession, resulted in a reduction in sawmill employment nationwide. In 1979

there were 223,000 people employed in sawmills in the United States, but by 1982 there
were only 157,000 -a 30 percent reduction (ASM various years). Following the recession,
employment levels increased somewhat but have not reached the 1979 level. For the Lake
States, employment levels have rebounded for the most part (Figure l-l). Particularly

notable is the large increase in employment in Minnesota during the mid 19905.

 

 

 

 

+M|
+MN

i W

J
\
'1
<..
%

 

 

 

 

 

Production Employees (000:)
/
b <)
\C
'<

R

 

 

 

 

1960 1965 1970 1975 1980 1985 1990 1995 2000
Your

Figure 1-1. Number of Employees by State 1963-1996, SIC 242
(Annual Survey of Manufactures, various years) Breaks in lines represent years for which
data were not available.

There were a total of 567 establishments in SIC 242 in the Lakes States in 1992
with 107 of them having twenty or more employees (Figure 1-2). Wisconsin had the

highest proportion of establishments with more than twenty employees at 21%. Michigan

had the least at 16%.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

300
250
57/
/
zoo / %
150 % M E1 Total Establishments (1992)
/ 7 mm Employees (1992)
r"
100 / V, 1%
/ / x/ %
/ iiééi‘ii‘if /// Wt“
529:?“ ' :I:-.3:§::.;o":= '3‘?”
o - “:5 , fl’g’ . M ’33?
Michigan Minnesota Wisconsin

Figure 1-2. Number of Establishments by State 1992, SIC 242
(Census of Manufactures 1992) .

Lumber output is probably the most important measure of the size of the industry
in each state (Figure 1-3). Total production in the Lake States in 1996 was 1,582 million
board feet (MMBF), approximately 75% of which was hardwood lumber (Census Bureau
1996). There was a sharp increase in production in all three states in 1993 (Figure 1-3).
For Wisconsin and Minnesota, part of the production increase can be explained by large
new capital expenditures in the mid 19903. Another reason was a reconciliation among
the MA24T (Lumber Production and Mill Stocks), the 1992 Census of Manufactures and
state sawmill directories in 1994 (Census Bureau 1994). This reconciliation was a review
of the statistical sample used to generate the state and national lumber production

statistics and led to large upward revisions for output for each of the Lake States starting

in 1993. A further reason for the sharp increase may be the large reduction of lumber
production in the Pacific Northwest around that time because of reduced sales of timber
from Federal lands that resulted from the strategy to protect northern spotted owl habitat.
It was unclear if the revisions have any effect on the output statistics for years prior to
1993, but if a smooth upward trend in output was assumed, productivity numbers for
years before 1993 have been underestimated to the extent that the reported output was

lower than actual output.

700

 

600

 

":71

§

 

A11

\
I
\'

 

 

-o—AM
+MN

F .W.

3

 

§

Lumber Production (mmbt’)
8
O

I?
I

 

 

X

S“

 

 

 

 

 

 

o T V T I 1
1960 1965 1970 1975 1980 1985 1990 1995 2000
Year

 

Figure 1-3. Lumber Production by State, 1963-1996, (MMBF)
(Census Bureau, MA24T, 1963-1996)

 

1.2 The Forest Resource

Within the Lake States there is variability in the timber resource. There are a total
of 47.4 million acres of timberlandl in the region and 56 billion cubic feet of growing
stock2 (Vasievich et al. 1997). Michigan has roughly double the timber volume of
Minnesota (Table l-l).

Hardwood forests predominate in the region (Table 1-1). The important hardwood
species are aspen, red oak, white oak, ash, hickory, hard maple, soft maple, and
basswood. Hardwoods are used typically for veneer, or for lumber for furniture, cabinets,
moulding and flooring. Aspen is used largely to produce pulp, reconstituted panel
products and oriented strand board. Overall, the region’s standing timber is 72 percent
hardwood by volume. In the softwood forest regions farther north, particularly in
Minnesota, wood for pulp dominates but there is still a softwood lumber industry.
Softwood is also used for wood products such as plywood and fiberboard.

. Tae l-l-Volume of 8“!qu Timber 96 n fee)

‘ STATE Softwood Hardwood

      

 

" Michigan 7,576 19,085

 

Minnesota 4,652 10,495

 

~ Wisconsin 4,452 14,059

 

    

 

 

 

7 Total 16,680 43,639
Source: USDA Forest Service FIA Database Retrieval System

The forestland in the Lake States is predominately privately owned and most is
non-industrial private forest (NIPF) (Figure 1-4). NIPF is private land not owned by the

forest industry.

 

' Timberland is forestland capable of producing a minimum of 20 cubic feet of merchantable
timber per acre annually and not subject to legal restrictions that preclude timber harvesting.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

  

 

 

 

 

12.000
10.000
8.000
g 0 Michigan
5 6.000 E] Minnesota
.7 EJWisconsin
2
<
4.000
2,000

 

 

 

 

 

 

 

Nata". a... ‘ 0.-.... ............. 55.5....“
Figure 1-4. Forestland Area by State and Ownership 1996, (thousands of acres).
(USDA, Forest Service)

Despite the fact that most forest land in the Lake States is privately owned, there
is significantly more public forest land than in states immediately to the south. This is
partly due to settlement patterns during the 19‘h century. Another significant factor was
the reverting of land back to the state as a result of delinquent property tax payments.
Serious delinquency problems resulted in a large area of land reverting to the state in the
cutover areas of the Lakes States (Barlowe 1986).

There were over eight hundred million cubic feet of timber harvested in the Lake
States in 1996 (Figure 1-5). The proportion of timber removals from each ownership type

closely matches the proportion of forestland area in each ownership type. Nevertheless,

 

2 Growing stock includes trees with a minimum diameter at breast height of 5 inches with
merchantable volume measured 1 foot above the ground up to a top diameter of 4 inches. Rot or other
defects that reduce merchantable yield are subtracted from that volume.

1......“
W ~ ~ ‘

for individual states there is more variation. In Michigan and Minnesota, National Forests
had a greater percentage of removals than their proportion of the forestland base. This is
an indication of the different resource management strategies and timber resources of the

National Forests in these states.

900

800

 

 

 

 

700
i 600
0
g 500 IWisconsin
g aMinnesota
g 400 DMichigan
g
g 300
:I:

§

100

 

National forest Other public Forest industry Other private All ownerships

Figure 1-5. Timber Removals by State and Ownership 1996, (million cubic feet)
(USDA Forest Service)

1.3 Timber Pricing

The cost-minimization model used in this study assumes that input and output
markets are perfectly competitive. Over the study period with the dataset used here,
materials have made up 64 percent of sawmill costs with the remainder being made up of
labor and capital costs. Materials is almost entirely sawlogs but some mills will plane
rough lumber so for them materials comprises both sawlogs and rough lumber. Baardsen

(2000) criticizes studies that aggregate sawmill production and cost data at the national

level, or regional level where the industry is a large contributor to the regional economy,
because this would violate the assumption that input and output markets are perfectly
competitive. In a region where the sawmill industry is large, wages may be determined
partly by the industry itself, that is, the labor price is endogenous to the industry. In this
case the sawmills are not price takers and this violates the assumption of perfect
competition. For this study, it seems clear that the industry does not affect or otherwise
determine wage rates because it is small compared to the rest of the economy in the Lake
States and it is reasonable to assume that sawmills are price takers in the labor market.
The same argument can be made for the capital market. Baardsen’s criticism is most
applicable to the market for materials (wood). This section examines the pricing
mechanisms for timber on national, state and private lands in the Lake States. Some
components of the pricing methods on public lands are determined within the region
(logging costs, transportation costs) but others such as output price are determined in the
lumber market as a whole and production from the Lake States sawmill industry is small
relative to world or national production and so it is unlikely that it influences output
price. Also, timber is bought and sold across state boundaries outside the study region.
This serves to mitigate the influence sawmills in the Lake States may have over timber
prices.

The method used to determine a sale price for timber depends on the ownership of
the timber or timberland. Public land managers are constrained by law and regulations as
to what methods they may use to sell public timber. Private landowners have very few, if
any, restrictions on how they can sell their timber. There are two kinds of private

forestland: industrial private forestland (IPF) and nonindustrial private forestland (NIPF).

10

IPF is land owned by pulp and paper companies or sawmills or some other owner that
uses the land for timber production. NIPF is made up of landowners such as farmers, or
other landowners for whom timber production is not the purpose of owning the land. IPF
is not prevalent in the Lake States (7% by area) while NIPF makes up 55% of forestland
and the rest, 38%, is public land (USDA Forest Service 1997). IPF area is not large
compared to other ownerships and it is mostly used for production of pulpwood so the
issue of transfer pricing for timber within vertically integrated lumber products
manufacturers is not an issue for this study. Some NIPF sales are done with competitive
bids with or without forester assistance, while others are not. Some sales may be made
only if a logger approaches the landowner and offers to buy a few trees.

Pricing for timber from National Forests follows a stricter format. According to
the National Forest Management Act of 1976, timber from National Forests cannot be
sold for less than its appraised value (USDA For. Serv. 1978). On National Forests the
traditional method of appraisal has been the residual value (RV) approach. In its simplest
form, the RV method determines a minimum bid price based on the following formula:

SP-(MC+LC+P&R)=S,

where SP is output price, MC is milling cost, LC is logging cost, P&R is a profit
and risk margin and S is stumpage. Once a minimum bid price is set, bids are accepted on
the timber sale (USDA For. Serv. 1982). The sale will normally be awarded to the
qualified bidder with the highest bid. Note that to a sawmill, the sawlog cost they will see
in a perfectly competitive market is:

LC+P&R+S+TC-MC=SLC,

ll

where P&R is profit and risk to the logger, TC is transportation cost to the mill
and SLC is sawlog cost.

Increasingly, a different approach for appraising stumpage value of a stand of
timber in National Forests is being used, although not in the East. The Transactions
Evidence Appraisal method (TEA), which is like a hedonic pricing model, is used as an
aid to timber appraisal. TEA uses actual sale prices from past sales to help determine the
final sale price of a current sale. Obviously, no two tracts of timber are identical and the
market conditions under which the sale is made will differ from previous sales.
Nevertheless, with a database of sale characteristics such as species, volume, quality,
terrain, distance from mills and market conditions, it is possible to predict the final
stumpage price for a particular sale with a reasonable degree of accuracy (Bare and Smith
1999). The TEA tries to estimate the final sale price for a timber sale but it is up to
individual timber buyers to determine their own willingness to pay and bid accordingly.

Pricing of timber from state lands in Michigan follows the “Comparative Method
of Stumpage Appraisal” (Michigan DNR, Forest Management Division 2000b). The
method is meant to give the State of Michigan fair stumpage return and the timber buyer
normal profit. The factors used to appraise stumpage value are based on costs of the
average operator for operations including felling and bucking, skidding, road
maintenance, hauling, distance to nearest mill, quantity of timber, quality of timber, and
market trend and competition (Michigan DNR, Forest Management Division 2000a).
Market trend and competition takes into account competition for timber and also the
supply of labor. When competition for timber is high and the labor supply is good, the

stumpage appraisal is higher.

12

In Minnesota, sales of timber from state lands are conducted by several methods.
These include regular auction sales, intermediate auction sales, informal sales, special
fuelwood permits and special product permits (Minnesota Department of Natural
Resources, Forestry 2000). Regular and intermediate auction sales can be conducted
using either oral or sealed bidding and the winning bidder must pay 15% of the appraised
value at the time of sale.

The Wisconsin Department of Natural Resources appraises stumpage rates based
on sales data collected by foresters (Wisconsin Department of Natural Resources 1999).
Stumpage rates vary based on local market conditions, distance to mills, and other site
and timber quality factors. This is a transactions evidence approach similar to that used
by the USDA Forest Service for estimating final sale prices for timber sold from national

forests.

1.4 Timber Supply

Sustainable forest management (SFM) is growing in importance to forest
managers and policymakers and some outcomes of the adoption of SFM may have an
effect on the supply and availability of timber for the sawmill industry of the Lake States.
The Great Lakes Forestry Alliance, as well as other governmental and non-govemmental
organizations, are involved in the development of principles, criteria and indicators for
sustainable forest management (Williams et al. 1998). These criteria typically involve
sustainability of ecosystems and biodiversity as well as the economic viability of forest
industries. There is a conflict between these two criteria in that improvement of
biodiversity may reduce the availability of timber for forest products industries. The

extent to which this occurs will vary by political jurisdiction but there is clearly a conflict

13

among many of the criteria for SFM developed by the United Nations and agreed upon in
what has become known as the Montreal process (Canadian Forest Service 1995).

There are reasons, other than SFM, that timber supply may be restricted in the
future. Changes in attitudes of private landowners in the future may restrict timber supply
from NIPF. Fifty-five percent of the forestland in the study region is NIPF. There is a
trend toward preservation of forest cover on these lands by new landowners and this
could affect availability. Overall, forest managers in “the Lake States foresee an 8 percent
decrease in area of land available for harvest by 2020 (Vasievich, et al. 1997). Apart from
potential decreases in overall volume of wood available, the size and quality of the
available timber may be decreasing. Smaller diameter logs have lower lumber recovery
factors (LRF) than larger diameter logs (Haynes 1990). This will be discussed in the next
section.

The price of timber is affected by its supply, but also by the demand for timber.
Changes in the price of lumber will affect the price paid for timber through the effect of
output price on minimum stumpage prices and also through the change in demand
brought about by output price changes. If output price increases, this will increase the
minimum bid price for a timber sale (ceteris paribus) and it will also increase the demand

for timber and therefore its price.

1.5 Productivity in the Sawmill Industry

In addition to the potential resource constraints outlined above, technological
change, or productivity is important for the continued competitiveness of the sawmill
industry. Until fifty years ago, labor productivity in the sawmill industry has lagged

behind that of manufacturing in general in the United States. Between 1899 and 1954,

14

labor productivity grew by 1.1 percent per year, approximately half the rate of the
manufacturing sector as a whole (Kendrick 1961). Nevertheless, between 1958 and 1974,
labor productivity in the forest products industries grew faster than that for all
manufacturing industries (Duke and Huffstutler 1977). But, between 1988 and 2000,
output per hour of labor for SIC 242 increased on average 1.8 percent per year,
considerably less than the average of 3.3 percent per year for all manufacturing (BLS,
Industry Productivity Database).

In addition to the increases in labor productivity, output of industrial wood
product per unit of industrial roundwood input increased 39 percent in the period 1900-
1998 (Ince 2000). This figure applies to all wood-using industries and is largely
explained by increases in the use of residual products such as woodchips, and the success
of paper recycling programs but innovations in sawmill technology during the study
period have reduced wood waste and allowed more precise control over how each log is
sawn. Improved milling technology resulted in better lumber recovery factors (LRF) in
lumber producing regions of the United States. In the Pacific Northwest, softwood LRF
increased from 6.67 to 7.87 board feet of lumber per cubic foot of timber from 1952-1985
and in the South, it increased from 5.05 to 6.02 during that same period (Haynes 1990).
One of the goals of this study is to measure the technological change in the sawmilling
industry of the Lake States and to determine if it is biased towards any particular input.
Other studies have found that materials-using technological change is partly the result of
decreased quality of the wood resource (Martinello 1987). One of the factors affecting
quality is the average log size and Haynes (1990) found that in the hardwood lumber

industry, LRF improves dramatically when the diameter of the logs being milled is larger.

15

In the late 19708, for 11 to 15 inch diameter hardwood logs, the LRF was 3.3 board feet
of lumber per cubic foot of timber but for logs greater than 19 inches in diameter, the
recovery was 5.6 board feet of lumber per cubic foot of timber. That is almost a 70%
improvement over the smaller diameter logs. Given the long history of timber harvests in
the Lake States, it may be possible that the average size of the logs is decreasing and
there may be decreasing LRF over the study period.

The improvement in productivity of labor and wood in the wood products
industry of the United States has allowed the industry to overcome any increasing
scarcity of those inputs but it is possible that further improvements may be difficult and
that the scarcity will begin to manifest itself in higher timber prices, decreased profits and
lower output. It is also possible that decreased supply will drive marginal mills out of

business.

1.6 Research Questions

A basic concept in economics is that a reduction in the supply of a good will
increase its equilibrium price, ceteris paribus. In the future, the supply of sawlogs to the
sawmill industry could well be reduced because of factors outlined in the previous
sections. Reduced supply of timber could lead to higher prices for wood which would
affect demand for labor and capital so: “What is the effect on equilibrium quantity
demanded in the sawmill industry of changes in factor price?”

The focus of this study is the production structure of the sawmill industry in the
Lake States, and an important aspect of the production structure is how it has changed
over time. The region is dominated by mixed hardwood forest, and hardwoods require

different technology or more basically a different input mix from softwoods in order to be

16

produced efficiently, given the characteristics of the input and output markets and
regulatory system to which the sawmill is exposed. This mix changes over time and
technological changes will have implications for employment and regional economies.
Consequently, the second research question is: “What has been the rate and nature of
technological change in the sawmill industry of the Lake States during the study
period?”

Regional sawmill industries with positive scale economies can be characterized as
having a small number of large producers. Constant returns to scale, or diminishing
returns to scale tend to keep individual plant sizes smaller but the number of firms larger.
In other words, output per mill is low relative to other regions. Therefore it is valuable to
know: “Does the sawmill industry of the Lake States exhibit any economies or
diseconomies of scale?”

There are no current studies of the production structure of the sawmill industry of
the Lake States so some quantification of the demand for inputs to the industry and
change in factor productivity will help policymakers assess the possible tradeoffs among
the various aspects of sustainable forestry and the effects of changes in relative input

prices.

