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This is to certify that the
dissertation entitled
ANALYsz ECONOMIC HULTIPLIERS FOR THE
HOOD PRODUCTS INDUSTRIES

presented by

PAUL R. BECKLEY

has been accepted towards fulfillment
of the requirements for

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MAY BE RECALLED with earlier due date if requested.

 

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ANALYZING ECONOMIC MULTIPLIERS FOR THE
WOOD PRODUCTS INDUSTRIES

By

Paul R. Beckley

A DISSERTATION

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

DOCTOR OF PHILOSOPHY

Department of Forestry

2002

ABSTRACT

ANALYZING ECONOMIC MULTIPLIERS FOR THE
WOOD PRODUCTS INDUSTRIES
By

Paul R. Beckley

With anticipated increased demand for economic impact analysis to support public policy
and investment decisions at all levels, steps to improve the efficiency of the economic
impact analysis process must be examined. Presently, the most common method of
impact analysis involves the use of ready-made interactive, input-output models. These
models along with the necessary data can be very expensive and require substantial skills
to use. The primary purpose of this study is to investigate the feasibility of providing
more readily available, situation-specific, economic multipliers, to assist in the economic
impact analysis process. The study focuses on the wood products industries and also

examines the response of multipliers to changes in the size of economic impact areas.

Regression analysis techniques are used to determine the relationship between several
types of multipliers and reasonably available explanatory variables including human
population, population density, number of economic sectors, total industry output,

personal income, and the physical size of the impact area.

Results of the study demonstrate that regression models, based on readily available

information, might not be the best approach to predict economic multipliers for the wood

products industries. These models vary greatly in their ability to predict multipliers. In
some specific situations the resulting models might be useful but at the same time risky.
Additional study would be needed to analyze the relative merits of alternative prediction
methods including costs and the extent and quality of results (e. g. statistical confidence)
needed to support decisions. Study results also highlight the effect of impact area size on
multipliers — as economic impact areas become relatively large, the growth of multipliers
rapidly culminates. Therefore, analysts should use caution when increasing the size of
impact areas to capture additional economic effects, especially in heavily populated areas

with large economies.

ACKNOWLEDGMENTS

I would especially like to thank my Ph.D. advisor, Dr. Larry Leefers, for his support and
advice. It was his effort and encouragement that led me back into the Ph.D. program at
Michigan State University. I am especially thankful for his patience and constructive

criticism in the completion of this dissertation.

In addition I would like to thank the other members of my graduate committee. They are
Dr. Daniel J. Stynes, Dr. Dennis B. Propst and Dr. Karen Potter-Witter. Their technical

leadership was extremely helpful.

Special thanks to my employer, USDA Forest Service, which provided valuable time and
resources necessary to complete this research and dissertation. Especially helpful was the
technical and moral support provided by my co-worker and good friend, Michael
Niccolucci of the Forest Service Inventory and Monitoring Institute. Assistance from Dr.
Susan Winter and Dr. Greg Alward of the Inventory and Monitoring Institute was also
extremely valuable as was the continuing wisdom of Dr. Michael Vasievich of the Forest
Service, Washington Office, Ecosystem Management group. Thanks is also due to
Shirley Hendrick, of Columbia Falls, MT who did much data entry and writing-editing

for this project.

Above all I would like to thank my wife PJ for all the sacrifices she has made while I

pursued this degree. Her patience has been admirable. I hope I can repay her someday.

iv

TABLE OF CONTENTS

LIST OF TABLES
LIST OF FIGURES
CHAPTER ONE: INTRODUCTION

Introduction

Problem Statement
Research Objectives
Organization of Dissertation

CHAPTER TWO: LITERATURE REVIEW

Introduction
Economic Impact Analysis
Multiplier Analysis
Economic base models
Input-output analysis
Common types of multipliers
IMPLAN —An Economic Impact Analysis System
Multipliers generated by IMPLAN
Types of multipliers
Economic variables
Other sources of multipliers
The Impact Area
Multiplier Studies Closely Related to this Study

CHAPTER THREE: RESEARCH METHODS

Introduction
Economic Impact Model Selection
Selecting the Study Area(s)
Economic Sectors Analyzed
Impact Model Construction
Trade flows
Types of multipliers to be analyzed — types of effects
Types of multipliers analyzed — economic variables
Response Variables Analyzed
Explanatory Variables Analyzed
Other explanatory variables considered
General Form of model
Statistical Analysis Methods

37

37
37
39
42
48
50
53
54
55
57
63
65
66

CHAPTER FOUR: ANALYSIS AND RESULTS
Introduction

Study Objective 1: Describe variations in multipliers
Number of Observations
Measures of Central Tendency
Measures of Variability

Study Objective 2: Identify the kefiactors that explain the
variation of economic multipliers.
Correlation Analysis
Measures of Normality

Study Objective 3: Determination of the feasibility of using
selected, readily available. explanatory
variables to estimate economic multipliers

 

Introduction
Procedures and Results

Regression Analysis
Best Subsets Process
Developing the Regression Equation
Improving the Regression Equation
Regional Differences/Adjustments
Elimination of Unusual Observations
Non-linear Alternatives
Additional Explanatory Variables
Multicollinearity and Heteroscedasticity
The Final Model
Examining Differences Between
Geographic Impact Levels

70

70

70
71
72
75

77
78
83

84

85

85

86
86
89
93
94
99
99
101
102
105

109

CHAPTER FIVE: CONCLUSIONS

Introduction
Research Summary
Discussion of Results
Study Objective 1: Describe variations in multipliers

Study Objective 2: Identify the key factors that

explain the variation of economic multipliers

Study Objective 3: Determination of the feasibility of using
selected, readily available, explanatory va_riables

to estimate economic multipliers
Policy Implications
Recommendations for Future Research

REFERENCES

vii

112

112
113
115
116

116

117
122
123

126

APPENDICES

APPENDIX A - Validation of Linear Models

APPENDD( B - Best Subsets Regression Analysis Results
APPENDIX C - Regression Equation Information —- Preliminary Model
APPENDD( D - Analysis of Variance Results

APPENDIX E — Study Area Map

APPENDD( F - States in USDA Forest Service Regions

APPENDIX G - Final Regression Analysis Results

APPENDIX H - Descriptive Statistics for Impact Area Levels

viii

133

137

149

155

167

168

169

175

LIST OF TABLES

TABLE 1.

TABLE 2.

TABLE 3

TABLE 4

TABLE 5.

TABLE 6.

TABLE 7.

TABLE 8.

TABLE 9.

TABLE 10.

TABLE 11.

TABLE 12.

TABLE 13.

TABLE 14.

TABLE 15.

TABLE 16.

TABLE 17.

TABLE 18.

Forest Products IMPLAN Sectors
Multiplier Response Variables
Wood Products Industry Production Functions
Regional Purchase Coefficients
Explanatory Variables
Explanatory Variable Codes
Number of Observations
Measures of Central Tendency
Measures of Variability
Standard Deviation and Coefficient of Variation
Correlation Coefficients and P-Values
Correlation Coefficients Between Explanatory Variables
Best-subsets Regression Analysis Results Summary

Regression Equations - Preliminary Model Coefficients
Effects of Regional Stratification on R2 Values
Multicollinearity Analysis

Final Model Coefficients

Mean and Maximum Absolute Percent Error

ix

45

47

51

57

57

71

73

74

76

79

82

88

90

95

104

105

108

LIST OF FIGURES

FIGURE 1. Distribution of Multiplier Means (LE2)

77

CHAPTER ONE: INTRODUCTION

Introduction

Planning and quantifying regional economic growth or determining economic effects of
public agency land management decisions has been a concern for quite some time, of
local, state and national planners (McKusick 197 8). The primary purpose of this study is
to evaluate the feasibility of providing more convenient input-output multipliers to assist

in conducting economic impact analysis for economic planning purposes.

Problem Statement

With anticipated increased demand for economic impact analysis there is also increased
demand to simplify the economic impact analysis process. This pressure to simplify and
streamline has been hastened by the development of new high-speed computers and
software, which have been of great assistance to those already skilled in economic impact
analysis. However, it has also encouraged analysts unskilled in economic analysis
methods to try their hand at impact analysis and also created a mindset that economic
analysis is now automated and can be done by most anyone. This has often resulted in
analysts shortcutting and oversimplifying the impact analysis process with little

awareness of the detrimental consequences.

The increased demand for more and better economic impact analysis exists not only at
the federal government level but also the state and local government level. In addition,

the private sector, which is applying for government assistance or providing the

government with analysis results, is in need of better and simpler analysis procedures and

a better understanding of the analysis process itself.

The wood products industry, on which this study focuses, is an industry that is
significantly affected by public agency decisions, especially those decisions by the
USDA Forest Service. Consequently, changes in this industry resulting from government
decisions can have significant effects on the social and economic environments of

affected regions.

The purpose of economic impact analysis, at least in the case of this study, is to
determine the nature and magnitude of the economic effects of the activities of the wood
products industries. These activities are fi'equently affected by decisions of federal and
state land management agencies that provide raw material to the industry. The economic
impact analysis process commonly specializes in answering the main questions that have
been found to be of concern to surrounding communities — how many jobs will be
gained/lost and how will income be affected by changes in the wood products industries?
And, more broadly, how will these potential changes eventually affect the economic

structure and health of the region?

In the past, it was relatively difficult to conduct impact analysis to any degree of
accuracy, and the process required extensive knowledge in the concepts of regional
economics. It also required access to models and data that were few and expensive.

These systems normally required the collection of primary data — taking new surveys.

Eventually secondary data based systems for use on desktop computers were developed
which made analysis much faster, easier, and cheaper. These systems include IMPLAN,
REMI, and RIMS II (Rickman 1995). Although these systems are a vast improvement
over what was previously available, they can still be expensive and require skills not
available in many smaller regions or organizations. An alternative approach has been to
use ready-made multipliers (U .S. Department of Commerce 1986). However, these
multipliers are normally heavily aggregated and geographically broad. Consequently,
these ready-made multipliers could be significantly different for a smaller region, for a
specific economic sector, or a small aggregation of sectors. In summary, there is little
help at the present time, in the form of ready-made impact information or alternatives to
input-output type model building for site-specific conditions. New models must be

developed which require skills frequently not available at the local level.

In addition to the above problem there has been the more specific and continual problem
of actually defining the region of economic impact. This is frequently affected by local
officials who each want to know how their jurisdiction will be affected by proposed
activities. Frequently, the analyst does not have enough information to properly
determine an area appropriate to help solve the problem at hand. These conditions have
lead to incorrectly designated geographic impact areas, inaccurate analyses, and
consequently incorrect results. Analysts designing the impact study also might be
unfamiliar with the behavior of economic outcomes or multipliers that are influenced by

changes in local or regional assmnpfions or conditions.

An example of the above problem is where there is always pressure, fiom certain interest
groups, or at least the tendency to expand the impact area, to capture every last possible
economic effect. Of course the price the analyst or decision maker must pay for this is
that the effects become diluted as the area increases. For example, are we willing to
double the size of the impact area to capture a 2 percent increase in effects at the expense
of diluting the locational Specificity on the first 98 percent? This mistake is continually
repeated because the behavior of economic multipliers is not very well understood by
many analysts. This is especially critical in the wood products industry because of the

complexity of the industry and its associated trade flows.

Until the past few years, the smallest unit of geography in available impact models, such
as IMPLAN and RIMSII, has been the county. Consequently, most impact areas have
been designated as individual counties or combinations of counties. In addition to the
tendency of making impact areas too large there is the opposite and equally important

error of making them too small.

The same political forces mentioned above that resulted in areas that might have been too
large, could also result in impact areas that are too small. This occurs as a result of
political leaders wanting to know what is happening in just their county. This creates a
situation where a significant amount of the effects associated with changes in that county
or county group might occur outside that area and be missed by the analyst. Part of the
problem is that there is a tendency to use readily available multipliers or simple rules of

thumb in designing impact areas. This occurs when the analyst does not have enough

information to design an impact area that fits the local situation. For example if the
analyst does not know where the raw materials (e.g. logs) originate, where the workforce
lives or spends its money, or what the byproducts of the industry might be, they might be
tempted to use a ready-made region such as a county, or a Bureau of Economic Analysis
(BEA) economic area or region. Occasionally, the analyst might not even know what the
question is that needs to be, answered. If there are not time or other resources to build a
model and estimate economic multipliers and other useful information there might be a
temptation to use a ready-made multiplier. These ready-made multipliers and regions

will be discussed in more detail in another section of this report.

Recently, the capability of designing models at the zip code level, has been available and
an irresistible temptation for some analysts. This could compound the problem of
designing impact areas that are too small. However, this study will not test models at that

smaller geographic level because data quality at the present is unacceptable for research

purposes

In summary, although vast improvements have been made in the process of economic
impact analysis, it can still be expensive. Economic multipliers used to estimate
economic effects can be generated in haste without adequate skills or information. The
implications of these problems remain unknown to many analysts. The feasibility of
ready-made multipliers at the local level needs to be investigated. The same type of
problem exists with identifying the appropriate economic impact areas. Where areas that

are too large have been designed, site-specific effects can be smoothed over and not

identified. The specific effects might be localized within a large impact area and the
advantages associated with a smaller impact area might be lost. With areas that are too
small a significant amount of the effects might occur in adjacent areas and be missed by
the analyst or decision maker. The objectives of this study and how some of the above

problems will be addressed are included in the next section.

Research Objectives

The goal of this study is to investigate the behavior of certain economic multipliers of the
wood products industry to determine the feasibility of providing more readily available,
situation-specific, economic multipliers to assist in the economic impact analysis process.
In conjunction with this, the study results should provide information that analysts can
use for testing the effectiveness of designing economic impact areas or how multipliers

respond to changes in the Size of the impact area.

The above goals will be addressed by creating economic response surfaces (geographic
regions) and examining how selected factors influence them. Regression analysis will be

the primary analysis tool to address these goals.

Currently, most timber industry analysts and economic development teams do not have
access to such information. AS previously discussed, existing multipliers are either very
general or they need to be determined through an extensive computer analysis by

someone with specialized training. Economic impact areas are frequently selected with

inadequate information or skill with little awareness of the implications of incorrectly

chosen areas.

The following specific questions need to be addressed in order to provide a better
understanding of multipliers useful to the wood products industry and to conduct this
study. These questions serve as a basis for the specific objectives.

0 What is the variation in economic multipliers for wood products sectors across
impact areas of differing sizes and characteristics, and what are the variables that
might be responsible for these differences?

0 Is there a detectible pattern for the variation? Do some variables cause multipliers
to increase while others cause multipliers to decrease or have no effect at all?

0 How can these findings be used? Can they be used to develop more site-specific
readily usable multipliers? Can they be used to establish or test the
appropriateness of selected impact areas?

0 How can analysts working for the government, private contractors, or the wood

products industry apply the appropriate multipliers for a given region?

Consequently, an approach is needed as explained above, that can simplify the problem
of generating multipliers for a given region and problem and take some of the uncertainty
out of estimating economic impacts. Because of the nature of the wood products
industry, with clear and significant backward linkages from the major producers to the

incidental producers, multipliers for the few most significant actors in the wood products

industry should be able to fairly represent the wood products industry as a whole and

address the questions being asked.

National Forests, administered by the USDA Forest Service, serve as the nuclei of the
economic impact regions in this study. They will also be the primary beneficiaries of the

results of this study.

There are three research objectives for this study:

1. Describe the range of variation in economic multipliers for representative sectors
in the wood products industry across geographic regions of varying size and
characteristics.

2. Identify the key factors that explain the variation of economic multipliers from
Objective 1, which might serve as variables in a multiplier prediction model.

3. Determine the feasibility of using selected explanatory variables from Objective 2

to estimate economic multipliers for the wood products industry.

Data used for explanatory variables must be readily available to provide an advantage
over constructing input-output or economic base models. The study will not develop a
ready-made set of multipliers or impact regions to be immediately applied. Rather it will

focus on the feasibility of doing so.

To achieve these objectives, the study has developed a set of various economic

multipliers representing selected wood products industry sectors and investigated the role

of selected explanatory variables that were used to predict those multipliers. The
multipliers, serving as response or dependent variables in the regression model, were
developed using the IMPLAN system. These multipliers served as the baseline, or were
deemed to be the true multipliers for purposes of this study. Regression techniques were

used to analyze the relationships between the multipliers and the explanatory variables.

Organization of Dissertation

This dissertation report begins with Chapter 1, which describes the problem and its
importance, along with specific questions the study is designed to answer and the
resulting study objectives. Can multipliers be developed to be useful for analysts that do
not require the time or resources to calculate multipliers or identify regions on their own?
Can economic multipliers be used to assist in determining the major extent of economic
impact areas? Chapter 2 presents a review of available literature dealing with the
subjects of economic impact analysis, input-output analysis, economic multipliers, and
regional delineation. Past use of these procedures for evaluating management decisions
for the wood products industry also are discussed. Chapter 3 describes the methods used
to collect and analyze data in this study. Chapter 4 discusses the analysis and study
results. Chapter 5 discusses the conclusion of the study and describes policy implications

and suggestions for further research.

CHAPTER TWO: LITERATURE REVIEW

Introduction

This chapter reviews basic literature on economic impact analysis, multiplier analysis,
and input-output analysis to provide a conceptual fi'amework for the study. The chapter
is divided into five sections. The first section briefly discusses economic impact analysis
— its uses and relationship to recent regulatory requirements. The second section reviews
the fundamentals of multiplier analysis — how multipliers are calculated and used. The
third section presents the fundamentals of the IMPLAN economic impact analysis
system, its history, products, and present capabilities in relation to calculating multipliers.
The fourth section discusses how economic impact areas are defined. The fifth section

discusses past studies.

The literature review begins with an extensive search of available databases. The most
significant are those available through the Rocky Mountain Research Station of the
USDA Forest Service. The Station uses a variety of specialized databases both on CDs
and through commercial online vendors, through several universities, with access to over
400 bibliographic databases. The databases that were most productive were TreeCD,
which has worldwide coverage of forestry literature — 1939 to present; Agricola, which
has worldwide coverage of agricultural/rangelands literature — 1970 to present and
Sociological Abstracts, which has worldwide coverage of literature on theoretical and

applied sociology/behavioral sciences (including econorrrics) — 1963 to present. The

10

Internet was also searched for applicable literature. The search results were reviewed and

the literature that appeared to be most useful for this study was acquired and reviewed.

Economic Impact Analysis

Input-output analysis is one of many tools available for economic impact analysis
although, for various reasons, the input-output approach is the most popular (Richardson
1979, 1985). Its popularity will continue to increase because the development of
computers and software has made impact analysis much easier and more informative than
it has been in the past. Input-output analysis will be discussed in more detail later in this

chapter.

With the assistance of computers and the availability of secondary data based models, the
potential and demand for higher quality economic impact analysis is on the rise. This is a
result of the increasing intensity of economic and community planning along with a

myriad of new governmental regulations and policies requiring economic impact analysis

prior to implementing new activities or proposals.

Moreover, economic impact analysis will be necessary to satisfy the requirements of the
most recent National Forest Management Act Regulations (USDA 2000). The purpose of
the regulations includes statements such as:
“Sustainability, composed of interdependent ecological, social, and economic
elements, embodies the principles of multiple-use and sustained yield without

impairment to the productivity of the land. Sustainability means meeting needs of

11

the present generation without compromising the ability of firture generations to
meet their needs (Section 219.1(b)(3))”.
The harvest of wood products plays a role in the sustainability goals. Section 219.21
elaborates on the importance of social and economic information to provide assessment

and economic impact information to aid in the planning and decision making process.

The recently released Interior Columbia Basin Final Environmental Impact Statement,
which could substantially change management direction on F8 and BLM lands for a large
geographic region, proposes agency decisions that “support economic and/social needs of
people, cultures, and communities, and provide sustainable and predictable levels of
products and services, fi'om lands adnrinistered by the Forest Service or the BLM”
(USDA, USDI 2000). Economic impact analysis using input-output analysis was used to
determine many of the economic effects of this new policy proposal (Quigley et al.

1996). Economic impact analysis is needed to assess the economic effects as the new
policy is implemented which will include various new roles (e. g., ecosystem restoration)
for the harvest of wood products.

A variety of social and economic disciplines call for economic impact analysis including
distributive justice (Phelps 1989, Wagner et al. 1992), social impact assessment (Burdge
1994, 1999, 1991, Bryan 1996), community planning (Rasker 1994, Hart 1999, Bauen
1996), rural development (Holland et al. 1995, 1997, Vasievich 1999, Fossum 1993) and

environmental economics (Ekins 1992, Power 1988, 1996).

12

Multiplier Analysis

Economic multipliers are most fi'equently generated from input-output analysis.
Economic multipliers are a way of measuring the economic interdependence of a region.
Multiplier analysis can be an important procedure in assessing the economic effects of
changes in the wood products industry on the economy of a region. Multipliers are used
to estimate the direct, indirect and total economic impacts resulting fi'om a change in
“final demand”. The idea is to multiply the multiplier by some economic measures in

order to get the total impacts (Aldwell 1984).

Economic multipliers generated by regional input-output models can be usefirl in
providing detailed information about an industry’s effect on the regional economy. By
computing various kinds of multipliers, one can measure the impact of an industry on
economic variables such as employment, income, and the activity level of all industries in

the region (Burford et el. 1981).

Economic multipliers vary according to the economic variables to which they apply (e. g.
total industry output, income, employment, etc.) and how they are defined (e. g. Type 1,
Type II, Type SAM). Type I multipliers address direct and indirect effects. Type II and
Type SAM multipliers address total effects. These types of multipliers can be referred to
as “ratio multipliers” because they are the ratio of total economic effects in relation to
direct economic effects. Multiplier variables and types of multipliers will be explained in

more detail later in this chapter under “Input-output Analysis”.

13

Multiplier Analysis

Economic multipliers are most frequently generated fi'om input-output analysis.
Economic multipliers are a way of measuring the economic interdependence of a region.
Multiplier analysis can be an important procedure in assessing the economic effects of
changes in the wood products industry on the economy of a region. Multipliers are used
to estimate the direct, indirect and total economic impacts resulting from a change in
“final demand”. The idea is to multiply the multiplier by some economic measures in

order to get the total impacts (Aldwell 1984).

Economic multipliers generated by regional input-output models can be useful in
providing detailed information about an industry’s effect on the regional economy. By
computing various kinds of multipliers, one can measure the impact of an industry on
economic variables such as employment, income, and the activity level of all industries in

the region (Burford et el. 1981).

Economic multipliers vary according to the economic variables to which they apply (e. g.
total industry output, income, employment, etc.) and how they are defined (e. g. Type I,
Type II, Type SAM). Type I multipliers address direct and indirect effects. Type II and
Type SAM multipliers address total effects. These types of multipliers can be referred to
as “ratio multipliers” because they are the ratio of total economic effects in relation to
direct economic effects. Multiplier variables and types of multipliers will be explained in

more detail later in this chapter under “Input—output Analysis”.

13

Various combinations of multipliers and types are possible. For example, it is possible to
derive a Type I income multiplier, a Type II value-added multiplier, and a type SAM
employment multiplier. Keynesian-type multipliers, can be derived from the IMPLAN
output and an independent estimate of the total amount of new dollars spent in a region as
a result of some action (Stynes 1999). These multipliers are commonly related to some
physical unit of change in production. An example of this would be the number of jobs
lost per million board feet reduction in timber harvest or million AUMS of grazing
(Kolison et al. 1992). Response coefficients are not addressed in this study. They need

to be calculated separately and locally because of the need to include physical output.

Among the most commonly used methods for estimating economic multipliers and ratios
are 1) economic base models and 2) input-output models (Richardson 1985). Of the two
methods input-output analysis has received the most use in recent years (Hastings 1993).
This is probably due to the availability of new software and high-speed personal
computers that make computations simple compared to the past as well as providing

more detailed sectoral information from secondary data.

Economic base models - The assumption for economic base models is that all
economic activity within a region must be classified as basic or non-basic. Basic sectors
export their output to markets outside the region therefore bringing new money to the
region. The derivative sectors arise fiom serving markets inside the region or it can be

said that the non-basic sectors are attributable to the basic sectors. Therefore the

14

. economic base multiplier (i.e. income) is expressed as the ratio of total income to the

basic income.

A frequent approach for identifying the basic component of an economy is
through the use of location quotients. The location quotient assumes that any production
in excess of local consumption is exported and that percent is applied to the economic
variable of interest to determine the basic component of the economy (Pleeter 1980,

Krikelas 1992).

One of the more consistent lines of criticism has been that base studies perform
well in description but poorly in prediction. Base/non-base classification is a useful way
to characterize or describe a regional economy. But it is not certain that a single
base/non-base ratio can yield a useful estimate of the multiplicative effects associated

with a change in export activity (Bills and Zygadlo 1978).

Several other shortcomings of economic base models include (1) failure of the model to
reckon with supply inelasticities, (2) drift over time of estimated parameter values due to
evolving local econonries, (3) focus on exports to the exclusion of other autonomous
sources of demand and, (4) weaknesses that any Keynesian consumption function
exhibits. In addition, estimated economic base multipliers exhibit wide variability (Frey

1989)

Economic base models will not be discussed frrrther because this approach cannot be

used to address the objectives of this study.

15

Input—output analysis — Francois Quesnay first described inter-industry
relationships in 1758. However, the empirical application had to wait until the 20th
century when Wassily Leontief developed the concept of multipliers from input-output

tables. He received a Nobel Prize in 1973 for his work.

Input-output analysis is frequently chosen for regional analysis because it provides
several types of information. It is an excellent descriptive tool showing in detail the
structure of an existing regional economy. It provides important information on
individual industrial sector size, and its behavior and interaction with the rest of the
economy. It shows the relative importance of sectors in terms of their sales, wages and
employment. It also provides a way to predict how the economy will respond to
exogenous changes or changes that are planned. Therefore, it is useful in prescriptive
exercises where various actions are being considered and the relative merits are to be

determined based on alternative outcomes (Hastings 1993).

Input-output analysis is a means of examining relationships within an economy both
between business and between businesses and final consumers. It captures all monetary
market transactions for consumption in a given period of time. The resulting
mathematical formulae allow one to examine the effects of a change in one or several

economic activities on an entire economy.

A primary input-output study is based on data collected directly from industries. An

example is the United States’ Benchmark Study on Input-Output Accounts (U .S.

16

Department of Commerce 2001). Secondary input-output studies rely on data collected
from other sources to construct the accounts. The inter-industry transaction information

usually comes from some other primary study. IMPLAN (Minnesota IMPLAN Group

1999) is an example of a secondary input-output modeling system.

Trade flows are also part of the descriptive input-output model. They describe the
movement of goods and services within a region and from and to the outside world

(regional imports and exports).

By adding, what is referred to by economists, as social accounting data an analyst can
examine non-industrial transactions such as payment of taxes by businesses and
households. Social accounting data includes tax collection by governments, and
payments to households and business. Input-output accounting describes the flow of
commodities fiom producers to intermediate and final consumers. Social Accounting

Matrices (SAMs) Show the flow of money between all institutions (Maki 1997).

The regional economic accounts are used to construct local level multipliers. Multipliers
describe the response of the economy to a stimulus (a change in demand or production).
Purchases for final use (final demand) drive an input—output model. That is, industries
producing goods and services for consumption purchase goods and services from other
producers, and these other producers in turn purchase goods and services (indirect
purchases). These indirect purchases (or indirect effects) continue until leakages from

the region stop the cycle.

17

The indirect effects and the effects of increased household spending (induced effects) can
be mathematically derived as sets of multipliers. The derivation is called the Leontief
inverse (Miemyk 1965). The resulting sets of multipliers describe the change of output

for each industry caused by a one-dollar change in final demand for any given industry.