1.7 Objectives

The research questions were answered by calculating elasticities of substitution,
own and cross-price elasticities of demand for the major inputs of the sawmill industry,
returns to scale and technological change including the bias of technological change.
These results are important because they describe the ease and degree with which inputs

can be substituted for one another when their relative prices change. Relative price

17

changes can occur for many reasons including reduced timber supply, national monetary
policy (interest rates) and the rate of growth of the economy. For the policymaker, the
calculated results can provide insights to how the sawmill industry will react when
policies are undertaken that may change relative prices of the inputs to the industry. The
rate and bias of technological change in the sawmill industry of the Lake States is also
important to policymakers because it gives an indication of the future demand for inputs
to the industry. For example, if the bias of technological change is materials-saving, then
there may be less pressure to increase timber harvests from public lands in the future.
This may give policymakers some room to set aside lands for uses other than timber

production or to reduce the emphasis on timber production on public land.

1.8 Dissertation Outline

The dissertation consists of three chapters in addition to the introductory chapter
plus literature cited and appendices.

Chapter 2 begins by describing the conceptual framework and behavioral model
used in developing the analytical model. A review of similar studies of the sawmill
industry in the United States, Canada and elsewhere is included here including a table
summarizing the important aspects of each study. This is followed by a description of the
theoretical background of the analytical methods and a description of the analytical
methods themselves. The data used in the model are discussed along with any data
manipulation used to prepare the data for analysis.

Chapter 3 contains the actual model and results. The model selection procedure

and all necessary statistical tests are included in this section. The calculation of the

18

elasticities, productivity measures and returns to scale are presented here. A discussion of
the results and comparison with other studies is also included here.

Chapter 4 includes a summary of the model results and conclusions based on the
discussion in Chapter 3. Policy implications of the results are also discussed and areas of

further research are identified.

19

2.0 THEORETICAL BACKGROUND, METHODS AND
DATA

This chapter includes the conceptual framework that guided the study. This
includes a description and discussion of the behavioral model and theoretical framework.
Following that is a discussion of specific empirical methods used to test hypotheses
related to the conceptual framework. The chapter ends with a discussion of the data,

including sources and transformations required to make the raw data usable in the model.

2.1 Behavioral and Theoretical Framework

2.1.1 Producer Behavior

The primary behavioral assumption in this study is that sawmill managers will
minimize costs with respect to a given output level and factor prices. This is a reasonable
assumption that is more behaviorally restrictive than the assumption that they are profit
maximizers. If we assume that sawmill managers are profit maxirnizers then they are able
to adjust the quantity of both inputs and output to maximize profit. If we assume that they
are cost minimizers, then they are only able to adjust the quantity of inputs to minimize
costs given a fixed output level.

By minimizing costs, the producers are being both technically and allocatively
efficient given an output level and input prices. When relative prices change, the rational
producer will use different amounts of each input in order to produce the given output
level at the minimum cost. In this case, we are allowing producers to vary the quantities

of labor, sawlogs and capital used in the production process. The interest here is in the

20

degree to which one input will substitute for another when relative prices change, or in
other words, the elasticities of substitution.

Another assumption of the model is that producers are price takers for inputs and
outputs. In other words, the input and output markets are perfectly competitive. There can
still be variability in input and output prices though as a result of an institutional factor
such as unionized labor forces in some areas or heterogeneity of the wood input based on
species composition, age and size and also transportation costs. The point is that those
factors are largely beyond the control of the mills and therefore they remain price takers

(Banskota er al. 1985).

2.1.2 Production Function

In order to model the production structure of an industry it is necessary to have a
conception of the underlying production function. In this case, lumber output Q is
assumed to be produced by the inputs labor (L), materials (M) and capital (K). Production
is also assumed to be a function of time (t). The time trend variable is meant to take
account of technological change. This is a common way of accounting for technological
change and the purpose is not to explain it but simply to measure it as a function of time.

The implicit production function is:

F(Q,L,M,K,t) (1)

All inputs are treated as variable. At the firm level capital is not variable in the
short run but the data used here are aggregated at the statewide industry level and new
capital expenditure decisions are made every year by mill managers based on the state of

their existing capital stock and the prices of other inputs which may be substitutes or

complements to capital. New capital expenditures may be made sooner or later depending

21

on those other factors. This leads to annual variability of the capital stock and therefore

the user cost of capital.

2.1.3 Duality

The theoretical framework for this model makes use of the duality of production
and cost. Rather than estimate a production function, this model estimates the dual cost
function to obtain results regarding the substitution of inputs, input demand,
technological change and returns to scale.

According to Varian (1992) the fundamental principle of duality in production is:
“the cost function of a firm summarizes all of the economically relevant aspects of its
technology”. The advantage of estimating a cost function as opposed to a production
function is that there exist several functional forms from which derived demand equations
can be determined and are flexible in their treatment of various aspects of the production

structure that we are interested in. One of these is discussed in the next section.

2.1.4 Transcendental Logarithmic Functional Form

The choice of functional form is important for applied economic research. The
decision of which of many possible functional forms to use to model an economic
process using a cost or profit function hinges on several considerations. These
considerations can be grouped into four categories according to whether they relate to
maintained hypotheses, estimation, data, or application (Griffin, er al. 1987).

Maintained hypotheses are a priori restrictions on the value and of the function
and its parameters. In economic production analysis, maintained hypotheses for a

production function could include homogeneity, homotheticity, restrictions on the

22

elasticities of substitution and concavity. Key properties of a well-behaved cost function
for a single-output technology are that it is homogeneous of degree one in input prices,
has strictly positive input factor demands and that it is concave in input prices (Varian
1992). Homogeneous of degree one in input prices means that if all input prices double,
for example, costs will double. This reflects the behavioral assumption that it is only
relative factor prices and not the level of each price that matter to the mill owner when
deciding how much of each input to employ. Strictly positive input factor demands means
that demand for an input can never be negative, which is intuitive, but it also cannot be
zero because it is not possible to create lumber without wood, for example. Concavity in
input prices means that as the price of an input increases, costs will increase but at a
decreasing rate as mill owners substitute away from the increasingly expensive input.
Global flexibility refers to the property of the functional form that does not
restrict its value at any point nor does it restrict the value of its first or second derivatives.
There is a tradeoff between flexibility and maintained hypotheses. On its own, greater
flexibility is more desirable, however it may present estimation problems from the
increased amount of information required and subsequent loss of degrees of freedom. We
want the cost function to conform to economic theory. This requires the imposition of
restrictions on the parameters to impose the properties of a well-behaved cost function.
The second category that needs to be considered when choosing a functional form
is estimation. Availability of data and data properties need to be considered when
choosing a functional form. A difficulty with many functional forms is that as a result of

their flexibility, there are many parameters to be estimated and consequently there may

23

be a problem with degrees of freedom. This can be mitigated somewhat by the imposition
of some maintained hypotheses as mentioned earlier.

The third category involves data-specific considerations such as goodness-of-fit.
In this case, the previous two categories have already limited the choice of functional
form to a few and so this is not an important category for choosing functional form.

The fourth category concerns the application in which the function will be used. The
application in this study was an optimization problem that minimized a cost function for
sawmills in the Lake States. The maintained hypotheses and flexibility were relevant to
the application. The goals of this study were to measure elasticity of substitution,
technological change, own and cross-price elasticities and allow for non-constant returns
to scale and the translog cost function allowed that.

The transcendental logarithmic (translog) function was chosen for all the reasons
cited above including its flexibility and suitability given the amount and type of data, in
addition to the preponderance of literature using it in one form or another. It was
necessary to use the translog in order to provide the flexibility to allow the data to
determine the returns to. scale as well as the nature and bias of technological change and
the elasticities of substitution and demand. The main difficulty with using the translog is
the relatively large number of parameters to be estimated, in this case, three variable
inputs and a time trend variable. This necessitated the estimation of twenty-one
parameters, including the constant. This large number of parameters can lead to a degrees
of freedom problem. This problem can be overcome by a sufficiently large dataset, but

also by restricting the flexibility of the functional form in areas that will not impinge

upon the prospective analysis. These restrictions were outlined in the model selection
section.

Other common alternative functional forms such as the constant elasticity of
substitution (CBS) functional form and the Cobb-Douglas functional form are not
appropriate for this study for a variety of reasons. The CBS function imposes difficulties
with regards to estimation because it is not linear in the parameters. Also, its namesake
characteristic is not applicable to this study as it holds for all input levels (Boisvert 1982).
The Cobb-Douglas functional form is subsumed in the translog functional form in that if
the parameters for the terms in the translog function that allow nonunitary elasticity of
substitution between inputs are zero, the translog function will exhibit unitary elasticity
of substitution (Griffin er al. 1987). The Cobb-Douglas functional form imposes unitary
elasticity of substitution between all inputs and this may not be a valid assumption for the
sawmill industry of the Lake States. The Cobb-Douglas function cannot be rejected out of
hand because of that trait because the data may support unitary elasticity of substitution

between inputs and the translog model will be tested for this behavior.

2.2 Applications of the Theory

There have been a number of papers written on the production structure and
demand for inputs in the wood products industries of North America and elsewhere. Most
focus on a specific region of the United States or Canada. It is typical in these analyses to
use a cost function of some type but a profit function may also be used. The profit
function method is rare but it may prove useful depending on data availability and the

assumed behavior of sawmill managers. This style of analysis was used by Caves et al.

(1981) in studying the railway industry of the US. and follows the duality relationship
between production functions and restricted cost functions derived by Lau (1978).

Among the studies of the sawmill industry outlined here are Stier (1980), Nautiyal
and Singh (1985), Singh and Nautiyal (1985), Banskota et al. (1985), Martinello (1985),
Abt (1987), Martinello, (1987), Meil and Nautiyal (1988), Puttock and Prescott (1992),
Bigsby (1994) and Baardsen (2000). All of these studies used translog cost functions to
estimate a variety of economic statistics of interest such as elasticities of substitution,
elasticities of demand, technological change and returns to scale. Several assumptions are
common to all these studies. It was assumed with this method that producers are efficient
in that they minimize costs given an output level. It was also assumed that they are only
able to minimize costs with respect to certain inputs. In the case of the above studies, the
inputs include materials (usually wood but Baardsen (2000) uses sawlogs, lumber and
“other materials” as separate inputs) labor, capital and sometimes energy. Table 2-1
summarizes the Characteristics of each of the above studies vary according to study
region, industry studied, time period, data type (time-series, cross-section, panel) inputs
and types of reported results (Table 2-1). All of the studies have imposed homogeneity of
degree one in input prices which is a fundamental property of a well-behaved cost
function (Varian 1984). They all also employ the translog functional form.

Research in other forest industry sectors has also been conducted by Stier (1985),
De Borger and Buongiomo (1985), Kant and Nautiyal (1997), Smith and Munn (1998),
and Andrade (2000). These are studies of the pulp and paper industry and the logging

industry and the methods follow closely those of the sawmill studies listed in Table 2-1.

26

Table 2-1a. Summa -,

omiIfSawl Prconoduti Structure Stdies

 

 

 

 

 

 

 

 

 

 

 

Author Study Region Industry Studied Time Data Type Inputs Reported Raul
Period
Stier U.S. SIC 242 1958- Time-series K, L ABS. elasticities of
(1980) Sawmills and 1974 demand, technical
planing mills (US change bias
Census Bureau)
Nautiyal Canada SIC 2513 1965- Time-series K, L, ABS. elasticities of
and Singh Sawmills and 1981 M, E demand
(1985) planing mills
(Statistics Canada)
Singh and Canada SIC 2513 1955- Time-series K. L. ABS. elasticities of
Nautiyal Sawmills and 1982 ‘ M. E demand. economies of
(1985) planing mills scale, individual input
(Statistics Canada) productivity
Banskota Alberta Sawmills 1978 Cross-section; K. L, ABS. elasticities of
er al. 83 mill-level M. E demand. returns to
(1985) observations scale
Martinello Canada Sawmills and 1963- Time-series K. L. ABS. elasticities of
(1985) shingle mills 1972 M, E demand. technical
change, returns to
scale
Abt US: SIC 242 sawmills 1963- Pooled time- K, L. M Elasticities of demand
(1987) Appalachian, and planing mills 1978 series (panel) and factor demand
Southern and decomposition
Western
regions
Martinello British SIC 2513 sawmills 1963- Time-series K, L, M ABS. elasticities of
(1987) Columbia and planing mills 1979 demand, returns to ‘
Coast and (Statistics Canada) scale. technical change ’
Interior
Meil and BC Coast, BC Sawmills 1968- Pooled time- K, L. ABS. elasticities of
Nautiyal Interior, 1984 series (panel) M. E demand, factor
( 1988) Ontario, demand
Quebec decomposition, returns
to scale, technical
change
Puttock Southem Hardwood 1980- Pooled time- K. L. AES, elasticities of
and Ontario sawmills 1984 series 21 M, E demand. returns to
Prescott sawmills scale
(1992)
Bigsby Australia Sawmills 1950- Time-series K. L, Elasticities of demand,
(1994) 1985 M, E returns to scale.
technical change.
Baardsen Norway Sawmills 1974- Pooled time- K. L. S, ABS, MES, elasticities
(2000)3 1991 series. Mill- E, F, of demand. retums to
level data W, M. 1 scale and technical

 

 

 

 

 

 

chane

K, L, M, E stand for capital, labor, materials (wood) and energy, respectively.
2AES is Allen Partial Elasticity of Substitution. MES is Morishima Elasticity of
Substitution.
3S, E, F, W, M, I stand for sawlogs, electricity, fuel oil, lumber input, other materials and
other inputs, respectively.

27

 

Study R_egion

Tale 2-lb. of Sawmill Pro cture Studies

 

Industry Studied

Production Characteristics

 

 

U.S.

SIC 242

Sawmills and planing mills

(US Census Bureau)

Non-Hicks neutral technological change.

 

Canada

SIC 2513

Sawmills and planing mills

(Statistics Canada)

Increasing returns to scale; nonunitary
elasticity of substitution.

 

Singh and
Nautiyal
(1985)

Canada

SIC 2513

Sawmills and planing mills

(Statistics Canada)

Increasing returns to scale; Hicks-neutral
technological change; nonunitary elasticity of
substitution.

 

Banskota
et al.
‘ (1985)

Alberta

Sawmills

Increasing returns to scale; nonunitary
elasticity of substitution.

 

Martinello
‘ (1985)

Canada

Sawmills and shingle mills

Increasing returns to scale; nonunitary
elasticity of substitution, non-Hicks neutral
technological change.

 

Abt
(1987)

US: Appalachian,
Southern and Western
regions

SIC 242 sawmills and
planing mills

Appalachian region exhibits decreasing
returns to scale.

 

Martiner
(1987)

British Columbia Coast
and Interior

SIC 2513 sawmills and
planing mills
(Statistics Canada)

Interior sawmills constant returns to scale;
Coast sawmills increasing returns to scale;
nonunitary elasticity of substitution; non-
Hicks neutral technological change.

 

‘ Meil and
‘ Nautiyal
(1988)

BC Coast. BC Interior,
Ontario. Quebec

Sawmills

Smallest mill-size class in Ontario decreasing
returns to scale; nonunitary elasticity of
substitution; non-Hicks neutral technological
change.

 

Southern Ontario

Hardwood sawmills

Smaller mills have increasing returns to scale .
while larger mills exhibit decreasing returns to f
scale; nonunitary elasticity of substitution. '

 

Australia

Sawmills

Increasing returns to scale; nonunitary
elasticity of substitution; non-Hicks neutral
technological change.

 

 

Norway

 

Sawmills

 

2.3 Empirical Methods

 

Increasing returns to scale; nonunitary
elasticity of substitution; non-Hicks neutral
technolo _ica1 chan ~ e.

The basic empirical method used in the articles described in section 2.2 was used

here. It was assumed that sawmill operators were cost minimizers and could adjust the

level of labor, capital and materials in order to produce the given output in the least cost

way.

28

The translog functional form was used in order to provide the flexibility with
regards to returns to scale, bias of technological change and non-constant elasticities of

substitution among inputs (Griffin er al. 1987).

2.3.1 Translog Cost Function Model

The input factor demands, elasticities of substitution, own-price and cross-price
elasticities, technological change and economies of scale were derived through the
estimation of a translog cost function. The inputs include labor, materials (sawlogs) and
capital. There was also a time trend variable used for measuring the current state of
technology. The model included the translog cost function and the cost share equations
for all but one of the variable inputs. Only two of the share equations are linearly
independent because by definition they sum to one. Therefore, one of the equations must
be dropped and it can be calculated using the remaining two. It does not matter which
input cost share equation is dropped. In this case, the capital cost share equation was
dropped.

The model that was estimated is shown below.

InVC=flC +flLInLP+flM In MP+,BK In KP+,B,I+,BQ an
gm“, In LP2 +13,“M In MP2 +13“ In KP2 +5,,:2 +509 In Q2]+,Bu In LP“:

2
+flLQ lnLPan‘l‘flM’ [UMP*t+flMQ lnMPan-fflkt anP*t+flKQ anan+ ()
fl:g’*1flQ+flm In LPln MP+flLK In LPln KP+,BMK 1n MPln KP
SL=flL +flulnLP+flm 1nMP+flLK anP+
flat-+1342 an

(3)

SM =,BM +flMM1nMP+flWInLP+flMK1nKP+
flMtt+flManQ

29

Where:

VC = variable cost defined as the sum of labor, materials and capital costs.

LP = labor price ($lhour)

MP = materials price (sawlog price) (SIMBF)

KP = capital price defined as the ratio between gross quasirent and capital stock
= time trend (year)

Q = lumber output (MMBF)

SL= labor cost share (labor cost divided by VC)

SM: materials cost share (materials cost (sawlogs) divided by VC)

The model was estimated using full information maximum likelihood (FIML)
estimation method using EViews 4.1g software. The maximum likelihood estimator has
several desirable properties. It is asymptotically unbiased and efficient and it is consistent
(Kennedy 1992). In the past, estimation by maximum likelihood methods was not popular
due to the algebraic manipulations of the data required for estimation with some software
packages. Nevertheless, it is increasingly popular as the computing power required for
estimation has become available. The translog model estimated here is a system of
equations and full information methods estimate the model equations together as opposed
to estimating the parameters of each equation separately. The advantage of this is that the
estimates will have a smaller asymptotic variance-covariance matrix (Kennedy 1992).
Three-stage least squares (BSLS) is another major systems method of estimation. Both
FIML and 3SLS incorporate all the information available in the system and estimate all
the equations simultaneously but FIML can be asymptotically more efficient. This
property makes the estimates invariable with respect to the cost share equation that was
deleted from the model (Greene 1990). It seems that the aforementioned lack of

computing power in the past has been the major reason that led other researchers to use

an estimation technique other than FIML.

30

2.3.2 Demand Equations

In order to derive the input demand equation for input i, Shephard’s Lemma was
used (Shephard 1953):

x. = aVC,(Q, p)
‘ ax. ’

l

 

(4)

Where x: is the optimal quantity of input 1'.
For the translog function used here, the equation is:

danC _ 8VC&_ 17er =
alnp, api VC VC — I

 

(5)

Where p,- is the price of input i.

This leads to the share equations used to estimate the model:
SL =,6L +flu InLP+flLM lnMP+flLK anP+

,6”! + flLQ In Q

SM =flM +flMM1nMP+flLM lnLP+flMK1nKP+
flurt+flManQ

The derivation of the capital cost share equation is analogous:

SK =flK +13“ lnLP+flLK lnLP+flMK1nMP+
flKrt + flKQ In Q (6)

The actual cost share for capital can be calculated as SK=1-SL-SM because the cost

shares must sum to one.

2.3.3 Elasticities

Several types of elasticities were calculated in order to describe the sawmill

industry of the Lake States. Elasticities of substitution between input pairs were

31

calculated to determine the extent to which inputs are technically substitutable for each
other. There are two common forms of these elasticities: Allen-Uzawa Partial Elasticity
of Substitution (ABS) and Morishima Elasticity of Substitution (MES). Traditionally, the
AES (Allen and Hicks 1934; Uzawa 1962) has been used but following Blackorby and
Russell (1989), there has been increasing use of the MES. In addition to the elasticities of
substitution, own and cross-price elasticities were calculated.

Explanation of the ABS and MES elasticities-of substitution and their calculation

is given below along with methods for calculating the own and cross-price elasticities.

2.3.3.1 Allen-Uzawa versus Morishima Elasticity of Substitution

The AES is calculated from the cost function as:

= VC(Q,p)VC,., (Q. p)
VC.(Q, p>VC,.(Q. p) ’

 

A.-,-(Q,p)

where subscripts represent partial derivatives with respect to inputs i and j, Q is output
quantity and p is the vector of input prices.

Then from this we can write:

_ 5.49.12)

A. , _
,(Qp) “Q,”

Where f” (Q, p) is the constant-output cross-price elasticity of demand and

S I (Q, p) = p j.VC I (Q, p)/ VC (Q, p) is the cost share of input j in total cost

(Blackorby and Russell 1989).
The criticisms of the AES are threefold:

1) It does not measure the curvature of the isoquant

2) Provides no information about relative factor shares

32

3) Cannot be interpreted as the derivative of a quantity ratio with respect to a
price ratio

Blackorby and Russell argue that the AES provides no information that is not
provided by the constant-output cross-price elasticity. The AES has been used to classify
net substitutes and complements but this application can be accomplished by the
constant-output cross-price elasticity. The constant-output cross-price elasticity is both
unit free and has a clear economic meaning. The AES is merely the constant-output
cross-price divided by the cost share of input j and they argue that this is meaningless.

Blackorby and Russell propose an alternative elasticity of substitution originally

derived by Morishima (1967). The MES is given by:

inCij (Q’p) _ inCu(Q9p)
VC,.(Q,p) VC.(Q,p)

 

 

Mij(Q’p)= =§ji(Q’p)—fii(Q’p)

One desirable property of the MES is that it allows for asymmetrical elasticities of

substitution (i.e. M u at M I... ) in cases with more than two inputs. The AES imposes
symmetry on the elasticity of substitution. This is counterintuitive. Variation of p, in the
ratio p, / p I. will have two corresponding effects on the ratio x: / x; : the change in x;
given by 6], (Q, p) and the change in x: given by 4:“. (Q, p). However, the effect of a
change in the price ratio p, / p j by holding pl. constant and varying p 1. is given by

M).- (Q, P) = 5,,- (Q, P) - 51-,(Q, p) , thus, there is no requirement for M0. = Mfl.

(Blackorby and Russell 1989).
In recent production studies of the sawmill industry (Smith and Munn (1998),
Baardsen (2000)) these criticisms of the AES were broached. In the case of Smith and

Munn (1998) only the MES were presented and in Baardsen (2000) both the ABS and

33

MES were presented. In this study, both types are presented in order to allow comparison

with other studies.
2.3.3.2 Elasticity Calculations

The own-price and cross-price elasticities are calculated based on the following

formulae:
iii = Aii * Si

(7)
513' = Air * S 1

Where S,- is the cost share for input i and A“- and A”. (the AES) are given by:

 

‘ (8)

Notice that the AES will vary with the relative factor Shares S.- and Sj, so its value
will depend on whether it is calculated at mean factor share levels or with individual
yearly observations (Nautiyal and Singh 1985).

From Blackorby and Russell (1989) the MES is calculated as such:

My :5}: -511

(9)
Mn = 4:17 — 511'

Once the estimation is complete the estimated parameters are used to calculate

own-price and cross-price elasticities using the above formulae.

2.3.4 Technological Change

The rate and bias of technological change in the sawmill industry is the second

research question answered by the study. In this model, the state of technology is

34

represented by the trend variable t in the cost function. The translog functional form
allows for biased technological change by relating each of the inputs to the time trend
variable.

An overall measure of technological change (total factor productivity) is given by:

 

=[l_aanC]dln(Q) _arnvc (10)

a In Q dt 3:

Where 1' is total factor productivity, VC is variable cost, Q is output and t is the
time trend variable (Kant and Nautiyal 1997). The first term is the scale effect and the
second term is the rate of technical change.

If r is positive for fixed input prices and output, costs are decreasing over time,
that is, productivity is increasing. If 2' is negative, then costs are increasing over time for
fixed input prices and output.

This statistic may be useful in some applications but generally it is more useful to
measure productivity of each input separately. With many factors of production,
productivity of some factors may increase over time while decreasing or remaining
unchanged for others. Binswanger (1974) demonstrates the method for measuring biased
technical change with many factors of production.

Technical change that affects all inputs equally is termed Hicks neutral. When
technological change affects inputs to differing degrees, it is termed biased technological
change. Single factor productivity is computed as:

_as,_1_

__— , 11
7' atS, ( )

Where S, is the cost share of factor i, t is the time trend variable and %— = ,6".
t

35

If ,6“ is <0, then the technological change is factor i-saving. If ,3“ is >0, then the

technological change is factor i-using.

2.3.5 Returns to Scale

A major characteristic of industrial processes is the efficiency with which they
transform inputs as input levels increase. An industrial process exhibits increasing returns
to scale if output increases by an amount greater than k when all inputs are increased by a
factor of k (k>1). If output increases by less than k, the process is said to exhibit
decreasing returns to scale. Constant returns to scale are exhibited when output increases
by exactly k.

It seems counterintuitive that output should increase by a factor greater or less
than k when all inputs are increased by k. If all inputs are increased, it should be possible
to replicate the output produced by the original input quantities. Varian (1992) points out
that not all inputs are under the producer’s control. For example, it may not be possible to
increase the area of land used for a plantation forest even though increasing other inputs
will increase timber production. Strictly speaking, this situation does not describe
decreasing returns to scale because all inputs are not being increased. In addition, the
model used here does not include all inputs to the production process and it does not
distinguish among differing quality of inputs. In the sawmill industry, increasing the
volume of sawlogs going through the mill often means harvesting lesser quality stands
with smaller trees or less desirable species. Despite the fact that the volume of wood may
be doubled, lumber recovery factors may decrease and so the milling technology will
exhibit decreasing returns to scale. Nevertheless, it is still possible to measure the returns

to scale for the included inputs.

36

Information on economies of scale in an industry can yield valuable insights into
the possible future structure of the industry in terms of number of plants and plant size. If
a technology exhibits increasing returns to scale there is an incentive to increase plant
size. On the other hand, decreasing returns to scale with respect to production labor and
capital may prevent plant size from increasing, but the number of plants per firm may
increase at the same time as the number of firms decreases because of increasing returns
to scale in management labor. In this case, a firm is taken to be one organization that may
operate more than one manufacturing facility.

A beneficial aspect of the translog cost function is that it does not restrict the

technology to constant returns to scale. A Cobb-Douglas production function of the form:

Q = A(L"K“"”)
0<a<1

restricts the technology to constant returns to scale (in addition to
constant rate of substitution between the inputs).

With the translog cost function, economies of scale are measured as the
proportional increase in cost as a result of a small proportional increase in output. This is
the elasticity of cost with respect to output. Christensen and Greene (1976) define scale

economics as:

aanC
(9an

 

SCE=1- (12)

This formulation will give positive numbers for increasing returns to scale and

negative numbers for decreasing returns to scale.

37

2.4 Data

The data required for the model include: quantity of labor and logs used in the
milling process, the prices of those inputs, new capital expenditures, the value of the
capital stock of the milling industry, the price of capital, user cost of capital and the
volume of output (lumber). Data were collected for three states (Michigan, Minnesota
and Wisconsin) for the period 1963—1996. All financial data was discounted to 1996
using the PPI for all commodities. There are a total of 66 observations. For Michigan,
there are 27 observations, 17 for Minnesota and 22 for Wisconsin. Each state had a
different number of observations because for some years, data for SIC 242 were not
published for some states. It was felt that rather than try to generate the missing data from
reported data for SIC 24 for each state or national SIC 242 data it was better to just omit .
those years from the dataset.

The time period of the study was chosen partly due to data constraints. Prior to
1963, data from the Annual Survey of Manufacturers were not as readily available for
SIC 242 at the state level. The time series ends at 1996 because at that time the Census
Bureau changed from the SIC system to the North American Industrial Classification
System (N AICS) and there is poor correspondence between SIC 242 and the new
classifications.

There is also the issue of the level of aggregation of the data and the assumption
of exogenous input prices. At the state level of aggregation it could be possible that the
industry itself determines prices of at least some inputs (particularly wood). Baardsen
(2000) claims that aggregating data beyond the mill level was inappropriate given the

assumption of exogenous input prices. He quotes Varian (1984) as saying this is

38

“unrealistic” (Varian 1984, p. 179). What Varian actually says is it “seems unrealistic”
(ibid). This is a slightly more mild criticism and may not be completely applicable to the
Lake States. In the case of the Lake States this may not be the case because there are no
restrictions for the transport of wood to neighboring states and so timber sellers can
simply sell to buyers across the state line if they feel that they can get a better price. This
does not apply to all areas of all the states because transportation costs and information
costs may become limiting factors for this movement of wood but there is export of
timber to Indiana and Illinois which are not part of this study. In addition, Stone (1997),
states that “changes in the supply of timber in other regions of the country (and world)
influences Lake States timber markets”. This is another indication that the timber market
in the Lake States is not a closed system and that the industry in the region has limited
influence on the prices it pays for inputs. Likewise, for labor, in most parts of the Lake
States there are more employment opportunities available outside the sawmill sector or
the wood products industry in general than there might be in the Interior of British
Columbia, so the labor price can be taken to be exogenous to the sawmill sector. With
11,000 employees total in the Lake States in 1996 it seems unlikely that the industry as a
whole can influence wage rates to any great degree. Certainly capital prices are not
determined within a market endogenous to the Lake States sawmill industry. Studies
aggregated at the national level or studies of regions such as the Pacific Northwest or

British Columbia may be more subject to this criticism.

39

2.4.1 Labor Quantity

Labor quantity is defined as man-hours of production labor in SIC 242 (sawmills
and planing mills) for each year. The data source was the Annual Survey of Manufactures

(ASM) and the Census of Manufactures (CoM) from the Census Bureau.

2.4.2 Labor Price

Labor price, or wages, is calculated easily frOm the Census Bureau data for SIC
242. Labor price was calculated as dollars per hour for production workers. It was simply

the payroll expense divided by the number of hours worked.

2.4.3 Sawlog Price

Sawlog price was calculated as the quotient of the cost of materials and volume of
sawlogs entering mills in each state for years when the Forest Service Timber Product
Output (TPO) data were available (USDA Forest Service North Central Forest
Experiment Station Resource Bulletins, various years). The Census Bureau collects data
on the gross cost of material inputs to the industry. This cost was almost entirely made up
of sawlog costs. In order to calculate a price per thousand board feet (MBF), the total
material cost was divided by the volume of sawlogs consumed in each year.

Sawlog prices for years when Forest Service TPO data for sawlog receipts were
not available (see Table A-5) were calculated based on price data from Timber Mart
North, state Departments of Natural Resources stumpage data, Forest Service stumpage
data, Minnesota Forest Products Price Report, Wisconsin County stumpage data, the

Wisconsin Forest Products Price Review and US. Timber Production, Trade,

40

Consumption, and Price Statistics, 1950-85 (Ulrich 1987). A weighted average price was

calculated based on proportions of each species and grade harvested in each state.

2.4.4 Capital Stock

The capital stock series was created using the perpetual inventory method
developed by Christensen and Jorgenson (1969).

With the perpetual inventory method, capitalstock in the current period (K, ) is a
function of the investment in the current period (1,), capital stock in the previous period
(K,- 1), and the depreciation rate (a):

K,=I,+(1-,u)K,-1 (13)

Investment was taken to be new capital expenditures (NCE) for structures and
equipment. Total NCE were available from both the CoM and the ASM for SIC 242 at
the state level. Nevertheless, not all years were available for all states. In years for which
NCE data were not available, data were generated by calculating the proportion of each
state’s NCE for SIC 242 to national NCE for SIC 242. The proportion for the years
immediately preceding and following the missing data were then averaged and multiplied
by the national NCE to arrive at NCE at the state level. NCE were further broken down
into NCE for buildings and structures, and NCE for machinery and equipment due to
different service lives for each type of capital. The breakdown into the two categories of
capital was accomplished by using the national SIC 242 data on NCE for each category.
Over the timeframe of the study, 17.5% of NCE were for buildings and structures and
82.5% for machinery and equipment. These proportions were fairly constant during this

period.

41

There are three types of depreciation methods that could be used to depreciate the
capital stock series: straight-line, geometric (of which double-declining balance
depreciation is one type) and hyperbolic. Computationally, all require an estimate of the
service life of the capital and in the case of geometric and hyperbolic depreciation, a
parameter that controls the rate of depreciation.

As the name suggests, straight-line depreciation is linear so the depreciation rate
is constant and equal to I/L where L is the service life of the capital. This assumes the
productive capacity of the capital decreases equally each year of its life.

Geometric depreciation is a form of accelerated depreciation which assumes that
the productive capacity of the capital decreases more rapidly in the early stages than it
does near the end of its service life. With geometric depreciation, the declining-balance
rate is the same every year: ébzR/L
where R is rate relative to the straight-line rate of I/L. Therefore, the double-declining-
balance rate is 2/L. As R increases, the depreciation rate increases and depreciation in the
early stages of the life of the capital is increased. Geometric depreciation is measured as:
dx.0=&}(1'60)x-1
Where x=1,2,3....,L

Hyperbolic depreciation is the opposite of accelerated depreciation. With
hyperbolic depreciation, the capital retains more of its productive capacity in the early
stages and as the capital ages, the depreciation accelerates. That is, the depreciation is
delayed (as opposed to accelerated) in the early stage of its life. The hyperbolic
depreciation rate is calculated as:

L-(x-l) _ L—x
L-flU-l) L-flx

 

(14)

d .0:

42

Where x=1,2,3. . ..,L and ,6 is the curvature parameter.

With a ,6 of zero, hyperbolic depreciation reduces to straight-line depreciation. If
,6 is I, there will be no depreciation throughout the course of the service life of the capital
with the exception of the final year when all depreciation will occur.

Intuitively, hyperbolic depreciation most closely matches the actual degradation
of productive services from buildings and machinery in the sawmill industry. As capital
ages, repairs become more frequent and more extensive. Abt (1987) employed hyperbolic
depreciation to create the capital stock series for this reason.

The Bureau of Labor Statistics has established procedures for estimating net
capital stock and depreciation profiles using hyperbolic depreciation (BLS 1997). The
curvature parameter for depreciation of structures is assumed to be 0.75 and for
equipment it is 0.5.

The service life of buildings and machinery for SIC 242 was also not easy to
estimate but BLS procedures assume buildings and structures in SIC 242 have a service
life of 28 years and machinery and equipment have a service life of 13 years.

In order to employ the perpetual inventory method of capital stock estimation, a
benchmark, or starting value of the capital stock is required. Once a starting value of K is
established, NCE and the depreciation rate are used to calculate the capital stock in each
subsequent period. The path of the capital stock series is somewhat sensitive to the
benchmark capital stock level at the beginning of the series, but any errors in the
estimation of the benchmark are quickly dissipated by the NCE data.

In this case, gross book value (GBV) data were not available for SIC 242 for the

Lake States. Capital stock data for SIC 242 in Kentucky and West Virginia are available

43

and the starting values for each of the Lake States are based on the capital stock levels in
those states. The majority of lumber produced in the Lakes States is hardwood and the
same is true of Kentucky and West Virginia. Also, the production levels are relatively
close as well. The input factor mix is assumed to be the same for the Lake States and
Kentucky and West Virginia for the purposes of calculating the initial capital stock.

The starting value for the capital stock series for each state was calculated by
determining the proportion of each of the Lake States’ lumber production to the lumber
production in Kentucky and also in West Virginia in 1963. After the proportions were
calculated, they were multiplied by the 1963 capital stock data for Kentucky and West
Virginia. The resultant figures were then averaged to arrive at an estimate of the capital
stock in 1963 for each of the Lake States. These figures were then used to begin the
estimation of capital stock in subsequent years using NCE data in the perpetual inventory
method. Once capital stock for each category of capital was calculated, the figures were
summed for each year and state to arrive at total capital stock.