There are a large number of references on input—output analysis covering an array of
inter-related matrices, matrix algebra, and trade flow mechanics (Miernyk 1965,
Minnesota IMPLAN Group 2000, Miller 1985, Otto and Johnson 1993, USDA 1978,
Rose et a1. 1989, Fjeldsted 1990, and Hewings 1985). Technical details, to the extent
necessary, will be discussed as part of the study methodology. However, this study
focuses primarily on the behavior of economic multipliers, which are described in the

following section.

Although input/output analysis has gained in popularity as the tool of choice for
economic impact analysis it is not without critics or shortcomings. A few of the concerns
associated with input/output analysis include
- Models are especially sensitive to trade flow assumptions.
- Multipliers are based on technology matrices that are often quite old.
- New sectors, not presently existing, have to be added to the model by the user
as increases in demand for certain commodities or industries reach threshold

levels. Otherwise these inputs are imported and outputs are exported resulting

l8

in incorrect impact analysis solutions. Information is usually not available as
to what the thresholds are or what sectors might emerge.

Production functions are assumed to have constant return to scale, which
means they are considered linear. If additional output is required, all inputs
increase proportionately.

Data for some individual sectors, especially those in agriculture, have a
substantial chance to be in error as the data is highly disaggregated based on
questionable variables.

There are no supply constraints. An industry is treated as having unlimited
access to raw materials and its output is limited only by the demand for its
products.

Another assumption is that there is a fixed commodity input structure which
means that price changes do not cause a firm to buy substitute goods which is
what would happen in real situations.

The model also assumes there is homogeneous sector output or the
proportions of all the commodities produced by that industry, remain the
same, regardless of total output. An industry will not increase the output of
one product without proportionately increasing the output of all its other
products.

The industry technology assumption comes into play when data is collected
on an industry-by—commodity basis and then converted to industry-by-

industry matrices. It assumes that an industry uses the same technology to

19

produce all its products. In other words, an industry has a primary or main

product and all other products are byproducts of the primary product.

Common Types of Multipliers

Type I - Type I multipliers give the direct and indirect effect only — that is, the
original expenditures resulting from the impacts plus the indirect effects of industries
buying from industries. An example of a direct effect would be a sawmill employing
workers. An indirect effect would be the local auto repair shop hiring another mechanic
who will work on the sawrnill’s vehicles. Whether or not an effect is direct or indirect
depends on the starting point of the analysis. For example if the starting point of the
analysis was the mechanics shop then the hiring of the mechanic would be a direct effect
and the hiring of an extra worker at the parts store (where the mechanics shop buys its
parts) would be an indirect effect. However, the starting point for this analysis was the
wood products sectors chosen for analysis. Household expenditure effects — i.e. induced
effects are not estimated with the Type I multiplier. The Type I multiplier can be defined
as the ratio of the direct and indirect changes in the variable of interest to direct changes

in that variable.

Type II — Type II multipliers account for the direct, indirect, and induced effects
where the induced effects are based on income. Examples of direct and indirect effects
are given above. Induced effects result from expenditures of the household sector on
final consumption. When the mill worker, or mechanic, and parts store worker spend

their income it generates new employment and income. These rounds of spending

20

continue until all the effects of the original spending eventually leak out of the selected

impact area.

The relationship between personal consumption expenditures (PCE) (induced effects)
and income is based on resident-only income from the Social Accounting Matrix (SAM)
accounts. The assumption is that there is a linear relationship between local income and
local expenditures. The Type II multiplier can be defined as the ratio of the direct,

indirect and induced changes in the selected variable, to direct changes in that variable.

Type II multipliers are created by incorporating household expenditures into the rounds
of inter-industry purchases. In this way, money flowing to the labor force is recycled
through the economy and is not lost as a leakage as it would be with the Type I

multiplier.

There are three different Type II formulations: “Standard” (which is not available in
IMPLAN software), “SAM Based” and “Specified Disposable Income”. The difference
in all three methodologies lies in how the denominator representing total household
expenditures is derived for conversion of household expenditures (the PCB vector) to
coefficients. Each dollar going to household income from either employee compensation
or proprietor income is spent through the PCB coefficients in each of the rounds of direct
and indirect effects. The household income row and PCB column coefficients can be
incorporated in the Leontief matrix the same as any other industry. Common to all three

methodologies is that:

21

1) The PCE final demand (the household expenditures column) represents
expenditures for goods and services made by residents of the region being
modeled.

2) The household row represents income earned by labor (usually employee
compensation plus self-employment income) paid by regional industries and

institutions for household production — i.e., labor.

Therefore, the household expenditures column is residence based and the household

income row is by place of work.

The “standar ” formulation for Type II multipliers can be found in the input-output
textbooks ( Miller and Blair 1985, Hoover et al. 1984). The denominator, by which the
PCB column coefficients are derived, is the sum of payments made by industry and
institutions for labor - i.e., employee compensation and proprietor income. The PCB
column represents expenditures by regional households (fiom income from all sources)
and that income is work place based. This creates problems in places that have large
retirement industries, and consequently, large amounts of retirement income ( Olson,
1997). This can coincide with high natural amenity areas that have significant wood
products industries — the subject of this study. The amount of PCB reflects both
retirement and labor income but the denominator only includes labor income. Resulting
coefficients and therefore multipliers, can be overstated unless a certain number of
retirees are assumed to come with each new job. Similar problems exist if a region does

not incorporate the labor force and has a significant number of commuters — i.e., changes

22

in regional household spending does not directly reflect changes in work-based labor
income, which are respent through PCE. These are important implications when dealing
with regions such as those occupied by National Forests or the timber industry where
aesthetic values are generally above average and consequently the retirement component

of the population is disproportionately high.

The above situation is important in respect to the proposed study because fiequently
workers will live in high amenity rural areas but commute into urban areas to work. As
the impact areas are enlarged, as will be the case in this study, we Should see this
situation reflected in the resulting induced (Type II) multipliers. Workers will tend to
spend much of their money in the larger area. This suggests that the design of impact
areas should take this situation into consideration and maybe include those areas where
much of the induced spending occurs. It also suggests that analyzing the multipliers

might help in the design of impact areas — part of the subject of this study.

IMPLAN models have an advantage over many earlier input-output models because data
are available for a complete set of “Social Accounting Matrices” (SAM) (Alward et al.
1996). The PCE expenditure vector in the “standard” input-output account only includes
expenditures for goods and services provided by industry sectors (local or imported). To
derive PCE coefficients the PCB coefficient column generated by the SAM is used. The
coefficients can now represent the disposal of each dollar of regional household income
regardless of the source. The Type II multiplier in this formulation, therefore, includes

spending and re-Spending of each dollar of labor income through the PCB coefficients —

23

transfer payments are no longer a part of the impacts. However, significant commuting
into the region may cause overestimation of multipliers, as the model will assume their
labor income will be spent locally instead of in the region fiom which the commuters

came.

When using the “Specified Disposable Income Ratio” method, IMPLAN borrows the
methodology from the BEA’s RIMS II project, which essentially is a SAM based
multiplier without the SAM data (Minnesota IMPLAN Group 1999). First the PCB
vector is normalized by summing the PCB values and dividing by the total (the BEA uses
the national PCE vector while IMPLAN models are regionalized). The resulting PCE
coefficients sum to one. Each dollar of labor income can now be spent through this
vector, but first we must account for the fact that each dollar in income is not spent solely
on PCE. Some of it is used to pay taxes and some goes to savings. This is simulated by
applying a disposable-to-total income ratio to the PCE coefficients. Nationally, this ratio
is 0.85. The PCE coefficients are reduced so that they now sum to 0.85 — i.e., every
dollar of labor income generates 85 cents of PCB. In IMPLAN, the user can edit the
disposable income ratio. This is useful for studying any policies affecting household
disposable income rates (taxes, savings). Type II multipliers simulating loss of income
through commuters from outside can be generated by proportionately reducing the

disposable income rate (Minnesota IMPLAN Group 1997).

Type SAM — Type SAM multipliers are the direct, indirect, and induced effects

where the induced effect is based on information in the social accounting matrix. This

24

relationship accounts for social security and income tax leakage, institution savings, and
commuting. It also accounts for inter-institutional transfers. The SAM multiplier was
the indirect multiplier used for this study because it has the capability of accounting for
all expenditures regardless of source. This is important because there are Significant
transactions between government institutions and the wood products industry and their

omission could result in inaccurate multipliers.

IMPLAN - An Economic Impact Analysis System.

This study used the IMPLAN economic impact analysis system to generate impact
models and resulting economic multipliers. IMPLAN (IMpact Analysis for PLAN ing),
was originally developed by the USDA Forest Service in cooperation with the Federal
Emergency Management Agency and the USDI Bureau of Land Management to assist
the Forest Service in land and resource management planning (Siverts et al. 1985). It is
one of the most widely used economic impact tools for wood products industry
applications (Flick and Teeter 1988, Aruna et a1. 1997, Zeng and Harou 1988, Lord and
Strauss 1993). This study used the IMPLAN Pro, Version 2.0 (hereafter referred to as
IMPLAN) economic impact system to generate impact models and resulting economic
multipliers. The multipliers generated by IMPLAN were used as the response
(dependent) variables in the regression models for this study. IMPLAN also served as a

source of data used as a few of the explanatory (independent) variables.

25

The IMPLAN system has been in use since 1979 and has evolved from a mainframe,
non-interactive application that ran in “batch” mode to a menu-driven microcomputer
program that is completely interactive (Minnesota IMPLAN Group 1999). The
Minnesota IMPLAN Group (MIG) began work on IMPLAN databases in 1987 at the
University of Minnesota. In 1993, MIG, Inc. (MIG) was formed to privatize the
development of IMPLAN data and software. Version 1 of the Windows software was

developed by MIG and released in June of 1996.

The IMPLAN database, created by MIG, consists of two major parts:

1) National-level technology matrices;

2) Estimates of regional data for institutional demand and transfers, value-added,
industry output and employment for each county in the US. as well as state
and national totals.

The IMPLAN data and accounts closely follow the accounting conventions used in the

“Input-Output Study of the US. Economy “ by the Bureau of Economic Analysis (1980).

There are two components to the IMPLAN system, the software and the database.
The software performs the necessary calculations using the impact area or region data to
create the models. It also provides an interface for the user to change the region’s

economic description, create impact scenarios and introduce changes to the local model.

26

The databases provide all the information needed to create regional IMPLAN models.
The IMPLAN system can be used to analyze a wide variety of issues including those

associated with Federal land management.

IMPLAN’S regional social accounting system allows a user to:

1) Develop a set of balanced economic/social accounts.

2) Develop multiplier tables.

3) Change any component of the system (i.e. production functions, trade flows or
database).

4) Create custom impact analysis by entering final demand changes.

5) Obtain any report in the system and examine the models assumptions and
calculations.

6) Define regions appropriate to address problems being analyzed.

7) Select and focus on just those sectors of interest.

Because the purpose of this study was primarily to determine the feasibility of predicting
multipliers, given certain explanatory variables, the discussion of the IMPLAN model
was limited to what is needed to understand the study. This included, the various types of
multipliers, and the economic variables generated by IMPLAN that the multipliers apply

to.

27

Multipliers generated by IMPLAN.
Types of multipliers
IMPLAN generates Type I, II, and SAM multipliers. If it is desirable for an analysis to
include the induced effects generated by indirect spending, the type of induced multiplier
to construct (e. g. Type II or SAM), must be selected. IMPLAN allows the user to select

what institutions to include in the calculation of the SAM multiplier.

Economic Variables
IMPLAN calculates economic ratios and multipliers for various impact measures that
include total industry output (sales); the components of value added such as labor
income, employee compensation, proprietor’s income, other property income and indirect

business taxes; and employment.

Total Industry Output — Total industry output (T 10) is the value of production by
industry(s) for a given time period. For IMPLAN, T10 is annual calendar year
production. Output can be measured either by the total value of purchases by
intermediate and final consumers, or by intermediate outlays plus value added. Output
can also be thought of as the value of sales plus or minus the changes in inventories. The
TIO multiplier is the change in output resulting from an increase of $1.00 in final
demand.

Value Added — Income multipliers (or for any of the value-added components) are
derived from the relationship between income and output. Study area data has the total

industry output and total income for each sector. From this, income per dollar of output

28

can be calculated. An industry multiplier is split into the direct and indirect effects and
then multiplied by the income per dollar of output ratio to get the income direct and

indirect effects.

Employment — The employment multiplier is created in the same manner as the
income multiplier, but using output per worker ratios instead of output per dollar of
income. First the employment per dollar of output is calculated, and then the direct and
indirect effects are estimated (Type I multipliers). The level of employment per million
dollars of output is then multiplied by the output multiplier. Employment data in the

IMPLAN model is from local sources.

It is important to know that employment, as reported by IMPLAN, is a single number of

jobs. It includes both full time and part-time workers — not full-time equivalents.

Other sources of multipliers.

In the mid-1970’s the Bureau of Economic Analysis (BEA) completed development of a
method for estimating regional Input-Output multipliers known as RIMS (Regional
Industrial Multiplier System). More recently BEA completed an enhancement of RIMS
known as RIMS 11 (Regional Input-Output Modeling System). A product of the RIMS II
system is a published set of multiplier tables by industry aggregation for each state in the
US. They are “total” multipliers for output, earnings and employment. These

multipliers are sometimes useful when resources are not available to calculate more

29

specific multipliers. However, inaccurate results can arise from these multipliers when
the situation at hand is different from the average. Also, these multipliers are not useful
to this study because they do not present geographic variation about an area of potential
change in production and the industry-sectoring scheme for the wood products industry is

not nearly as useful as in IMPLAN (U .S. Department of Commerce 1986).

The Impact Area

One of the first tasks in economic impact analysis is identifying the impact area or
describing the spatial context of an impact analysis. In this study it was essential to get a
wide variety of impact regions for analysis so identifying the most appropriate areas for
impact analysis was only a product of chance rather than purposive or biased. The
procedure used for this particular study will be explained in the next chapter. When
normally selecting the appropriate impact area the analyst will usually define a county or
groups of counties (and/or states) for conducting the economic impact analysis. Also,
parts of counties (zip code areas) can now be included with other areas or analyzed

separately (Olfert et al. 1994, Goldman et al. 1997)

The following factors are presented as guides in selecting the appropriate counties for the
analysis. There are no hard-and-fast rules that can be mechaniCally applied to determine
the area to use. However, using information contained in the impact system database, the
user’s own knowledge of the area, and the question being evaluated, appropriate areas

can be developed.

30

The impact area should be defined as (l) a functional economic unit of a size appropriate
to the policy issue and (2) an area that includes most of economic factors that are most

directly affected by the policy (USDA 1988).

In terms of size the area should be large enough to:
1) Include all relevant activities (forward and backward linkages) related to the
question, and
2) Serve as a functional economic area.
But the area should be small enough to:
1) Be geographically oriented to the question, and
2) Represent the individuals, institutions and industries most affected by the

proposed action.

Factors to consider include:

1) Problem definition. - What question is the study expected to address? Region
definitions depend on the issues under study. The boundaries depend on the
purpose of the analysis. However, there is a tendency where regional
boundaries are drawn for narrow purposes to end up with regions that
geographers call “lifeless”. A lifeless region offers little reason for its
definition beyond the narrow purposes for which it is defined (Robison 1997).

2) Trade patterns - What are the principal trading patterns of key industries or
institutions? This includes governments and households. Where do local

residents spend their money? Where does the labor force live? Where are the

31

3)

4)

5)

6)

travel corridors? What is the location of supporting industries and services

(USDA 1988)?

Targeted audience - Is the analysis being conducted for a particular group or
audience as opposed to being prepared for general public knowledge? If a

particular group is targeted, a study area that represents their interests should
be used. For example a Board of Commissioners might only be interested in

economic effects in their particular county.

Spatial grouping. - Generally the impact area is made up of contiguous
counties. However, for some purposes leaving gaps or holes may be
appropriate. If impacts are desired both at a local level and a broader regional
or state level it may be necessary to develop several models with increasingly

larger areas included. This is similar to what was done in this study.

Leakages. - Generally, the smaller the area, the less diverse the economy and
the more spending leaks from the area. It might be useful to increase the size
of the impact area to reduce the leakage. This will also increase the income

and employment impact.

Functional economic areas. - This type of area is considered to be an ideal

strictly from an economic perspective. It contains a resident labor force for

local industries, 3 source for consumer purchases, and essential support

32

services. However, it may not be the ideal for a particular impact analysis if

some other (e.g., political) consideration takes precedence (USDA 1992).

Predefined Study Areas - The US. Bureau of Census and the Department of Commerce
have predefined study areas such as the Census Commuting Area or the Metropolitan
Statistical Areas (MSA). Both of these are based on counties. The MSA’S capture
metropolitan regions quite well, whereas the commuting areas tend to be large (USDA

1 999).

Tolbert and Kizer (1990) have defined 382 labor market areas (875 sub-market areas) for
the US, based on county-level journey to work data fiom the 1990 Census. There are
also Bureau of Economic Analysis economic regions and areas based on counties but
each is centered on a Census defined Metropolitan area. The BEA areas are defined to

have a minimum population of 100,000.

The USDA Forest Service has identified a network of impact areas for the purpose of
accomplishment reporting for several forest resources. An example of this is that done

for several National Forests in Minnesota, Wisconsin and Michigan (Retzlaff et al. 2000).

At the present, a doubly constrained gravity model is being developed by the Minnesota
IMPLAN Group and the USDA Forest Service Inventory and Monitoring Institute to
estimate trade flows for over 500 commodities between all counties in the US. The

IMPLAN software and national database of counties will be used to create the attracting

33

masses (supply and demand). Irnpedances will be derived from the Oakridge National
Laboratory’s Transportation Network model between centroids for all US. counties to
represent distances between the masses. The resulting trade flow estimates between
counties will allow for the replacement of the current IMPLAN methodology of
econometrically derived Regional Purchase Coefficients with “observed” county level
RPCs. This will be a substantial improvement in the identification of impact areas and

determination of trade flows (Olson 2000).

Multiplier Studies Closely Related to this Study.

One of the objectives of the literature review was to be reasonably assured that the
proposed study was not a duplication of an already completed study as well as acquire
ideas useful to this study. The search indicated that there were similar studies but each of
these studies had some major differences from this study. Several studies investigated
the possibility of estimating multipliers through regression models but did not apply it to
the wood products industry. Several other studies analyzed wood products industry
multipliers but did not propose alternatives to using existing input/output models. These

studies are briefly discussed in the following section.

Burford and Katz (1981) felt that acceptable input-output models could be built by using
census data to determine the regional purchase coefficients and then using these in
conjunction with a technical coefficient matrix could estimate the matrix of regional
coefficients. These results could then be used as explanatory variables in a regression

model to predict multipliers. Their study showed merit but is not presently useful

34

because the effort required to develop the explanatory variables is probably more costly

than using a secondary data model such as IMPLAN.

A study by Zheng and Harou (1988) successfully estimated multipliers in the wood
products industry by using the “internal purchase ratio” and the “intra-regional sale ratio”
as explanatory variables in a regression model. Again, these variables are not readily
available outside the input/output model and their acquisition and use would require
Special skills. This technique is similar to what is used by the US. Department of
Commerce, Bureau of Economic Analysis (1986) to set up their modeling systems
(RIMS and RIMSII) that was then used to develop their regional multiplier tables. The
above approach arose from the work done by Drake (1976) whose idea was to estimate

multipliers without the creation of an entire regional input-output model.

Regression analysis was used by Mulligan and Gibson (1984) to estimate economic base
multipliers for small communities. Their objectives were similar to this study in that the
authors were looking for readily available explanatory variables but still ended up

including components of the input-output model itself.

A study by Wen-Huei Chang (2001) describes and explains how multipliers used to
analyze recreation and tourism impacts vary across a wide range of conditions.
Conditions included population, population density, area, and geographic location. These

variables were also included in this study.

In summary, there have been a number of studies to simplify the estimation of economic
multipliers. Generally, they have depended on regression models that required data that

was not readily available. Moreover, a number of studies used input-output model data

35

as explanatory variables for estimating multipliers. Since the completion of those studies
secondary data models have become relatively available, fast and inexpensive.
Moreover, contemporary models do not require the skills that input-output analysis
methods previously required. This study does not replicate those studies because this

study proposes using information that is readily available.

One of the purposes of the literature review was to identify explanatory variables that
would be useful in explaining changes in economic multipliers. It was found that
variables used in past studies were either not generally available or had already been
considered for inclusion in this study prior to the review of the existing literature.
However, it did reinforce the notion that the selected variables were worthy of analysis.

Discussion of the variables used in this study begins in Chapter 3.

36

CHAPTER THREE: RESEARCH METHODS

Introduction

The research objectives of this study are to describe the range of variation in economic
multipliers in the wood products industries, to identify the key factors that explain the
variation, and to determine the feasibility of using these key factors in building a model
that could be used as an inexpensive tool to predict economic multipliers. To achieve
these objectives 650 economic impact regions were selected that varied in size and
economic characteristics. Input-output models, using IMPLAN, were developed for
determining multipliers for each of these regions for selected sectors of the wood
products industries. Variations in multipliers were examined by comparing
characteristics of the regions selected including industry production functions.
Regression models were developed to identify regional characteristics that explain the
variations in multipliers and evaluating the potential for generating multipliers from

readily available explanatory variables.

Economic Impact Model Selection

The 1997 IMPLAN database, which is the most recent year available, was used to build
all the regional models. For purposes of this study IMPLAN multipliers are treated as
representing the actual interactions within a local impact area. However, the multipliers
are derived from the national-level technology matrix, which serves as a basis for each

sector’s production functions and resulting multipliers. Regional data is applied to

37

national matrices (absorption and byproducts) to create a set of regional accounts. The
value added and final demand components of the transactions table are from regional
data. Thus, the assumptions used to calculate the multipliers may influence the direction
and magnitude of local interactions if the national production functions do not resemble

the local production functions (local interactions).

In an attempt to determine if there was the potential to have major differences in
production functions from region to region, the average firm size was examined. It was
assumed that significantly different sizes of operations would lead to different economies
of scale and possibly different production functions from region to region. This was done
by determining the number of firms and total jobs for SIC 24, Lumber and Wood
Products sector from County Business Patterns. From this the average firm size in terms
of employment for different regions was determined. It was found that there was very
little difference in firm size from region to region. The average firm size for the United
States for 1997 was 21.3 workers. For regions of the United States the average was as
follows: western, 21.8, northcentral, 23.8, southeast, 21.9, and northeast, 16.1. These
differences are not large enough to suspect they would cause major differences in

production functions.

The IMPLAN data files are available at the county, state and national levels. Models can
also be developed at the zip code level (Olson 1997). For this study only county-level
databases were used and combined as described as follows to form the appropriate impact

regions. The current version of IMPLAN (IMPLAN Pro 2.0), was used in this study to

38

generate economic multipliers. The only other feasible available system to use was
RIMSII. However, it was not used because of the initial investment required and lack of
technical support for using the model. The IMPLAN software program and data is

presently accessible fiom the USDA Forest Service along with technical support.

Selecting the Study Area(s)

Because the primary use of the results of this study will be for economic effects analysis
for timber management programs for units of the USDA Forest Service, the impact areas
were centered around National Forests. Impact regions were designed for each National
Forest. Although all National Forests do not have a timber program, all were included
because they at least had the potential to have a timber sale program (Appendix E).

The National Grasslands were not included because they generally had no potential for
timber sale programs. Alaska and Puerto Rico were not included in the study because
conditions in those states are vastly different than other states and it was felt that any
attempt to develop meaningful predictors for Alaska and Puerto Rico based heavily on
mainland data would be unsuccessful. This resulted in 155 sets of impact areas being

designed.

For each National Forest a set of up to five impact areas, were developed where data
was available. The reason five areas were developed for each National Forest was to
assure an adequate sample size and to also assure an adequate range in the size of impact

areas — in terms of the explanatory variables to be used in the analysis.

39

The first impact area (Level A) consisted of the most populous of all individual cOunties
that contain any lands within the designated National Forest. This was the smallest of the
set of 5 impact areas. Although this region might exclude much of the NF land in some

cases it could capture a significant amount of the economic activity.

The second impact area (Level B) included all the counties having lands within the
designated National Forest. This model might show that only including the geographic
source of raw materials could exclude much of the economic activity resulting from the
wood products industry. This was usually the next to smallest impact region and always

included the county comprising Level A.

The third impact area (Level C) included all the counties in Level B along with all the
counties adjacent to the counties in Level B. This was an attempt to view the
effectiveness of a mechanical construct that attempts to capture most of the economic
activity without knowing where the impact variables (e. g. where do people work, spend

their money etc.) actually are. It also provides additional diversity in impact area size.

Level D is the impact region that is used by the Forest Service for the TSPIRS (Timber
Sale Program Information Reporting System) report system. TSPIRS was developed in
response to Congressional direction contained in the Conference Committee Report on
the 1985 Interior Appropriations Bill as a result of concern over “below cost” timber
sales. One part of the annual report displays the economic impact of the Forest Service

timber program, for the year of the report, in terms of employment and income. Of the

40

five levels of impact area used in this study this is thought to be the most appropriate
impact area and is constructed pursuant to criteria in the Forest Service Handbook
1909.17 and Retzlaff et a1. (2000). However, this level covers only approximately half

the National Forests in the study because of missing data.

Level B consists of all the counties in the Bureau of Economic Analysis (BEA) Economic
Area (8) that the National Forests predominantly fall within (BEA 1995, Johnson 1995).

This was usually the largest of the impact areas and often occurred in several states.

IMPLAN models were developed for each of the impact areas described above (650
models). Some Forests had only four impact areas because of the lack of information
needed to design the Level D impact area. The study objectives require that a wide
variety of conditions among impact areas exist in order to evaluate the effects of those
conditions on the resulting economic multipliers. It would also provide a realistic array
of impact areas. This was evaluated by the first objective that describes the range of
variation in the multipliers and the second objective that looks at the range of conditions

within the impact areas that could cause the variation.

Another approach considered, to design economic impact areas, was an expanding core
in the form of concentric circles or layers of counties. For example another layer of
adjacent counties would be added to Level C. The feasibility of this approach was tested
and found to be somewhat possible in the east and south where counties are relatively

small. However, in the remainder of the country the resulting impact areas were often

41

enormous and frequently crossed several states. A modification of this approach would
be to add counties one at a time, each time creating a new model. However, there is no
clear criteria as to what sequence the counties would be added and it could create a
substantial amount of extra work with no obvious benefit. Also, the study objectives
should still be achievable without this extra model-building as there remains a large range

of situations within the existing design.

One of the reasons for including a wide variety of regions is to get an ample range in the
value of multipliers to see how the variation is related to the various characteristics of
regions. This is an important assumption in linear regression that will be addressed later
in this report (Appendix A). The list of impact areas is available fi'om the author upon

request.

Economic sectors analyzed

The purpose of the study was to analyze the behavior of the economic multipliers of the
wood products industry in response to a number of variables. Several assumptions were
made in identifying what economic sectors are normally considered part of the “wood
products industry”. This is necessary to determine which sectors this study should focus

on.

The main assumption is that the primary use of multipliers is to measure the marginal

effects resulting from management decisions that might affect the “wood products

42

industry” and consequently the surrounding economy. In the Forest Service or other
federal agencies this would normally be a decision that would affect the timber supply to
local processors. Therefore we must ask the question - will there be any direct effects on
a particular sector from a change in timber supply? For example, should the home
construction industry, which uses wood, be considered part of the wood products
industry? In this study it would not be included because it is not directly affected by a
change in the local timber supply. The home construction industry would I

exist even if the timber industry were not present. The presence of the industry is a
function of local demand for housing, not the supply of raw materials. Beckley (1998)
showed that a Si gnificant part of the lumber used in housing, even in those regions where
the lumber supply exceeds demand, is imported from outside the region. There is a
substantial amount of cross hauling. The same can be said for other wood-using sectors
such as millwork, wood kitchen cabinets, wood containers, and furniture. Their existence
is not a function of favorable wood prices because of the presence of a local sawmill.
Using the above logic, Table 1 shows the IMPLAN sectors that could potentially be
considered part of the wood products industry for the production and analysis of
economic multipliers in this study. These sectors need to be located reasonably close to

raw materials because of high transportation costs.