After capital stock was calculated for each year and state, the price of capital was
calculated. Following Stier (1985) capital price was calculated as the ratio between gross
quasi-rent and capital stock. Gross quasi-rent was defined as value of shipments minus
total employee compensation minus materials costs. Capital price is a ratio of two dollar
values and as such has no units. It is the ratio of revenues (value of shipments), net of
labor and materials cost, to capital stock. Value of shipments and employee compensation
data came from the Census of Manufactures and the Annual Survey of Manufactures.
Materials cost data were constructed as described above. Capital price does not need to

be calculated for every year for every state because the final data set had some years

missing for each state due to missing Census Bureau data. For Michigan, there were no
Census Bureau data for SIC 242 for the years 1968, 1979-1981 and 1984-1986.
Minnesota was missing Census Bureau data for SIC 242 for the years 1966, 1968-1971,
1973-1976, 1978-1981 and 1983-1986. Wisconsin was missing 1965-1966, 1968-1971,
1979-1981 and 1984-1986.

Gross-quasi rent (returns to capital) may be negative in some years and so it was
necessary to smooth the capital price series by fitting a line using OLS estimation. The
data for capital price presented in Appendix A is the smoothed capital price trend. It was
necessary to calculate NCE for every year in order to employ the perpetual inventory
method of estimating capital stock.

The user cost of capital was also calculated in order to create the cost variable for'
the left hand side of the cost function and to determine cost shares for each of the three
inputs. Bigsby (1994) calculates the user cost of capital services in the Australian
sawmilling industry as:
uc=(r +gn'dPn/Pm)Pm n! (15)

Where,

UC is user cost,

r is the interest rate on lO-year government bonds

g" is the declining balance depreciation rate for capital it

dPn/Pm is the annual rate of change of capital price for capital n

Pm is the price of capital it at time t and,

K", is the value of the capital stock of capital n at time t.

For this study, Bi gsby’s formula needed to be modified to incorporate the

hyperbolic depreciation scheme for depreciating the two kinds of capital used to construct

the capital stock variable.

45

The final values were then converted to 1996 dollars using the PPI for all

commodities.

2.4.5 Lumber Output

Output volumes came from the Census Bureau publication MA24T: Lumber
production and nrill stocks. Volumes are in MMBF International 1/ ” log rule. A point to
note regarding the lumber output statistics is that in 1994 the Census Bureau undertook a
reconciliation among the MA24T, the 1992 Census of Manufactures, and state sawmill
directories (Census Bureau 1994). The results of this reconciliation were large upward
revisions of the output statistics from 1993. This may have the effect of underestimating

productivity gains earlier in the study period relative to later in the study period

2.4.6 Variable Cost and Input Cost Shares

The left-hand side variables of the translog cost function and share equations were
derived from the cost data for the inputs labor, materials and capital. Variable cost was
the sum of labor, material and capital costs which were in turn the product of the price
and quantity of each input. The input cost shares were the proportion of variable cost

made up by each of the three inputs.

46

0.8

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

0.7
0.6
W‘ w‘ 4
2 0.5
I
g \ + Labor
3 o 4 Wk A + Materials
5 M +Capital
a. A
0.2
o. 1 M
o 7 Y T V 7 T T
1980 1965 1970 1975 1980 1985 1990 1995 2000

Year

Figure 2-1. Input Factor Cost Shares for Michigan (1963-1996)

From examining the slope of the input cost shares and their change over time in,
certain relationships are apparent (Figures 2-1, 2-2 and 2-3). Capital is a relatively
unimportant input in terms of its contribution to costs and its share of input costs is
reasonably steady, suggesting low substitutability between capital and the other inputs.
On the other hand, there appears to be strong substitutability between labor and materials.
The only significant aberration is for Wisconsin in the early late 19705 and early 19805
when there was a spike in the cost share for capital as a result of particularly large new
capital expenditures in the late 19703. The figures also seem to show a general increase in

the cost share of materials and a decrease in the cost share of labor.

47

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

0.9
0.8
0.7 A )\\I’/\\\
. A.“
2 V
0
lg 0:5 -O-Labor
+Materials
g 0.4 A A A +Capital
3 \/ \ -/ \N
03 X \/\ /AV v
0.2 V
0.1
o ”f; fi+ VA
1960 1965 1970 1975 1980 1985 1990 1995 2000
Year
Figure 2-2. Input Factor Cost Shares for Minnesota (1963-1996)
0.8

 

 

 

0.5
K + Labor
+ Materials

 

 

 

 

Input Coot Share
0
A

W + Capital
0.3

 

 

 

 

 

 

0.2
0'1 /A\+Hw
o r 7 r r r fir r
1 960 1 965 1 970 1975 1980 1 985 1 990 1 995 2000

Year

Figure 2-3. Input Factor Cost Shares for Wisconsin (1963-1996)

48

For Michigan and Minnesota, there was a decrease in the cost share of materials
and a consequent increase in the cost share of labor around 1989. Wisconsin did not
exhibit this same pattern. A possible explanation is that there was an increase in materials
price in those two states that Wisconsin did not experience to the same degree. The

reason for this increase is not known.

49

3.0 MODEL RESULTS AND DISCUSSION

This chapter presents the econometric model results including the results of the
model that is homogeneous of degree one in input prices and several versions of the
model in which increasingly restrictive assumptions have been imposed and tested for
validity. Those restrictive assumptions include constant returns to scale and unitary
elasticity of substitution. In addition to presenting the results of the model, the results are

discussed and compared to results from other studies.

3.1 Maintained Hypotheses

There are several restrictions imposed on the model in order for it to conform to
the theoretical requirements of a cost function. A cost function must be homogeneous of
degree one in input prices. This means that if all input prices dOuble, cost will double,
holding output constant. In order for that condition to hold, the following parameter

restrictions are imposed on the translog cost function (Nautiyal and Singh 1985):

and (16)
2.5.) =Zflji :25“ :0
r j l

Wherei and j represent the inputs labor, materials and capital,
Q is production and t is the time trend.

These restrictions are necessary for theoretical reasons but they provide the
benefit of reducing the number of parameters that need to be estimated. The unrestricted
model has twenty-one parameters and the imposition of the above restrictions reduces the

number of parameters to be estimated to fifteen.

50

The original model that was estimated is shown below.

anC=flC +(l—flM -,6K)lnLP+,BM InMP+,BK In KP+fl,r+,BQ InQ

+%[(—flw --,13L,()InLP2 +(-flm -,BMK)InMP2 +(—flLK -,BMK)In KP2 +fl,,:2 +,6QQ 1:192].-
flKQ In K In Q+ flat * In Q+ [3”, In LPIn MP+ 51.x In LPln KP+ flux 1n MPln KP

SL =(l-fiu -flx)+(-flm -flLK)ln LP+flm InMP+flLK In KP+ (17)

(‘flm ‘ fix, )1 + (”fling ‘ 161m) 1" Q

flMrt+flManQ

3.2 Model Selection Procedure

The model selection procedure is a stepwise testing of model assumptions in order
to select the most appropriate model for the data set. The translog cost function used to
model the production structure of the sawmill industry of the Lake States is flexible in
that it allows for nonconstant returns to scale and nonunitary elasticities of substitution
among the inputs. The modeling procedure starts with the unrestricted model and then
adds successively more restrictive assumptions. Model (1) is the model that includes
restrictions on the parameters that impose homogeneity of degree one in input prices.
Considering that a well-behaved cost function must behave in that way, we take this
model to be the unrestricted model in terms of testing the more restrictive assumptions of
the other models. Model (2) imposes homogeneity of degree one in output. In other
words, it imposes constant returns to scale. Model (3) imposes unitary elasticity of
substitution among the inputs but relaxes the constant returns to scale assumption. Model
(4) includes both the constant returns to scale and unitary elasticity of substitution

restrictions.

51

The homogeneity restrictions were discussed in Chapter 2 and reiterated in
equation (16) above. To restrict the model to constant returns to scale, (Model 2, below)
the following parameter restrictions are imposed:

fliQ =0andflQQ =0 (18)

Where I equals labor, materials and capital.

In order to impose unitary elasticity of substitution restrictions, (Model 3, below)
the following parameter restrictions are imposed (Nautiyal and Singh 1985):

a). = o (19)
Where I and j equal labor, materials and capital.

The parameters of the translog cost function and the labor and materials share
equations were estimated as a system of equations using Full Information Maximum
Likelihood (FIML) estimation with EViews 4.1© software. Table-3-I shows the values of
the estimated parameters for each model along with the values of parameters calculated

from the estimated parameters based on the restrictions of the corresponding model.

52

 

Table 3-1. Estimates of the

Be

BM
Bx
fir

at

function

%

 

2108.314

-2.375
86.

l***

-0.000996
4.27E-05

9.53E-04
1
-0.0420***

132

0.00720
156

-0.00564

IIOIIC

NA
NA

Function Parameters

.81

4.411019

-0.102
1
-2.498
41
78.231***
.1

0.00137

0.036323
—0.0221
1

1.2141
-2.50249
18
45354***

-0.03804***

0.00

NA
NA

NA

NA

NA

19

1
0.007813
1
-0.00231
11
3
471
21.615
11.341

 

l

1**

1.503421

1
-2.50049
7461
78.

-0.00279
12***

0.000682

141
NA
NA
NA
NA

NA

NA

NA

NA
NA

NA

6
279.4977

112

Table 3-1 continued,

Notes: 1.Figures in parentheses are the standard errors of estimates. 2. A single
asterisk signifies significance at the 10 percent level, a double asterisk at the 5 percent
level, and a triple asterisk at the 1 percent level. 3. Parameters without standard errors
were calculated from other parameters based on the imposed restrictions.

Two of the parameters are significant at the 5% level. This is not unusual for
models of this type. Abt (1984) had two variables significant at the 5% level and five
with standard errors less than the coefficient estimate in his model of the Appalachian
region of the US. Justification of such models was made on economic grounds where
theory dictates the economic properties of a well-behaved cost function and those
properties were imposed on the statistical model. The estimation procedure first satisfied
the imposed parameter restrictions and then attempted the best statistical fit of the data.
Also, many of the variables used the same data (e. g. labor price and labor price squared)
so there was a fair amount of multicollinearity built into the model. These factors had the
effect of increasing the standard errors on the parameter estimates. Therefore, the
calculated results should be treated with caution because of the low number of parameters
that are significant at the 5% level.

The hypothesis testing in the model selection process was done using the
likelihood ratio test. The likelihood ratio statistic was calculated as:

LR = 2(LLu, - LL,) (20)

Where LL“, was the log of the likelihood function for the unrestricted model and
LL, was the log of the likelihood function for the restricted model. Multiplying the
difference between the log likelihoods of the unrestricted and restricted models by two

makes the LR statistic approximate a xz distribution (Wooldridge, 2000). The critical

value for the test was the value of the x2 distribution at the preferred level of significance

54

(1% in this case) and with the proper number of restrictions. Models (2) and (3) each had
three linearly independent restrictions and Model (4) had six.

According to the likelihood ratio tests on each of the three restricted models, we
could not reject the assumption of constant returns to scale (Model (2)) whereas the
hypothesis of unitary elasticity of substitution among the inputs (Model (3)) was rejected
at the 1% level. The model with constant returns to scale and unitary elasticity of
substitution (Model (4)) was also rejected at the 1% level.

While the translog cost function that has had homogeneity of degree one in input
prices imposed can allow for nonconstant returns to scale, the empirical evidence here
suggests that the production structure of the sawmill industry in the Lake States can be
estimated with a cost function that imposes constant returns to scale. The following
calculations of elasticities of substitution, own and cross price elasticities among the

inputs and technological change are based on the results from Model (2).

3.2.1 Other Cost Function Properties

In addition to being homogenous of degree one in input prices, a well-behaved
cost function must have input demand functions that are strictly positive (Bemdt and
Wood 1975). Cost shares can never be zero or less than zero. The input demands (cost
shares) of each input were calculated based on the parameter estimates of Model (2) and
all were positive for each annual observation.

Another property of a well-behaved cost function is that it must be concave in
input prices. In order to be concave, the principal minors of the Hessian matrix of the
second order partial derivatives be negative definite. Nautiyal and Singh (1985) show that

an equivalent test of concavity is that the matrix of ABS be negative semi-definite. Given

55

the reported AES (Table 3-2) the matrix fulfills that requirement with the principal

minors alternating sign beginning with negative.

3.3 Data Pooling

All of the models estimated combined times-series data with cross-sectional data
(i.e. panel data) in order to increase the number of observations and improve the degrees
of freedom. Observations from the period 1963-1996 for Michigan, Minnesota and
Wisconsin were combined into one dataset of 66 observations. Michigan has 27
observations, Minnesota has 17 and Wisconsin has 22. With this type of data pooling we
assumed that the production structures of the sawmill industry in the three states were
similar enough that they could be estimated together in one model Abt (1987). There are
several methods available to test whether or not this is the case. One is the Chow test
which requires that the three pooled cross-sections be run as separate models and then an
F-test is used to determine if they are significantly different (Gujarati 1995). Another is
the dummy variable method. Dummy variables for Michigan and Minnesota were added
to Model (2) to measure possible shifts in the intercept as a result of differences related to
the cross-section (state) represented by each observation. If the coefficient for one or both
of the dummy variables is statistically significant, then the assumption of identical
production structures is not valid. The results of this regression (Appendix B) showed
that the coefficients on the dummy variables were not significant at the 10% level and so

the cross-sections may be estimated together.

3.4 Elasticities of Substitution

From equations (8) and (9), the ABS and MES can be calculated (Table 3-2).

56

Table 3-2. The Allen-Uzawa Partial Elasticity of Substitution and Morishima
Elasticity of Substitution based on FIML estimates of Model (2) (at mean level of

Labor Price if Maerati “CaprtaIPrcei
Price

 

NA 0.89 -1.36
(0.80) (0.037)

 

0.89 NA 0.91
(0.89) (0.23)

 

-1.36 0.91 NA
(0.13) (0.90)

Note: Morishima elasticities are in parentheses.

    

 

 

 

The AES suggested that all input pairs were substitutes except for labor and
capital which were complements. The MES on the other hand suggested that all input
pairs were substitutes. The MES are generally lower than their AES counterparts. Note
that the MES allows for nonsymmetrical elasticity of substitution. That is, M,-,- does not
have to equal Mfi. This is more flexible than the AES which imposes symmetry on the
elasticities of substitution between input pairs. *

Nautiyal and Singh (1985) presented results for AES for the lumber industry in
Canada and found that all inputs are substitutes for each other. Most other studies of the
sawmill industry, including Stier (1980), Martinello (1987), and Puttock and Prescott
(1992) had the same finding. Nevertheless, Banskota et al. (1985) found that in the
Alberta sawmill industry, capital and materials are complements while all other input
pairs are substitutes. Likewise, Campbell and Jennings (1990) found materials to be
complements of both energy and capital in the Tasmanian sawmill industry. Baardsen
(2000) also found many complementary input pairs, in particular between sawlogs and
energy, labor and energy, and sawlogs and labor in his study of the Norwegian

sawmilling industry. Studies of the substitutability between capital and labor in other

57

industries also indicate that capital and labor are substitutes, with the exception of Denny
and May (1977).

All of the own-price AES are negative. This is necessary for the corresponding
own-price elasticities of demand to be negative and consequently for the input demand
curves to be downward sloping. Most authors do not report the own-price AES but it is
necessary to calculate them in order to calculate the own-price elasticities of demand.

The elasticity of substitution results are discussed in the following sections and

the results of other authors are summarized (Table 3-3).

3.4.1 Labor-Material Substitution

The AES between labor and material calculated in this study was 0.89. The MES
was 0.80 for labor/material and 0.89 for material/labor. There is a wide range of values in
the literature for the AES between labor and material. Banskota et al. (1985) calculated it
to be quite inelastic at 0.0614. Nautiyal and Singh (1985) found a value almost ten times
greater at 0.60. In Meil and N autiyal (1988) the values range from 0.248 to 0.488.
Martinello (1987) estimated it to be 0.203 for BC Coast mills and 0.053 for BC Interior
mills. Martinello (1985) estimated the elasticity to be zero for sawmill and shingle mills
in Canada while Puttock and Prescott (1992) calculated a value of 0.595 for the
hardwood sawmill industry of Southern Ontario. Abt (1984) found quite high values for
each region of the US. he studied. The AES for labor and material for the Appalachian,
Southern and Western regions was 0.80, 0.95 and 0.60 respectively. Except for Abt, the
other studies are all of the Canadian lumber industry. The relatively high values for the
US. industry indicate that it is more able to react to price changes than is the Canadian

industry. The industry as modeled in this study is more able to substitute away from labor

58

or materials if their prices increase than are the Appalachian and Western regions as
modeled by Abt but the AES for the Lake States and Abt’s Appalachian region were
quite close. The value for the hardwood industry in Southern Ontario was also quite high
indicating a similar substitutability between labor and materials. Baardsen (2000) was the
only study that calculated an AES indicating that labor and materials were complements
with a value of -0.10. Nevertheless, his estimate of MES for labor/materials was 0.66 and

materials/labor was 0.55, indicating that they were substitutes.

3.4.2 Labor-Capital Substitution

The AES between labor and capital was negative, indicating that they are
complements. The calculated value was -1.36. The MES calculations indicated that labor.
and capital are substitutes and the substitutions are quite inelastic with a value of 0.037
for labor/capital and 0.13 for capital/labor. Baardsen (2000) had the
substitute/complement relationship differ between ABS and MES for labor and materials
with the AES results indicating they were complements and the MES results indicating
they were substitutes. All other studies show labor and capital to be substitutes with the
exception of Denny and May (1977). They estimated the AES between labor and capital
for the Canadian manufacturing sector to be -0.533, indicating that they are complements.
Nevertheless, the absolute value of the AES is in the range calculated by other authors.
Martinello (1987) reported AES between labor and capital of up to 1.669 for the wood
industries of BC. The ABS and MES estimates of Baardsen (2000) were similar in
magnitude to this study with an AES of 0.73, a labor/capital MES of 0.70 and a

capital/labor MES of 0.75.