The next step is to decide which, if not all, of these sector’s multipliers should be
analyzed. The first, alternative might be to form an aggregate of all the wood products
industries. Although aggregating speeds up the model development process, and reduces

the size of reports, it can introduce substantial error due to the loss of data detail. Errors

43

'l'ahlc l — l’orcst Products |\ll’l..\\ Sectors

 

 

 

 

 

 

 

 

 

 

 

 

IMPLAN Sector IMPLAN Sector Name (1987 SIC Codes)a

22 Forest Products (Commodity — no SIC code)

24 Forestry Products (0810, 0830, 0970)

26 Ag, Forestry, and Fishery Services (710, 720, 750, 760,
0254, 0850, 0920)

133 Logging Camps and Contractors (2410)

134 Sawmills and Planing Mills (2421)

135 Hardwood Dimension and Flooring Mills (2426)

139 Veneer and Plywood (2435, 2436)

146 Reconstituted Wood Products (2493)

161 Pulp Mills (2610)

162 Paper Mills (2620)

163 Paperboard Mills (2630)

 

 

 

 

a
Detailed descriptions of each of these sectors can be found in the Standard Industrial
Classification Manual —- 1987. Executive Oflice of the President, Office of Management
and Budget.

are introduced from production functions, output per worker averages, and other value
added ratios. Aggregating the region’s industry sectors before generating multipliers has
the effect of taking several individual industries and combining them to form a totally
new industry. Dramatic errors can happen when multipliers are derived from the
production functions of aggregated industries. The production function of the new

aggregated industry becomes the weighted average of the individual production

44

larhle 2 ~ Multiplier Response Variables

 

 

 

 

 

 

 

 

 

 

 

 

 

 

a Type Variable
Economrc Sector (IMPLAN Code) Multrplrer Class Multiplier Code
LoggingCamps and Contractors (133) Employment Type I LE1
Type SAM LE2
Personal Income Type I LPl
Type SAM LP2
Sawmills and PlaninLMills (134) Employment Type I SE1
Type SAM SE2
Personal Income Type I SP1
Type SAM SP2
Veneer and Plywood (139) Employment Type I VEl
Type SAM VE2
Personal Income Type I VPl
Type SAM VP2

 

 

 

 

 

a First Digit ---- Economic Sector

Logging Camps and Contractors = L
Sawmills and Planing Mills = S
Veneer and Plywood = V

Second Digit-u- Multiplier Class
Employment Multiplier = E
Personal Income Multiplier = I

Third Digit --- Multiplier Type
Type I Multiplier = 1
Type SAM Multiplier = 2

functions. Industries with the greatest outputs have the greatest influence on the
aggregated industry, but the new industry’s production function may not truly represent
an industry being impacted. This generates an aggregation-induced error (Olson 1995 ,
1995a). Test runs on several counties showed that there is a significant variation in Type

SAM employment multipliers among the 11 wood products sectors. Some are

45

considerably above and some considerably below the Type SAM aggregate multiplier.
Another problem with an aggregated multiplier is that it would be difficult to extrapolate
to other regions because it is doubtful that the sector proportions would be the same or

that the region would even have the same combinations of sectors.

For the above reasons no attempt was be made to aggregate sectors in calculating
multipliers. In addition, only the most significant sectors in the wood products industry

(Table 2) were analyzed.

There are several reasons for examining a subset of the sectors. First, there are 11 sectors
identified, which could make the study too burdensome. Many of the sectors are already
backward linked. For example the sawmills and planing mills (sector 134) sector has
backward linkages to four other wood products sectors. This was determined by
examining the production function in the absorption matrix generated by IMPLAN
(Table 3). For example the logging sector (133) buys 32 percent of its inputs fi'om the
forestry products sector (24) and the sawmills sector (134) buys 28 percent of its input
from the logging sector. All wood products sectors buy more fiom other wood products
sectors than all other sectors combined. These transactions will all be accounted for as
indirect effects. Employee compensation varies from 16 percent for the logging sector

(the least labor intensive) to 25 percent for the veneer sector (the most labor intensive).

46

l

 

'I'alrle 3 — \\ uurl Products Industry l’r'urluetiuu Functions

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Industry Logging Sawmills Veneer
Commodity Demand:
Forest Products Sectors:
Forestry Products (24) .32 .09 .09
Logging (133) .08 .28 .16
Sawmills (134) .00 .08 .01
Veneer (139) .00 .00 .08
Total Forest Industry .40 .45 .34
Other Commodity Demand .22 .25 .28
Total Commodity Demand .62 .70 .62
Value Added:
Employee Comp .16 .18 .25
Proprietary Income .02 .02 .04
Other Property Income .19 .08 .08
Indirect Business Taxes .01 .00 .01
Total Value Added .38 .30 .38
Total 1.00 1.00 1.00

 

 

 

 

a
Data in Table 3 are Gross Absorption Coemcients from the IMPLAN Industry
Balance Sheet from report united statesiap. 1997 data.

The study will focus on the sectors that are normally significant and higher on the

processing ladder.

The study will include Sector 133, Logging Camps and Contractors; Sector 134,

Sawmills and Planing mills; and Sector 139, veneer and plywood.

47

These sectors are described as follows:1
Logging Camps and Contractors (133) — Establishments primarily engaged in
cutting timber and in producing rough, round, hewn, or riven primary forest or wood raw

materials, or in producing wood chips in the field.

Sawmills and Planing Mills (134) — Establishments primarily engaged in sawing
rough lumber and timber from logs and bolts, or resawing cants and flitches into lumber,
including box lumber and softwood cut stock; planing mills combined with sawmills; and
separately operated planing mills which are engaged primarily in producing surfaced

lumber and standard workings or patterns of lumber ......

Veneer and Plywood (139) — Establishments primarily engaged in producing
commercial veneer and those primarily engaged in manufacturing commercial plywood
or pre-finished plywood. This includes non-wood backed or faced veneer and plywood,

from veneer produced in the same establishment or from purchased veneer.

Sector 146, Reconstituted Wood Products; Sector 161, Pulp Mills; Sector 162, Paper
Mills; and Sector 163, Paperboard Mills will not be included in the analysis because they
occur so infiequently it would be difficult to statistically evaluate. Those sectors that are
minor and well represented as indirect effects will not be included in the analysis (Sector
22, Forest Products; Sector 24, Forestry Products; and Sector 26, Agricultural, Forestry

and Fishery Services). Finally, if a sector occurs very infrequently and is also probably

 

' Descriptions of wood products sectors are from the Standard Industrial Classification Manual — 1987.
Executive Ofice of the President, Office of Management and Budget.

48

independent of local raw material supply, it is excluded (Sector 135, Hardwood

Dimension and Flooring Mills).

Impact Model Construction

There are two different impact model components that are normally constructed by
IMPLAN for each of the impact areas selected. The descriptive component describes the
transfers of money between industries and institutions for the impact area being analyzed.
It contains the social accounts and the input-output accounts. The social accounts include
variables such as employment, income, and total industry output for the impact area
being analyzed. The input-output accounts show the flow of funds between economic

sectors (intermediate and final demand).

The predictive component is the set of input-output multipliers, which “predict” total
regional activity based on a change in consumption or demand. This includes the
calculation of the econonric multipliers. For this study, all that was needed fi'om the
predictive component were the economic multipliers, which were used as the only
response variables in regression analysis. The descriptive component must be generated

before IMPLAN generates the predictive component.

The following sections discuss several decisions and assumptions that were made which

affect the multipliers that were generated and analyzed.

49

Trade Flows

When constructing the social accounts, certain assumptions must be made with respect to
trade flows (imports/cxports/transshipments). This is an important assumption in that it
determines how much is spent within the impact region, how much is spent outside the
impact region from activity originating within the impact region, and consequently how
large the resulting multipliers will be. In this study, trade flows will be estimated using
the Regional Purchase Coefiicient (RPC) approach. RPCS are derived with an
econometric equation that predicts local purchases based on the region’s characteristics.
The RPC is the percent of local demand satisfied by local production. For example, an
RPC of 0.75 for a given commodity means that for each $1 of local need, 75% will be
purchased from local producers. This method is based on the characteristics of the region
and describes the actual trade flows for the region mathematically. IMPLAN software
generates RPCS automatically with a set of econometrically based equations. There is a
different equation for each commodity with variables filled by study area data. The
RPCS are limited by the supply/demand-pooling ratio (explained below). The ratio of
locally purchased to imported goods is perhaps the most significant factor affecting
subsequent multipliers (MIG 2000). The greater the quantity of goods purchased locally,
the more local economic activity will be stimulated and hence the larger the resulting
multipliers. IMPLAN allows RPCS to be edited if the user feels they have better
information. This has not been done in this study as there is no known better secondary

data.

50

Table 4 shows an example of RPCS for four different states in different regions of the
United States. For example in Georgia economic impact areas, 76 percent of what the
sawmills sector buys fi'om the logging sector is bought locally. Table 4 also shows there
is little difference from region to region with exception of the sawmill sector in
Michigan, which is significantly smaller. It also shows that the logging and sawmill
sectors do not buy anything locally. This is consistent with Table 3, which shows that the
production frmctions for both logging and sawmills do not include the veneer sector. The

production functions and regional purchase coefficients must both be examined when

State/Industry Logging (133) Sawmills (134) Veneer (139)

133 .96 .96 .97

134 .76 .76 .76

139 .00 .00 .81
hdkflu

133 .93 .93 .93

134 .43 .43 .43

139 .00 .00 .60
Nhnuana

133 .93 .93 .93

134 .78 .78 .78

139 .00 .00 .76

133 .98 .98 .98
134 .78 .78 .78
139 .00 .00 .83

 

a
Data in Table 4 are RPCS from the IMPLAN Industry Balance Sheet from report united statesiap. 1997
data.

51

considering the economic effects of changes in the wood products industry. The
production function for an industry could show a particular industry to provide significant

inputs. However, if the RPC is small the effects on the impact area will be small.

An alternative to using RPCS to calculate trade flows is the Supply/Demand Pooling
approach, which is offered by IMPLAN. Supply/demand pooling assumes that local
demand will get as much locally as possible; all local need that can possibly be met by
local producers will be purchased locally. Since this minimizes imports it will maximize
local economic activity and the reSulting multiplier. The percent of local usage is based
on physical capacity for the region. The total commodity supply is divided by the
demand. If the resulting ratio is 0.8 then 80% of local needs will be met by local
demand. If supply is greater than demand, 100% of that demand will be met by local
production and the remainder is exported. Because this scenario is not realistic it will not
be used in this study as the primary trade flow assumption. However, as mentioned

above, it will serve as the upper limit for the RPC ratio.

The third potential assumption for trade flows is the Location Quotient approach. This
approach is also offered by IMPLAN and based on commodity output. The location
quotient equation is a fixed equation. It compares the ratios of local production to
national production ratios or other base regions as desired. This implies that the base
region is self-sufficient. If commodity production for a region approaches the similar
proportion as the base region, the RPC approaches 1. For example if the veneer and

plywood sector is 2.3% of the US. economy anything in excess of this in the region

52

being analyzed would be assumed to be exported. This again has the same weaknesses as
the supply/demand pooling approach, in that it ignores cross hauling/transshipments, and

consequently was not used in this study.

When dealing with multi-state regions some additional assumptions were made with
respect to trade flows. IMPLAN offers three alternatives. The first is Maximum RPC,
which says that the combined region’s RPCS will be at least equal to the maximum of the
individual RPCS. The second option, First RPC is an arbitrary system previously used
by the US Postal Service that simply takes the first state from a multi-state list. The last
alternative is Average RPC, which is a weighted average based on output for all the states
in the selected region. This is the assumption that was used in this study because it is the

only one that resembles reality and is the IMPLAN recommended default.

As previously mentioned in this report the Forest Service in conjunction with the
Minnesota IMPLAN Group is developing a gravity model that will determine trade

flows. However, this will not be available as part of the IMPLAN model until 2002 at

the earliest.

Types of multipliers to be analyzed — types of effects.
One study objective focuses on the behavior of economic multipliers of a region as
various selected economic characteristics are changed (e. g. population, size, geographic
region etc.). Of the multipliers available, only the Type 1, Type II and the Type SAM are

developed by IMPLAN. They are also the most useful current method of measuring

53

economic impacts. The Type SAM multiplier option in IMPLAN allows the user to
select what institutions to include or not include. The Type I multiplier, which is used
to determine direct and indirect effects, is a prerequisite and is generated regardless of

whether the Type II or Type SAM multiplier is selected.

The Type I multiplier was one of the two multipliers selected as a dependent variable in
regression analysis and analyzed in this study. It was anticipated that it might display
different behavior than the multipliers that include induced effects. The Type I multiplier
is usually a good indicator of the development of the industry being analyzed; that is the

more diverse the industry is the higher will be the Type I multiplier.

The Type SAM multiplier was chosen as the other dependent variable to be analyzed. It
was selected over the Type II multiplier because it gives a more realistic view of the
economy in that it can account for transactions for all institutions, including households

and government transactions.

This study was limited to analyzing the Type I multiplier and the Type SAM multiplier.
This is consistent with the objectives of the study as these are the multipliers most

commonly used by Forest Service and other analysts at the present.

Types of multipliers to be analyzed - economic variables.

Multipliers, including the Type I and Type SAM multipliers, are commonly expressed in

terms of several economic variables. These include employment, output (sales), and

54

value added. Value added includes employee compensation, proprietor income (self-
employed income), other property income and indirect business taxes. All of these
multiplier variables can be generated by IMPLAN. However, in the interest of keeping
the study focused, only employment and personal income (determined by adding
employee compensation and proprietor income) multipliers were analyzed. This was
determined based on the demand by analysts for employment and income multipliers and
the lack of demand for value added multipliers. Value added data is rarely encountered
in economic impact studies and not well understood by the concerned public or many

analysts determining economic impacts.

Response variables analyzed

Table 2 shows the structure of the multipliers used in the study. The first and
most basic statement is that the multipliers will eventually be used as the response
(dependent) variables for regression analysis in this study. The explanatory

(independent) variables will be discussed later in this section.

Three economic sectors from the IMPLAN economic impact model were chosen
for the study. Rationale for this selection was presented earlier in this chapter under
section “Economic Sectors Analyzed” (pg 42). For each of these three sectors both the
Type I and Type SAM multipliers were calculated for both the employment multiplier
and the personal income multiplier. This means that up to a total of 12 multipliers were
generated for each impact model. Less than 12 were generated if some of the wood

products sectors were not present. Up to five impact area models were generated for each

55

National Forest therefore up to 60 multipliers could be developed for an individual
National Forest impact area. However, every multiplier will fall into one of the 12
classes listed below. Also, each of the multipliers listed below will be analyzed separately

throughout this study.

Each of the 12 different classes of multipliers was given a descriptive variable code
(Table 2, pg 45). This ‘code will be used for descriptive purposes throughout this study
for the simple reason of saving space. The code is somewhat easy to follow. For
example the first multiplier shown in Table 2, LE1 is a multiplier for, Logging Camps
and Contractors sector for Employment, Type 1.

Explanatory variables to be analyzed
Introduction
One of the objectives of the study was to identify key factors that explain the variation of
economic multipliers. The explanatory variables chosen for analysis were a result of the
literature review, discussion with experts, and reviewing the industry production
functions to get a better understanding of the industry structures. Another objective was
to determine the feasibility of using these variables individually or in combination to
predict the economic multipliers (response variables). The impact areas analyzed have
been described by a number of characteristics that helped in analyzing and classifying
multipliers. These explanatory variables served as the initial independent variables in the
study and were analyzed using regression techniques to determine if they are usefirl in

predicting multipliers (Table 5).

56

I'ahle 5 - lixplanalor} \ ariahles

 

 

 

 

Variable Indicator Used Source
. Total population 1997 Population from
Human Populatron .
Populatron Density US. Census estimate.
Total Industry Output IMPLAN
Size of Economy Total Personal Income
Number of Economic Sectors
Geographic Size Square miles US. Census

 

 

 

 

 

Each of the variables in Table 5, were included with other information for each economic
impact area analyzed, in an Excel spreadsheet. They were then transferred to MINITAB
for statistical analysis. The independent or explanatory variables (Table 5) were
analyzed, through regression analysis, in relation to the economic multipliers described

earlier. The economic multipliers were modeled as the dependent variables.

Explanatory variables analyzed

 
 

'lahle o li\pla|rator) \ arialile ('orles

   

 

 

Explanatory Variables Variable
(Base year-1997) Code
Population (millions ) (+) a P0P
Population Density (+) PopDen
Number of Economic Sectors (+) Sect
Total Industry Output (billions$) (+) TIO
Personal Income (billionSS) (+) Perlnc
Economic Impact Area (million acres) (+) EIA
Geographic Region Reg

 

a
Sign in brackets indicates the anticipated direction of change of

multiplier. For example (+) means that the multiplier will be
expected to increase as the value of the explanatory variable
increases.

57

Table 6 shows the variables that have been chosen to analyze as potential explanatory
variables, the unit of measure, the code used to identify the variable in this report, and the
expected direction of change. Although much of the data was taken from the IMPLAN
databases, it is available from alternate sources as described below. The use of IMPLAN
data was mostly a matter of expedience. A brief discussion of each of the variables

follows.

Population - The expectation is that as human populations increase, so will
economic multipliers. This would be especially true for the Type SAM multiplier, which
includes induced effects. As the population increases the economy becomes more
diverse and spending leakage is reduced. As more local money is spent within the
economic impact region the multipliers Should increase. However, this assumption is not
as obvious with the Type I multiplier. Does the wood products industry become more
developed in larger impact areas therefore have larger multipliers? The analysis should

answer this question.

The human population for each county was determined from the County
Population Estimates Program of the US. Census Bureau for the year 1997. The
program estimates populations along with demographic components of change for each
year between decennial censuses. The year 1997 was used because it is the latest year
reflected in the most recent IMPLAN model. All impact areas were either individual

counties or in most cases aggregates of counties where populations were simply summed.

58

Population Density - AS the human population becomes more dense (more
people per unit of land area) how do the economic multipliers change? Prior research
investigating the behavior of multipliers for the tourism industry, showed Type II
multipliers increase with increasing population density (Chang 2001). It was assumed

the same direction of change will occur with the wood products industry.

Human population density, in terms of people per square mile, was determined by
dividing the total population, explained above for 1997, for each impact area, by the area
(square miles) in each impact area. The area (square miles) was determined as explained
below under Economic Impact Area. The US. Census Bureau computation of population
density was not used because the latest computation was from 1990, which is not

consistent with the base year 1997 used for other variables.

Number of Economic Sectors - It is assumed that the larger the number of
economic sectors in the region being analyzed, the larger will be the Type SAM
multiplier for that region. As sectors are added, the economy becomes more diverse and
spending leakage is reduced. As more local money is spent within the economic impact
region the multipliers should increase. This assumption was based on previous research
(Zheng et al. 1988). However, this assumption is not as obvious with the Type I
multiplier. It is not intuitive or apparent that the wood products industry becomes more

developed in impact areas with more sectors. The analysis addresses this issue.

59

The number of economic sectors used as an explanatory variable is based on the number
of sectors in the IMPLAN economic impact model. The IMPLAN basic impact area data
report shows the total number of sectors for each model. A non-IMPLAN substitute for
this variable could be the number of sectors at the 3-4-digit level for Bureau of Economic
Analysis data. Another source would be the E8202 state and county employment and
income data collected under the guidance of the Bureau of Labor Statistics, US.

Department of Labor.

Total Industry Output - The total industry output is the total value of production
by industry for a given time period -— in this case, a year, for the selected impact area. It

is the total value of purchases by intermediate and final consumers including exports.

The assumption is that as an economy grows, it becomes more diverse and there is less
spending leakage from the economic impact area For this reason, at least the Type SAM
multiplier should increase as the total industry output increases. . This assumption was
based on previous research (Zheng et al. 1988). Whether or not the Type I multiplier
increases (normally a function of the complexity of the wood products industry) will need

to be answered by the analysis.

The total industry output information is taken from IMPLAN Report #SA050, Output,

Value Added and Employment. An alternative source of this information would be the

Bureau of Econorrric Analysis Annual Survey of Manufactures (U SDC 2001).

60

Personal Income - Personal income in this case, is the sum of employee
compensation and proprietor income, for the selected impact area. It is assumed that as
personal income increases so will population and the diversity of the economy. This will
result in less spending leakage to other econonries and result in larger multipliers — at
least the Type SAM multiplier. It is uncertain at to whether the Type I multiplier will
increase. This information is taken from IMPLAN Report #SA050, Output, Value Added
and Employment. Other Property Income was not included because it does not have a
direct relationship or influence on economic multipliers. A non-IMPLAN source of this

data would be the REIS CA5 tables (U SDC 2001).

Economic Impact Area — The physical size of the economic impact areas (square
miles) was determined for each county and aggregated as necessary for each multi-county
impact area. As the size of the impact area increases it is assumed that the size and
diversity of the economy will increase resulting in larger multipliers - at least for the
Type SAM multiplier. The direction of change for the Type I multiplier is uncertain
without further analysis. The size of the impact areas was taken from the US. Census
Bureau, Table 1. Land Area, Population, and Density for States and Counties from 1990

Summary Tape File 1C.

Geographic Variables

To address one of the study objectives (Objective 3), it was necessary to look at possible

regional differences to determine if separate equations for different regions would

61

improve the ability to predict multipliers. Two sets of regions were identified as
potentially useful. These delineations are not used as explanatory variables in the study.
They are potential criteria to be used to develop sub-populations through analysis of
variance to determine if there are differences between geographic regions and used as

dummy variables in the model building process. They are as follows:

USDA Forest Service Regions — Impact areas and resulting multipliers were
determined for all Forest Service Regions with the exception of the Alaska Region (R-
10). All multipliers have been attributed by F8 Region and can be reviewed for certain
regional differences. These will be discussed in later sections. Forest Service Regions
were chosen because they are well distributed throughout the US, and the benefit of this

study accrues primarily to that agency (Appendix E and F).

Bureau of Economic Analysis Economic Regions - The entire US. is divided
into Economic Regions by the Bureau of Economic Analysis . Regions are then
subdivided into economic areas. All multipliers for all levels are attributed by the
primary BEA Economic Regions within the economic impact area for which the
multiplier applies. Also, the level five impact area (Chapter 3) is based on BEA
Economic areas. Economic areas are generally centered around metropolitan areas

(U SDC 1995).

It was expected that the complexity of the wood products industry could change

throughout the US. with some areas more developed than others. This could result in

62

better predictive models. Analysis of variance techniques were used to address this
possibility. However, there were no specific expectations as to where multipliers of all

types might be higher or lower or where the effects of explanatory variables differ.

Other explanatory variables considered
Another variable considered , in addition to those in Table 1, was the size of the timber
industry in the impact area — both relative and absolute. However, this was dropped as it
was not possible to collect this information in a reasonable time at a reasonable cost, and
it would not serve as a reasonably available explanatory variable to use in lieu of impact
model building. The objectives of the study require that data must be reasonably
available, outside the IMPLAN system. Although, IMPLAN data was used for some of
the explanatory variables, it was done for expediency reasons — the data could have been

acquired from an additional source, but at additional expense to the study.

The number of sectors in the wood products industry (as opposed to all economic
sectors), was also considered as an explanatory variable, and is closely related to the
variable discussed above. There were several problems with this idea. The first problem
was that it is difficult and time-consuming to deternrine how many wood products sectors
there actually are in a particular impact area without using IMPLAN. The objectives of
this study require alternative and reasonably available sources of data The second
problem is the degree of connectedness among wood products sectors. Based on

reviewing the production functions of each wood products sector in an impact region, the

63

amount of economic transactions among wood products sectors is often less than half of

the of the total value of purchases.

In addition to the number of economic sectors as an indicator of economic diversity, the
use of the Shannon-Weaver index (USDA Forest Service 2001) as an indicator, was also
considered. However, this idea was dropped because the indices are only available for
individual counties and cannot be aggregated. The calculation of multi-county indices
is complicated and requires the analysis of the IMPLAN multi-county data matrix. There

are plans to have this automated by IMPLAN in the near future.

Another independent variable considered was the acres of timberland in an impact area
and the timberland acres as a percent of total impact area acres. This variable was not
used because of the unavailability of timberland data. However, this data will be

available from the USDA Forest Service in the near future.

Interaction variables (cross-product terms) were also examined. For example, population
was multiplied by the number of economic sectors and then evaluated as an independent

variable. The new interaction terms were evaluated with and without the original terms.

Where original terms remained the model produced slightly higher adjusted R 2
(regression coefficient) values but introduced significant additional multicollinearity
indicated by variance inflation factor (V IF) values greater than 5.0. The VIP is used to
detect whether one explanatory variable has a strong linear association with the

remaining explanatory variables (the presence of multicollinearity among the explanatory

variables). VIF measures how much the variance of an estimated regression coefficient
increases if your explanatory variables are correlated. The presence of this condition

resulted in eventually eliminating the interaction variables in favor of more significant

individual variables. Where original terms were excluded, adjusted R 2 values were
slightly lower than they were when in the original model where the original terms were

separate and the interaction term was excluded.

General Form of Model

Given the data described above, it was possible to represent the models in a general form.

The general linear form of a multiple regression model is:
multipliers, = 30+ Xflj‘XfiE;
1
where multipliers, is the value of the economic multiplier i, (Table 2), ’60 is the

intercept, ZfljIXj is the sum of all coefficients multiplied by the respective variable
I

attribute for each attribute j , (Table 5), and 8,- is the error for each multiplier i. The

focus of the study is determining the feasibility of predicting multiplier S i .

Although the functional form y = x (linear) was selected for the preliminary models other
forms were considered. These included lny = lnx (double log), lny = x (dependent) single

log) and y = lnx (independent) single log.

65

Statistical Analysis Methods

The statistical analysis done for this study was based on techniques fiom several sources.
They include Koutsoyiannis (1979), Gujarati (1995), Freedman et a1 (1991), Snedecor et
a1 ( 1980), Mendenhall et al. (1994), and the MINITAB users guide (1999). The statistical
analysis methods will be described as they are applied for each of the study objectives. A
summary of analysis procedures leading up to statistical analysis will precede the

discussion of the statistical analysis used in this study.

Study Objective 1: Describe Variations in Multipliers.

The IMPLAN economic impact system was used to generate the economic multipliers to
be analyzed as dependent variables in regression analysis. Type I and Type SAM
multipliers were generated to reflect indirect, induced, and total economic effects. Type I
and Type SAM multipliers were generated to reflect effects in terms of employment and
personal income. The multipliers analyzed were limited to the three predominant sectors
of the wood products industries: logging camps and contractors, sawmills and planing
mills, and veneer and plywood. Trade flows were estimated using the Regional Purchase

Coefficient option in IMPLAN.

The study areas, to be used as samples, were based on National Forests with each
National Forest serving as a center for up to five, different sized, impact areas. This
resulted in 155 sets of impact areas for 650 separate impact areas to be analyzed. Impact

areas varied from single counties to aggregates of more than 20 counties. Sets of data,

66

including economic multipliers, were developed for each of the 650 impact areas.
Geographic regions were established based on USDA Forest Service regions and impact

areas grouped accordingly for additional comparison.

Descriptive statistics generated consisted of means, trimmed means, medians, ranges,
maximums, minimums, and standard deviations of multipliers. These were computed for
each type of multiplier for each sector selected for all geographic regions (listed in Table

2).

Study Objective 2: Identify the key factors that explain the variation of economic
multipliers.

The second study objective is to identify the key factors that explain the variations in
economic multipliers under varying conditions. The explanatory variables selected as
possible factors that might help to explain the variation in multipliers were: population
(human), population density, total number of economic sectors, total industry output,
personal income, and the physical size of the economic impact area. Other explanatory
variables considered but not used were: total acres of timberland within the impact area,
percent of total acres in an impact area consisting of timberlands, the size of the timber
industry, and cross-product terms. Non-linearity was tested using natural log
transformations. Dummy variables were used to investigate possible regional
differences. Building separate models for separate geographic regions was also

investigated.

67

Correlation coefficients were computed between all response and explanatory variables to
determine the direction and strength of relationships among these variables. This process
also helped identify those variables that had the best chance for inclusion in the model
developed for Objective 3. At the same time the relationship between explanatory
variables and other explanatory variables was examined through correlation analysis to

determine the potential for multicollinearity.

Study Objective 3: Determine the feasibility of using selected, readily available,
explanatog variables to estimfiate economic multipliers.

Linear regression techniques were used to quantitatively evaluate the relationship
between the explanatory variables and the response variables (multipliers). MINITAB

Best Subsets process was used to identify the best combinations of variables to be used in

potential regression models to predict multipliers. R2 , adjusted R2 , and Mallow’s Cp
values were generated by MINIT AB to measure the quality of the models. Regression
models were examined for the presence of heteroscedasticity by visual analysis of the

residual plot graphs.

After the preliminary regression models were established for each multiplier group
additional procedures were used in an attempt to improve the models. Analysis of
variance procedures were used to determine if there were differences in multipliers
between geographic regions (based on USDA Forest Service regions) that might improve
the models. Regions or the best combinations of regions were represented as dummy

variables in the regression analysis process. Additional variables such as the size of the

68

wood products industry and the percent of the region bearing harvestable timber crops
were analyzed as explanatory variables. Natural log transformations were used to
generate non-linear explanatory variables in an attempt to improve the predictive strength
of the models. Multicollinearity was measured using variance inflation factors (V IF ). If
A VIF greater than 5.0 indicated that multicollinearity was a problem. Models were then

adjusted to reduce multicollinearity.

The analysis produced 12 final models designed to predict two types of multipliers, for

two categories of economic effects, for each of three wood products industries sectors.

69

CHAPTER FOUR: ANALYSIS AND RESULTS

Introduction

Results of the study are presented for each of the three objectives of the study. The
objectives are: describe variations in the multipliers of the wood products industries,
identify the key factors that explain the variations in multipliers, and determine the
feasibility of using selected explanatory variables to predict multipliers. The following
discussion applies to all National Forest impact regions in the US. unless otherwise

indicated.
Study Objective 1: Describe Variations in Multipliers.

This section describes the response variables (multipliers) in terms of generally used
descriptive statistics discussed in Chapter 3, Methods. These parameters were generated
with the use of the MIN ITAB statistical software program. This information is generally
referred to as “descriptive statistics” as opposed to “inferential statistics” which will be
discussed under Study Objective 3, later in this chapter. The review of the data
characteristics is important in order to evaluate potential use of the data for statistical

inferences.

Descriptive statistics “consists of procedures used to summarize and describe the
important characteristics of a set of measurements” (Mendenhall et al. 1994). The
following section describes each selected characteristic for each multiplier group and

each of the explanatory variables.

70

The relationship between the multipliers and the individual explanatory variables is
reported and discussed under Objectives 2 and 3. This was done by correlation analysis
and also regressing each explanatory variable on each individual multiplier in the Best

Subsets procedure.

Number of Observations
As can be seen in Table 7, the number of observations (impact models) varies among the
three economic sectors studied. A total of 674 impact areas were modeled in IMPLAN.

Twenty-four of these impact areas had none of

‘l'ahle 7 Number of Observations

 

the 3 wood products economic sectors therefore

were not represented in the models. Almost all Multiplier Number of
Variable Code Observations
impact areas that had Logging Camps and
LE1 650
Logging Contractors (650 areas) also had LE2 650
LP] 650
Sawmills and Planing mills (647 areas). In LP2 650
SE1 647
contrast, only 384 impact areas were represented 552 647
SP 1 647
by the Veneer and Plywood sector. This is SP2 647
VEl 384
econorrrically logical as the economic threshold VE2 384
WI 384
to enter this sector is much greater than the other VP2 384
Pop 674
sectors and the scale of operation must be much PopDen 674
Sect 674
larger to continue operations. There is no such T10 674
Perlnc 674
thing as a small veneer and plywood mill. BIA 674

 

 

 

71

Measures of Central Tendency

Means - MIN ITAB calculates the arithmetic mean, or average. The mean is a
commonly used measure of the center of a population or sample of numbers (Table 8).
An explanation of the multipliers in Table 8 can best be given by an example. The mean
multiplier for LEI (logging, employment, Type I), is 1.39. This means that for each
direct job created or lost from change in output another .39 indirect jobs will be created
or lost. For example, an increase in raw material availability from a local National Forest
might have the potential to create another 100 jobs in the logging industry. It would also
create another 39 indirect jobs in those industries that the logging industry buys from.
The multiplier for LE2 (logging, employment, Type SAM) creates an additional 32 jobs
(1.71-1.39) from induced spending (household spending of wages paid by firms causing
direct and indirect effects). Total direct, indirect, and induced effects would result in 171

additional jobs in the selected economic impact area.

72

The first procedure performed after the means were calculated was to review the
relationship between the Type 1 and Type SAM multipliers. The mean Type SAM
Multiplier is and should be in all cases larger as it includes the induced as well as direct
and indirect effects. Also, an important procedure was to review all the resultant
multipliers to see if they appeared to be reasonable for the given circumstances. This was
done by ordering the multipliers from top to bottom and vice versa to search for extreme
values. All multipliers of all types were found to be above 1.0 and below 4.0. Anything

below 1.0 would have

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

indicated a technical error. 'l‘ahle 8 ~ Measures of (‘entral ’l‘entlene)
ytlrrng above 4 0 would be Multiplier Means Trrmm' ed Medrans
. a
possible but highly unlikely. Variable Code Means
Multiplier means of all types LE1 1.39 1.39 1.40
LE2 1.71 1.71 1.71
are consistently larger in the LP] 1.35 1.34 1.32
LP2 1.60 1.59 1.57
sawmill and planing mills SE1 1.76 1.77 1.80
SE2 2.24 2.25 2.26
sector than the other sectors SP1 1.68 1.67 1.65
SP2 2.00 1.99 1.96
(Table 8). They are lowest in VEl 1.53 1.53 1.54
. VE2 1.99 1.99 2.00
the 10881118 sector- vr>1 1.46 1.46 1.46
, , VP2 1.75 1.75 1.75
Employment multrplrers are
consistently higher than a See Table 2 (pg 45) for variable code descriptions.

personal income multipliers. This might suggest that income per job for the direct and

induced effects is lower on the average than the wood products sectors.

73

Trimmed Mean - A 5% trimmed mean is calculated by MINITAB, which removes the
smallest 5% and the largest 5% of the values, and then averages the remaining values as

it does for the arithmetic mean. The value of this calculation is to determine if there is a

 

Table 9 - Measures of Variabilit)
Multiplier Minimum Maximum Range
Variable Code Value Means Value (difference)
LE1 1.09 1.39 1.59 0.50
LE2 1.18 1.71 2.13 0.95
LPl 1.10 1.35 1.87 0.77
LP2 1.18 1.60 2.26 1.08
SE1 1.35 1.76 2.05 0.70
SE2 1.58 2.24 2.91 1.33
SP1 1.23 1.68 2.99 1.76
SP2 1.38 2.00 3.51 2.13
VEl 1.24 1.53 1.69 0.45
VE2 1 .47 1.99 2.44 0.97
W] 1.15 1.46 1.90 0.75
VP2 1.33 1.75 2.29 0.96

 

 

 

significant effect on the arithmetic mean from the presence of unusual values/outliers.
Table 8 indicates the possibility that there is little difference between the 2 sets of means
therefore suggesting that unusual values to one side of the mean or the other, might not

have very much effect on the arithmetic mean.

Median — The median is the middle measurement in a set of measurements. Half the

observations are less than or equal to it.

74

The median can be very similar or exactly the same as the arithmetic mean or it can be
very different depending how individual observations (multipliers, etc.) are distributed
about the mean. It is a rough indicator of whether or not a population is “normally
distributed”. A comparison of the aritlnnetic means and medians in Table 8 shows very
little difference. Graphs, generated by MINITAB, showed the distribution of median

values about their means to be sinrilar to the distribution of the value of the means.

Measures of Variability

Range — The range is the difference between the largest and smallest data value.
It is one of several measures of the distribution of observations (multipliers etc.) about
the population means.

The minimum and maximum value and range for each class of multiplier shows a fairly
broad range of values (Table 9). However, by itself, range is not a good predictor of a
normal distribution about the mean because it depends on only 2 values, which might be
outliers and not very representative of the population. A normal distribution is essential
in evaluating the predictive qualities of the data. The sawmill and planing mills type
SAM multiplier shows the widest range and this seems reasonable because the industry
exists over a wide range of conditions (population, number of sectors, etc.). Generally,
the minimum values occurred in counties with small econorrries and the maximum values
occurred in medium to large counties. The absolute smallest multiplier (1 .09) is for the
Level 1 area for the William F. Bankhead National Forest in a rural area of Alabama.

The absolute largest multiplier (3.51) is for the Level 3 impact area for the Appalachicola

75

National in the heavily populated Florida panhandle. The area has both a large

population and well developed wood products industry.

I able 10 — Standard Deviation and (‘oel'l'ieient ol'

 

\ ariation
Multiplier Standard Coefficient
Variable Code Means Deviation of
Variation

LE1 1.39 0.10 .07
LE2 1.71 0.17 .10
LP] 1.35 0.13 .10
LP2 1.60 0.18 .1 1
SE1 1.76 0.14 .08
SE2 2.24 0.26 .12
SP1 1.68 0.18 .11
SP2 2.00 0.24 .12
VEl 1.53 0.10 .07
VE2 1.99 0.21 .11
WI 1.46 0.10 .07
VP2 1.75 0.15 .09

 

 

 

Standard Deviation - The standard deviation is another method, which provides a
measure of how Spread out the data are (dispersion). While the ”range” explained above
was based on only the 2 most dispersed observations, the standard deviation considers all

observations and their relationship to the mean (Table 9).

Comparing the ranges from above to the standard deviations for each multiplier category
shows many similarities. The major similarity is that the Type SAM multipliers Show
more dispersion than the Type 1 multipliers under both income and employment
measures and whether expressed as an absolute (standard deviation) or as a percent

(coefficient of variation) . This is probably due to the inclusion of induced effects that

76

vary more over a wide range of conditions. Also, sawmills and planing mills show more
dispersion than the other two sectors therefore being consistent with the behavior of the

means.

Figure 1 - Distribution of Multiplier Means

Frequency

 

1.15 1.25 1.35 1.45 1.55 1.65 1.75 1.85 1.95 2.05 2.15
Multipliers (LE2)

Figure 1 is an example of the normal shaped distribution of the means and the small

degree of deviation.

Study Objective 2: Identifl the key factors that explain the variation of economic

multipliers.

While Study Objective 1 identified differences in multipliers throughout the impact areas

established for the study, Study Objective 2 evaluates the relationship of the multipliers

77

to a variety of explanatory variables (Table 5). The reason for this analysis was to

determine their potential as explanatory variables in the final regression model.

Correlation Analysis — Closely related to but conceptually different from

regression analysis (to be discussed under Study Objective 3 ) is correlation analysis
where the primary objective is to measure the degree of linear association between two
variables. The correlation coefficient is the quantitative measure of the linear association

Mendenhall et al. 1994).

Correlation analysis was used to quantify the relationship between the explanatory
variables and response variables (multipliers). Correlation analysis was also used to
compare the explanatory variables to each other to measure the potential for

multicollinearity. The presence of multicollinearity was measured by variance inflation

factors (VIF).

Correlation analysis was used (MINIT AB) to calculate the coefficient of correlation for
pairs of variables. This was done to determine the degree of the relationships between
the explanatory variables and the response variables. The correlation coefficient assumes
a value between -1 and +1. If one variable tends to increase as the other decreases, the

correlation coefficient is negative. Conversely, if the two variables tend to increase or

78

l‘ahle l I ~ (‘orrelalion (‘oel'l'ieients and l’-\'alues

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

vanables Pop PopDen Sect T10 Perlnc BIA
LE1 0.193 a 0.020 0.517 0.193 0.193 0.463
0. (x) 0 b 0.612 0.000 0.000 0.000 0.000

LE2 0.172 -0031 0.509 0.172 0.173 0.423
0.000 0.437 0.000 0.000 0.000 0.000

LPl 0.323 0.206 0.510 0.322 0.317 0.360
0.000 0.000 0.000 0.000 0.000 0.000

LP2 0.405 0.220 0.643 0.402 0.397 0.422
0.000 0.000 0.000 0.000 0.000 0.000

SE1 -0.214 -0312 0.118 -0212 -0213 0.273
0.000 0.000 0.003 0.000 0.000 0.000

SE2 -0.109 -0.227 0.251 -0.105 -O.106 0.305
0.006 0.000 0.000 0.008 0.007 0.000

SP1 0.022 -O.128 0.204 0.025 0.019 0.224
0.583 0.001 0.000 0.519 0.625 0.000

SP2 0.143 -0071 0.392 0.145 0.138 0.319
0.000 0.072 0.000 0.000 0.000 0.000

VEl -0.309 -O.318 0.021 -0.312 -0317 0.032
0.000 0.000 0.688 0.000 0.000 0.537

VE2 -0205 -0.234 0.122 -0204 -0207 0.211
0.000 0.000 0.017 0.000 0.000 0.017

VP1 0.079 -0052 0.296 0.075 0.067 0.102
0.124 0.312 0.000 0.145 0.193 0.046

VP2 0.236 0.024 0.535 0.233 0.226 0.248
0.000 0.644 0.000 0.000 0.000 0.000

 

 

a
Correlation coeficients are presented in the top row of data for each variable.

b
P-values are presented in the bottom row for each variable.

decrease together, the correlation coefficient is positive. In Table 10 the top number in
each set of rows is the correlation coefficient. The bottom number is the p-value for
individual hypothesis tests. P-values are often used in hypothesis tests where you either
accept or reject a null hypothesis. The p-value represents the probability of rejecting the

null hypothesis when it is true. The smaller the p-value, the smaller the probability that

79

you would be making a mistake by rejecting the null hypothesis. The null hypothesis in
this case is that the correlation coefficients in Table 10 are zero. A cutoff value often
used is 0.05, that is, reject the null hypothesis when the p—value is less than 0.05.
Technically, the p-value is defined as the lowest significance level at which a null

hypothesis can be rejected.

Table 11 shows that in most cases there is little chance that you would be making a
mistake by rejecting the null hypothesis. However, in some cases (i.e. VEl/IS = 0.688)
the p-value is quite large suggesting there is a high probability that rejecting the null
hypotheses would be a mistake. Some p-values are unusually high for population
density. High p—values are associated with low correlation coefficients —— this is to be

expected. Other than that there is no obvious pattern.

The strongest positive linear relationships, between the response variables (multipliers)

i and the explanatory variables (Table 5) indicated by the correlation coefficients, was
between the multipliers and the number of economic sectors. This would be expected as
the more diverse the economy the more spending, direct, indirect, and induced, will
probably occur in the impact area. Also, consistently positive was the relationship
between the multipliers and the geographic size of the area. It would be expected that the
larger the area the more econonric sectors it would have — on the average. This would be
consistent with the findings that the more economic sectors in an impact area, the larger
the multipliers. Negative correlations were dominant for population density suggesting

that areas with higher population density have less developed wood products industries

80

although the industry was present throughout a wide variety of population densities. This
would also seem logical as many wood harvesting and processing centers are in rural
areas - but areas that are apparently economically diverse. Overall, negative correlations
were most frequent in the sawmills and planing nrills sector followed by the veneer and
plywood sector. The logging camps and contractors sector was positively correlated in
most all cases. The reasons for this are not apparent. The veneer and plywood sector,
employment variable, for both types of multipliers, are mostly negative. In the same
group but only for personal income, the correlations coefficients are mostly positive. The
same pattern occurs for the sawmills and planing mills sectors. Why employment is
positively correlated and personal income negatively correlated is not clear but it is fairly
consistent. This might suggest that incomes on the average tend to be lower in wood
products industry dominated regions. Other than the observations above there is not a
significant pattern of highs and lows, positives and negatives. Why negative values exist
for some variables and not others is not apparent. The lowest correlation coefficients are
for industry output. This is probably due to the fact that industry output is not a good
indicator of income or employment when examined in the aggregate. A region could
have a large value for industry output but low income, employment, population and

economic diversity resulting in low multipliers - or just the opposite could occur.

Although the relationships of individual variables might show small correlation

coefficients, their predictive powers could be significant when combined with other

explanatory variables in multiple regression analysis. In summary, Table 11 shows that

81

there are definitely relationships
between the variables selected and
firrther analysis is justified.

Sect TIO Perlnc
The next step was to look at the

relationships among the

explanatory variables to
investigate the potential for 0.396

. . . 0.000 0.000 0.000
multrcollrnearrty.

. . . . Perlnc 0.994 0.387 0.615 0.998
Mulficollrnearrty exrsts where 0.000 0.000

explanatory variables overlap. For

EIA 0.365 -0.157 0.491 0.346 0.347
0.000 0.000 0.000

 

example the relationship between
. Correlation coefficients are presented in the top row of
an explanatory variable such as data for each variable.

population and a particular type of van a1":’-1\‘:'alues are presented in the bottom row of data for each
economic multiplier may be very similar to another explanatory variable such as total
industry output or the number of econonric sectors. The implication of this condition
generally means that the confidence in the models ability to predict multipliers will be
less. Sometimes one variable can predict as well as two or more variables and the fewer
variables necessary the less the cost of collecting and managing data.

Correlation coefficients were estimated for each pair explanatory variables (Table 12). It
can be seen that there are several high correlation coefficients therefore potential

multicollinearity. This is most noticeable between the number of economic sectors , total

industry output , and personal income. The only negative correlation is between

82

population density and geographic area and this value is low. This would seem logical
because areas that are physically large, normally have less dense populations. P-values
were low indicating a high level of confidence in the coefficient values. This
multicollinearity problem will be dealt with during the regression analysis process. All of

the variables in Table 11 were carried into regression analysis.

In summary, it is expected that the number of economic sectors and population density
will serve as the best explanatory variables in predicting multipliers of all types.
Population, industry output, and total income should increase the strength of the model

but may represent the same conditions and cause excessive multicollinearity.

Measures of Normality - In order for standard statistical assrunptions to be valid in
making statistical inferences, the response (dependent) variables need to be “normally”
distributed about their means. There are several methods in assessing the normal
distribution. They include comparing the means to the medians, determining the range of
the observations, and standard deviations. However, there are several other more
accurate methods of determining the degree of normality. The first method is by simply
reviewing histograms for each variable to see how closely they resemble a bell curve.
This was done for all response variables, and the bell shape pattern of the histogram
existed in all cases. Figure 1 is an example of the normal distribution of multiplier

values.

83

The second method is more complex and systematic. The method used was the Ryan-
Joiner test, which is a correlation-based test (available in MINITAB), similar to the
commonly used Shapiro-Wilke test (not available in MIN ITAB). The graphical output is
a plot of normal probabilities versus the data. The input data are plotted as the x-values.
Then the probability of occurrence is calculated, assuming a normal distribution, and then
calculated probabilities are plotted as y-values. The grid on the graph resembles the grids
found on normal probability paper, with a log scale for the probabilities. A least-squares
line is fit to the plotted points and drawn on the plot for reference. The line forms an
estimate of the cumulative distribution firnction for the population from which data are

drawn.

In this study, the data departed from the fitted line most evidently in the extremes, or
distribution tails. In most cases there was a slight tendency for the data to be lighter in
the tails than a normal distribution because the smallest points are below the lines and the

largest points are just above the lines. The test indicated that all multiplier classes

showed a high degree of normality with all R2 values above 0.96 and several above 0.99
and most p-values less than 0.00100. In summary, the data distributions were found to be
highly normal and fit for developing statistical inferences using regression analysis

without any need for scale transformation (log scale, square root etc) or firrther analysis.

Study Objective 3: Determine the fea_sibility of usinggelected, readily available,

explanatog variables to estimate economic multipliers.

84

Introduction

One of the primary objectives of this study was to investigate the feasibility of estimating
economic multipliers using variables such as population and industry output (Table 5).
This would allow the analyst to enter a few variables into an equation and generate
various types of multipliers to estimate the economic impacts of a particular decision for

a particular area

This analysis used “inferential” statistical methods as opposed to “descriptive” methods
as previously described in study objectives 1 and 2. However, descriptive statistics have
been included in the report to give a better understanding of the characteristics of the
variables. “ Inferential statistics” consists of procedures used to make inferences about
population characteristics (Mendenhall et al. 1994). In this particular case we would

“infer” a particular multiplier fiom characteristics of the population being studied.

There are certain assumptions that must hold when constructing linear least squares
models (1995). Each of these ten assumptions was addressed in respect to this study to

validate the models constructed (Appendix A).

Procedures and results

Linear regression analysis was used to determine the relationship between the
explanatory (independent) variables and the response (dependent) variables. The
following sections will describe the processes used to eventually develop
predictive/probabilistic models through the use of regression and other associated

techniques.

85

Regression Analysis
Regression analysis is concerned with the study of the dependence of one variable (in this
case - economic multipliers), on one or more other variables, the explanatory variables,
(in this case population, number of economic sectors, etc.) with a view to estimating and
or predicting the mean value of the former in terms of the known or fixed values of the
latter (Gujarati 1995). The end product of regression analysis is a multivariate equation
useful in predicting the dependent variable along with the associated probability
distribution. This is different than correlation discussed earlier where the end product
was a measure of the strength of the association between the dependent variable and an

explanatory variable with no attempt at prediction.

The “least squares” linear regression method was used (as opposed to “logistic
regression”) because of the continuous nature of the dependent variable (multipliers).
The least squares method estimates parameters in the model so that the fit of the model is
optimized by minimizing the sum of squared errors. This means that the linear
regression line is positioned so the sum of the distances between the actual measurement

and the regression line are equal above and below the regression line.

Best Subsets Process - The first step in the regression analysis process was to evaluate
the explanatory variables using the MINITAB Best Subsets process. Best Subsets

regression generates regression models and then selects the two models giving the
largest adjusted R2 . MINITAB displays information on these models, again examines

all two-predictor models, and again selects the two models with the largest adjusted R 2 .

86

The process continues so all possible combinations are evaluated. In this analysis each
dependent variable (multiplier) is evaluated (regressed) with respect to every combination
of explanatory variables — individually and in combinations. The Best Subsets regression
procedure can be used to select a group of likely models for further analysis. The general
method is to select the smallest subset that fulfills certain statistical criteria. The reason
that you would use a subset of variables rather than a full set is because the subset model
may actually estimate the regression coefficients and predict future responses
(multipliers) with smaller variance than the full model using all the explanatory variables.
Also, the more variables used, the more expensive the process of generating, analyzing

and managing data.

The statistics R2 , adjusted R2 , Mallow’s Cp, and 8 (square root of MSE) were

calculated by the Best Subsets procedure and were used for comparison criteria.
Normally, analysts might only consider subsets that provide the largest R 2 value.
However R2 always increases with the size of the subset therefore R2 is most useful
when comparing models of the same size. This study uses adjusted R2 and Mallow’s
Cp to compare models with different numbers of explanatory variables. The adjusted R2

is the regular R 2 adjusted by the degrees of freedom. Mallow’s Cp, which is used to
determine goodness of fit of the model, is the ratio of the standard error of the model
divided by the number of independent (explanatory) variables in the equation. The lower
the Cp the better the model. Generally, it is good to have a Cp value lower than the

number of response variables in the model (Draper et al. 1981).

87

In general this study favored models where Cp is small and close to or less than the
number of explanatory variables in the model. In the case of this study it should be
between 1 and 6 for the range of models being evaluated. A small value of Cp indicates
that the model is relatively precise (has small variance) in estimating the true regression

coefficients and predicting future responses.

The output for the Best Subsets process is quite lengthy (12 tables) and is presented as
Appendix B. The analysis of each dependent variable (multiplier) generates a separate
report showing the results of the regression analysis in respect to the explanatory
variab1e(s) in all possible combinations. Using adjusted R2 and Mallow’s Cp as criteria

the best model was picked for each multiplier. Table 13 presents a summary of each of

the best models.

 

 

Table I3 _ Best Subsets Regression ,\nalysis Results Summary

ultiplier Number of Pop Per
Models Variables R2 R2 adj Cp 8 Pop Den Sec TIO Inc EIA
LE1 4 37.6 37.3 4.9 0.07702 X X X X
LE2 6 36.6 36.0 7.0 0.13587 X X X X X X
LP] 3 28.9 28.5 3.5 0.10629 X X X
LP2 3 43.6 43.3 3.3 0.13769 X X X
SE1 5 27.5 26.9 5.3 0.12202 X X X X X
SE2 5 27.6 27.0 5.1 0.21814 X X X X X
SP1 5 10.7 10.0 6.5 0.17518 X X X X X
SP2 5 21.9 21.3 6.8 0.21701 X X X X X
VB] 4 25.3 24.6 3.5 0.08366 X X X X
VE2 4 20.0 19.2 4.1 0.18610 X X X X
W] 6 16.2 14.8 7.0 0.09601 X X X X X X
VP2 5 34.2 33.3 5.6 0.11940 X X X X X

 

 

88

The Best Subsets process does not generate a regression equation, but yields an R2 and
adjusted R 2 value and shows which variables have the best opportunities to produce the

most useful and efficient equations. Table 13 shows a range of adjusted R 2 values from

43.3 for LP2 to only 10.0 for SP1. With the exception of LPl and LP2, all multiplier

groups have better adjusted R 2 values using four or more explanatory variables. The
number of economic sectors appears in all multiplier groups. Population density is only
absent fi'om LE1. At the other extreme is total industry output that is only present in 6
multiplier groups. This is consistent with what was found in correlation analysis. Table
13 also shows that most of the models have a Cp value slightly greater than the number

of variables.

Developing the Regression Equation — The next step in the model building process was
to develop the preliminary regression equation for each of the Best Subsets of variables in
Table 12. Because of the length of the MINITAB output for each regression equation
and associated data only a summary is presented in Table 14. The detailed tables are

shown in Appendix C.

All type SAM multipliers were, as they should be, larger than Type 1 values.

89

Table 14 - Regression liqualions —- Preliminary Model (.‘oeflieients

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Explanatory Variables
Intercept Pop Pop Sect TIO Perlnc Area
Multiplier (Beta) (mil) Dens (milS) (bilS) (mil ac)
Model

LE1 1.23 —.05 l 2 .000517 .000002 00129
LE2 1.42 -. 1000 -.000089 .001010 -. 137 .000006 00165
LP] 1 . 1 8 .000092 .000474 00103
LP2 1.29 .000095 .000961 00136
SE1 1.64 -.0788 -.000210 .000508 .000002 00139
SE2 1.93 -.1640 -.00031 1 .001210 .000005 00223
SP1 1.55 -.000181 .000472 .248 -.000006 00089
SP2 1.69 -.000238 .001070 .305 -.000007 00123
VEl 1.44 -.000140 .000397 .104 -.000003
VE2 1.75 -.03 00 -.000202 .000913 .00081
VP1 1.33 .0374 -.000103 .000484 .157 -.000005 00044
VP2 1.46 .0322 -.000123 .000986 .167 -.000005

 

 

 

 

 

 

 

 

 

 

The population coefficient was negative in most of the models it was included. This
means that as the population increased, multipliers decreased. This result seems
reasonable in that most timber industry activities are in less populated areas. Exceptions
were VP1 and VP2 where multipliers increased slightly with increasing population.
However, it is expected that veneer and plywood plants be in larger areas than the other

SOCIOI'S.