59

The only unusual result of the AES calculations from the model is the finding of
complementarity between labor and capital. Complementarity between materials and
capital, and energy and capital are found in other studies that used time series data and it
may be the result of capacity expansion. The study period in this study (1963-1996)
includes recessions in the early 19803 and 19903 that saw lumber output drop
substantially, particularly in the early 19803. At the same time, interest rates were very
high and many sawmill workers were laid off. In this case it appears that the capital price
and consequently the user cost of capital were increasing during this time while quantity
of labor and of output were decreasing. The AES, nevertheless, assumes that output
remains constant. A possible explanation is that the complementarity is due to labor and
capital being used in fixed proportions. If mill-level data were available they may reveal
that the labor used was directly proportional to the number or type (band or circular) of
saws used at the mill which can be used as a proxy for capital stock (Puttock and Prescott
1992). Denny and May (1977) gave no explanation of their finding of complementarity

between labor and capital except that it was unusual.

3.4.3 Materials-Capital Substitution

For materials and capital, the AES results indicate that they are inelastic
substitutes with a value of 0.91. The MES value for materials/capital is more inelastic
with a value of 0.23 but the MES for capital/materials is 0.90. The results for MES
indicate that the sawmill industry of the Lake States reacts more to changes in material
price than changes in the price of capital. This is in part because of the large share of
costs comprised by materials. Materials make up 62% of costs on average over the study

period. Labor represents 34% and capital only 4% of variable costs as defined in the

60

model. Nautiyal and Singh (1988) found a more inelastic value of 0.17 for the Canadian
lumber industry. Martinello (1985) calculated the AES between materials and capital to
be 0.575 for sawmills and shingle mills in Canada and Baardsen’s AES estimate for the
Norwegian sawmill industry was close to that at 0.73 while his MES estimates for
materials/capital and capital/materials were 0.70 and 1.00 respectively. Banskota et al.
(1985) found materials and capital to be slightly complementary in the Alberta sawmill
industry with an AES of 00544. Other authors have explained such results as a
demonstration of an overall material and capital using expansion in the industry over the
study period (Meil and N autiyal 1988) but the Banskota et al. study used strictly cross

sectional, rnill-Ievel data for the year 1978.

3.4.4 Elasticity of Substitution Discussion Summary

The AES presented above show that labor and capital are elastic complements in
the Lake States and all other input pairs are substitutes. The own-price AES are all
negatively signed which is necessary for the own-price elasticities of demand to be
negative and the corresponding input demand curves to be downward sloping. There is a
quite consistent rate of substitutability between labor and material for both the AES and
MES. Also, the asymmetric nature of the MES shows that capital is much more reactive
to price changes in labor and materials than the other way around.

Overall, the values calculated in this study are comparable to those calculated for
other regions but there is particular concurrence with the Ontario and Québec regions
studied by Meil and N autiyal (1988), the southern Ontario hardwood sawmill industry
studied by Puttock and Prescott (1992) and the Appalachian region studied by Abt

(1987). The regions studied by Puttock and Prescott, and Abt are particularly of interest

61

because they are most similar to the Lake States in terms of forest resources and land
ownership. While most forest land in Canada is publicly owned, southern Ontario has a
similar development pattern to the nearby states, which is characterized by many small
landowners. This, combined with the differences between a hardwood forest resource and
a softwood forest resource which predominates in most of the other regions modeled in
the literature may be a reason for the differences between the two types of regions in
terms of the substitutability of inputs, particularly materials and labor.

For ease of comparison, a summary of the elasticity of substitution results of other
authors is below (Table 3-3).

Tabk 3-3 Aline Elasi __of SusnLn SWIM”! _
Study Labor/Materials Labor/Capital Capital/Materials .

Stier, 1980 NA 0.105 NA

. Nautiyal 0.60 0.93 1.24
and Singh,
1985
Singh and 0.24 2.58 -0.62
Nautiyal,
, 1985

. Banskota et 0.0614 1.7274 -0.0544
“aL,1985
Martinello, 0.00 0.226 0.575
1985 ‘
Martinello, 0.203 1.669 0.246
‘ 1987' 0.053 1.254 0.572
. Meil and 0.337
‘ Nautiyal,
; 19882

1 Puttock and 0.595 NA NA
; Prescott,
.1992

; Baardsen, -O.10 0.73 0.71
l 2000
McQueen, 0.89 -1.36 0.91
‘ 2003
T0p numbers are for BC Coast and bottom numbers are for BC Interior.
2Number is for smallest mill-size class in Ontario.

     
 

    

     

 

  

 

 
      

 

 
   
    

 

 
 

 

 
      

 

    
    

 

 
   
    

 

 
   
    

 

 
   
 

 

  
     

 

 

 

62

The complementarity of labor and capital indicates that they are employed in
fixed proportions and this is again similar to the findings for the smaller mill size classes

of Ontario and Québec modeled by Meil and Nautiyal.

3.5 Price Elasticities

The own-price and cross-price elasticities are calculated according to equation
(7). The signs of the price elasticities are dependent on the signs of the AES. Therefore,
the results in terms of whether inputs are substitutes or complements for each other
rrrirror the results of the AES (Table 3-4).

Table 3-4. Own and Cross-Price Elasticities (at mean level of observations) 1963-
' Input Labor Price Material Price Capital Price
Labor -0.50 0.55

 

 

‘ Material 0.30 -0.34
-0.46 0.56

 

 

 

 

 

All of the own-price elasticities are negative, indicating downward sloping
demand curves. The cross-price elasticities are all positive indicating that the inputs are
substitutes except for those between capital and labor which are negative indicating that
those two inputs are complements. This is in accordance with the AES results. All the

calculated elasticities are inelastic.

3.5.1 Own-Price Elasticities

Own-price elasticity of demand measures the percentage change in the quantity
demanded of a good when its price changes by one percent. In this model, the change in
quantity demanded of an input was measured as the change in the size of its cost share.

The labor own-price elasticity of demand calculated in this study was -0.50 and was

63

correctly signed for a downward sloping demand curve. It was also within the range
reported in the literature. Nautiyal and Singh (1985) calculated an own-price elasticity of
demand for labor of -0.48 for the Canadian lumber industry while Banskota et al. (1985)
found it to be slightly more inelastic at -0.3644 for the Alberta sawmill industry. Abt
(1987) calculated it to be -0.11 in the Appalachian region, -0.47 in the South and -0.39 in
the West. Meil and Nautiyal (1988) calculated values for different regions of Canada
ranging from -0.264 to -0.494. As with many of the elasticities of substitution calculated
by them in that study, the values for the Ontario and Québec industries more closely
matched the ones calculated for the Lake States as opposed to those of British Columbia.
Baardsen (2000) reported the highest value in the reviewed literature with a value of
-0.57 for the Norwegian industry.
The calculated own-price elasticity of demand for materials was -0.34. Nautiyal
and Singh (1985) calculated a less inelastic value of -0.44. Meil and Nautiyal (1988)
calculated a range of values from -0.065 to -0.229. The least inelastic value was for large
mills in Québec. Unlike many of the elasticity of substitution results, their results for
Ontario rrrills were not close to the findings of this study. The own-price elasticity for
materials in Ontario mills ranged from -0.076 to -0.110. As with the other results that
show elasticities quite a bit more inelastic than for the Lake States, one reason may be
institutional factors that require mills to continue to process wood despite market
conditions. In Canada, provincial governments typically require mills to harvest and
process a certain amount of their annual allowable cut each year in order to ensure
community stability and for forest management reasons. This makes them less able to

substitute away from wood when the price increases. Nevertheless, Abt (1987) found the

materials own-price elasticity for the Appalachian region in the US. to be very inelastic
at -0.08. Abt’s results for the Southern and Western regions were less inelastic at -0.25
and -0.20 respectively. Puttock and Prescott (1992) calculated it to be -0.202. Both Abt’s
and Puttock and Prescott’s results are more inelastic than that of this study which
contradicts some of the evidence that the Appalachian region of Abt and the Southern
Ontario hardwood sawmill industry are close matches for the industry in the Lake States.
It could be that the Lake States have somewhat of a hybrid industry in that hardwood
lumber predominates in the southern areas of each state and softwood lumber becomes
more prevalent as you move north and this is affecting the model results. In addition,
NIPF dominates the forestland ownership classes in the southern parts of the states while
state, national and commercial forestland is more prevalent farther north. Overall, the
hardwood lumber industry predominates in the Lake States with over 75% of the total
production by volume in 1996 (Census Bureau 1997). Baardsen (2000) found the least
inelastic value in the literature with an own-price elasticity for sawlogs of -0.70. The
Norwegian industry is dominated by softwood lumber.

The capital own-price elasticity is -0.19. N autiyal and Singh (1988) found that the
own-price elasticity of demand for capital in the Canadian industry was elastic with a
value of -l.2l. Martinello (1985) calculated a value of -0.297 for sawmills and shingle
mills in BC. Singh and Nautiyal (1985) calculated a similar value of -0.2426 for the
Canadian lumber industry using a long-run translog cost function. The result from
Banskota et al. (1985) was -0.7590. Surprisingly, Baardsen (2000) did not find the largest

value in the literature for this elasticity which be estimated to be-0.66 for Norwegian

65

sawmills. Abt (1987), Meil and Nautiyal (1988) and Puttock and Prescott (1992) did not

calculate price elasticities for capital.

3.5.2 Cross-Price Elasticities

Labor and materials were inelastic substitutes with a labor/materials cross-price
elasticity of 0.55. This means that for a one percent increase in the price of materials, the
quantity of labor demanded increases by 0.55%. The materials/labor cross-price elasticity
was 0.30. Nautiyal and Singh (1985) found these two elasticities were more inelastic than
those in this study with values of 0.30 and 0.14 respectively. Martinello (1985) found
both of these elasticities were zero in keeping with his estimates of the AES between
labor and materials. Banskota er al. (1985) determined that labor and material were
substitutes, but very inelastic ones, with values of 0.0225 for labor/materials and 0.0258
for material/labor. Meil and N autiyal (1988) also found these values to be inelastic but
much less so than Banskota et al. with results for labor/materials ranging from 0.173 on
the BC Coast to 0.278 in Québec. Their results for materials/labor ranged from 0.069 on
the BC Coast to 0.240 in Québec. The Ontario numbers were in the 0.115 to 0.159 range.
For the hardwood industry of southern Ontario, Puttock and Prescott (1992) calculated a
labor/materials elasticity of 0.106 and a materials/labor elasticity of 0.227. For the
Appalachian region of the US, Abt (1984) found the labor/materials elasticity of
demand to be 0.47 and the materials/labor elasticity to be 0.35. The corresponding
elasticities for the Southern and Western regions were 0.61 and 0.37, and 0.39 and 0.20.
This study produced the same result as all the other studies in that labor and materials are
substitutes but the degree of that substitutability is greater in the Lake States than the

other regions. Although not a production study of the sawmill industry, McGuire et al.

66

(1999), also found that increased scarcity (both physical and economic) of veneer logs in
Indiana, Illinois, Michigan, Minnesota and Wisconsin led to increased demand for
sawmill labor in the form of increased effort to procure veneer logs.

The sign of the labor/capital and capital/labor cross-price elasticities indicate that
they are inelastic complements. The value for the labor/capital elasticity is -0.06 and for
capital/labor it is 046. Therefore the demand for labor is much less sensitive to the price
of capital than the demand for capital is to the price of labor. As with the AES for
labor/capital, most other studies reported cross-price elasticities that indicated they were
inelastic substitutes. The exceptions are Banskota et al. (1985) and Meil and Nautiyal
(1988). Banskota et al. reported a labor/capital cross-price elasticity of 0.6319 and a
capital/labor elasticity of 02389. It is unclear how it was possible to have different signs
on these two elasticities given that they were calculated as the product of the AES and the

cost share for the second input: (5,]— = Au *5 I.) . They reported a positive AES between

labor and capital and all cost shares must be positive. Meil and Nautiyal also reported a
number of results indicating that in some regions of Canada and for some mill size
classes, labor and capital were complements. In BC, the larger mill size classes exhibited
this trait and for Ontario and Québec almost all the mill size classes had a negative
labor/capital cross-price elasticity. Only the smallest mill size class in Ontario had a
result indicating they were substitutes with a value of 0.053. For the mill size classes in
Ontario and Québec that indicated labor and capital were complements, the value of the
elasticity varied from 0033 up to -0.603. These values are in the range of those
calculated in this study indicating that the labor and capital input markets in these regions

are similarly sensitive to changes in their prices. The elasticities for the Lake States,

67

nevertheless, indicate that capital is more sensitive to labor price changes than the other
way around. This result follows from the AES between labor and capital and the fact that

capital has a cost share of only 4% on average compared to 34% for labor.

The material/capital and capital/material elasticities are similar in magnitude but
different in sign from the labor/capital and capital/labor elasticities. The value of the
material/capital elasticity is 0.04 and the capital/material elasticity is 0.56. The results
indicate that material and capital are substitutes and that capital is more sensitive to
changes in material price than the other way around. The sensitivity to their respective
price changes is the same as for labor and capital and for the same reason in that
materials make up a much larger share of costs than capital. Nautiyal and Singh (1985)
had results for Canada that reflect similar relative sensitivity to changes in cross-price
with a material/capital elasticity of 0.17 and a capital/material elasticity of 0.63. Banskota
et al. (1985) found material and capital to be complements with a material/capital
elasticity of -0.0075 and a capital/material elasticity of -0.0228. This result is opposed to
the result from Banskota (1984) that found material and capital to be substitutes.
Banskota (1984) was a time series study while Banskota et al. (1985) was a mill-level
cross-sectional study. He hypothesized that the differing results “reflects perhaps the
long-run adjustments (cross-sectional studies) vis-a-vis short-run adjustments (time-series
studies)” Banskota et al. (1985). Martinello (1985) also found the two inputs to be
substitutes for the Canadian lumber industry with a material/capital elasticity of 0.078
and a capital material elasticity of 0.242 and Martinello (1987) found similar results for
the BC Coast and Interior. Meil and Nautiyal (1988) had mixed results for the BC Coast

and BC Interior with some mill-size classes indicating substitution between materials and

68

capital and some indicating a complementary relationship. All of those elasticities were
very small nonetheless with a range in absolute value of 0.002 to 0.065. For Ontario and
Que’bec, material and capital were generally complements and the complementary
elasticities varied from -0.078 to -0.869. For Norway, Baardsen (2000) had results similar
to the others with a sawlog/capital elasticity of 0.04 and a capital/sawlog elasticity of
0.30. Abt (1987) found materials and capital to be complements in all three regions: the
Appalachian region had a value of -0.10 while the Southern region’s value was -0.03 and

for the West it was -0.19.

3.5.3 Elasticity of Demand Discussion Summary

As with the own-price AES, all the own-price elasticities of demand are less than
unity and negative indicating inelastic downward sloping demand curves. The cross-price
elasticities are all inelastic and positive except between labor and capital which are
inelastic and negative, in concurrence with the AES for those two inputs. Changes in the
price of capital do not have very large effects on the demand for any of the inputs,
including capital, whereas changes in the prices of the other two inputs have a much
greater effect on the demand for capital.

Given that materials and labor are substitutes, the earlier discussion of reduced
timber availability in the Lakes States as a result of changing forest management or
landowner attitudes means that to a point, increases in materials prices may actually
increase employment in the sawmill sector of the Lake States, assuming that output
remains constant. There had been an increase in wood use and employment in the
industry over the study period along with an increase in output. It is possible that part of

the increase was the result of changing characteristics of the wood resource which

69

required more of both inputs to produce the same amount of lumber. Decreasing average
log diameter may be one characteristic that has changed over the course of the study
period. Smaller diameter logs have lower lumber recovery factors (LRF) than larger
diameter logs and so not only more wood, but more labor may be required to maximize
the quantity of high grade lumber out of the smaller logs. This study is unable to
determine how high or for how long timber prices can increase for this effect to hold. The
substitutability of labor for materials and vice versa is higher in the Lake States than for
the softwood producing regions of Canada. This may be due to the institutional factors
controlling harvesting in the two jurisdictions. Almost all the timber harvested in Canada
is from public land and sawmills are committed to harvest a certain percentage of their
annual allowable cut (AAC) each year. This limits their response to price changes.
Likewise, particularly in British Columbia, the labor force is unionized and so they are
more limited in their response to labor price changes. In the United States, even in the
Northwest where there is a large amount of federal land, sawmill managers have more
leeway in adjusting to input price changes. Likewise in the Appalachian region and the
South, the preponderance of private forestland means that sawmill operators can react to
input price changes as opposed to being required to harvest when market conditions may
not warrant because of other public policy reasons such as community stability.

For ease of comparison, a summary of the elasticity of demand results of other

authors is presented below (Table 3-5 and Table 3-6).

70

Table 3-5 Own-Price Elasticit of Demand Results of Selected Studies

 

 

 

 

 

 

 

 

 

 

 

Study Labor Materials Capital
Nautiyal -0.48 -O.44 -1.21
and Singh,

1985

Singh and -0.8607 -0.6936 -0.2426
Nautiyal,

1985

Banskota et -0.3644 -0.0228 -0.7590
al., 1985 ’
Martinello, -0.238 -0.374 -0.297
1985

Martinello, -0.309 -0.069 -0.528
1987' -0323 -0.146 0594
Abt, 19872 011 -0.08 NA
Meil and 0440 -0.076 NA
Nautiyal,

19883

Puttock and -0.489 0202 NA
Prescott,

1992

Bigsby, -0.58 -0.30 -0.69
1994

Baardsen, -0.57 -0.70 -0.66
2000

McQueen, -0.50 -0.34 -0.19 l
2003

 

 

 

Top numbers are for BC Coast and bottom numbers are for BC Interior.
2Numbers are for Appalachian region (Kentucky, Pennsylvania, West Virginia).
3Numbers are for smallest mill-size class in Ontario.