The population density coefficient was negative in most of the models it was included
(included in 11 of 12 models). This means that areas with higher population densities
will have lower multipliers. This seems reasonable in that most wood products
operations are in rural regions. This is consistent with what was found in correlation

analysis.

90

The coefficient for the number of economic sectors occurs in all models and is positive
in all cases. This means that the more total economic sectors a region has the higher will

be the economic multiplier

The coefficient for total industry output occurs in only 6 models. Five of the six models
are positive meaning that as total industry output becomes larger the multipliers increase.
The primary reason for its exclusion in half the models is that it is highly collinear with

population and income and its exclusion lowers the VIP of the model.

The regression coefficient for total personal income occurs in 9 of 12 models. Four are
positive and five are negative. There is no apparent reason why some are positive and
some are negative in light of the fact that closely related variables and are substantially

positive.

The regression coefficients for the physical size of the analysis area occur in 10 of 12
models and in all cases vary positively with the multipliers. As the physical size of the
analysis area increases so does the multiplier. This would be expected - the economy
would, on the average, get larger and more diversified (more sectors) as the size of the

area increased.

The Type SAM multiplier is larger that the Type 1 multiplier in all cases. This is because

the SAM multiplier includes induced effects as well as the indirect effects.

91

Statistical parameters that explain statistical significance were calculated for each term in
the regression equation. Because of the large volume of data, the statistical parameters for
the model coefficients shown in Table 14, are included in Appendix C. Each of these

parameters is briefly discussed as follows:

P-Value — The p-value was used to determine which of the effects in the model
are statistically significant. The p-value was calculated for each of the regression
equation coefficients. The traditional procedure was to:

- Identify the p-value for the effect or coefficient you want to evaluate.
- Compare this povalue to your selected significance level. In the case
of this study the significance level is .05.

0 If the p-value was less than or equal to .05, conclude that the
effect is significant -— therefore there is a significant linear
effect for the coefficient of interest (e. g. population).

O If the p-value was not less than .05, there is no significant
effect, that is the multiplier does not change with changes in

the coefficient of interest (e. g. personal income).

VIF - VIF (variance inflation factor) measures how much the variance of an
estimated regression coefficient increases if your explanatory variables are correlated. A
VIF in excess of the number of independent variables, as a general rule, is deemed

unacceptable. For this study a VIP greater than 5.0, a common level used in practice, is

92

deemed to be excessive. How excessive VIF values were dealt with is explained in

Chapter 3.

Because of the large number of samples taken, p-values were almost always less than
0.05 and therefore deemed significant at the 5.0 percent level for the preliminary
regression equations in Table 14. P-values can be seen in Appendix C. In brief,
coefficient values are likely to be what is shown in Table 14. For this reason only the
few exceptions where p-values exceeded 0.05 will be briefly discussed. For Type 1
multipliers only VP1 for the area variable exceeded 0.05. This is consistent with the
result of it also being the only negative “area” variable coefficient for the preliminary
models. The area variable coefficient is positive for all the other models. Other
coefficients that are non-significant are VP2 - population coefficient with a p-value of
0.110; LE2 — output coefficient with a p-value of 0.056; VE2 — area coefficient with a

p-value of 0.1 3 1.

Improving the Regression Equation - After the preliminary equations/models shown in
Table 14 were established additional variations were examined to improve their
predictive strength. Several factors were taken into consideration. These include
possible regional differences, eliminating some of the observations, testing for natural log
transformations, and reducing multicollinearity. These will be discussed separately in the

following sections.

93

Regional Differences/Adjustments — In an attempt to improve the models, possible
regional differences were examined. Analysis of variance (ANOVA) was used to explore
the possibility of subdividing the observations into geographic regions to determine if

there are real differences between regions.

ANOVA is similar to regression in that it is used to investigate and model the
relationship between a response variable (multipliers) and one or more explanatory
variables. However, analysis of variance differs from regression in that the independent

variables are qualitative (categorical) (Minitab 2000).

To look at possible regional differences in multiplier observations, one-way analysis of
variance was used. One-way analysis of variance tests the equality of population means
when classification is by one variable (such as Forest Service (FS) Regions). The
classification variable, or factor, usually has three or more levels, where the level
represents the treatment applied. In this case there were seven FS Regions. FS Regions
were set up as dummy variables for regression analysis. The regions were based on
USDA Forest Service Regions, because they are discretely distributed throughout the
continental US. The resulting geographic regions can be seen in Appendix D. The states

in each FS Region are in Appendix E and F.

Multiple comparisons of means allowed for the examination of which means are different

and to estimate by how much they are different. These differences can be examined in

94

Appendix D of this report. Because of the need to examine all pairwise comparisons of

means, Fisher’s least significant difference (LSD) method was used.

All multipliers benefited from regional differentiation. All multiplier groups were
separated into either two or three sub-groups. Although differences in means were quite

small the standard deviations were also quite small allong for a separation of regions.

Table 15 shows adjusted R2 values before and after regional differentiation. Absolute
and percent changes were substantial in some cases. In other cases changes were
minimal but in all cases changes were positive. There is no clear pattern as to what
caused some areas to benefit more than others other than the wood products industry in
some regions must increase with the size (population, income etc ) of the region on a
relatively predictable basis.
Multiplier means are different
enough from region to region

that stratification reduces the

variation enough, with the result Multiplier
Before
being better regression results. LEI 37-3 - 354%
LE2 36.0 . 56.1%
LPl 28.5 . 65.6%
LP2 43.3 . 27
Some of the more notable SE1 . 13.4%
27.0 . 27.0%
differences between regions 10.0 . 1
21.3 . 68.5%
disclosed through analysis of 24.6 , 41.9%
19.2 . 83.3%
variance are as follows. 14.8 17.6%

 

5.7%

Employment multipliers for the logging camps and contractors sector (LE1, LE2) are
significantly lower in the east than in the west. Type SAM multipliers follow the same
pattern as the Type I multipliers therefore attributing the regional differences to the Type
I multiplier. This could be a result of a lesser-developed logging industry in the east.
Also, with counties being smaller in the east so would the impact areas likely be smaller.
This study has already shown that areas that are geographically smaller will likely have
smaller multipliers. The personal income multipliers for the logging sector (LPl , LP2)
follow a similar pattern but with one major difference — the northwest (F S Regions 1 and
6) are lower than the east. The Type SAM multipliers again follow the same pattern as
the Type 1 multiplier. This could be due to low income to output ratios in the northwest
from advanced technology and the effect of low local wage structure in parts of the
northwest. Logging industry multipliers in the southwest remain high in all cases. This

could be due to the extremely large impact area size in the southwest.

AS previously mentioned, multipliers for the sawmills and planing mills sector, as a
group, are higher than multipliers for the logging, and veneer and plywood sectors. The
multiplier patterns for sawmills and planing mills are somewhat similar to those for the
logging sector. Employment multipliers for sawmills and planing mills (SE1, SE2) for
the northeast are lower than the other regions. This is probably due to the same reasons
logging sector multipliers are lower. The southwest and California regions are also quite
low. Again, Type SAM multipliers follow the same pattern as Type I multipliers. This

Suggests there is little difference in the induced component of the multipliers. Personal

96

income multipliers (SP1, SP2) do not follow the same pattern as the employment
multipliers but loosely follow the same pattern as the personal income multipliers for the
logging industry. An exception is that the Rocky Mountain region has relatively high
personal income multipliers while having below average employment multipliers. This
difference might be the result of high income to output ratios for the sawmills and

planing mills sector.

Employment multipliers for the veneer and plywood sectors (VEl , VE2) are lowest in the
arid regions of the southwest and the Rocky Mountains (F S Regions 2,3,4). The industry
is small and not well developed or diverse, due to the scarcity of raw materials (large
diameter logs). The large impact areas do not compensate for the lack of industry
development Employment multipliers are highest in the northeast and south where the
industry is well developed due to the proximity to raw materials. Personal income
multipliers (VP1, VP2) have similar patterns to the employment multipliers. They are
highest in the east and south and lowest in the central Rocky Mountains and Great Basin.
Patterns for the Type SAM multipliers, for both employment and personal income of all
types, fi'om region to region are similar to the Type I multipliers therefore being

consistent with the other wood products sectors studied.

In summary, the differences in the total (SAM) multipliers, throughout all three wood
products sectors, are primarily a result of differences in the direct (Type 1) multipliers.
This is evident because the Type SAM multipliers follow the same pattern from region to

region as the Type 1 multiplier. This suggests there is little difference in the induced

97

multiplier component of the Type SAM multipliers of all types from region to region. It
also appears that differences in impact area sizes affect the size of multipliers fi'om region
to region. Some regions have much larger impact areas (larger counties) on the average

and consequently higher multipliers.

Another approach in lieu of using dummy variables to investigate regional difierences
originated fi'om the review of the US. map in Appendix B. One of the most obvious
features is that the geographic size of counties in the west is much greater than the east.
This would cause impact areas in the west to be larger than the east and might be the
cause of differences in econonric multipliers. This difference was investigated by
dividing the sample data (multipliers) into two separate populations — east and west. The
cast consisted of Forest Service Regions 8 and 9. The west consisted of Forest Service
Regions 1,2,3 ,4,5, and 6. Separate models were developed for the east and west for each
multiplier group - 12 models for the east, 12 for the west. These models were then

compared to the results in Table 15. In almost all cases the dummy variable approach to

regional differentiation produced better models. Adjusted R 2 values were higher for all
but one model. P-values were equally significant. Another benefit of the dummy
variable approach is that there is just one set of 12 models instead of 24 models. For the
above reasons the idea of separate sets of regional models to account for different regions

was not pursued any further.

98

Elimination of Unusual Observations - Another strategy considered to improve the
model, involving geographic adjustments, was to look at unusual observations (outliers)
that might not contribute to the model and could be eliminated without endangering the
objectives of the study. A visual review of scatter plots of regression residuals was done
for all models. A formal method (e. g. Studentized Residual) was deemed unnecessary as
the outliers appeared to be obvious in the scatter plots. The review showed extreme
values for the impact areas in Southern California. The explanatory variables such as
population, total industry output, and total personal income were significantly higher than
other areas. To determine the effects of this situation, the impact areas in Southern

California were eliminated from the study population and the regression analysis was

repeated. The new adjusted R2 values showed only a minimal improvement -— in most
cases less than 1%. It was assumw that although these values were extreme there were
too few of them to make a difference. Given the small effects of excluding the outliers,

the Southern California impact areas were kept in the study.

Non-linear Alternatives — Further efforts to improve the model included natural log
transformation to test the possibility of non-linearity. Independent (explanatory) and
dependent (response) variables were tested individually and in unison. Of special interest
were the population, industry output, and personal income variables. It was originally
assumed that these explanatory variables were positively correlated with the multipliers.
The results of the correlation analysis (Table 11) show differently with either low or
negative correlation. Because the number of economic sectors showed strong positive

correlation with the multiplier values it was considered a possibility that the other

99

economic magnitude variables might show the same results if transformed to natural log

form. This transfonnation did result in most of the signs changing from negative to
positive. However, improvement (less than 2% adjusted R2 ) resulted in only a few of

the models. Most models showed no improvement or a reduction in adjusted R2 values.
The most significant problem was a substantial increase in p—values. Almost all models
resulted with non-significant natural log variables. This further substantiated the position

that the proper functional form is linear.

Potential non-linearity was also tested by graphical analysis of residuals. These tests

also indicated the best overall fit and functional form was linear.

Interaction effects (cross-product terms) were also tested. For example, population was
multiplied by the number of economic sectors and then evaluated as an explanatory
variable. This was done for all combinations of two explanatory variables. Three-
variable combinations were not attempted because of the inability to explain the

interactions. The new interaction terms were evaluated with and without the original

terms. Where original terms remained, the model produced slightly higher R 2 values
but introduced significant additional multicollinearity indicated by variance inflation
factor (VIF) values greater than 5.0. The presence of this condition resulted in eventually
eliminating the interaction variables in favor of more significant individual variables.
When interaction terms and original terms were retained in the model the same Situation

again occurred. Given the presence of multicollinearity and the limited increase in

100

significance led to eventually eliminating the interaction variables in favor of more

significant individual variables.

Additional Explanatory Variables - After completion of the preliminary models there
was evidence that additional explanatory variables might improve the model. These
ideas came from further literature review and consultation with experts. These variables
were 1) total acres of timberland within the impact area and 2) percent of total acres in

an impact area consisting of timberlands.

It was hypothesized that the more heavily timbered an area was the more developed the
timber industry would be and consequently have higher economic multipliers - at least
the Type I multiplier. Because of the labor involved in populating a database with
timberland areas for over 700 impact areas, the analysis was done on a sample basis (242
impact areas). The USDA Forest Service Forest Inventory and Assessment (FIA) Data
Base was the source of the area of timberlands. The FIA program is an inventory of
vegetation on all lands in the US. Total area (acres) of the economic impact areas has

already been discussed in a previous section of this report.

The acres of timberland and the percent of acres of timberland were analyzed using the
same methods used to analyze the other explanatory variables. Best Subsets regression
was used to test the new variables by themselves and in conjunction with all
combinations of the original explanatory variables. There was no clear evidence, in the

aggregate, that the additional variables significantly improved the existing models.

101

Adjusted R2 values were only slightly improved (less than 2%) for some of the
multipliers and actually decreased for others. Even where improvement occurred, it was
done at the expense of increased VIFs - substantial in some cases. For this reason the
timberland acres and percentages were not used as explanatory variables in the final

models.

The National Resources Inventory (NR1) coordinated by the Natural Resources
Conservation Service (NRCS) was evaluated as a source of timberland data. However,

the survey does not include Federal lands therefore it is not useful for this study.

Another approach to improve the regression models was to treat the different impact area

levels (Level A — E) as dummy variables. The results were mixed. In several of the

models the adjusted R2 increased by as much as 8 %. Some increased by no more than
2%. Multicollinearity was not a problem as VIF values were well below 5.0. However,
p-values were very large for the Level regression coefficients with most all well
exceeding the .05 significance level. Therefore the final models in this study have not

been adjusted to include this idea.

Multicollinearity and Heteroscedasticity - Correlation analysis, indicated a great degree
of correlation among several of the explanatory variables. These included total personal
income, total industry output, and total economic sectors (Table 12). The regression
analysis process in MINITAB also generates a variance inflation factor (V IF), which is

used to detect correlation amongst variables (i.e. multicollinearity). VIF measures how

102

much the variance of an estimated regression coefficient increases if your explanatory
variables are correlated. A VIF of 1.0 indicates no correlation; greater than one,
otherwise. It has been suggested that when the VIP is greater than 5 to 10, the regression
coefficients standard errors are inflated (Gujarati 1995). If this occurs recommendations
to mitigate these effects include: collecting additional data, deleting explanatory variables
that are causing the multicollinearity, using different explanatory variables, or an
alternative to least squares regression (Montgomery et al. 1982). The most expedient
alternative, as a first step, is to reduce the VIP to acceptable levels by systematically
excluding those explanatory variables that are the greatest cause of multicollinearity

(Table 16).

The VIF factors for each explanatory variable for each final model are included in
Appendix G of this report. The next step in the analysis was to eliminate the explanatory

variable with the highest VIP and then re-determine the regression equation to see if VIF

values are all below 5.0 without a substantial reduction in the adjusted R2 value. Table
16 is a summary of the results of adjusting the model to reduce VIF values to less than

5.0. Detailed data is presented in Appendix G.

103

‘Inhlc IO -\Iulticollincaril) .\II;I|)sis

 

Multiplier Explanatory Explanatory Adjusted Adjusted
Variables Variables R2 R2

Group Eliminated Retained Before After

LE1 PerInc PerInc,Sect,Area, 50.5% 50.5%
RegDum

LE2 PerInc PopDen,SecLTIO 56.2% 56.1%
Area,RegDum

LPl None PopDen,Sect, 47.2% 47.2%
Area,RegDum

LP2 None PopDen,Sect 55.2% 55.2%
Area,RegDum

SE1 PerInc Pop,PopDen,Sect, 30.5% 29.8%
Area,RegDum

SE2 PerInc Pop,PopDen,Sect, 34.3% 33.4%
Area,RegDum

SP1 PerInc PopDen,Sect,TIO 28.4% 28.4%
Area,RegDum

SP2 PerInc PopDen,Sect,TIO 35.9% 35.8%
Area,RegDum

VEl TIO PopDen,Sect, 34.9% 34.2%
Perlnc,RegDum

VE2 TIO Pop,PopDen,Sect, 35.2% 35.2%
RegDum

T10, PerInc,PopDen, 17.4% 15.0%

VP1 PerInc Sect,Area,

RegDum
TIO, Pop,PopDen,Sect, 35.2% 33.9%
VP2 PerInc RegDum

 

 

 

Only in two cases (VP1, VP2) did more than one variable need to be eliminated to reduce
the VIF value to less than 5.0. Eliminating total personal income was the most common
remedy. Regression coefficients either did not change at all or only declined slightly in
all cases. Therefore, the resulting models are significantly free of multicollinearity.

Also of concern is the possible presence of heteroscedasticity. Heteroscedasticity

generally means that the residual values (differences between the regression line and the

104

actual measured values) are not evenly distributed over the range of values of the
independent variables. This was addressed by a graphical analysis of the residuals for
each model. In most cases heteroscedasticity was not a problem. An exception existed at
the extremes of the regression model where extreme values existed (e. g. large population
in Los Angeles County). Other statistical parameters, remained relatively constant
(Appendix G).

The Final Model — Table 17 shows a summary of the final models. Details of the
final regression analysis are included in the report as Appendix G. All SAM multipliers,

as they should, remained larger than their Type I counterpart.

The population coefficient remained negative in all models. The population density

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

luhlt- l7 l’inzll .\ I 0(ch ( ‘ocl'l'icicnls
Explanatory Variables
Inter Pop PopDen Sectors TIO PerInc Area RegDum
Multiplie cept- (mil) (bilS) (bil$) (mil ac) Variable
r Model Beta
LE1 1.25 -.0110 .000603 .0003 87 -.0855
LE2 1.48 -.000120 .001180 -.3240 -.0003 80 -.1840
LPl 1 .01 .000072 .000476 .000748 .1020
LP2 1.08 .000072 .000964 .001040 .1 190
SE1 1.53 -.0228 -.000193 .000473 .001280 .0626
SE2 1.78 -.0459 -.000326 .001270 .001000 .0933
SP1 1.25 .000157 .000588 -.0552 .000310 .1470
SP2 1.42 -.000223 .001 100 -.1 1 10 .000846 .1560
VEl 1.32 -.000130 .004000 -.0000 .0683
VE2 1.24 -.0277 -.000220 .001040 .2330
VP1 1.15 -.000076 .000478 -.0000 .000041 .0920
VP2 1.35 -.0075 -.000123 .000995 .0583

 

 

 

 

 

 

 

 

 

105

 

coefficient remained negative in 9 of the 11 models it occurred, which is similar to the
preliminary model. The coefficient for the number of economic sectors occurred

in all 12 models and remained positive in all models. Total industry output coefficients
remained in three of the final models and all those coefficients were negative. This
reduction was a result of efforts to reduce multicollinearity. The personal income
coefficient only remained in 2 of the12 final models and had very slight negative values.
The absence of the personal income coefficient was also a result of reducing
multicollinearity. The regression coefficients for the physical size of the area occur in 9

of the 12 models. All but one of the coefficients (LE2) are positive.

The regional variable coefficients R which were based on USDA FS regions, and

included in the regression analysis as dummy variables, are included in all models.

Reliability parameters such as standard errors, p-values and variance inflation factors

indicate that the R2 values and adjusted R2 values are highly reliable (Appendix G).

This is mostly due to a large number of samples. Enlarging the survey would add very

little to the confidence in the analysis. However, R 2 values and adjusted R 2 values are

quite low, indicating a large portion of the variation is unexplained (Table 16). Only

three multiplier groups have R 2 and adjusted R 2 values exceeding 50%. Three groups

are less than 30% with one of those at 15%.

The Logging Camps and Contractors sector has significantly higher R2 and adjusted R2

values than the other sectors (> 50%). This could be because the logging industry is

106

more consistently found in small rural economies than are the other two sectors, which

are usually found throughout a variety of circumstances. SAM multipliers have higher

R2 and adjusted R2 values than Type 1 multipliers. This is probably because the Type
SAM multiplier includes the effects of induced spending ( i.e. spending by households)
which increases with increases in variables directly related to the size of the economy
(i.e. personal income, number of sectors, population). There is no clear pattern to the
relationship between employment multipliers and income multipliers. As previously
mentioned, high income does not necessarily mean a high number of jobs and just the
opposite can also be true.

Statistical parameters that explain statistical significance were calculated for each term in
the regression equation. Because of the large volume of data, the statistical parameters for
the model coefficients shown in Table 17, are included in Appendix G. Definitions are
covered earlier in this chapter. As in the preliminary models, p-values are quite small in
relation to the chosen significance level of 0.05. The largest p-value is for VP1 for the
area variable coefficient at 0.892. Others are : LE2 — area with p-value of 0.139; SP1 —
industry output with p-value of 0.406; SP1 - area with p-value of 0.346; SP2 — industry
output with a p-value of 0.184. The conclusion is that in most cases there is high
probability that most of the coefficients in the models are correct. The remainder, with

large p—values, do not meet the standards for confidence.

Absolute Percent Error

In addition to the measures taken above, the absolute percent errors were calculated to

provide further evidence as to the validity of the regression models. The results were

107

examined in respect to both mean and maximum percent error. This was done by taking
the difference between the IMPLAN generated multipliers and comparing them to the
multipliers generated by the regression models (T able 18). The mean absolute percent
error is the mean of the percent differences for each multiplier group. The maximum

absolute percent error is the individual maximum percent difference for each multiplier

group.

Multiplier Mean Absolute Maximum Absolute
Percent Error Percent Error
LE1 3.9% 17.9%
LE2 5.3% 33.1%
LPl 5.0% 29.0%
LP2 5.7% 31.0%
SE1 5.4% 36.0%
SE2 7.5% 48.7%
SP1 6.5% 45.1%
SP2 6.8% 45.5%
VB] 4.1% 19.4%
VE2 7.5% 36.6%
VP1 4.8% 22.9%
VP2 5.0% 28.9%

 

The results in Table 18 are somewhat similar to the regression results in Table 17 in some
respects and very different in others. The mean absolute percent errors are generally
small (good) varying fiom a low of 3.9% for the LE1 Group to a high of 7.5% for both
the SE2 and VE2 Groups. Maximum percent errors vary fi'om a low of 17.9% for LE1 to

a high of 48.7% for SE2. The sawmill sector has the highest mean absolute percent
errors, the highest maximum absolute percent errors, and the lowest R 2 values. While

the logging sector had the highest R 2 values it had the highest (poorest) absolute percent

108

errors. The absolute percent errors are higher for the Type SAM multipliers than for the

Type I multipliers. This is just the opposite of the R2 values.

In general the mean absolute percent errors are quite small. However, most of the
maximum percent errors are quite high. This suggests that there is high potential for
variation about the mean values and the potential for substantial error in the prediction

models.

Examining Differences Between Geographic Impact Levels. Previous sections of this
analysis demonstrated the relationship between economic multipliers and an array of
explanatory variables. The purpose was to analyze their potential in measuring the values
of various types of economic multipliers. The intent was to determine the feasibility of
building statistical regression models that might forgo the need to build formal input-

output impact models.

The objectives of this study, stated in the beginning of this report, also included
explaining the differences in impact area characteristics (multipliers and explanatory
variables) as they expanded from impact region Level A to Level B around each National

Forest impact centroid and how they might be used in designing future impact areas.
Each National Forest was the geographic focal point for the design of 5 separate

economic impact areas. The criteria used to design these areas are described earlier in

this report but generally it was expected that they would increase in physical size from

109

Level A to Level E. Initial review showed that Level D (FS TSPIRS criteria) was an
exception in that they were on the average larger than level E but also showed great

fluctuation. For these reasons Level D was not included in this part of the study.

The initial idea was to visualize the impact areas growing as a series of concentric circles,
which have been historically used to explain the concept of central place theory (Isard
1975). However, political boundaries, which are also data area boundaries, did not in
most cases, produce a configuration resembling concentric circles. The addition of a
00st) produced results that were unpredictable. They varied from sparsely populated

areas to major metropolitan areas with little relationship to the preceding impact area.

On the average, the expected patterns held true. As the geographic area was enlarged the
multipliers became greater. This is consistent with regression analysis findings where
the coefficient for the size of the geographic area was positive in 11 of 12 models (Table
17). With the exception of population density, all of the explanatory variables increased
on the average along with increases in geographic area. This is consistent with the
correlation analysis done to validate potential explanatory variables (Table l 1).
Population density would be expected to be higher in Level A than B because A is the

most populated county in the Level B aggregate.

The discussion above verifies the results of the regression analysis earlier in this report, at

least fiom the perspective of direction of change. Although the extremes were quite

dispersed, the standard deviations indicated the multiplier populations were tightly

110

distributed about their means. However, the explanatory variables were quite diverse.
As areas grew quite large or populated, multipliers grew slowly. This suggests that
although the appropriate functional form was determined to be linear, the upper range of
the regression line flattens to a non-linear configuration. The implications of this will be
discussed further in the next chapter. Appendix H shows the descriptive statistics of the

analysis described.

111

CHAPTER FIVE - CONCLUSIONS

Introduction

An increased demand for economic impact analysis has increased the need to simplify the
economic impact analysis process. Much of this demand has resulted from recently
developed laws and regulations requiring government agencies to determine the

economic impacts of their proposed projects, programs, and policies.

The general goal of this study was to investigate the behavior of certain economic
multipliers of the wood products industries and the feasibility of providing more readily
available, situation-specific, economic multipliers to assist in the economic impact

analysis process.

The three research objectives are to describe the range of variation in economic
multipliers for certain sectors of the wood products industries, to identify the key factors
that explain the variation of economic multipliers, and to determine the feasibility of
using selected explanatory variables to simplify the determination of economic
multipliers used for economic analysis. The study was not intended to develop a system
to be used immediately by analysts but only determine whether or not such tools might be

feasible.

112

Research Summary

The first step in the research study was a literature review. The literature provided the
theoretical foundation for the eventual analysis. The literature also provided many ideas
as to what variables could be used to achieve the desired results as well as what analysis

techniques might be available and the appropriate functional form to use.

The first operational step in the research process was to determine the scOpe of the study.
It was decided that it would not be feasible to analyze all the sectors of the wood products
industry —- there were just too many and conclusions could probably be reached with just
analyzing the major, most frequently occurring sectors. A variety of explanatory
variables were then selected. This selection was based on discussions with subject area
experts and a review of the literature. These were variables that were thought to be
closely related to the complexity of the wood products industry and the economy as a
whole as well as being variables that could be easily measured fiom readily available
data. Additional variables were tested as the study progressed. Other decisions that
were made included the kind of multipliers to be tested (Type 1, Type SAM, etc.), the
economic parameter that the multiplier should represent (income, employment, value
added etc.), and how the impact area boundaries were determined and sampled. These

processes are described in detail in previous sections of this dissertation.

Twelve separate models were developed representing three wood products sectors, two
types of multipliers, and two economic variables. Regional differences were accounted

for via dummy variable values within each of the twelve models.

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The first step in the statistical analysis was to determine and review the basic descriptive
statistics of the multipliers and explanatory variables. Means, medians, standard
deviations, distributions, ranges, and measures of normality of economic multipliers
were analyzed for all selected wood products sectors. These analyses set the stage and

provided guidance for further analysis.

The next step was to do correlation analysis to determine the strength of the relationships
between the explanatory variables and the multipliers to validate the selection of
explanatory variables. Also correlation analysis was done among the explanatory

variables to determine the potential for multicollinearity.

Best-subsets linear regression analysis was then performed to determine the linear
relationships between and among all combinations of explanatory and response
(multipliers) variables. The end product of this process was a “preliminary” regression

equation or model. The models were examined for the presence of heteroscedasticity.

The next steps were done to try to improve the model. An analysis of variance was done

to determine whether or not there were regional differences - and there were.

Non-linear assumptions were tested by using logarithm scales on both and each axis. The
original correlation analysis and the best-subsets regression analysis indicated a high
potential for multicollinearity between explanatory variables. Sets of explanatory
variables were reviewed and excluded of unnecessary variables to reduce variance

inflation factors (V IF) to acceptable levels.

114

Several additional potential response variables were tested for their predictive ability.
The most significant of these was the magnitude of the timber supply within the
economic impact area represented by the total acres of timberland in the economic impact.

area and timberland acres as a percent of total acres within the impact area.

An attempt was also made to develop interaction variables (e. g. cross-product terms) by
multiplying explanatory variables by each other to create a new and unique explanatory

variable.

Another approach to improve the regression models was to treat the different impact area

levels (Level A — E) as dummy variables. The results were mixed. Some models were

reasonably improved with higher adjusted R 2 s and others were not. However, p-values

were very large for the Level regression coefficients so the idea was not carried further.

The last analysis procedure was to examine the statistical differences between different
geographic impact levels originating from the same event. This was done to answer the
question of what happens to the multiplier as the same impact area is systematically

expanded and what are the implications.

Discussion of the results

Twelve different regression equation models were developed to predict economic

multipliers for three different wood products industry sectors (Table 17). The final

llS

results and notable findings as the models were developed are discussed in this section.
The development of the least squares regression model was based on the set of

assmnptions in Appendix A.

Study Objective 1: Describe Variations in Multipliers.

The number of observations (impact areas) in the study for each multiplier group, varied
from a low of 384 to a high of 674 observations. Most impact areas had Logging Camps
and Contractors (Sector 133) and Sawmills and Planing Mills (Sector 134) but many
impact areas did not have Veneer and Plywood (Sector 139). The number of
observations was more than adequate for the objectives of the study with standard
deviations and standard errors being quite small. A wide variation in multiplier values

occurred, which is a prerequisite to regression models.

Study Objective 2: fientifv the l_<ev factors that explain the variation of economic

multipliers.

Normality of the response variable (multipliers) was analyzed by visual observation and
the use of the Ryan-Joiner test. Results showed good normal distribution allowing for the

necessary statistical inferences.

116

Correlation analysis results (Tables 11 and12) indicated a low to moderate degree of
correlation among most of the variables. The strongest linear relationships were between
the multipliers and the number of economic sectors and the geographic size of the area.
Correlation coefficients were highest for the logging sector and lowest for planing mills.
Correlation coefficients for personal income multipliers were generally larger than for
employment multipliers and larger for Type SAM multipliers than Type 1 multipliers.
Correlation coefficients were very high between several of the explanatory variables
suggesting potential for multicollinearity. This situation was especially pronounced
between population and number of economic sectors, total industry output, and total
personal income. However, this was to be expected and the problem was addressed later

in the analysis.

Study Objective 3: Determine the feasibility of using selected. readily available,

 

explanatory variables to estimate economic multipliers.

The purpose of regression analysis, was to develop a set of regression equations to serve
as predictive models. The first phase of Best-Subsets analysis generated a set of models
for each of the twelve multiplier groups based on all the possible combinations of the
explanatory variables and their relationship to the multipliers. Non-linear relationships
were considered by examining residual plots and logarithmic transformation. The results

can be seen in Appendix B. The single strongest variables, those with the highest

adjusted R2 value, are the same as those with the highest correlation coefficients; the

number of economic sectors and the geographic size of the area. The single weakest

117

explanatory variables do not follow a pattern and vary depending on the type of

multiplier and industry sector. However, as explanatory variables are aggregated the

adjusted R2 values increase with corresponding decreases in the Cp values. The best of
each set is then selected for preliminary regression model development (Table 14). The
best model could have as few as three or as many as six explanatory variables. The most
common explanatory variable was the number of sectors, which occurs in every model.

The least common variable is total industry output, which occurs in only half the models.

Models for the SAM multipliers are generally stronger (have higher adjusted R2) than
for the Type I multipliers. This is because leakage from indirect expenditures is less in
regions with more people and economic sectors. Models for the Logging Camps and
Contractors (sector 133) are the strongest. Models for Sawmills and Planing Mills (sector
134) are the weakest. There is no consistency between the personal income and

employment multipliers across the economic sectors analyzed.

Regional differences (Forest Service Regions were used) were analyzed using one-way
analysis of variance. The outcome can be seen in Appendix D. Regional groupings were

done based on the graphic illustrations in Appendix D and new models were developed.

Substantial improvement was made with all models with some of the R2 values more
than doubling (Table 15). As previously mentioned non-linearity was addressed with no

potential improvement apparent.

Multicollinearity, which was suggested as a potential problem in predictive models,

during the discussion of correlation analysis, became a reality as a result of regression

118

analysis. All but two of the multiplier variables needed at least one of the highly
collinear explanatory variables removed from the model to reduce VIF values below the
acceptable standard of 5.0 (Table 15). Only two of the multiplier variables required two
explanatory variables to be removed. The most frequently removed explanatory variable

was personal income, which was removed from six of the models. Removal of these

variables resulted in very little decrease of R 2 values. The number of sectors was still
the most common explanatory variable in the final models, personal income, the least

frequent.

The models were examined for the presence of heteroscedasticity. This was done with a
visual examination of graphs of the regression residuals. The presence of

heteroscedasticity was not to the extent that it would affect the results of the study.

As previously mentioned, interaction variables or cross-product terms were tested. This

only resulted in slight increases in adjusted R2 values but substantially increased
multicollinearity (VIF). Therefore, the interaction variables were not carried any further

in the analysis.

Afier the final models in Table 17 were developed, another potentially viable explanatory
variable was analyzed. Timber supply in the impact area was thought to possibly have an
effect on the magnitude and complexity of the timber industry. This might influence the
size of the economic multipliers. This element was represented by two variables — total

timberland area and timberland area as a percent of total area in the impact region. The

119

details of this analysis are included in a previous section of this report. The results were

inconclusive because of several factors including the absence of reliable data. In some

cases the adjusted R 2 values slightly improved the models, but introduced a substantial
amount of additional variation (higher VIF values). In other cases there was little or no
improvement. No conclusions can be made on the usefulness of this variable until a full

set of reliable data is available.

Among the objectives of the study was the intent to analyze the behavior of multipliers as
specific impact areas are systematically increased. The descriptive statistics developed
by this analysis are in Appendix H. With the exception of population density, all the
explanatory variables increased as the impact area increased in size. As expected, as the
geographic area was enlarged the multiplier usually also got larger, but in the extremes of
its range, not in a linear fashion. For example the geographic area (mean) between level
B and C approximately tripled while the increase in the multiplier is very small. The
main point here is that, at least on the average, additional area past a certain point, tends
to dilute the effects of the impact analysis. Therefore, indiscriminately using the
mechanical rules to build impact areas (e. g. all counties with National Forest land) or
aggressively expanding the impact area in the fear of missing something, is not

recommended.
The question remains - how feasible is it to construct ready-made, situation specific

economic multipliers for the wood products industry. The study shows that predictive

models can be developed from readily available data (Table 17). Reliability parameters

120

such as standard errors, p-values and variance inflation factors indicate that the R 2
values and adjusted R2 values are highly reliable. However, R2 values and adjusted
R 2 values are quite low indicating a large portion of the variation is unaccounted for

(Table 16). Only three multiplier groups have R 2 and adjusted R 2 values exceeding

50%. Three groups are less than 30% with one of these groups at 15%.

The Logging Camps and Contractors sector has significantly higher R2 and adjusted R2
values than the other sectors (> 50%). This could be due to the logging industry being
more consistently found in small rural economies than are the other two sectors, which

can be found throughout a greater range of regions with more diverse characteristics.

SAM multipliers have higher R2 and adjusted R2 values than Type 1 multipliers. This
is probably because the Type SAM multiplier includes the effects of induced spending
(i.e. spending by households) which increases with increases in variables directly related
to the size of the economy (i.e. personal income, number of sectors, population). There is
no clear pattern to the relationship between employment multipliers and income

multipliers.

In addition to the measures taken above to determine the validity of the regression
models, the results were also examined in respect to mean and maximum percent error.
This was done by taking the difference between the IMPLAN generated multipliers and
comparing them to the multipliers generated by the regression models (Table 18). While

mean absolute percent errors were small the maximum values were quite large meaning

121

that for any particular multiplier estimate the multiplier estimated by the regression
models could be substantially different than the actual multiplier estimated by IMPLAN.

This analysis did not serve to invalidate the regression results.

The information above indicates that only those willing to take high risks might chose to
use the models for Logging Camps and Contractors to estimate the multipliers for just

that economic sector. However, there is usually very little demand for just a single sector

multiplier within the wood products industries. R 2 and adjusted R2 values for the
other sectors are so low that they should not be considered a viable alternative. This
leaves the analyst with the undesirable option of using a regression model derived
multiplier for one sector (Logging Camps and Contractors) and multipliers from another

source (i.e. input-output model) for the remaining sectors.

This study suggests the feasibility of generating economic multipliers from regression
models, using readily available explanatory variables, is limited. The risk of error is
high and must be weighed against more expensive methods with lower risk. However,
there are still potential ways to improve the models (see Recommendations for Future

Research).

Policy Implications

Based on this research, the development of predictive regression models to estimate

economic multipliers appears to be questionable. Also, is it practical in light of other

122

alternatives? The primary alternative at the present time is developing site-specific
multipliers using model-building software programs such as IMPLAN and RIMSII. Both
approaches require substantial initial investments. To develop a set of predictive models
requires skills in econometric modeling. Software systems like IMPLAN are already
developed. However, systems like IMPLAN have high acquisition costs and also require

skilled analysts to develop dependable results.

The use of regression models requires the user to have access to the data representing the
model variables. The IMPLAN user already has most of the information they need in the
IMPLAN data set. However, it would be possible to build a regression based software
model where all the basic information is in the model data set just as it is in IMPLAN.
Policy decisions would depend heavily on the total relative costs of the alternative
approaches and the quality of the results. This is beyond the scope of this study. The
behavior of multipliers resulting fiom changes in explanatory variables should be

considered in writing guidelines for economic impact area design.

Recommendations for Future Research

Economic feasibility and assumption of risk seems to be the primary issue as to whether
regression model multipliers should be used in lieu of models such as IMPLAN. To
make this decision research needs to be done looking at the total costs in relation to the

product needed. For example IMPLAN is expensive but can do a great many things.

123

However, many of these products of IMPLAN are rarely used. A regression-based model
could be designed to produce only those reports that are commonly used and require less
skill/expense. If the results from developing regression-based models do not justify the
expense then further development is likely doomed unless it makes the model more

economically feasible.

A second recommendation is to further explore timber supply as an explanatory variable.
Within the next year the USDA Forest Service should have complete coverage of the
US. for timberlands. The present inventory that is available for use does not include
some substantial timbered areas such as Oregon and Washington. Other vegetation
inventories do not separate out timberlands. Actual timber harvest levels could also be

used as an explanatory variable if this data could be found in a readily usable form.

A third recommendation is to analyze more of the multipliers such as those for value-
added. It was not included in this study because of an attempt to keep the number of
variables within reason and value-added is not a commonly used measure of economic

activity for economic impact analysis.

A fourth recommendation is to evaluate employment as an explanatory variable. It was
not included in this study because of the concern about the different definitions of
employment and what jobs are included in the readily available data. However, there
might be some merit to looking at the definition in terms of total employment as

determined by the Bureau of Economic Analysis.

124

A fifth possibility for future research is to generate sales or output multipliers and use
these multipliers as the dependent variables in regression models. Then analyze for
correlation and regression coefficients. Employment and income multipliers could then

be created from local or regional output to jobs or income ratios.

A final recommendation is to further investigate the non-linear characteristics of
multiplier predictions. Part of this study looked at the behavior of multipliers as specific
impact areas were expanded. There was evidence to demonstrate that as the size of
specific impact areas reached certain levels, multipliers grew slowly. This has important

implications where analysts are trying to geographically focus on impacted areas.

125

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--. Bureau of Economic Analysis. 1995. BEA Economic Area Component County List.
Available at www.bea.doc.gov/bea/regionaUdocflmnlisthtm.

---. Bureau of Economic Analysis, Inter-industry Division. 2001. Annual Input-Output
Accounts Of The US. Economy, 1997. Washington, DC.

Vasievich, Mike. 1999. Here comes the neighborhood — a new gold rush and eleven
other trends affecting the Midwest. NC News (Aug/Sept):l-3. St. Paul, MN:USDA
Forest Service, North Central Research Station.

Wagner, John E., Steven C. Deller, and Greg Alward. 1992. Estimating economic

impacts using industry and household expenditures. Journal Of The Community
Development Society 23(2).

131

Zheng, Chinlong, and Patrice A. Harou. 1988. A method to estimate input-output
multipliers for the forestry sector without an I-O table. Forest Science 34(4):882-893.

132

Appendix A — Validation of Linear Models

Assumptions Underlying the Method of Least Squares - There are 10 basic assumptions
that must be met to have a valid least squares regression model (Koutsoyiannis 1979).

Each is discussed relative to this research.

Assumption 1: Linear regression model. The regression model is linear in the
parameters. The parameters, which are economic multipliers and associated explanatory
variables are assumed to be linearly related and are analyzed accordingly. In addition,

the X and Y variables were put in natural log form and tested for non-linearity.

Assumption 2: X values are fixed in repeated sampling. Values taken by regressor X are
considered fixed in repeated samples. More technically, X is assumed to be non-
stochastic. The X values in this study are fixed known constants such as population,
number of economic sectors etc. The Y values are economic multipliers and are

stochastic.

Assumption 3: Zero mean value of disturbance U; Given the value of X, the mean, or
expected, value of the random disturbance term L],- is zero. Technically the conditional
mean value of Q is zero. The analysis was designed to produce a least squares linear

equation therefore equally distributing the observations about the regression line. This,

by definition, produces a net zero value for the residuals.

133

Appendix A (Cont)

Assumption 4: Homoscedasticiy or gual variance of UL- . Given the value of X, the
variance of L1,- is the same for all observations. That is, the conditional variances of L4-
are identical. This was confirmed by examining scatter plots with residual values plotted
along the X values. A slight amount of heteroscedasticity was observed in some of the
models but it was not significant enough to justify using a procedure such as the
Lagrange-Multiplier test. The implications of non-constant variance which leads to non-
constant standard errors affects our ability to make precision statements in hypothesis

testing.

Assumption 5: No autocorrelation between E dism Given any two X values, Xi]-

(i not = j), the correlation between any two g, (i not = j) is zero. The assumption of
ordinary least squares is that the successive values of the random variable u are
temporally independent, that is, that the value which U assumes in any one period is
independent fiom the value which it assumed in any previous period. In brief, this is a
problem associated with time series data. This study does not include time series — it is

cross-sectional therefore autocorrelation is not a problem.

Assumption 6: Zero covariance between U; and X_,-. The disturbance u and explanatory

variable X are uncorrelated. This is similar to homoscedasticity in Assumption 4. As X
changes, the magnitude of the error terms should not change. Examination of the

arrangement of the error terms around their mean (zero) shows this not to be a problem.

134

Appendix A (Cont)

Assamntion 7: The number of observations n must be ggeater than the number of
parameters to be estimated. Alternatively, the number of observations n must be greater
than the number of explanatory variables. In this study there are at from 3 to 6
explanatory variables plus the Y intercept. There are a minimum of 384 observations

thus satisfying this assumption.

Assumption 8: Mbilitv in X values. The X values in a given sample must not all be
the same. Technically, variable (X) must be a finite positive number. For example, if
there was little variation in population or any of the other explanatory variables, we
would not be able to explain much of the variation in the multipliers. There is significant

variation in all the explanatory variables in this study.

Assumption 9: The regression model is correctly specified. Alternatively, there is no
specification bias or error in the model used in empirical analysis. Specification should
be addressed in terms of the variables chosen and the form of the variables chosen. The
variables chosen were the result of experience in the economic impact field and and the
available literature. It was felt there were no other readily available variables that would
strengthen the model. The assumption of linearity was tested by looking at the graphic

distribution of the residuals and natural log transformations.

135

Appendix A (Cont)

Assumption 10: There is no perfect multicollinearig. That is, there are no perfect linear
relationships among the explanatory variables. This was tested with correlation analysis
among the explanatory variables. Although some R-values were very high in the draft
models, none were close to perfect. All of the highly collinear values were removed in
the final model. Remaining variables in the final model showed very low collinearity.
The effects of multicollinearity include enlarging the standard error and variance, which
is measured by the variance inflation factor (V IF). Variables with high VIF values were

usually removed in the regression analysis process.

136

Appendix B — Best Subsets Regression Analysis Results

B-t. Regression:

 

Best Subsets ‘

 

    

 

 

 

 

 

LE1 versus Pop, PopDen, Sect, TIO, Perlnc, EIA
Response (dependent variable) is LE1
Pop Per
Vars R-Sq R-Sq (adj) Cp 8 Pop Den Sect TIO Inc EIA

1 26.9 26.8 109.4 0.083181 X
1 21.5 21.4 165.5 0.086214 X
1 3.7 3.6 349.0 0.095477 X
1 3.7 3.6 349.2 0.095488 X
1 3.7 3.6 349.3 0.095491 X
2 32.8 32.6 50.7 0.079821 X X
2 29.9 29.7 80.3 0.081510 X X
2 29.7 29.5 82.9 0.081654 X X
2 29.6 29.4 84.0 0.081716 X X
2 29.1 28.8 89.5 0.082026 X X
3 36.6 36.3 13.7 0.077606 X X X
3 36.1 35.8 18.9 0.077912 X X X
3 36 35.7 19.6 0.077954 X X X
3 33.2 32.9 48.5 0.079641 X X X

-- ~' ‘ xx“x..x::
4 37.1 36.7 X X X X
4 36.6 36.2 15.7 0.077666 X X X X
4 36.1 35.7 20.5 0.077953 X X X X
4 36.1 35.7 20.9 0.077973 X X X X
5 37.8 37.3 5.0 0.076972 X X X X X
5 37.7 37.2 6.7 0.077072 X X X X X
5 37.1 36.6 12.5 0.077421 X X X X X
5 36.1 35.6 22.5 0.078013 X X X X X
5 31 .8 31 .3 66.7 0.080584 X X X X X
6 37.8 37.2 7.0 0.077030 X X X X X X

649 cases used, 86 cases contain missing values.b

 

Shaded row was selected as best subset for regression model development.

Cases with missing values are those impact areas that did not have the sector being analyzed.

137

Appendix B (Cont)

8-2. Regression:
Best Subsets

 

 

 

 

 

  

 

LE2 versus Pop, PopDen, Sect, TIO, Perlnc, EIA
Response (dependent variable) is LE2
Pap Per
Vars R-Sq R-Sq (adj) Cp S Pop Den Sect TIO Inc EIA

1 26 25.9 104.6 0.14625 X
1 17.9 17.8 186.5 0.15402 X
1 3 2.8 337.7 0.16745 X
1 2.9 2.8 338.0 0.16748 X
1 2.9 2.8 338.1 0.16748 X
2 30 29.8 65.5 0.1429 X X
2 29.8 29.6 67.8 0.14252 X X
2 29.7 29.5 68.9 0.14263 X X
2 29.5 29.3 71 .4 0.14288 X X
2 29.3 29.1 73.4 0.14308 X X
3 34.5 34.2 22.7 0.13782 X X X
3 34 33.7 27.5 0.13833 X X X
3 33.8 33.5 29.2 0.13850 X X X
3 31.9 31.6 48.4 0.14046 X X X
3 31 .8 31 .5 49.6 0.14059 X X X
4 35.6 35.2 13.3 0.13675 X X X X
4 34.9 34.5 19.9 0.13743 X X X X
4 34.8 34.4 21.3 0.13758 X X X X
4 34.5 34.1 24.8 0.13794 X X X X
4 34.4 33.9 25.9 0.13806 X X X X
5 36.3 35.8 8.7 0.13615 X X X X X
5 36.1 35.6 10.0 0.13629 X X X X X
5 35.4 34.9 16.8 0.13701 X X X X X
5 34.6 34.1 25.4 0.13790 X X X X X
5 _ 33.3 32L§mammw 38.8w 0.13929 Xena-9&1 . X an h

;444 ’3“ ' ' ommafigmm-egaaz‘geesnmvxtnXXr .XX. . l

649 cases used, 86 cases contain missing values.

 

138

Appendix B (Cont)

B-3. Regression:

 

Best Subsets

 

 

   

  
  

  
  

 

 

 

P1 versus Pop, PopDen, Sect, TIO, Perlnc, EIA
Response (dependent variable) is LP1
Pop Per
Vars R-Sq R-Sq (adj) Cp 8 Pop Den Sect TlO Inc EIA

1 26.1 26.0 24.4 0.10815 X
1 13.0 12.8 143.6 0.11739 X
1 10.4 10.3 166.7 0.11910 X
1 10.3 10.2 167.5 0.11915 X
1 10.1 9.9 170.1 0.11935 X
2 27.8 27.6 1 1.4 0.10702 X X
2 26 4 26.2 23.9 0.10804 X X
2 26.1 25.9 26.3 0.10823 X X
2 26.1 25.9 26.4 0.10823 X X
2 26.1 25.9 26.4 0._1_9823 X_ _ X m

' f .- -3 .1~ -- * 24:3
3 27.8 27.5 13.3 0.10709 X X X
3 27.8 27.5 13.3 0.10710 X X X
3 27.8 27.5 13.4 0.10710 X X X
3 26.4 26.1 25.7 0.1081 1 X X X
4 29.1 28.7 3.6 0.10621 X X X X
4 29.1 28.6 3.7 0.1062 X X X X
4 29.1 28.6 3.9 0.10624 X X X X
4 28 0 27.5 13.7 0.10704 X X X X
4 28.0 27.5 13.9 0.10706 X X X X
5 29.1 28.6 5.2 0.10626 X X X X X
5 29.1 28.6 5.2 0.10627 X X X X X
5 29.1 28.5 5.5 0.10629 X X X X X
5 28.0 27.5 15.3 0.10710 X X X X X
5 26.5 25.9 29.1 0.10823 X X X X X
6 29.2 28.5 7.0 0.10633 X X X X X X

649 cases used. 86 cases contain missipgalues.

 

 

139

Appendix B (Cont)

B-4. Regression:

 

Best Subsets

LP2 versus Pop, PopDen, Sect, TIO, Perlnc, EIA

Response (dependent variable) is LP2

 

 

649 cases used, 86 cases contain missigq values.

 

 

 

Pop Per
Vars R-Sq R-Sq (adj) Cp 8 Pop Den Sect TIO Inc EIA

41.3 23.5 0.14004 X

17.6 293.6 0.16593 X

16.2 309.7 0.16735 X

16.0 312.3 0.16758 X

15.6 316.6 0.16796 X

42.8 7.6 0.13825 X X

41.3 24.8 0.14007 X X

41.3 25.5 0.14015 X X

41.3 25.5 0.14015 X X

. 41.3 25.5 0.14015 X X
_;- iii: '11:":- ., :- ., flint::i‘me"wm&mriecavemana_f~47§uart'~rx;:::rz.wi ’"Pfjfé'

3 43.0 42.8 9.4 0.13834 X X X
3 43.0 42.7 9.5 0.13835 X X X
3 43.0 42.7 9.5 0.13836 X X X
3 41.5 41.2 26.7 0.14016 X X x
4 43.7 43.3 3.7 0.13762 X X X X
4 43.7 43.3 3.8 0.13764 X X X X
4 43.7 43.3 4.0 0.13766 X X X X
4 43.1 42.8 10.0 0.13830 X X X X
4 43.1 42.8 10.1 0.13831 X X X X
5 43.7 43.3 5.2 0.13768 X X X X X
5 43.7 43.3 5.3 0.13769 X X X X X
5 43.7 43.3 5.5 0.13771 X X X X X
5 43.2 42.7 1 1 .6 0.13836 X X X X X
5 41.6 41.1 30.1 0.14033 X X X X X
6 43.8 43.2 7.0 0.13777 X X X X X X

 

140

 

 

Appendix B (Cont)

B-5. Regression:

Best Subsets

 

 

 

 

         

 

 

SE1 versus Pop, PopDen, Sect, TIO, Perlnc, EIA
Response (dependent variable) is SE1
Pop Per
Vars FI-Sq R-Sq (adj) Cp S Pop Den Sect TIO Inc EIA
1 10.3 10.2 148.6 0.13527 X
1 7.4 7.3 174.2 0.13745 X
1 4.6 4.4 199.2 0.13953 X
1 4.6 4.4 199.4 0.13956 X
1 4.5 4.3 200.1 0.13961 X
2 18.6 18.4 77.5 0.12897 X X
2 18.1 17.8 82.4 0.12941 X X
2 17.9 17.7 83.7 0.12952 X X
2 15.6 15.3 104.0 0.13133 X X
2 15.4 15.2 105.5 0.13147 X X
3 23.6 23.2 35.8 0.12508 X X X
3 23 22.6 41 .3 0.12559 X X X
3 22.8 22.5 42.2 0.12567 X X X
3 22.7 22.3 43.7 0.12581 X X X
3 22 21.6 49.9 0.12638 X X X
4 26.7 26.2 10.6 0.1262 X X X X
4 25.7 25.2 19.0 0.12341 X X X X
4 25.5 25.1 20.6 0.12357 X X X X
4 24.2 23.7 32.6 0.12469 X X X X
4 24.2 23.7 32.6 0.12469 X X X X
5 27.4 26.9 5.7 0.12206 X x X x X
5 25.8 25.2 20.3 0.12345 X X X X X
5 24.2 23.6 34.3 0.12476 X X X X X
5 23.4 22.8 41 .0 0.12538 X X X X X
6 27.5 26.8 7.0 0.12209 X X X X X X
646 cases used, 89 cases contain missinpvalues.

 

 

141

Appendix B (Cont)

B—6. Regression:
Best Subsets

 

 

 

 

           
 

 

SE2 versus Pop, PopDen, Sect, TIO, Perlnc, EIA
Response (dependent variable) is SE2
Pop Per
Vars R-Sq R-Sq (adj) Cp 8 Pop Den Sect TIO Inc EIA
1 9.3 9.1 158.8 0.24343 X
1 6.3 6.2 184.8 0.24734 X
1 5.2 5.0 195.2 0.24890 X
1 1 .2 1 .0 230.2 0.25405 X
1 1.1 1.0 230.8 0.25413 X
2 18.2 18.0 81 .7 0.23128 X X
2 17.6 17.3 87.7 0.2323 X X
2 17.4 17.2 88.8 0.23240 X X
2 16.6 16.4 95.9 0.23354 X X
2 14.8 14.5 112.5 0.23615 X X
3 23 9 23.5 34.1 0.22336 X X X
3 23.8 23.5 34.2 0.22337 X X X
3 23.0 22.6 41 .9 0.22465 X X X
3 22.9 22.6 42.3 0.22471 X X X
3 22.8 22.4 43.7 0.22495 X X X
4 26.3 25.8 14.9 0.21998 X X X X
4 25.2 24.7 24.5 0.22159 X X X X
4 25.1 24.7 24.9 0.22167 X X X X
4 24.9 24.4 26.8 0.22198 X X X X
4 24.8 24.3 . 27.6 0.22212 X XMW X 7
5 27.2 26.6 8.8 0.21877 X X X
5 25.2 24.6 26.5 0.22176 X X X X
5 24.9 24 3 28.6 0.2212 X X X X X
5 24.9 24.3 28.8 0.22215 X X X X X
6 27.6 26.9 7.0 0.21830 X X X X X X
646 cases used, 89 cases contain missingvalues.