71

 

Tale 3-6088_Peri8 Em of Demnd Hts" of WSW ,

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Top numrsbe are for BC Cast and bottom mismbere for BCIonterir. i

 

. Study Labor/ Materials Labor/ Capital Materials Capital] 1
. Materials [Labor Capital [Labor ICapital Materials
~ Stier, 1980 0.047 0.058
, Nautiyal 0.30 0.14 0.13 0.23 0.17 0.63
and Singh,
1 1985
Singh and 0.1264 0.7659 0.2925 0.6085 -0.703 -0.3266
‘ Nautiyal,
1985
Banskota et 0.0225 0.0258 0.6319 -0.2389 -0.0228 -0.0075
‘ al., 1985 '
Martinello, 0.000 0.000 0.031 0.050 0.078 0.242
1985
1 Martinello, 0.138 0.044 0.171 0.361 0.025 0.167
w 19871 0.028 0.012 0.294 0.288 0.134 0.306
Abt, 19872 0.11 -0.08 0.11 NA -0.10 NA
~ Meil and 0.199 0.115 0.053 NA 0205 NA
Nautiyal,
19883
Puttock and 0.106 0.227 NA NA NA NA
Prescott,
‘ 1992
Bigsby, 0.56 0.24 0.02 0.14 0.04 0.53
1994
, Baardsen, -0.04 -0.02 0.04 0.18 0.04 0.30
2000
. M°Queen, 0.55 0.30 -0.06 -0.46 0.04 0.56
. 2003

   

2Numbers are for Appalachian region (Kentucky, Pennsylvania, West Virginia).

3Number is for smallest mill-size class in Ontario.

3.6 Productivity Growth

Growth in productivity, or technical change, is measured as the change in demand

for inputs as a function of time holding output and prices constant. For example, if

demand for labor is decreasing over time, that is an indication of labor-saving

technological change. If demand for labor is increasing over time, then the technological

change is labor-using. Improving productivity is an important way for the sawmill

72

industry of the Lake States to remain competitive during a time of increasing resource
constraints. This section includes a calculation of total factor productivity for the region
as well as a measure of the bias of technological change among the inputs. This is useful
information for policymakers as different policies will be required to enhance

productivity of different inputs.

3.6.1 Total Factor Productivity

Total factor productivity is the overall measure of productivity for the given

production technology and is measured by equation (10). In this model we cannot reject

am VC

2)an

 

the assumption of constant returns to scale so [ ] equals 1 making the first term of

equation (10) equal zero leaving:

__ Bln VC
3:

 

(20)

The derivative of the variable cost function with respect to t yields the following
equation:

31 VC ~
3. = fl, +fl,,r+(—,6M, -,6K,)ln LP+,6M,1n MP+flK, ln KP+,B,Q ln Q (21)

 

Evaluated at the mean level of observations, total factor productivity as measured
by Model (2) was 0.008. The interpretation of this number is that productivity is
increasing because variable costs, holding output and input prices constant, are
decreasing by approximately 0.8% per year. This is a small increase in overall
productivity for the industry as a whole over the period of the study. It should be noted
that this is an average rate of change over the study period while in reality technological

change tends to be “lumpy”. The goal of including a time trend in this study is to test for

73

the existence of technological change and its effect on production costs. Under these
circumstances, the constant rate of change assumption is not as limiting (Lopez 1980).
Most other studies report improvement in productivity to varying degrees.
Martinello (1987) calculated annual total factor productivity improvement of 0.903% for
British Columbia (BC) Coast sawmills but only 0.072% for BC Interior sawmills for the
period 1963-1979. Nautiyal and Singh (1985) found no evidence of technological change
in the Canadian lumber industry as a whole. In a study of individual softwood lumber
producing regions in Canada from 1968-1984, Meil and Nautiyal (1988) found
improvements in total factor productivity from 0.7% to 1.0% per year for BC Coast
sawmills and from 0.2% to 0.4% in the BC Interior depending on the mill-size class. In
Ontario, they found improvements of 0.6% to 1.0%. Québec also demonstrated
improvements of 0.8% to 1.0% except in the largest mill-size category where there was
an annual reduction of productivity of 0.1% per year. For British Columbia, the
productivity improvements generally increased as mill-size class increased. There was no

such correspondence for Ontario and Quebec.

3.6.2 Technical Change Bias

In addition to overall change in productivity, the bias of that change can be
calculated as well and is more interesting in terms of the policy implications of
technological change. Bias of technological change is calculated as in equation (11).

The bias of technological change for each of the inputs as well as annual total
factor productivity change show that technology has been improving over the study
period (Table 3-4). The bias of technical change is interpreted as the annual percentage

change in the cost share of the particular input.

74

Bias of Technical Total Factor Productivity
Chang: (%lyr) Change (%lyr)
Labor -0.62 0.80

Material 0.31

81813-7-T888h8ichhan'

      
   
 

  

 

 
   
 

 

 

 

 

 

Ca ital 0.30

  

    

 

The bias of the technical change in the sawmill industry as calculated here
appears to be labor-saving and capital and materials-using. These results show that the
cost share for material was increasing by 0.31%lyear over the study period and for capital
the increase is 0.30%lyear. The cost share for labor is decreasing by 0.62%/year which is
lower than most other studies. These values are quite low but nevertheless concur with
previous information on the relatively low lumber recovery factor (LRF) in hardwood
regions, the North Central region in particular, and the findings of other authors
specifically modeling regions where hardwoods predominate. In the Appalachian region
Abt (1987) found technical change to be labor-saving and material-using with values of -
15%/year for labor and 0.8%/year for materials. Meil and Nautiyal (1988) had similar
results for their study of the softwood producing regions of Canada. They found that for
the smallest mill size class in Ontario, the bias of technological change for materials was
0.8%/year and -1.7%/year. for labor. That is, the cost share for these inputs was changing
by that amount each year on average. Most other studies found that the bias in
technological change was labor-saving and capital-using but it was also usually material-
saving.

Meil and N auti yal (1988) state that an alternative way to interpret factor-using
technical change bias is that technical progress decreases with factor price increases.

Therefore, in the Lake States, where the technical change bias is materials and capital

75

using, industry and policymakers should pay attention to factors affecting the price of
these inputs, particularly materials, if the sector is to maintain or improve productivity
and competitiveness in the future.

The technological change bias in the Lake States is labor-saving but not as much
as was found in other studies. In the studies that disaggregate mills into two or more mill-
size classes, the general finding was that labor was more productive in larger mills. The
model selection process used here was unable to reject the assumption of constant returns
to scale but nevertheless it behooves mill managers to explore possibilities for improved
labor productivity via scale expansion or other means.

The results for technical change bias for materials may indicate a change in the
composition of the timber resource over time that is leading to greater wood use to
produce the same amount of lumber. Perhaps the logs being milled are becoming smaller,
or the species mix is becoming less favorable over time. This is a point that requires
further research to clarify. Martinello (1987) cites decreasing size and quality of timber in
British Columbia as the reason for his results that showed technological change being
capital-using, labor-saving and (approximately) material-neutral in Coastal sawmills. The
finding of materials using technological bias is also a concern given the prospect of
reduced timber availability in the future in the Lake States. According to Skog (1997)
computer-aided manufacturing and computer controlled processing are the key to
reducing the effect of timber scarcity. He points out that the technology won’t necessarily
decrease the amount of wood consumed but will increase the proportion of high-grade

material that is recovered and therefore offset the increasing price of sawlogs.

76

3.7 Returns to Scale

The model selection procedure found that the production structure of the sawmill
industry of the Lake States could be estimated with a model that imposes constant returns
to scale. This result concurs with the findings of studies for other regions of North
America, but of particular note is the concurrence with the results of other studies of the
hardwood lumber industry.

In the Lake States, lumber output per mil] has generally increased over the study
period but there have been several declines and increases in average output over that
period (Figure 3-1).The chart of output per mill may distort the truth to the extent that the
reconciliation of the lumber production fr gures reported in MA24T with the Census of
Manufactures and the state sawmill directories resulted in upwards revisions to the
production numbers starting in 1993. In that case, the output per mil] before 1993 was
understated relative to the years after 1993. Also, as stated earlier, there were large new
capital expenditures in the 19908 in the Lake States for several large sawmills and this
will increase the average output even though most mills may not be producing more

lumber.

77

350

 

 

 

 

 

 

 

 

 

300 \
g 250 4
E W
- 200
E V +establishments MI
-I— I'h t IAN

3 ‘>>‘ eflabm mens
g 150 ' + Establishments WI
E
a
2 100 _..___ ,_ _—

50

 

 

 

 

j ‘Y

1960 1965 1970 1975 1980 1985 1990 1995
Your

Figure 3-1. Number of Establishments, SIC 242 (1963-1992)
Source: Census of Manufactures (various years)

Given the number of establishments in each state over the study period (Figure 3-
1) and the lumber output per mill (Figure 3-2), it is clear that the sawmill industry of the
Lake States has not had the kind of reductions of mill numbers and increase in average
output that other regions of the United States, Canada and other countries have had. For
example, in Australia, numbers of sawmills decreased by two thirds between 1951 and
the mid 19808 while output per mill increased almost four times over that same time
period (Bi gsby 1994). In Washington, the number of establishments decreased by 41%
from 1963-1992 and output per mill increased 108%. Also, in West Virginia, the number
of establishments decreased 50% over the same time period and output per mil] increased
by 79%. In the Lake States, the number of establishments decreased by 23% and output

per mil] increased by 52% (Census of Manufactures, various years).

78

2.500

2,000

1.500 14 \ A;
+ output per mill MI
+ output per mill MN
+ output per mill WI

1.000 . . \

500

 

 

 

 

 

 

 

Lumber Output (MBF)

 

 

 

 

1960 1965 1 970 1975 1980 1 985 1990 1 995
Your

Figure 3-2. Lumber Output per mill. MI, MN and WI, 19625-1992. (MBF/mill)
Source: Census of Manufactures and MA24T, Lumber Production and Mill Stocks
(various years)

Nautiyal and Singh (1985) reported constant returns to scale for their models of
the lumber industry in Canada. Meil and Nautiyal (1988) reported constant returns to
scale for some of the softwood lumber regions of Canada but not all. Martinello (1987)
also calculated constant returns to scale for the lumber industry of the BC Interior but the
Coastal region exhibited increasing returns to scale. Puttock and Prescott (1997) found
constant returns to scale for the southern Ontario hardwood lumber industry for mills
producing less than 1600 MBF of lumber per year but increasing returns to scale for mills
producing more than that. Banskota et al. (1985) found a similar result in a study of the
Alberta sawmill industry. No mills with production less than 850 MBF had significant

scale economies while almost all mills with production greater than 850 MBF exhibited

increasing returns to scale. In the only study of the sawmill industry in a hardwood region

79

in the United States, Abt (1987) found decreasing returns to scale for the period 1963—
1978 for the Appalachian region comprising Kentucky, Pennsylvania and West Virginia.

The average annual output of sawmills in the Lake States is 1600 MBF per mill.
This figure is less than the output level required to exhibit increasing returns to scale in
Puttock and Prescott’s model of the hardwood industry in Ontario but almost double that
of the model of the Alberta lumber industry by Banskota et al. The Lake States lumber
industry is primarily based on hardwoods whereas that of Alberta is primarily softwood-
based. The softwood lumber industry is characterized in comparison to the hardwood
industry as having larger, more capital intensive mills in general. Nevertheless, the
smaller mill size exhibiting increasing returns to scale in Alberta as opposed to southern
Ontario may indicate the relative ease with which softwood logs can be handled and
milled compared to hardwood logs.

The model selection process determined that the hypothesis of constant returns to
scale cannot be rejected at the 1% level. The following analysis demonstrates the method
of determining returns to scale with a restricted variable cost function as used in this
study. The results from Model (1) were used to show how returns to scale may be
calculated.

Recall that returns to scale is calculated as the percentage change in costs given a
percentage change in output as given in equation (12). The derivative of the cost function
in Model (1) with respect to output yields equation (22):

aanC
<3an

 

= flQ + ,BQQ in Q + (-,6MQ - am ) 1n LP+ ,BMQ ln MP+ am In K + £0: (22)

Evaluated at the means of observations and using the parameter values from

Model (1), equation (22) yields a value of 0.93. Therefore, the overall returns to scale

80

estimated by the model is 0.07, or 7%. This means that for a 100% increase in output,
variable costs will increase by only 93%. Therefore, there was a cost saving of 7%. This
is a slightly positive returns to scale indicating that sawmills in the Lake States are on the
declining portion of the average cost curve. This calculation must be interpreted with
caution because the model selection process determined that the industry could be
modeled assuming constant returns to scale and the coefficients on a number of the
variables used to make the calculation are not significant at the 5% level.

Even though constant returns to scale cannot be rejected with this dataset, there
could still be incentives for sawmills to expand based on other inputs not explicitly
modeled in the variable cost function such as managerial skill. Given that the study
period is over thirty years long and the assumed service lives of both machinery and
structures are less than that, there has been opportunity for mills to increase in size
without premature retirement of productive capital. It may be that the periodic recessions
that have hit the industry, particularly in the early 1980s have made risk-averse mill
owners reluctant to expand their operations or buy out competitors despite possible

reductions in average costs.

81

4.0 CONCLUSIONS AND POLICY IMPLICATIONS

This chapter summarizes the main findings of the study and draws conclusions
based on those findings. Some policy implications of the findings are discussed. A brief

discussion of future research to answer questions raised by this research is also included.

4.1 Summary of Results

This study determined estimates of elasticities of substitution, elasticities of
demand, technological change, the bias of technological change and returns to scale for
the sawmill industry of the Lakes States from 1963-1996. Based on the results presented
in Chapter 3, a homothetic, homogenous (constant returns to scale), nonunitary elasticity
of substitution cost function can be used to model the production structure of the
sawmilling industry of the Lake States (Michigan, Minnesota and Wisconsin). This
estimated cost function satisfies all of the properties of a well-behaved cost function and
the results are consistent with economic theory and the estimates found in the literature.

Based on Allen Partial Elasticities of Substitution (AES), labor and materials, and
materials and capital are inelastic substitutes while labor and capital are elastic
complements in the Lake States sawmilling industry. The complementarity between labor
and capital indicates that these factors are employed in fixed proportions. The
substitutability between labor and materials is relatively high in relation to most other
studies, but comparable to studies of hardwood regions in North America.

The Morishima Elasticities of Substitution (MES) indicate that all inputs are
inelastic substitutes. The MES allows for asymmetrical elasticities of substitution

between input pairs and the results demonstrate that changes in the price of capital have

82

relatively little effect on labor and materials use, whereas changes in labor and materials
price have a relatively large effect on the use of capital. The MES between labor and
materials are similar in magnitude to the AES results.

The elasticities of demand show that labor and materials, and materials and
capital are substitutes while labor and capital are complements. All of the own-price
elasticities are negative which is necessary for downward sloping demand curves. All of
the own and cross-price elasticities are inelastic.

There was a small annual decrease in variable costs holding output constant over
the study period. This indicates that total factor productivity was increasing. The results
for bias of technical change indicate that the technological change over the study period
has been materials and capital-using and labor-saving although the labor savings have not
been as dramatic as other regions.

The model selection procedure found that the assumption of constant returns to
scale (homogeneity of degree one in output) could not be rejected at the 1% level and so
all the results are based on that model. This is not uncommon in the literature although
some regions exhibit increasing returns to scale (e. g., BC Coast) while the Appalachian

region exhibited decreasing returns to scale.

4.2 Conclusions and Policy Implications

The results also seem to indicate, and this is corroborated by Abt (1987), that
there are significant differences in the production structure of the sawmill industry
between regions. This is understandable given the differences in the wood resource in the
Pacific Northwest for instance, and the Lake States. The findings of the study show that

there is greater substitutability between labor and materials in the Lake States than in the

83

 

softwood lumber regions. Therefore, policies affecting the sawmill industry should be
tailored to the region they are located. The same policy will affect sawmills differently in
Washington than it will in Michigan. For example, in the Lake States and other hardwood
regions, policies that promote research and development on sawmill technology may help
increase the productivity of the industry more than similar investments in softwood
regions which typically are already more capital intensive than the hardwood industry. In
general, policies that address the weaknesses of the Lake States’ industry with respect to
the sawmill industry in other regions will be more effective in improving its efficiency
than national policies. Naturally, for state governments, the results of this study point to
some weaknesses or peculiarities of the hardwood industry and these findings can be
used to gauge the applicability of policies implemented in other jurisdictions to the Lake
States.

To the extent that decreased harvest levels on public land increases timber prices,
such a policy may actually increase employment given the substitution effect reported in
this study. It is difficult to say to what extent this effect may apply because the results for
the substitution between inputs are contingent on output levels remaining constant. Large
decreases in timber harvests could lead to the shutdown of mills that have less of an
ability to substitute away from wood and consequently have higher costs.

Given that such a large amount of forestland in the Lake States is privately
owned, policies affecting harvest levels on public land are only part of the picture. As
was discussed in Chapter 1, there is concern that harvests from private lands will
decrease as landowners’ preferences shift towards the aesthetic value of standing timber

as opposed to the financial value of harvested timber. In this case, government

84

policymakers have no direct control over harvest patterns and so instruments such as tax
incentives for forest management would be necessary. These types of incentives already
exist to help achieve forest management goals on private land. Using the results of this
study it may be possible to gauge the effects of such policies more accurately.

The finding that labor and capital are complements in the sawmilling process of
the Lake States also differentiates the region from other lumber producing regions of the
United States. Changes in the price of all inputs affects the demand for all other inputs
and so policymakers must be cognizant of this. In the case of labor and capital, the effects
are synergistic. Apart from the direction of demand changes when the price of labor or
capital changes, the magnitude is important. Changes in the price of capital have less of
an effect on the demand for labor than the other way around. Therefore policies affecting
one or other of these two inputs will have a varying degree of effect depending on which
input they apply to. For example, changes in the Federal Reserve prime rate will not
directly affect employment in the sawmill industry as much as changes in payroll taxes
will affect demand for capital.