 

 

142

Appendix B (Cont)

B-7. Regression:

Best Subsets

 

 

       

 

 

 

SP1 versus Pop, PopDen, Sect, TIO, Perlnc, EIA
Response (dependent variable) is SP1
Pop Per
Vars R-Sq R-Sq (adj) Cp S Pop Den Sect TIO Inc EIA
1 5.0 4.9 39.6 0.18015 X
1 4.1 4.0 45.8 0.18096 X
1 1 .6 1 .5 63.7 0.1833 X
1 0.1 0.0 75.0 0.18477 X
1 0.0 0.0 75.2 0.18479 X
2 8.2 7.9 18.7 0.17723 X X
2 6.2 5.9 33.1 0.17916 X X
2 6.0 5.7 34.2 0.17931 X X
2 6.0 5.7 34.6 0.17936 X X
2 5.9 5.6 35.1 0.17943 X X
3 8.9 8.5 15.3 0.17664 X X X
3 8.9 8.4 15.9 0.17673 X X X
3 8.8 8.3 16.7 0.17683 X X X
3 8.7 8.3 16.9 0.17685 X X X
3 8.4 8.0 19.1 0.17716 X X X
4 9.9 9.3 10.5 0.17585 X X X X
4 9.8 9.3 1 1 .0 0.17592 X X X X
4 9.7 9.1 11.9 0.17605 X X X X
4 9.5 9.0 13.1 0.17621 X X X X
' " i " .-- , -' mrvsrammmamxmxxnx
5 10.5 9.8 8.2 0.17541 X X X X
5 10.0 9.3 11 .5 0.17586 X X X X X
5 10.0 9.3 11 9 0.17591 X X X X X
5 9.1 8.4 18.1 0.17676 X X X X X
6 10.9 10.1 7.0 0.17511 X X X X X X
646 cases used, 89 cases contain missing values.

 

143

Appendix B (Cont)

B-8. Regression:

 

Best Subsets

5
5
5
5
6

 

{finesseewwwowmmmmm-s-s-s-t-s

20.7
Khan .-'
I t
we

Vars R-Sq

15.4
10.2
2.1
2.1
1.9
19.5
17.6
17.2
17.1
17.0
20.2
20.1
20.1
20.0
19.7
21.1
21.0
21 .0
20.9

 
 

22.1

Response (dependent variable) is SP2

SP2 versus Pop, PopDen, Sect, TIO, PerInc, EIA

 

646 cases used, 89 cases contain missing values.

Pop Den Sect TIO

POP

R-Sq (adj) Cp S
15.3 52.1 0.22514
10.0 95.0 0.23199
2.0 161.1 0.24217
1.9 161.5 0.2424 X
1.8 162.6 0.24240
19.2 20.5 0.21980 x
17.3 36.3 0.2241
16.9 39.3 0.22290 X
16.9 39.7 0.22297
16.7 40.9 0.2316
19.8 16.9 0.21903 X X
19.7 17.4 0.2191 1 X
19.7 17.6 0.21914 X
19.6 18.5 0.21930 X
19.3 20.7 0.21966 X
20.6 1 1.0 0.21789 X X
20.5 12.1 0.21806 X
20.5 12.2 0.21808 X
20.4 13. 3 0.21826 X
‘ “W, _ ' f 20 2 amm14 5 mgggmsfgsrmoésm x
, ~.-5‘.:’:x.\;»' 1: 354.4 .. , 513.3131}. , g . , g
21.1 7.9 0.21719 X X
20.7 11.7 0.21783 X X
20.5 13.1 0.21807 X X
19.7 19.8 0.21920 X
21.4 7.0 0.21687 X X

133;
E

><><><><><1

X
X
X
X
X
X
X X
X
X
X
X
X
X
X
X
X
X
. TL

5

Per
Inc

 

EIA

 

 

 

144

Appendix B (Cont)

B-9. Regression:

 

Best Subsets

Response (dependent variable) is VE1

 

VE1 versus Pop. PopDen, Sect, TIO, Perlnc, EIA

 

 

 

 

 

 

 

  

383 cases used, 352 cases contain misflg values.

 
 
 

Pop Per
Vars R-Sq R-Sq (adj) Cp S Pop Den Sect TlO Inc
1 10.1 9.9 74.4 0.091452 X
1 10.1 9.8 74.5 0.091457 X
1 9.8 9.5 76.1 0.091622 x
1 9.6 9.3 77.1 0.091721 X
1 0.1 0.0 124.8 0.096400
2 18.7 18.2 33.2 0.087095 X X
2 18.2 17.8 35.3 0.087320 X X
2 17.8 17.4 37.3 0.087535 X X
2 14.3 13.8 55.3 0.089416 X X
2 14.0 13.6 56.6 0.089553 X X
3 24.3 23.7 6.5 0.0841 12 x X X
3 23.9 23.3 8.7 0.084349 X X X
3 23.7 23.1 9.7 0.084462 X X X
3 19.6 19.0 30.3 0.086689 X X
3 19.1 18.5 . 0.086977 X
4 24.4 23.6 8.4 0.084203 X X X X
4 24.3 23.5 8.5 0.084222 X X X
4 23.9 23.1 10.6 0.084453 X X X x
4 23.9 23.1 10.7 0.084458 X X X
5 25.4 24.5 5.0 0.083722 X X X X X
5 25.4 24.4 5.4 0.083768 X X X X
5 24.4 23.4 10.4 0.084315 X X X X
5 23.9 22.9 12.6 0.084563 X X X x
5 20.1 19.0 31.9 0.086665 X X X X
6 25.4 24.3 7.0 0.083831 x X X X X

EIA

X

><X><><><

 

 

145

Appendix B (Cont)

B-10. Regression:

Best Subsets

 

VE2 versus Pop, PopDen, Sect, TIO, Perlnc, EIA

Response (dependent variable) is VE2

  

 

 

       

 

 

Pop Per
Vars R-Sq R-Sq (adj) Cp S Pop Den Sect TIO Inc EIA
1 5.5 5.2 66.6 0.20149 X
1 4.3 4.0 72.2 0.20276 X
1 4.2 4.0 72.5 0.20282 X
1 4.2 3.9 72.7 0.20287 X
1 1 .5 1 .2 85.4 0.20569 X
2 15.3 14.9 22.1 0.19095 X X
2 15.3 14.8 22.3 0.19099 X X
2 15.2 14.8 22.6 0.19107 X X
2 10 1 9.6 46.9 0.19678 X X
2 9.6 9.1 49.1 0.19729 X X
3 19.5 18.9 4.4 0.18641 X X X
3 19.4 18.7 5.2 0.18661 X X X
3 19.1 18.4 6.6 0.18695 X X X
3 17.4 16.8 14.2 0.18882 X X
3 17.2 16.6 15.1 0.11904 2‘..-
4 19.8 18.9 5.3 0.18638 X X
4 19.6 18.7 6.0 0.18657 X X X
4 19.6 18.7 6.2 0.18662 X X X X
4 19.5 18.7 6.4 0.18666 X X X X
5 20 1 19.0 5.8 0.18627 X X X X X
5 20.0 19.0 5.9 0.18630 X X X X X
5 20.0 18.9 6.1 0.18634 X X X X X
5 19.7 18.7 7.4 0.18667 X X X X X
5 17.5 16.4 18.0 0.18927 X X X X X
6 20.2 19.0 7.0 0.18632 X X X X X X

 

 

383 cases used, 352 cases contain missingvalues.

 

146

Appendix B (Cont)

B-11. Regression:
Best Subsets

 

 

 

 

VP1 versus Pop, PopDen, Sect, TIO, Perlnc, EIA
Response (dependent variable) is VP1
Pop Per

Vars R-Sq R-Sq (adj) Cp S Pop Den Sect TIO lnc EIA
1 8.8 8.5 30.1 0.09949 X
1 1.0 0.8 64.8 0.10362 X
1 0.6 0.4 66.7 0.10384 X
1 0.6 0.3 67.0 0.10387 X
1 0.5 0.2 67.5 0.10393 X
2 11.4 11.0 20.3 0.09816 X X
2 11.4 10.9 20.6 0.09820 X X
2 11.1 10.6 21.7 0.09835 X X
2 10.9 10.4 22.6 0.09845 X X
2 8.9 8.5 31 .4 0.09953 X X
3 12.9 12.2 15.6 0.09747 X X X
3 12.6 12.0 16.8 0.09761 X X X
3 12.6 1 1.9 17.0 0.09764 X X X
3 124 117 177 0.09773 X X X
3 12.4 11.7 18.0 0.0976 X X X
4 14.6 13.7 9.9 0.09663 X X X X
4 13.6 12.7 14.5 0.09721 X X X X
4 13.6 12.7 14.6 0.09722 X X X X
4 13.4 12.5 15.5 0.09733 X X X X
4 13.2 12.3 16.4 0.09745 X X X X
5 15.6 14.5 7.5 0.09619 X X X X X
5 15.0 13.9 10.3 0.09655 X X X X
5 14.3 13.1 13.6 0.09697 X X X X
5 13.6 12.4 16.5 0.09734 X X X X
5 13.2 12.0 18.3 0.09756 X X X X ., A _

' ; 141* $13.70.. i ix: . 1x1 X I x ‘ x .

 
 

 

 

   

7383 cases used, 352 cases contain missinjq values.

147

Appendix B (Cont)

B— l 2. Regression:

Bust Subsets

 

  

 

          

 

 

VP2 versus Pop, PopDen, Sect, T10, PerInc, EIA
Response (dependent variable) is VP2
Pop Per
Vars R—Sq R-Sq (adj) Cp S Pop Den Sect TIO Inc EIA
1 28.7 28.5 29.2 0.12365 X
1 6.2 5.9 158.0 0.14182 X
1 5.6 5.4 161.2 0.14225 X
1 5.5 5.2 162.0 0.14235 X
1 5.2 4.9 163.8 0.14259 X
2 31.5 31.2 14.7 0.12129 X X
2 31.0 30.6 17.8 0.12177 X X
2 30.8 30.5 18.8 0.12192 X X
2 30.7 30.3 19.6 0.12204 X X
2 28.7 28.3 31.2 0.12381 X X
3 32.8 32.3 9.7 0.12035 X X X
3 32.6 32.1 10.7 0.12050 X X X
3 32.6 32.1 10.7 0.12052 X X X
3 31.9 31.4 14.6 0.12112 X X X
3 31.5 30.9 17.2 0.12153 X X X
4 33.7 33.0 6.2 0.11965 X X X X
4 33.1 32.4 9.9 0.12023 X X X X
4 32.9 32.2 11.1 0.12042 X X X X
4 32.7 32.0 12.0 0.12056 X X X X
4 32.7 32.0 12.2 0.12059 X X X X
,Q’TI'” > . 1.12.4.0... ' ? ......X....................J
5 33.8 32.9 7.9 0.11975 X X X X X
5 33.2 32.4 11.1 0.12026 X X X X X
5 32.7 31.8 14.0 0.12072 X X X X X
5 32.1 31.2 17.6 0.12129 X X X X X
6 34.3 33.3 7.0 0.11946 X X X X X X
383 cases used, 352 cases contain missing values.

 

148

Appendix C — Regression Equation Information — Preliminary Model

 

( -|.l{cgrcsxiull \n;H}~ds: liil \waulsl’UIL Sect.|’crlnix El.\

The regression equation is
LE1 = 1.23 — 0.0512 P0p +0.000517 Sect +0.000002 PerInc + 0.00129 EIA

650 cases used 85 cases contain missing values

Predictor Coef SE Coef T P VIF
Constant 1.23082 0.01041 118.22 0.000

Pop -0.05119 0.01254 -4.08 0.000 95.4
Sect 0.00051656 0.00004123 12.53 0.000 1.9
PerInc 0.00000158 0.00000048 3.29 0.001 92.8
EIA 0.0012899 0.0001490 8.66 0.000 1.3
S = 0.07720 R-Sq = 37.4% R-Sq(adj) = 37.0%

 

 

 

 

( -2.I{cglIW\inll \nzfl)~ds: IJCZ \crslvslhip.lflipl)cln Siwfl.'1l().l’crlnc.l] \

The regression equation is
LE2 = 1.42 - 0.100 Pop —0.000089 PopDen + 0.00101 Sect - 1.37 TIO
+0.000006 PerInc + 0.00164 EIA

649 cases used 86 cases contain missing values

Predictor Coef SE Coef T P VIF
Constant 1.42122 0.01848 76.92 0.000

Pop ~0.10010 0.02218 -4.51 0.000 96.3
PopDen -0.00008941 0.00004018 —2.23 0.026 1.5
Sect 0.00101245 0.00007515 13.47 0.000 2.0
TIO -1.3717 0.7161 -1.92 0.056 290.7
PerInc 0.00000605 0.00000176 3.44 0.001 400.9
EIA 0.0016483 0.0002837 5.81 0.000 1.6
S = 0.1359 R-Sq = 36.6% R—Sq(adj) = 36.0%

 

 

 

149

 

Appendix C (Cont)

 

( —3. Regression .\Il;l|)\i\: |.I’I \crslls I’nplh'n. Sect. ICI.\

The regression equation is
LP1 = 1.18 +0.000092 PopDen +0.000474 Sect + 0.00103 EIA

649 cases used 86 cases contain missing values

Predictor Coef SE Coef T P VIF
Constant 1.18059 0.01288 91.66 0.000

PopDen 0.00009170 0.00002914 3.15 0.002 1.3
Sect 0.00047360 0.00005229 9.06 0.000 1.6
EIA 0.0010269 0.0002168 4.74 0.000 1.5

s = 0.1063 R-Sq = 28.9% R-Sq(adj) = 28.5%

 

 

 

( ~4.|{curcsshnl \n;H}\is:l.P3 \crsus PUIH)CIL Secl.|il\

The regression equation is
LP2 = 1.29 +0.000095 PopDen +0.000961 Sect + 0.00136 EIA

649 cases used 86 cases contain missing values

Predictor Coef SE Coef T P
Constant 1.28837 0.01669 77.22 0.000
PopDen 0.0000946? 0.00003775 2.51 0.012
Sect 0.00096086 0.00006774 14.18 0.000
EIA 0.0013628 0.0002809 4.85 0.000
S = 0.1377 R-Sq = 43.6% R-Sq(adj) = 43.3%

VIF

l—‘HH
mmw

 

150

 

 

Appendix C (Cont)

   

(‘-5. Regression \naluis: Slil wrsus l’up. PopDen. Sect. Perlnc. l'l|.\

The regression equation is
SE1 = 1.64 - 0.0788 Pep —0.000210 PopDen +0.000508 Sect +0.000002 PerInc
+ 0.00139 EIA

646 cases used 89 cases contain missing values

 

Predictor Coef SE Coef T P VIF
Constant 1.63906 0.01651 99.31 0.000

Pop -0.07876 0.01987 -3.96 0.000 95.9
PopDen -0.00021024 0.00003510 -5.99 0.000 1.4
Sect 0.00050794 0.00006723 7.55 0.000 2.0
PerInc 0.00000207 0.00000076 2.70 0.007 94.0
EIA 0.0013856 0.0002556 5.42 0.000 1.6
S = 0.1220 R-Sq = 27.5% R-Sq(adj) = 26.9%

 

( wh.1{11;r0\sinll,\llfl|)\l\2§\l _

 

$32 =
+ 0.00223 EIA

 

3

The regression equation is
1.93 - 0.164 Pop -0.000311 PopDen + 0.00121 Sect +0.000005 PerInc

646 cases used 89 cases contain missing values

\cr\U\ PUIL PU'”)CIL Sccl.lkw1lug l].\

Predictor Coef SE Coef T P VIF
Constant 1.93169 0.02951 65.46 0.000

Pop -0.16438 0.03553 -4.63 0.000 95.9
PopDen —0.00031113 0.00006275 -4.96 0.000 1.4
Sect 0.0012079 0.0001202 10.05 0.000 2.0
PerInc 0.00000471 0.00000137 3.44 0.001 94.0
EIA 0.0022270 0.0004569 4.87 0.000 1.6
S = 0.2181 R-Sq = 27.6% R—Sq(adj) = 27.0%

 

151

 

 

Appendix C (Cont)

 

( -7. Regression .\ll:l|)\1\2 Sl’l wrsus l’nplk-n. 8001.1“). Perlnc. Iil \

The regression equation is
SP1 = 1.55 -0.000181 PopDen +0.000472 Sect + 2.48 TIO -0.000006 PerInc
+0.000889 EIA

646 cases used 89 cases contain missing values

Predictor Coef SE Coef T P VIF
Constant 1.54900 0.02380 65.09 0.000

PopDen -0.00018108 0.00005085 -3.56 0.000 1.5
Sect 0.00047173 0.00009601 4.91 0.000 2.0
TIO 2.4813 0.9124 2.72 0.007 283.9
PerInc —0.00000553 0.00000189 -2.92 0.004 279.4
EIA 0.0008890 0.0003648 2.44 0.015 1.6
S = 0.1752 R-Sq = 10.7% R-Sq(adj) = 10.0%

 

 

 

(-X.|{curcsshin \lhd}sis:f$P2 \crsuslhiplhni.Sch ll(L Pcrlnc.lil\

 

The regression equation is
SP2 = 1.69 -0.000238 PopDen + 0.00107 Sect + 3.05 TIO -0.000007 PerInc
+ 0.00123 EIA

646 cases used 89 cases contain missing values

Predictor Coef SE Coef T P VIF
Constant 1.69454 0.02948 57.48 0.000

PopDen -0.00023813 0.00006299 -3.78 0.000 1.5
Sect 0.0010699 0.0001189 9.00 0.000 2.0
TIO 3.046 1.130 2.69 0.007 283.9
PerInc -0.00000681 0.00000234 -2.90 0.004 279.4
EIA 0.0012273 0.0004519 2.72 0.007 1.6
S = 0.2170 R-Sq = 21.9% R-Sq(adj) = 21.3%

 

 

 

152

Appendix C (Cont)

    

 

(—U.l{cgrcsshnl \nul1sh: \lfl\11\us Pnjfl)cn.80cl.11().lkw1nc

The regression equation is
VE1 = 1.44 -0.000140 PopDen +0.000397 Sect + 1.04 TIO -0.000003 PerInc

383 cases used 352 cases contain missing values

Predictor Coef SE Coef T P VIF
Constant 1.44065 0.01686 85.45 0.000

PopDen -0.00014037 0.00002452 -5.72 0.000 1.3
Sect 0.00039712 0.00005731 6.93 0.000 1.7
TIO 1.0431 0.4632 2.25 0.025 293.6
PerInc -0.00000276 0.00000096 -2.88 0.004 288.5
S = 0.08366 R-Sq = 25.3% R-Sq(adj) = 24.6%

 

 

 

( —10.Itcgrcsxhin.\lnfl)sisz\‘FZ \crsUslNrp.|Niplhnl.Scct.i] \

 

The regression equation is
VE2 = 1.75 - 0.0314 Pop -0.000202 PopDen +0.000912 Sect +0.000812 EIA

383 cases used 352 cases contain missing values

Predictor Coef SE Coef T P VIF
Constant 1.75302 0.03730 47.00 0.000

Pop -0.031417 0.004603 -6.83 0.000 2.0
PopDen —0.00020185 0.00005785 -3.49 0.001 1.4
Sect 0.0009125 0.0001356 6.73 0.000 2.0
EIA 0.0008123 0.0005372 1.51 0.131 1.6
S = 0.1861 R-Sq = 20.0% R-Sq(adj) = 19.2%

 

 

153

  

 

Appendix C (Cont)

(-ll.l{curcsshni \nul1sh: \l’l\cr\Us|NqL Pujfl)cn.\c L lltL Pcrlnc.l].\

 

The regression equation is
VP1 = 1.33 + 0.0374 Pop -0.000103 PopDen +0.000484 Sect + 1.57 TIO
-0.000005 PerInc -0.000437 EIA

383 cases used 352 cases contain missing values

Predictor Coef SE Coef T P VIF
Constant 1.33386 0.01941 68.71 0.000

Pop 0.03741 0.01632 2.29 0.022 94.8
PopDen —0.00010326 0.00003042 -3.39 0.001 1.5
Sect 0.00048424 0.00007036 6.88 0.000 2.0
TIO 1.5675 0.5358 2.93 0.004 298.3
PerInc —0.00000486 0.00000133 -3.65 0.000 421.8
EIA —0.0004367 0.0002786 -1.57 0.118 1.6
S = 0.09601 R-Sq = 16.2% R-Sq(adj) = 14.8%

 

 

 

( -|2.|{curcsshln \IHH}\1\Z\ P2 \crsus PulLl’npl)cn.Fuwfl. lI(L Perlnc

 

The regression equation is
VP2 = 1.46 + 0.0322 Pop —0.000123 PopDen +0.000986 Sect + 1.67 TIO
-0.000005 PerInc

383 cases used 352 cases contain missing values

Predictor Coef SE Coef T P VIF
Constant 1.45712 0.02406 60.56 0.000

Pop 0.03225 0.02013 1.60 0.110 93.3
PopDen -0.00012316 0.00003508 -3.51 0.000 1.3
Sect 0.00098639 0.00008216 12.01 0.000 1.8
TIO 1.6679 0.6655 2.51 0.013 297.6
PerInc -0.00000497 0.00000166 -3.00 0.003 421.8
S = 0.1194 R-Sq = 34.2% R-Sqladj) = 33.3%

 

 

154

Appendix D — Analysis of Variance Results

   

L1
D-l. Analysis of Variance tor LE1

 

 

Source DF SS MS F P
GF 7 151825021689 30.11 0
Error 6424.62528 0.0072
Total 6496.14353
Individual 95% Cls For Mean
Based on Pooled StDev
Level N Mean StDev + + +
1 75 1.3947 0.0785 (--*---)
2 59 1 .4350 0.0777 (---*---)
3 39 1.4261 0.0714 («.1 ..... )
4 81 1 .4637 0.0872 (---*--)
5 63 1 .4323 0.0728 (mt---)
6 103 1.4038 0.1010 (“1...
8 154 1.3302 0.0861 (--*--)
9 76 1.3355 0.0827 (---*--)
Pooled StDev = 0.0849 1.350 1.400 1.450

Family error rate = 0.507
Individual error rate = 0.0500

Critical value = 1.964

 

 

 

a The distribution of means and standard deviations in the one-way analysis of variance
above shows clearly that the multipliers for Forest Service Regions 1-6 (dummy = 0) are
different than those for Regions 8 and 9 (dummy = 1). This presents an opportunity to
divide the samples into two groups to try to improve the strength of the model. This was
done by inserting dummy variables in the regression equation. This has been labeled the
LElDum.

155

Appendix D (Cont)

{’1
D-2. Analysis of Variance for LE2
Source DF SS MS F P

GF 7 5.7783 0.8 40.94000 0
Error 642 12.9444 0.0
Total 649 18.727

Individual 95% Cls For Mean
Based on Pooled StDe
Level N Mean StDev 1 1 + 1
75 1 .7767 0.1455 (---*---)
59 1 .7227 0.1028 (mt---)
39 1.6637 0.1109 ( ----- * ----- )

81 1 .7984 0.1338 (---*---)
63 1 .7993 0.1244 ("3---)
103 1.8177 0.1747 (-2---)

154 1.5915 0.1515 («t--
76 1.6034 0.1307 (---*---)

 

CDQGU'IROJN-e

 

T

Pooled StDev = 0.1420 1.600 1.680 1.760 1.840
Fisher's pairwise comparisons

Family error rate = 0.507
Individual error rate = 0.0500

 

Critical value = 1.964

 

 

a The distribution of means and standard deviations in the one-way analysis of variance
above shows clearly that the multipliers for Forest Service Regions 1-6 (dummy = 0) are
different than those for Regions 8 and 9 (dummy = 1). Also, Region 3 seems to be
separated from other regions. This presents an opportunity to at least divide the samples
into 2 groups to try to improve the strength of the model. This was done by inserting
dummy variables in regression equation. This has been labeled the LE2Dum.

156

Appendix D (C0nt.)

a
D-3. Analysis of Variance for LP1

 

Source DF SS MS F P
GF 7 3.2130 0.4590 41.84 0.000
Error 642 7.0424 0.01 10

Total 649 10.2554

Individual 95% Cls For Mean
Based on Pooled StDev

 

 

Critical value = 1.964

 

Family error rate = 0.507
Individual error rate = 0.0500

Fisher's pairwise comparisons

Level N Mean StDev + + + +
1 75 1.2666 0.0746 (--‘-)

2 59 1 .4279 0.1030 (--*-)

3 39 1 .5459 0.1457 (---*--)

4 81 1 .3954 0.1604 (--*-)

5 63 1.3460 0.1009 (--'-)

6 103 1.2745 0.0686 (-*-)

8 154 1.3275 0.0899 (-*)

9 76 1 .3350 0.1034 (--*-)

Pooled StDev=0.1047 1.30 1.40 1.50 1.60

 

 

a The distribution of means and standard deviations in the one-way analysis of variance
above shows clearly that the multipliers for Forest Service Regions 1 and 6 (dummy = 0)
are different than 2,4,5,8,9 (dummy = l) which are different than those for Region 3
(dummy = 2). This presents an opportunity to at least divide the samples into 3 separate
groups to try to improve the strength of the model. This was done by inserting dummy

variables in the regression equation. This has been labeled the LPlDum.

157

Appendix D (Cont)

Cl
04. Analysis of Variance for LP2

Source
GF
Error
Total

75
59
39
81

Level N

DF
7
642

5.2676
16.4065

SS MS F
0.7525 29.45

0.0256

649 21.6741

Individual 95% Cls For Mean

Based on Pooled St Dev

Mean StDev + + +

1 .4940
1 .7104
1 .8493
1 .6676
1 .6232

p
0

 

0.1 148 (--*---)
0.1543
0.1943
0.2325
0.1575

103 1.5226
154 1.5606
76 1.5836

0.1232
0.1473
0.1585

1
2

3

4

5 63
6

8

9

Pooled St Dev = 0.1599
Fishers pairwise comparisons

Family error rate = 0.507
Individual error rate = 0.0500

Critical value = 1.964

 

 

 

a The disuibution of means and standard deviations in the one-way analysis of variance
above shows clearly that the multipliers for Forest Service Regions 1 and 6 (dummy = 0)
are different than 2,4,5,8,9 (dummy = l) which are different than those for Region 3
(dummy = 2). This presents an opportunity to at least divide the samples into 3 separate
groups to try to improve the strength of the model. This was done by inserting dummy
variables in the regression equation. This was labeled the LP2Dum.

158

Appendix D (Cont)

2'1
D—5. Analysis of Variance for SE1

 

 

Source DF SS MS F P
GF 7 1.3002 0.1857 10.01 0
Error 639 1 1.8528 0.0185
T0131 646 1 3.1 53
Individual 95% Cls For Mean
Based on Pooled St Dev
Level N Mean St Dev 4 4 1
1 73 1 .8286 0.0928 (nun---)
2 61 1 .7899 0.1 176 (----*-----)
3 38 1.7157 0.1676 (------*------)
4 76 1.7815 0.1574 (nun---)
5 65 1.7288 0.1731 (----* ----- )
6 102 1.7994 0.1084 (----*---)
a 155 1.7667 0.1417 ("n")
9

77 1.6733 0.1312 (me...)

I l
T T

 

Pooled St Dev = 0.1362 1.680 1.740 1.800
Fisher's pairwise comparisons

Family error rate = 0.507
Individual error rate = 0.0500

Critical value = 1.964

 

 

 

a The distribution of means and standard deviations in the one-way analysis of variance
above shows clearly that the multipliers for Forest Service Regions 3 and 5 and 9
(dummy = 0) are different than the other regions which are fairly similar (dummy = 1).
This presents an opportunity to at least divide the samples into 2 geographic groups
which might improve the strength of the model. They have been labeled the SElDum.