The results for technological change bias in the Lake States indicate that the
technology change is material-using. This may be the result of a degradation in the size,
quality and/or species composition of the forest resource in the Lake States. If this is the
case, adaptation of the types of computer-aided processing systems common in modern
softwood lumber mills could help overcome negative changes in the quality or
availability of the wood resource.

The technical change was also capital-using and labor-saving which was a

common finding in the literature for the sawmill sector. The labor savings are not as high

85

as in other regions and this could limit the competitiveness of Lake States sawmilling in
the future. Also, although this model does not consider quality of labor, the capital-using
labor-saving technological change bias tends to leave the less-skilled workers behind.
Problems like this are not as grave in the Lake States as they might be in a region more
dominated by the forest industry where there are fewer alternative employment
opportunities.

The industry exhibits constant returns to scale although the exact reason for this is
unclear. It may be the result of uncertain and unstable market conditions and the ability of
small mills to use fully depreciated capital equipment. This finding makes sense in light
of the relatively small change in mill number and output per mil] compared to other
states. Until the reasons for the lack of improvement in output per mill and technological
progress compared to other regions are determined, it does not make sense to employ
policies that encourage larger mills. On the other hand, if there were diseconomies of

scale, then larger mills would improve the overall efficiency of the industry.

4.3 Further Research

The above conclusions indicate that further research into the reasons for the
limited technological change and lack of economies of scale would be beneficial for
policymakers to determine ways to maintain the competitiveness of the sawmill industry
in the Lake States.

It would be beneficial to model the hardwood and softwood industries of the Lake
States separately as it seems clear from the literature that they exhibit differing

production structures. In the Lake States, hardwoods make up over 75% of the volume

86

harvested so the results are biased in favor of hardwood sawmills but it would be
interesting to compare the two industries within the same region.

This model used lumber as the only output of the sawmilling sector. Due to lack
of data, other outputs such as wood chips could not be included. Woodchips are an
increasingly important joint product for sawmills and in the United States, the large
harvest reductions on National Forests, particularly in the West, may increase the

importance of wood chips even for hardwood sawmills.

87

LITERATURE CITED

ABT, RC. 1984. Regional production structure and factor demand in the US lumber
industry. Unpublished Ph.D. Dissertation. Department of Wildland Resource
Science. University of California, Berkeley. 98pp.

ABT, RC. 1987. An analysis of regional factor demand in the US. lumber industry.
Forest Sci. 33:164-173.

ALLEN, R.G.D., and J .R. HICKS. 1934. A reconsideration of the theory of value, pt. II.
Econornica. February-May 1934, 1, N .S. p.196—219.

ANDRADE, LC. 2000. Production technology in the pulp and paper industry in the
European Union: factor substitution, economies of scale, and technological
change. J. For. Econ. 6:1:23-40.

BAARDSEN, S. 2000. An econometric analysis of Norwegian sawmilling 1974-1991
based on mill-level data. Forest Science 46:537-547.

BANSKOTA, K., W. PHILLIPS, and T. WILLIAMSON. 1985. Factor substitution and
economies of scale in the Alberta sawmill industry. Can. J. For. Res. 15: 1025-
1030.

BANSKOTA, K. 1984. An economic analysis of the production structure of the
sawmilling industry in Alberta. Unpublished Ph.D. dissertation, University of
Alberta, Edmonton, Alta.

BARE, BB, and R.L. SMITH. 1999. Estimating stumpage values from transaction
evidence using multiple regression. Journal of Forestry. 99:32-39.

BARLOWE, R. 1986. Land resource economics: the econorrrics of real estate 4th edition.
Prentice-Hall, Englewood Cliffs, NJ. 559 p.

BEA'ITIE, B. R., and C. R. TAYLOR. 1985. The economics of production. John Wiley
and Sons, New York. 258 pp.

BERNDT, E.R., and DO. WOOD. 1975. Technology, prices and the derived demand for
energy. Rev. Econ. Stat. 57(3):259-268.

BIGSBY, HR. 1994. Production structure and the Australian sawmilling industry.
Australian Journal of Agricultural Economics. 38(3):271-288.

BINSWANGER, HP. 1974. The measurement of technical change biases with many
factors of production. American Economic Review. 64:964-976.

88

BLACKORBY, C., and RR. RUSSELL. 1989. Will the real elasticity of substitution
please stand up?: A comparison of the Allen/Uzawa and Morishima elasticities.
Am. Econ. Rev. 79(4):882—888.

BLYTH, J .E., WHIPPLE, J .W., MACE, T., and SMITH, W.B. 1985. Wisconsin timber
industry--an assessment of timber output trends. Resource Bulletin NC-90. St.
Paul, MN: US. Dept. of Agriculture, Forest Service, North Central Forest
Experiment Station.

BLYTH, J .E., WEATHERSPOON, AK, and SMITH, W.B. 1988. Michigan timber
industry--an assessment of timber product output and use. Resource Bulletin NC-

109. St. Paul, MN: US. Dept. of Agriculture, Forest Service, North Central Forest
Experiment Station.

BLYTH, J .E., WHIPPLE, J.W., and SMITH, W.B. 1989. Wisconsin timber industry--an
assessment of timber output trends. Resource Bulletin NC-112. St. Paul, MN:
US. Dept. of Agriculture, Forest Service, North Central Forest Experiment
Station.

BOISVERT, RN. 1982. The translog production function: its properties, its several
interpretations and estimation problems. Dept of Agricultural Economics. Cornell
University, Ithaca, New York. 35p.

BUREAU OF LABOR STATISTICS. 1997. BLS Handbook of Methods. Bureau of
Labor Statistics. Washington, DC.
http://www.bls.gov/opub/hom/homtoc_pdf.htm Accessed 06/21/03.

BUREAU OF LABOR STATISTICS. 2003. Office of Productivity and Technology.

Data from Industry Productivity Database.
ftpzllftp.bls.gov/pub/special.requests/opt/dipts/oaeh3drt.txt Accessed 07/03/03.

CAMPBELL, HF, and JENNINGS, S.M. 1990. Cost, technology and input demand in
the Tasmanian sawmilling industry. Australian Economic Papers 29:(55):273-
282.

CANADIAN FOREST SERVICE. 1995. Criteria and indicators for the conservation and

sustainable management of temperate and boreal forests : the Montreal process.
Canadian Forest Service. Hull, Quebec. 27p.

CAVES, D.W., L.R. CHRISTENSEN, and J .A. SWANSON. 1981. Productivity growth,
scale economies, and capacity utilization in US. railroads, 1955-1974. Am. Econ.
Rev. 71:994-1002.

CENSUS BUREAU, ECONOMICS AND STATISTICS ADMINISTRATION. 1995.
Current Industrial Reports: Lumber Production and Mill Stocks, MA24T 1994.
Washington, DC.

89

CHRISTENSEN, L.R., and D.W. JORGENSEN. 1969. The measure of US real capital
input, 1929-1967. Rev. Inc. Wealth 15:293-320.

CHRISTENSEN, L.R., and W.H. GREENE. 1976. Economics of scale in US electric
power generation. J. Polit. Econ. 84:655-676.

DE BORGER, B., and J. BUONGIORNO. 1985. Productivity growth in the paper and
paperboard industries: a variable cost function approach. Can. J. For. Res.
15:1013-1020.

DENNY, M., and D MAY. (1977). The existence of real value-added function in the
Canadian manufacturing sector. Journal of Econometrics. 5:55-69.

DIEWERT, W.B. 1971. An application of the Shephard duality theory: a generalized
Leontief production function. J. Polit. Econ. 79:481-507.

DUKE, J ., and C. HUFFSTUTLER. 1977. Productivity in sawmills increases as labor
input declines substantially. Mon. Labor Rev. 100:33-37.

EXTENSION FORESTRY OFFICE, COLLEGE OF AGRICULTURE, UNIVERSITY
OF WISCONSIN. Various Years. The Wisconsin forest products price review.
Cooperative Extension Service, University of Wisconsin-Extension.

GREENE, W.H. 1990. Econometric analysis. Macmillan, New York.

GRIFFIN, R.C., J .M. MONTGOMERY, and ME. RISTER. 1987. Selecting functional
form in production function analysis. Western Journal of Agricultural Economics
12(2): 216-227.

GUJARATI, D.N. 1995. Basic Econometrics. McGraw-Hill. New York. 838p.

HACKETT, R.L. and DAHLMAN, RA. 1993. Minnesota timber industry--an
assessment of timber product output and use, 1990. Resource Bulletin NC-l43.
St. Paul, MN: US. Dept. of Agriculture, Forest Service, North Central Forest
Experiment Station.

HACKETT, R.L. and PILON, J. 1993. Michigan timber industry--an assessment of
timber product output and use, 1990. Resource Bulletin NC-l44. St. Paul, MN:
US. Dept. of Agriculture, Forest Service, North Central Forest Experiment
Station.

HACKETT, R.L., and WHIPPLE, J .W. 1993. Wisconsin timber industry--an assessment
of timber product output and use, 1990. Resource Bulletin NC-l47. St. Paul, MN:
US. Dept. of Agriculture, Forest Service, North Central Forest Experiment
Station.

HACKETI‘, R.L., and WHIPPLE, J .W. 1995. Wisconsin timber industry--an assessment
of timber product output and use. Resource Bulletin NC-164. St. Paul, MN: US.
Dept. of Agriculture, Forest Service, North Central Forest Experiment Station.

90

HACKE'I'I‘, R.L. and DAHLMAN, RA. 1997. Minnesota timber industry--an
assessment of timber product output and use, 1992. Resource Bulletin NC-186.

St. Paul, MN: US. Dept. of Agriculture, Forest Service, North Central Forest
Experiment Station.

HACKE’IT, R.L., and WHIPPLE, J .W. 1997 . Wisconsin timber industry--an assessment
of timber product output and use, 1994. Resource Bulletin NC-187. St. Paul, MN:
US. Dept. of Agriculture, Forest Service, North Central Forest Experiment
Station.

HACKE'IT, R.L. and PILON, J. 1997. Michigan timber industry--an assessment of
timber product output and use, 1994. Resource Bulletin NC-189. St. Paul, MN:
US. Dept. of Agriculture, Forest Service, North Central Forest Experiment
Station.

HAYNES, R.W. 1990. An analysis of the timber situation in the United States: 1989-
2040. USDA Forest Service. General Technical Report RM-199.

INCE, P. 2000. Industrial wood productivity in the United States, 1900-1998. Res. Note
FPL—RN-0272. Madison, WI: US. Department of Agriculture, Forest Service,
Forest Products Laboratory. 14 p.

KANT, S., and J.C. NAUTIYAL. 1997. Production structure, factor substitution,
technical change, and total factor productivity in the Canadian logging industry.
Can J. For. Res. 27: 701-710

KENDRICK, J.W. 1961. Productivity trends in the United States. Princeton Univ Press,
Princeton. 630 p.

KENNEDY, P. 1992. A guide to econometrics. Third edition. MIT Press. Cambridge,
MA. 410p.

LAU, L.J. 1978. Applications of profit functions. In Production economics: A dual
approach to theory and applications, Vol. I, Fuss and McFadden (eds.). North-
Holland. 469 p.

LOPEZ, RE. 1980. The structure of production and the derived demand for inputs in
Canadian Agriculture. AM. J. Agric. Econ. 42:38-45.

MARTINELLO, F. 1985 Factor substitution, technical change, and returns to scale in
Canadian forest industries. Can. J. for. Res. 15: 1116-1124.

MARTINELLO, F. 1987. Substitution, technical change and returns to scale in British
Columbian wood products industries. Applied Economic. 19:483-496.

MAY, D.M. and PILON, J. 1995. Michigan timber industry--an assessment of timber
product output and use, 1992. Resource Bulletin NC-162. St. Paul, MN: US.
Dept. of Agriculture, Forest Service, North Central Forest Experiment Station

91

MCGUIRE, M., J. STEVENS, and K. POTTER-WITTER. 1999. Assessing scarcity of
the North Central veneer log resource. North. J. Appl. For. 16(3): 160-166.

MEIL, J .K., and J .C. NAUTIYAL. 1988. An intraregional economic analysis of
production structure and factor demand in major Canadian softwood lumber
producing regions. Can. J. For. Res. 18:1036-1048.

MICHIGAN DEPARTMENT OF NATURAL RESOURCES, FOREST
MANAGEMENT DIVISION. 2000a. Sawlog stumpage appraisal factors and
definitions. Information Circular 4207. Michigan Department of Natural
Resources, Forest Management Division.

MICHIGAN DEPARTMENT OF NATURAL RESOURCES, FOREST
MANAGEMENT DIVISION. 2000b. Procedure for presale stumpage appraisal.
Information Circular 4209. Michigan Department of Natural Resources, Forest
Management Division.

MINNESOTA DEPARTMENT OF NATURAL RESOURCES. Various Years.
Minnesota forest products price report. Division of Forestry, Minnesota
Department of Natural Resources.

MINNESOTA DEPARTMENT OF NATURAL RESOURCES, FORESTRY. 2000.
Summary of forest products permit provisions. Minnesota Department of Natural
Resources, Forestry.

MORISHIMA, M. 1967. A few suggestions on the theory of elasticity. (in Japanese)
Keizai Hyoron (Economic Review). 16:144-150.

NAUTIYAL. J .C., and BK. SINGH. 1985. Production structure and derived demand for
factor inputs in the Canadian lumber industry. Forest. Sci. 31 :42871-881.

PUTTOCK, G.D., and D.M. PRESCOTT. 1992. Factor substitution and economies of
scale in the southern Ontario hardwood sawmilling industry. Can. J. For. Res.
22:1139-1146.

SHEPHARD, R.W. 1953. Cost and production functions. Princeton University Press.
Princeton, N .J .

SINGH, B.K., and J .C. NAUTIYAL. 1985. A comparison of observed and long-run
productivity of and demand for inputs in the Canadian lumber industry. Can. J. of
For. Res. 16:443-455.

SKOG, K. 1997. Opportunities to change timber demand in the Lake States through
altered timber utilization. In Lake States regional forest resources assessment:
technical papers, Vasievich and Webster (eds.). General Technical Report NC-
189. St. Paul, MN: US. Department of Agriculture, Forest Service, North Central
Forest Experiment Station. 314 p.

92

SMITH, W. B., WEATHERSPOON, AK. and PILON, J. 1990. Michigan timber
industry--an assessment of timber product output and use, 1988. Resource
Bulletin NC-121. St. Paul, MN: US. Dept. of Agriculture, Forest Service, North
Central Forest Experiment Station.

SMITH, W.B., and WHIPPLE, J .W. 1990. Wisconsin timber industry--an assessment of
timber product output and use, 1988. Resource Bulletin NC-124. St. Paul, MN:
US. Dept. of Agriculture, Forest Service, North Central Forest Experiment
Station.

SMITH, W.B. and DAHLMAN, R. 1991. Minnesota timber industry--an assessment of
timber product output and use, 1988. Resource Bulletin NC-l27. St. Paul, MN:
US. Dept. of Agriculture, Forest Service, NOrth Central Forest Experiment
Station.

SMITH, P., and LA. MUNN. 1998. Regional cost function analysis of the logging
industry in the Pacific Northwest and Southeast. Forest Sci. 44:4:517-525.

STEARN S, F.W. 1997. History of the Lake States forests: natural and human impacts. In
Lake States regional forest resources assessment: technical papers, Vasievich and
Webster (eds.). General Technical Report NC-189. St. Paul, MN: US.
Department of Agriculture, Forest Service, North Central Forest Experiment
Station. 314 p.

STIER, J .C. 1980. Estimating the production technology in the US. forest products
industries. Forest Sci. 26(3):471-482.

STIER, J .C. 1985. Implications of factor substitution, economies of scale, and
technological change for the cost of production in the United States pulp and
paper industry. Forest Sci. 31(4):803-812.

STONE, RN. 1997 Great Lakes forest trends, 1952-1992. In Lake States regional forest

resources assessment: technical papers, Vasievich and Webster (eds.). General
Technical Report NC-189. St. Paul, MN: US. Department of Agriculture, Forest
Service, North Central Forest Experiment Station. 314 p.

ULRICH, A. 1987. US. timber production, trade, consumption, and price statistics,
1950-85. US. Dept. of Agriculture, Forest Service, Washington, DC.

USDA For. Serv. 1978. The principal laws relating to Forest Service Activities. Agric.
Handbook NO. 453. GPO, Washington, DC. 359 p.

USDA For. Serv. 1982. Forest Service appraisal handbook FSH-2402, Region 2 (Pacific
Northwest Region). GPO, Washington, DC. (loose-leaf).

USDA For. Serv. 1997. Spreadsheet tables for forest resources of the United States. FIA
website: http://ncr52.fs.fed.us/4801/fiadb/rpartabler/2002 {pa draft tables.htm
accessed 20/08/03.

93

UZAWA, H. 1962. Production functions with constant Elasticities of substitution.
Review Economic Studies 29:291-299.

VARIAN, HR. 1992. Microeconomic analysis 3rd edition. W.W. Norton & Company.
New York and London. 506 p.

VASIEVICH, J .M., K. POTTER-WITTER, and LA. LEEFERS. 1997. Timber supply
and market trends in the Lake States. In Lake States regional forest resources
assessment: technical papers, Vasievich and Webster (eds.). General Technical
Report NC-189. St. Paul, MN: US. Department of Agriculture, Forest Service,
North Central Forest Experiment Station. 314 p.

WASHBURN, CL, and CS. BINKLEY. 1990. InfOrmational efficiency of markets for
stumpage. American Journal of Agricultural Economics. 72:394-405.

WILLIAMS, J .W., P. DUINKER, and C. WEDELES. 1998. Assessing progress in
sustainable forest management: proposed criteria and indicators for the upper
Great Lakes region. Great Lakes Forest Alliance. Hayward, WI.

WISCONSIN DEPARTMENT OF NATURAL RESOURCES. 1999. NR 46.30
Stumpage rates-2001. Wisconsin Department of Natural Resources.

WOOLDRIDGE, J .M. 2000. Introductory Econometrics: A Modern Approach. South-
Westem College Publishing. 824p.

94

APPENDIX A: Model Data

95

 

Table A-1. Summary of Data Calculations

 

 

 

 

 

 

 

 

 

Variable SourceI Units Calculation
Labor CoM, ASM hours Raw data
Quantity
Sawlog Forest Service TPO Millions Converted to millions of board feet
Quantity reports(see Table 5 of cubic using a conversion factor of 158
Appendix A) feet cubic feet per thousand board feet
International scale
Labor Price CoM ASM $lhour Total production labor hours divided
by production labor cost
Sawlog Price CoM, ASM, Timber $lthousan Prices for years in which Forest
Mart North, state d board Service Timber Product Output data
Departments of feet were available were calculated by
Natural Resources dividing materials cost (reported in
stumpage data, CoM and ASM) by the volume of
Forest Service sawlog receipts at sawmills as
stumpage data, reported in the publications listed at
Minnesota Forest the bottom of Table 5 in Appendix A.
Products Price For other years, sawlog price was
Report, Wisconsin calculated from prices reported by the
County stumpage sources listed in column two. The
data, the Wisconsin price used in the model was a
Forest Products weighted average price based on the
Price Review and volume of each species harvested in
US. timber that year. For years in which harvest
production, trade, data are not available, it was assumed
consumption, and that the proportion of each species
price statistics, volume in the total harvest was the
1950-85 by Alice H. same as the closest year for which
Ulrich. harvest data were available.
Capital Stock CoM and ASM Millions The capital stock series was
of dollars calculated as described in Section
2.4.4.
Capital Price $l$ The capital price was calculated as
Capital described in Section 2.4.4.
price was
a ratio of
the gross
quasirent
to capital
stock
User cost of Millions The user cost of capital was
Capital of dollars calculated as described in Section

 

 

 

2.4.4.

 

ICoM is the Census of Manufactures; ASM is Annual Survey of Manufactures;

96

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Re mod 3.: mmSmm Nms _m.vw 2 .m2 3%
1mm $6 5.9 ENS“ S .m vcsm 0563 .32
Em cod 3.2 3+3 Saw 8.3 3.2: 32
Nvm 36 v2: Envo— wa mi; wfiwn Goa
mmm wed ad— 2 62 Saw mmhv 3...? 33
E m 86 and 3.3: 2; mg? 9 .8— wwi
3m No.0 3.0 362 am: adv wade 59
«mm 36 ohm ocsN— mud GNV omda mwafi
3N wmd m_.w Nwd: mm: amen 3.2. mm?
mom de mwd nmwofi 92m 3 dv mmNn MKS
Omm mmd wow v33 $5 02% 3.8 :3
Em». and v3. $58 $1. 00.: $2: 39
Em _md woe 3:5 36 3.8 993 m3“
Em 86 8.5 5.3 ewe 3.3 mode :2
.3 ate mww mmén One 3.8 8.2: m8—
owm med 5.2 emf» mow ovwm Eda N3—
mov wed 8.2 33K mm.m 3.9m wwfl. :3
now $6 mm.w 3.8 mw.m Qumm 8.2 93.
mov ovd wad Nthm ohm. Sawm “NE $2
mom 36 mw.w 9 Sn $.m mm. _ m 3.9. $3
own 93 5.x. mmmm mm.m She mafia coa—
onm mvd ww.w :Lm cod 5.? 5.3. 39
Rm 33 em.» Sim mw.m wmflm ciao 33
Ohm ovd wS. 84m mod hmdm code 83
Qm—Eé 8E Eta Egan—:85 GEE—=5 25:55 GEE—=5 an;
:eugueum heap—:1— :Emao 85m $55 huge 32.. MAS—Bum .538 he «moo new: .80 gene‘— ameU worsam

 

 

£23.. :2 5 2a 8...“... =< 2:23:88 5 swag: .8 as. .252 .~.< 2.3.

97

“1H... FIFE

 

 

 

wafl
v8 25 mwd 5. SN mew 3.00 3&2 32
NS 00.0 3.3 DWNVN and Nwdo mp. _2 voo—

 

 

 

 

 

 

 

 

..eo=:_.:eu N.< 939—.

98

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

2m med 3.: swam eN.w 0002 gem: e00:

01m ee 0 50 : 5.: _m 0N0 v0.3. mm.:0~ moo:

Em we 0 mm 0: R 3N Nve mm 00 mm mm: v00:

mom med : 0: 3:2 Nw.m 3 en E em mam—

mo me 0 3.0: N00: mmé :0 mm mm mm N00:

3 0e 0 mm 0: woe: mm...q 0e 0m 05 um 30:

00: mm 0 we a flaw: mmé N0 em mm an 000:

02 he 0 mm 0: 00 we: v0.0V 8 em oe _m 93:

we: em 0 v0 w 8» of Sam M: vm ween mm»:

mm: we 0 mm 0 mm 3: mm.m mm mm mo 3 >00:

mm: Cu 0 mm N. e0 mm: e0.m Q. : hm.0m Nwfl

mom 0v 0 mm m mm mm em: we a: N_ ev 2.9

we: ~00 2.: 3.? 0: wZN vase N3—

03 mmd e_.w 3.0m 5.0 3.: e3: sea—

0: NN.0 55w moem 3.0 N00: 8.: meo—

N: 0N0 _m.m 3.mm 3.0 eve me.:m we:

mm: 3.0 hme w0.wm 000 $0 3.: meme:
Pam—220 8th 5:0 3555535 AES—=50 AES—.50 Amp—2:05 39>

cozy—.095 :3an 85— «we?» ram—>5 3:0 weesum _SES “web .50“.— .80
.508...— 06 38 ..8: “23am
due—.3. e3: 5 8a mun—.mp0 =< $509.53.. 50 582.52 .50 52. .252 .m-< 935,—.

99

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

:e 2.0 mmd: mwdvm eve: 0md: Eyewm edd—
mme Ed 2d— mwdmm 3.: mod: 0.3mm mod:
eve 05d wmd: m2? 2 .3 30.8: vamm woo:
mme 05d evd_ ehdmm mw.: mmdw emwd— mod:
mom med N: d: 0v.ewm exam: 5.3 Samoa mad:
Ndm ded dad 0e.wwm 3:: made end: 32
mam med 3d 0wddm mew: 5.2. 3.3: 09:
E m wed 0ed mfiedm mme: e52. 3.0mm dwa—
Sm wed 3.0 :v. : mm 0m..: 00am Sewn $0.
a? 5d Nod: wedmm we.3 3.: Knew: go:
edm med de fins: 3.: emdv wfima mwo:
dwm med dew e: .mi mmdm mmev film mwd:
Sm med wad dado: 3.: 3.3 wed: wha—
vov med 0nd N53 3e mode 3.3 2.0:
mg Ned ES 3.: 2 .m nmdm 0e.vw e8:
0mm _ed med dedn new emwv v0.2. m3:
hem :ed wmd E .3. $6 NW? 2.4.0 3.0:
Km ded vow mnde mm.m om: 00.va m3—
Ndm 0ed and: 0w.wm ddé vedv nmdh m3:
ewm wmd 00d 00.ev _0.v 36m _e.mm bed:
mam emd 0N8 00M...V med whdm :ev wed:
emm end N05 2.? mmd v0.1.V Dem med:
Pam—220 3:0 Eta 3:222:85 GEE—E0 95:55 AES—__Ed 23>
552.095 1996 8am 905$ “3:5 92.:— meEam .538 :80 .50“.— :80
.508...— ._e as hum: 02.55

 

 

 

 

 

 

 

 

dun—.00 e03 E a...“ mouawc =< 3:303:30 NNV 53°35» .8.— Sad .25: .v.< v.05.

 

Table A-5. Sawlo

Recei ts b Sawmills in the Lake States (million cubic feet)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Year Miclgan Minnesota Wisconsin

1963 NA NA NA
1964 NA NA NA
1965 57.4 NA NA
1966 NA NA NA
1967 NA NA 47.8
1968 NA NA NA
1969 62.3 NA NA
1970 NA NA NA
1971 NA NA NA
1972 64 NA NA
1973 NA 30.9 68
1974 NA NA NA
1975 NA 30.9 NA
1976 NA 72.7 NA
1977 78.7 NA NA
1978 NA NA NA
1979 NA NA NA
1980 NA NA NA
1981 NA NA 94.4
1982 NA NA NA
1983 NA NA NA
1984 83.2 NA NA
1985 NA NA NA
1986 NA NA 93.2
1987 NA NA NA
1988 98.3 55.7 93.4
1989 NA NA NA
1990 107.4 40.7 97.8
1991 NA NA NA
1992 100.1 52.3 105.7
1993 NA NA NA
1994 99.4 NA 1 17.4
1995 NA NA NA
1996 93.7 NA NA

 

 

 

NOTE: Michigan data are from US. Forest Service publications NC-109, NC-121, NC-
144, NC-162 and NC-189. Minnesota data are from US. Forest Service publications NC-
127, NC-l43 and NC-186. Wisconsin data are from US. Forest Service publications NC-
90, NC-112, NC-124, NC-l47, NC-l64 and NC-187.

101

APPENDIX B: Model Output

102

 

Table B-1. Model of one in

TRAN SLOG
Full Maximum

 

1
observations:

Likelihood
residual

l

+C(4)*T
.5*((-C(12)—C(13))*LNLP"2+(-C(12)-
-C(l3)—C(23))*LNKP"2+C(55)*LNPROD’\2
2*C(12)*LNLP*LNSLP+2*C(13)*LNLP*LNKP+
-C(25)-C(35))*LNLP*LNPROD
—C(24)-C(34))*LNLP*T+C(25)*LNSLP*LNPROD
)*LNSLP*T+C(35)*LNKP*LNPROD+C(34)*LNKP*T

Mean var .9599]
SD. var

of S um
Watson 1.732487

103

Table B-1 continued,

 

‘ I uation: LCSHR=(l-C(2)-C(3))+(-C(12)-C(13))*LNLP+
(12)*LNSLP+C( l3)*LNKP+(-C(25)-C(35))*LNPROD+(-

(24)-C(34))*T

 

_ Observations: 66

 

0.336903 I

 

 

 

 

I’ -scLuared 0.459702 Mean dependent var
‘ djusted R- H0.394494 S.D. dependent var 0.061467
1 t $12113d 1
.E. of regression 0.047830 Sum squared resid 0.13268 0 ‘
ID urbin-Watson 1.192809 7
L s tat

 

 

 

”I uation: SLCSHR=C(2)+(-C(12)-
(23))*LNSLP+C(12)*LNLP+C(23)
*LNKP+C(25)*LNPROD+C(24)*(T)

 

‘ O bservations: 66

 

 

 

 

 

'I' -squared 0.363991 Mean dependent var I0.620487 '
, . djusted R- 0.322285 S.D. dependent var 10.06106
1 quared

.E. of regression 0.050273 Sum squared resid 0.15417
II urbin-Watson 1.295637
. tat

 

 

104

 

Table B-2. Model (2) Homogeneous of degree one in input prices; Constant returns

to scale
CRS
Method: Maximum
1

observations:

otal observations 198
Error

1

1

2.49841 1 1.035080

11

1

1 176
1.094570

1 1 17
131813

13672 2.853637

LNVC=C(30)+(l-C(2)-

.5*((-C(12)—C(l3))*LNLP"2+
-C(12)-C(23))*LNSLP"2+(-C(l3)-C(23))*LNKP"2+C(44)*T"2
2*C(12)*I_.NLP*LNSLP+2*C(13)*LNLP*LNKP+2*C(23)*LN
-C(24)-C(34))*LNLP*T+C(24)*LNSLP*T

+

66
1292 Mean var
. dependent var

1 Sum resid
Watson 1.597738

l-C(2)-C(3))+(-C( 13))*LNLP+

421001 Mean

 

105

 

 

 

 

Table B-2 continued,
‘ djusted R- 0.372751 S.D. dependent var 0.061467 1
1 quared ,1
.E. of regression 0.048681 Sum squared resid 0.142190 .7
ID urbin-Watson 1.122292

1 \ tat

 

 

 

I a nation: SLCSHR=C(2)+(-C(12)-C(23))*LNSLP+
(12)*LNLP+C(23)*LNKP+C(24)*(T)

 

O bservations: 66

i
i
J

 

 

 

 

 

,. -squared [0.335968 Mean dependent var 10.620487
, . djusted R- I0.303838 S.D. dependent var 10.061068
quared '
‘ .E. of regression 0.050953 Sum squared resid 0.160965 1
3 II urbin-Watson 1.216725 1

. tat

 

 

106

i

.wz-t

 

‘ ‘_.

Table B-3. Model (3) Homogeneous of degree one in input prices; Constant elasticity
of substitution

UNIELASTICITY
Method: Full Information Maximum Likelihood

1 66
observations:
otal observations 198
Error

1.308943 141
18127
45354 1.58155
1 1.424815
1367 15222
13 17006
11845

1.097292
1861

Likelihood
residual

1 +C(2)*LNSLP+
+C(5)*I_.NPROD+.5*(C(55)*LNPROD"2
—C(25)-C(35))*LNLP*LNPROD
-C(24)—C(34))*LNLP*T+C(25)*LNSLP*LNPROD+
+C(35)*LNKP*LNPROD+

66
var

dependent var

of resid
Watson 1.749547

var
. dependent var

 

107

Table B-3 continued,

 

.E. of regression

0.049991

Sum squared resid

[0.14991-

 

‘ ID urbin-Watson

1.173326

 

 

 

 

 

10.279240

Mean dependent var

 

0.256358

S.D. dependent var

 

10.052662

Sum squared resid

 

 

1.188819

 

 

108

 

 

 

 

ystem: CRSUNIELASTICITY

Table 84. Model (4) Homogenous of degree one in input prices; Constant returns to
scale; Constant elasticit of substitution f

 

I stimation Method: Full Information Maximum Likelihood

Marquardt)

 

ample: 1 66

 

1 Included observations: 66

 

otal system (balanced) observations 198

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

I - uation: LNVC=C(30)+(1-C(2)-

1
1
1
Coefficient Std. Error z-Statistic Prob.
(30) 2264.806 2674.889 0.846692 0.3972
(2) 3.570305 1.503421 -2.374787 0.0176
(3) -l.308860 0.925175 4.414717 0.1572
(4) 2.500494 2.746168 0.910539 0.3625
(5) 78.45342 25.78444 3.042666 0.0023 1
(44) 0.001368 0.001410 0.970449 10.3318 1
(24) 0.002112 0.000758 2.785713 0.0053 1
(34) 0.000682 10.000466 1.463747 10.1433
(45) 0.039126 0.012977 3.015044 10.0026 1
3| . g Likelihood 279.4977 1
ID eterrninant residual 4.21E-08 1
, ovariance 1
I

(3))*LNLP+C(2)*LNSLP+C(3)*LNKP+C(4)*T+
(5)*LNPROD+.5*(C(44)*T"2)+(-C(24)-C(34))*LNLP*T+

(24)*LNSLP*T+C(34)*LNKP*T+C(45)*T*LNPROD

 

O bservations: 66

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1 I' -squared 0.869116 Mean dependent var 4.959911
‘ djusted R- 0.850747 S.D. dependent var 0.636805
quared 1
' .E. of regression 0.246019 Sum squared resid 3.44994 1
II urbin—Watson 1.574837 1
, tat 1
I - uation: LCSHR=(l-C(2)—C(3))+(-C(24)—C(34))*T 1
‘ O bservations: 66
1' -squared 0.371778 Mean dependent var I0.336903
‘ djusted R- 0.341380 S.D. dependent var 0.061467
‘quared
1 .E. of regression 0.049883 Sum squared resid 0.154278
1| urbin-Watson 1.125985
tat
9 I . uation: SLCSHR=C(2)+C(24)*(T)
O bservations: 66
21' -squared [0.258612 [Mean dependent var [0.620487

 

109

—|q|

Mil... .

5 \.. ‘ tit-v-4; .-

fid .

.‘jib J

Table B-4 continued,

 

0.247028

S.D. dependent var

 

.E. of regression

0.052991

Sum squared resid

 

 

urbin-Watson
tat

 

1.146907

 

110

 

 

Table B-5. Model (2) with State dummy variables; Homogenous of degree one in
returns to scale

CRSSTATEDUMMY
Method: Maximum Likelihood

 

input

 

1
observations:
198
Error
.575 1.0
14909

otal

186002
138 1.085957
796335

1 189

1188 .152995
1 155
1 11

134032

Likelihood
residual

l
)*T+C(5)*LNPROD+
-C(12)-C(l3))*LNI_.P"2+(-C(12)-C(23))*LNSLP"2
—C(l3)—C(23))*LNKP"2+C(44)*T"2+2*C(12)*LNLP
+2*C(13)*LNLP*LNKP+2*C(23)*LNSLP*LNKP)
-C(24)-C(34))*LNLP*T+C(24)*LNSLP*T+
+C(45)*T*LNPROD+C(66)*MIDUM

var .95991
. dependent var

of 19 resid
Watson 1 1137

111

Table B-5 continued,
* I o uation: LCSHR=(1-C(2)-C(3))+(-C(12)-

(13))*LNLP+C(12)*LNSLP

(13)*LNKP+(-C(24)-C(34))*T

 

O bservations: 66

 

 

 

 

 

 

 

 

 

 

 

 

 

 

ID urbin-Watson

_ tat

1.248145

 

 

112

I' -squared F).417108 Mean dependent var 0.336903

‘ djusted R- 10.368533 S.D. dependent var 0.061467 1

~ - uared 1
.E. of regression 0.048844 Sum squared resid 0.14314t1

‘ 0 urbin-Watson 1.114952 1
tat 1
I cuation: SLCSHR=C(2)+(-C(12)- 1

(23))*LNSLP+C(12)*LNLP+C(23)

‘ *LNKP+C(24)*(T) 1
O bservations: 66 .
I’ -squared 0.353613 Mean dependent var 0.620487 1
- djusted R- 0.322336 3.13. dependent var 0.061068 1

- ~ 1 uared 1

W .E. of regression 0.050271 Sum squared resid 0.156688 1

   

11111111111111111111111