159

Appendix D (Cont)

a
D-6. Analysis of Variance for SE2

 

Level
73
61
38
76
65

1 02

1 55

2.3904
2.1737
2.1020
2.3071
2.2656
2.4122
2.1768

Individual 95% Cls For Mean
Based on Pooled StDev
N Mean StDev

0.1738
0.1707
0.2168
0.2998
0.2831
0.21 16
0.2251

1 l I
T T T

Source DF SS MS F P
GF 7 9.3939 1 .342 26.22 0
Error 639 32.7006 0.0512

Total 646 42.0945

COQQU'IrhWM-t

77 2.0518 0.1934 (---*--)

T

 

Pooled StDev = 0.2262 2.10 2.25 2.40

Fisher's pairwise comparisons

Family error rate = 0.507
Individual error rate = 0.0500

Critical value = 1.964

 

 

 

a The distribution of means and standard deviations in the one-way analysis of variance
above shows clearly that the multipliers for Forest Service Regions 2,3,8 and 9 (dummy
= 0) are different than 1 and 6 (dummy = 1) which are different than 4 and 5 (dummy =
2). This presents an opportunity to at least divide the samples into 3 geographic groups
which might improve the strength of the model. They have been labeled the SE2Dum.

160

Appendix D (Cont)

   

t]
D-7. Analysis of Variance for SP1

Source DF SS MS F P
GF 7 4.8545 0.6935 25.84 0
Error 639 17.1475 0.0268

Total 646 22.002

Individual 95% Cls For Mean
Based on Pooled StDev
Level N Mean StDev 4 4 4 4

 

1 73 1.6369 0.1111 (.3.--)
2 61 1.9066 0.1814 (mm)
3 38 1.6899 0.1403 (----*---)

4 76 1.6841 0.2316 (--*--)

5 65 1.5807 0.0972 (---*--)

6 102 1.5892 0.0772

8 155 1.6936 0.1630 (-*-)

9 77 1.7105 0.2361 (---*--)

 

Pooled StDev = 0.1638 1.56 1.68 1.80 1.92
Fisher's painivise comparisons

Family error rate = 0.507
Individual error rate = 0.0500

 

 

Critical value = 1.964

 

a The distribution of means and standard deviations in the one-way analysis of variance
above shows clearly that the multipliers for Forest Service Regions 5 and 6 (dummy = 0)
are different than 1,3,4,8 and 9 (dummy = 1) which are different than Region 2 (dummy
= 2). This presents an opportunity to at least divide the samples into 3 geographic groups
which might improve the strength of the model. They have been labeled the SPlDum.

161

Appendix D (Cont)

a
DB. Analysis of Variance for SP2

 

Source DF SS MS F P
GF 7 7.0007 1 .0001 20.23 0
Error 639 31 .5845 0.0494

Total 646 38.5852

Individual 95% Cls For Mean
Based on Pooled St Dev
Level N Mean St Dev 4 4 4
73 1.9302 0.1592 (---*--)
61 2.2828 0.2464 (---*---)
38 2.0243 0.1831 (nut...)
76 2.0156 0.3167 4*---)
65 1.9051 0.1390 (---'---)
102 1.8974 0.1279 (-'--
155 1.9900 0.2262 (--*-)
77 2.0271 0.2945 (--'--)

 

CDQGU'IAQN-t

 

T

Pooled St Dev = 0.2223 1.95 2.10 2.25
Fisher's pairwise comparisons

Family error rate = 0.507
Individual error rate = 0.0500

 

 

Critical value = 1.964

 

a The distribution of means and standard deviations in the one-way analysis of variance
above shows clearly that the multipliers for Forest Service Regions 1,5 and 6 (dummy =
0) are different than 3,4,8 and 9 (dummy = 1) that are different than Region 2 (dummy =
2). This presents an opportunity to at least divide the samples into 3 geographic groups
that might improve the strength of the model. They have been labeled the SP2Dum.

162

Appendix D (Cont)

 

a
D-9. Analysis of Variance for VE1

Level
41 1 .5953
1 1 1 .481 1
12 1 .4143
17 1 .4620
42 1.4805
96 1.5587

Individual 95% Cls For Mean
Based on Pooled StDev
N Mean StDev

0.0483
0.0523
0.1032
0.1198
0.1135
0.0858

1

l l
T T T

Source DF SS MS F P
GF 7 0.70949 0.10136 13.44 0
Error 376 2.83474 0.00754

Total 383 3.54423

11-

117 1.5412
48 1.4911

0.0889
0.0689

@flOM#QN-§

 

T

Pooled StDev = 0.0868 1.400 1.470 1.540 1.610
Fisher‘s painivise comparisons

Family error rate = 0.505
Individual error rate = 0.0500

Critical value = 1.966

 

 

 

a The distribution of means and standard deviations in the one-way analysis of variance
above shows clearly that the multipliers for Forest Service Regions 2,3,4,5 and 9 (dummy
= 0) are different than 1,6, and 8 (dummy = 1). This presents an opportunity to at least
divide the samples into 2 geographic groups which might improve the strength of the
model. They have been labeled the VE1 Dum.

163

Appendix D (Cont)

 

a
D-10. Analysis of Variance for VE2

Source DF SS MS F
GF 7 4.3638 0.6234 19.53
Error 376 12.0036 0.0319

Total 383 16.3674

011

Individual 95% Cls For Mean
Based on Pooled StDev

Level N Mean StDev 4 4 4
41 2.2058 0.1336 (-*--)

11 1.9261 0.1212 (----* ----- )

12 1.7311 0.1889 (----*----)

17 1 .9303 0.1982 (-—--‘---)

42 1.9344 0.2151 (--"-)

96 2.0681 0.1859 ('-)
117 1.9577 0.1913 (-"-)
48 1.8685 0.1217 (-*--

l
T T T

 

COCDQM§QNA

Pooled StDev = .1787 1.80 2.00 2.20
Fisher’s pairwise comparisons

Family error rate = 0.505
Individual error rate = 0.0500

 

 

Critical value = 1.966

 

a The distribution of means and standard deviations in the one-way analysis of variance
above shows clearly that the multipliers for Forest Service Regions 3 (dummy = 0) is
different than 2,4,5,6,8,and 9 (dummy = l) which is different that region 1 (dummy = 2).
This presents an opportunity to at least divide the samples into 3 geographic groups
which might improve the strength of the model. They have been labeled the VE2Dum.

164

Appendix D (Cont)

a
D-I 1. Analysis of Variance for VP1

 

Level

41
1 1
12
17

1.4218
1.4468
1.4750
1.3837
42 1.4397
96 1.4723

Individual 95% Cls For Mean
Based on Pooled StDev
N Mean StDev

0.0568
0.0265
0.1569
0.1315
0.0965
0.0738

Source DF SS MS F P
GF 7 0.3268 0.0467 4.6 0
Error 376 3.8115 0.0101

Total 383 4.1383

l l
T

(---*--)
1 * )
( * >

 

 

<-------*------)

<------)

117 1.4777
48 1.5064

0.1182
0.1139

(OQU’UI#ODN-t

 

T

Pooled StDev = 0.1007 1.380 1.440 1.500
Fisher's pairwise comparisons

Family error rate = 0.505
Individual error rate = 0.0500

Critical value = 1.966

 

 

 

a The distribution of means and standard deviations in the one-way analysis of variance
above shows clearly that the multipliers for Forest Service Region 4 (dummy = 0) is
different than 1,2,3,5,6,8,and 9 (dummy = 1). This presents an opportunity to at least
divide the samples into 2 geographic groups which might improve the strength of the
model. They have been labeled the VPlDum.

165

Appendix D (Cont)

   

a
D-12. Analysis of Variance for VP2

Source DF SS MS F P
GF 7 0.4308 0.0615 2.99 0.005
Error 376 7.7449 0.0206

Total 383 8.1757

Individual 95% Cls For Mean
Based on Pooled StDev
StDev 4 4 4

Level N Mean

 

41-

41 1.6955
11 1.7929
12 1.7747
17 1.6597
42 1.7385
96 1.7615

0.0877
0.0313
0.2043
0.1745
0.1363
0.1236

 

117 1.7483
48 1.8009

0.1634 (-----
0.1578

CODQU'I#WN-5

 

Pooled StDev = 0.1435 1.600 1.680 1.760 1.840
Fisher's pairwise comparisons

Family error rate = 0.505
Individual error rate = 0.0500

 

 

Critical value = 1.966

 

a The distribution of means and standard deviations in the one-way analysis of variance
above shows clearly that the multipliers for Forest Service Regions 1 and 4 (dummy = 0)
are different than 2,,5,6,8,and 9 (dummy = 1). This presents an opportunity to at least
divide the samples into 2 geographic groups which might improve the strength of the
model. They have been labeled the VP2Dum.

166

 

 

APPENDIX E — Study Area Map

 

3:: go“ 98.. o 08..

tau—50m 3.500 D
2.1. see". .28.: I
5.258 8.9.x $.33 D

 

oi coin”. Eo.uoi5:om

   

3.x Siam

  

mi 52522 563.

mi coaom Eofimw

    

  

7m 5.3m E6562

 

9m 3.2.x 8.2.82

 

 

 

167

Appendix F - States in USDA Forest Service Regions

REGION 1 — NORTHERN REGION
Idaho Montana North Dakota
REGION 2 — ROCKY MOUNTAIN REGION

Colorado South Dakota
Nebraska Wyoming

REGION 3 — SOUTHWESTERN REGION
Arizona New Mexico
REGION 4 - INTERMOUNTAIN REGION

Idaho Utah
Nevada Wyoming

REGION 5 — PACIFIC SOUTHWEST REGION
California

REGION 6 — PACIFIC NORTHWEST REGION
Oregon Washington

REGION 8 -— SOUTHERN REGION
Alabama Georgia Mississippi
Arkansas Kentucky North Carolina
Florida Louisiana South Carolina

REGION 9 — EASTERN REGION

Illinois Minnesota Ohio

Indiana Missouri Pennsylvania
Michigan New Hampshire Vermont

REGION 10 — ALASKA REGION

Alaska

168

Tennessee
Texas

Virginia

West Virginia
Wisconsin

Appendix G — Final Regression Analysis Results

     

(.—|.i n1a||{curcxshn1 \n;d1xis:|.[l \\ PHIL \rcl.lll\.l.hll)urn
The regression equation is

LEI = 1.25 - 0.0110 Pop +0.000603 Sect +0.000387 EIA

- 0.0855 LElDum.

650 cases used 85 cases contain missing values

Predictor Coef SE Coef T P VIF
Constant 1.25381 0.00938 133.72 0.000

Pop -0.010950 0.001471 -7.44 0.000 1.7
Sect 0.00060279 0.00003712 16.24 0.000 2.0
EIA 0.0003873 0.0001443 2.68 0.007 1.6
LElDum. -0.085494 0.006205 -13.78 0.000 1.2
S = 0.06843 R-Sq = 50.8% R-Sqladj) = 50.5%

 

 

 

       

   

(i-Z.|1h1a||{cgrcsxhin.\|ufl1sis: IJSZ \slhiplhul.80cl.ll().l{l\. ll 2|)u1n

 

The regression equation is
LE2 = 1.48 -0.000120 PopDen + 0.00118 Sect - 0.324 TIO -0.000380 EIA
- 0.184 LE2Dum

649 cases used 86 cases contain missing values

Predictor Coef SE Coef T P VIF
Constant 1.47588 0.01543 95.62 0.000

PopDen -0.00012024 0.00003296 -3.65 0.000 1.4
Sect 0.00118375 0.00006276 18.86 0.000 2.1
TIO -0.32382 0.04752 -6.81 0.000 1.9
EIA -0.0003796 0.0002565 -1.48 0.139 1.9
LE2Dum -0.18431 0.01025 -17.98 0.000 1.2
S = 0.1126 R-Sq = 56.4% R-Sq(adj) = 56.1%

 

 

 

169

Appendix G (Cont)

 

(1-3.I‘hiullicgrcxxhnl.\nzd}sisz Ll’|\s Po'fl)crL?$ch.l].\.l.Pll)urn

The regression equation is
LP1 = 1.01 +0.000072 PopDen 40.000476 Sect 40.000748 EIA
+ 0.102 LPlDum.

649 cases used 86 cases contain missing values

Predictor Coef SE Coef T P VIF
Constant 1.00563 0.01601 62.83 0.000

PopDen 0.00007240 0.00002508 2.89 0.004 1.3
Sect 0.00047649 0.00004495 10.60 0.000 1.6
EIA 0.0007485 0.0001873 4.00 0.000 1.5
LPlDum 0.101804 0.006727 15.13 0.000 1.0
S = 0.09136 R-Sq = 47.5% R-Sq(adj) = 47.2%

 

 

 

    

(.44. I‘lllzll Regression .\Il;ll)si\: I.I’2 \\ I’uplk'n. SL‘L‘I. ICI.\. |.l’2|)llnl
The regression equation is

LP2 = 1.08 40.000072 PopDen 40.000964 Sect 4 0.00104 EIA

+ 0.119 LP2Dum.

649 cases used 86 cases contain missing values

Predictor Coef SE Coef T P VIF
Constant 1.08465 0.02143 50.61 0.000

PopDen 0.00007220 0.00003358 2.15 0.032 1.3
Sect 0.00096423 0.00006018 16.02 0.000 1.6
EIA 0.0010385 0.0002507 4.14 0.000 1.5
LP2Dum 0.118536 0.009007 13.16 0.000 1.0

s = 0.1223 R-Sq = 55.5% R-Sq(adj) = 55.2%

 

 

 

170

 

Appendix G (Cont)

  

The regression equation is

SE1 =

+ 0.00128 EIA + 0.0626 SElDum.

1.53 - 0.0228 Pop -0.000193 PopDen +0.000473 Sect

646 cases used 89 cases contain missing values

Predictor Coef
Constant 1.53447
Pop —0.022765
PopDen -0.00019295
Sect 0.00047331
EIA 0.0012831
SElDum 0.06261
S = 0.1196 R-Sq

SE Coef
0.02422 63
0.002758 -8
0.00003420 -5.
0.00006578 7
0.0002498 5.
0.01077 5.
= 30.3% R-Sq(adj)

T

.35
.26

64

.20

14
82

.000
.000
.000
.000
.000
.000

000000

29.8%

(i-S.I*hlnll{curtwsiuli \n;fl1sis: Slil\~.lN1p.lNipl)cn.?$ch l].\.$d{ll)urn

VIF

reranaksH

00101ka

 

 

 

(.-h.|5hlu||{cgrcsshnl \n1H)\i\: SI 2‘1slN1p.lNlpl)cn.lfich [I \.5HC21)UIH

The regression equation is

SE2 =

+ 0.00100 EIA + 0.0933 SE2Dum.

1.78 - 0.0459 Pop -0.000326 PopDen + 0.00127 Sect

646 cases used 89 cases contain missing values

Predictor Coef
Constant 1.77667
Pop -0.045871
PopDen -0.00032552
Sect 0.0012687
EIA 0.0010022
SE2Dum 0.09327
S = 0.2083 R-Sq

SE Coef
0.03345 53
0.004737 —9
0.00005972 -5
0.0001150 11
0.0004532 2
0.01080 8
= 34.0% R-Sq(adj)

T

.12
.68
.45
.04
.21
.64

.000
.000
.000
.000
.027
.000

000000

33.4%

VIF

HiebokéH

I—‘QOlka

 

171

 

 

 

 

Appendix G (Cont.)

 

(i-".|*hinll{cgrcxshnl \nafl)\i\: SI’Ixx Pnjfl)cn.f\ch Il().lfl\.f~Pll)u1n

The regression equation is
MSPl = 1.25 -0.000157 PopDen +0.000588 Sect - 0.0552 TIO
40.000310 EIA + 0.147 SPlDum.

646 cases used 89 cases contain missing values

Predictor Coef SE Coef T P VIF
Constant 1.25007 0.03067 40.76 0.000

PopDen -0.00015717 0.00004502 -3.49 0.001 1.4
Sect 0.00058816 0.00008583 6.85 0.000 2.0
TIO -0.05522 0.06642 -0.83 0.406 1.9
EIA 0.0003097 0.0003283 0.94 0.346 1.6
SPlDum 0.14724 0.01114 13.22 0.000 1.1
S = 0.1563 R-Sq = 29.0% R-Sq(adj) = 28.4%

 

 

 

 

(1-8.IVHIaIl<cgrcsshni_\n;fl)sis:fSPZ \slfliplhnl.5ccl.ll().|{l\.§$P2|)u|n

The regression equation is
SP2 = 1.42 -0.000223 PopDen + 0.00110 Sect - 0.111 TIO +0.000846 EIA
4 0.156 SP2Dum.

646 cases used 89 cases contain missing values

Predictor Coef SE Coef T P VIF
Constant 1.41916 0.03420 41.49 0.000

PopDen -0.00022334 0.00005646 -3.96 0.000 1.4
Sect 0.0011006 0.0001072 10.26 0.000 2.0
TIO -0.11053 0.08303 —1.33 0.184 1.9
EIA 0.0008461 0.0004092 2.07 0.039 1.6
SP2Dum 0.15555 0.01249 12.45 0.000 1.0
S = 0.1960 R-Sq = 36.3% R-Sq(adj) = 35.8%

 

 

172

Lula.

Appendix G (Cont.)

  

(LJL lllnlllicurcssiUIl.\H1H}\I\2 \ I |\-lNipl)0|L Stwfl.l’crlntz'\lill)u1n

 

The regression equation is
VE1 = 1.32 -0.000130 PopDen 40.000400 Sect —0.000000 PerInc
4 0.0683 VElDum.

383 cases used 352 cases contain missing values

Predictor Coef SE Coef T P VIF
Constant 1.32105 0.02153 61.35 0.000

PopDen -0.00012976 0.00002235 -5.81 0.000 1.2
Sect 0.00040029 0.00005334 7.50 0.000 1.7
PerInc -0.00000049 0.00000007 -6.72 0.000 1.9
VElDum 0.068341 0.008729 7.83 0.000 1.1
S = 0.07813 R-Sq = 34.9% R-Sqiadj) = 34.2%

 

 

 

 

(i-IH.l’hinlItcgrcsshui.\n;fl)sis: \liZ \slhlp.lhipl)cn.fsch \I 2|)urn

The regression equation is
VE2 = 1.24 - 0.0277 Pop -0.000220 PopDen 4 0.00104 Sect
4 0.233 VE2Dum

383 cases used 352 cases contain missing values

Predictor Coef SE Coef T P VIF
Constant 1.24418 0.06098 20.40 0.000

Pop -0.027703 0.003933 —7.04 0.000 1.8
PopDen -0.00022042 0.00004743 -4.65 0.000 1.2
Sect 0.0010385 0.0001142 9.10 0.000 1.7
VEZDum 0.23262 0.02355 9.88 0.000 1.0
S = 0.1664 R-Sq = 36.0% R-Sq(adj) = 35.4%

 

 

 

173

 

Appendix G (Cont.)

(i-ll.l9h1a|Itegressuln.\rufl)sis: \l’l\s Perlne.lNiplh31.SeeI.l].\.\ Pll)urn

 

The regression equation is
VP1 = 1.15 -0.000000 PerInc —0.000076 PopDen +0.000478 Sect
40.000041 EIA + 0.0920 VP1Dum.

383 cases used 352 cases contain missing values

Predictor Coef SE Coef T P VIF
Constant 1.14964 0.05459 21.06 0.000

PerInc -0.00000024 0.00000009 -2.62 0.009 2.1
PopDen -0.00007592 0.00003016 -2.52 0.012 1.5
Sect 0.00047818 0.00007047 6.79 0.000 2.0
EIA 0.0000413 0.0003033 0.14 0.892 1.9
VP1Dum 0.09198 0.02628 3.50 0.001 1.2
S = 0.09592 R-Sq = 16.1% R-Sq(adj) = 15.0%

 

 

 

 

(i-IZ. l’inal Regression .\n:1|1six: \ 1’2 \\ Pop. PopDen. Seel. \'|’2|)um

The regression equation is
VP2 = 1.35 - 0.00751 Pop —0.000123 PopDen 40.000995 Sect
4 0.0583 VP2Dum.

383 cases used 352 cases contain missing values

Predictor Coef SE Coef T P VIF
Constant 1.35134 0.03855 35.06 0.000

Pop -0.007508 0.002813 -2.67 0.008 1.8
PopDen -0.00012342 0.00003402 -3.63 0.000 1.2
Sect 0.00099530 0.00008151 12.21 0.000 1.7
VP2Dum 0.05834 0.01726 3.38 0.001 1.0
S = 0.1189 R—Sq = 34.6% R-Sq(adj) = 33.9%

 

 

174

Appendix H - Descriptive Statistics for Impact Area Levels

 
 

H-I. Descriptive Statistics for Impact Area Levels - Population

 

Impact Level?l Mean Median StDev SE Mean Minimum Maximum
A 321474 79039 1 107081 91310 9004 91 16506
B 579538 1 87058 1 649802 1 36073 6639 1 1 446843
C 1688949 689737 3209368 264704 89040 1 9743435
E 1926399 789207 2883554 237831 92639 1 7078752

 

 

 

H-2. Descriptive Statistics for Impact Area Levels - Population Density

Impact Level Mean Median StDev SE Mean Minimum Maximum
A 151.4 47.7 317.9 26.2 1.8 2245.4
B 49.19 24.3 74.67 6.16 1.7 488.6
C 55.4 36.7 62.51 5.16 3.8 384.7
E 75.73 44.9 94.08 7.79 4.2 ' 647.7

 

 

H—3. Descriptive Statistics for Impact Area Levels - No. of Economic Sectors

 

 

Impact Level Mean Median StDev SE Mean Minimum Maximum
A 191.68 175 76.76 6.33 95 483
B 236.41 222 82.8 6.83 61 495
C 338.57 335 76.28 6.29 182 505
E 345.37 338 83.06 6.85 183 502

 

 

H-4. Descriptive Statistics for Impact Area Levels - Total Industry Output

 

Impact Level Mean Median StDev SE Mean Minimum Maximum
A 16297 3340 62339 5142 229 513996
B 27180 7696 87046 7179 175 614238
C 80868 29706 164582 13575 3923 1008888
E 103669 32777 164357 13556 4310 874502

 

 

 

 

 

a Impact Level A - Most populous county in National Forest
Impact Level B - All counties in National Forest.
Impact Level C - Level 2 plus all adjacent counties.
Impact Level E - BEA economic areas.

175

Appendix H (Cont.)

 

H-S. Descriptive Statistics for Impact area Levels - Personal Income

Impact Level
A

B
C
E

 

Mean
7.792E+09
1 .35E410
3.92E410
4.86E410

Median
1.65E409
3.635409
1 .46E410
1 .64E410

StDev SE Mean
2.85E410 2.35E+09
4.145410 3.41 E409
7.98E410 6.58E409
7.83E410 6.46E409

Minimum Maximum
962092 2.34E411

83153000 2.90E+11

1.66E-1-09 4.91E+11
1.775-1-09 4.25E+11

 

 

 

H-6. Descriptive Statistics for Impact Area Levels - Area (sq mi)

Impact Level

 

1110!!!)

Mean
2958

12700
37780
33543

Median

1909

1 0335
31 482
3201 9

StDev SE Mean Minimum Maximum
3317 274 251 20062
9852 813 428 48674
30367 2505 3489 189303
22810 1881 3430 87808

 

 

H-7. Descriptive Statistics for Impact Area Level Multipliers - LE1

Impact Level
A

 

B
C
E

Mean
1.3518
1.357
1.4183
1.4318

Median
1 .3579
1 .3521
1 .4186
1.4422

StDev SE Mean Minimum Maximum
0.1046 0.0092 1.0868 1 .5554
0.0941 0.0078 1.1661 1 .5775
0.0903 0.0074 1.1946 1.5863
0.0849 0.007 1 .2409 1 .5592

 

 

H-8. Descriptive Statistics for Impact Area Level Multipliers - LE2

 

Impact Level

morn)

 

Mean
1 .6253
1 .6509
1 .7664
1 .7782

Median
1 .6375
1 .6534
1 .7632
1 .7787

StDev SE Mean Minimum Maximum
0.1679 0.0148 1.1825 2.0092
0.1614 0.0134 1.2699 2.1341
0.1648 0.0136 1.3524 2.1144
0.1533 0.0127 1.3962 2.0955

 

 

176

 

 

 

Appendix H (Cont.)

 

H-9. Descriptive Statistics for Impact Area Level Multipliers - LP1

 

Impact Level

 

“100)

Mean
1 .31 16
1.3103
1.3677
1.3943

Median
1 .2709
1 .281
1 .3524
1 .387

StDev
0.1301
0.1 179
0.1 165
0.1202

SE Mean

0.01 15

0.0098

0.0096
0.01

Minimum
1.0966

1.156

1.1905
1.1858

   

            

 

Maximum
1 .7477
1 .8096
1.8338
1 .8688

 

 

 

H-IO. Descriptive Statistics for Impact Area Level Multipliers — LP2

Impact Level

ITIOU>

Mean
1.5296
1.5333
1.6465
1 .6869

Median
1.4886
1.5052
1.6313
1.6824

StDev
0.1815
0.1656
0.1652
0.166

SE Mean
0.016
0.0138
0.0136
0.0138

Minimum Maximum
1 .1789 2.0935
1.2778 2.1882
1 .3764 2.2553
1 .3897 2.2496

 

 

H-II. Descriptive Statistics for Impact Area Level Multipliers — SE1

 

Impact Level

1110!!!)

Mean
1 .6651
1 .7363
1 .8044
1 .8095

Median
1 .6887
1 .7627
1 .8173
1 .8345

StDev
0.1535
0.1262
0.1271
0.1342

SE Mean

0.0137
0.0105
0.0105
0.01 1 1

Minimum

1 .3521

1.3792

1.4443
1 .448

Maximum
1 .9333
2.0281

2.032
2.0476

 

 

 

 

H-12. Descriptive Statistics for Impact Area Level Multipliers - SE2

Impact Level

"1003)

Mean
2.07
2.1665
2.31 99
2.3276

Median
2.1 167
2.1753
2.3223
2.3392

StDev
0.2539
0.2156
0.2406
0.2318

SE Mean

0.0227
0.018
0.0198
0.0192

Minimum
1 .5777
1.6984

1 .8343
1 .7588

Maxim um
2.6335
2.7162
2.91 18

2.907

 

 

177

 

Appendix H (Cont.)

 

H-13. Descriptive Statistics for Impact Area Level Multipliers — SP1

Impact Level

"100!)

 

Mean

1 .5945
1 .6648
1 .7189
1 .7297

Median

1 .5527
1 .6037
1 .696
1 .7071

StDev
0.2069
0.2127
0.1462
0.1551

SE Mean

0.0185
0.01 78
0.0121
0.0128

Minimum

1 .231 4
1 .2824
1 .3076
1 .3803

Maximum
2.5955
2.9886
2.2151
2.0308

 

 

 

H-14. Descriptive Statistics for Impact Area Level Multipliers — SP2

Impact Level

"100)

Mean
1 .8572
1 .9476
2.0676
2.0925

Median
1 .7952
1 .8942
2.0455
2.0651

StDev
0.2514
0.2669
0.1898
0.2077

SE Mean

0.0225
0.0223
0.01 57
0.01 72

Minimum

1.3758
1.5184
1.5774
1.6683

Maxim um
2.977
3.5145
2.6687
2.4792

 

 

 

 

H-IS. Descriptive Statistics for Impact Area Level Multipliers — VE1

Impact Level
A

B
C
E

Mean
1.456
1.5019
1.5406
1.5416

Median
1.4447
1.5177
1.5443
1.5482

StDev
0.1 162
0.0853
0.0907
0.093

SE Mean
0.01 81
0.01
0.0089
0.0092

Minimum
1.2406
1.268
1.3333
1.31 19

Maximum
1 .6551
1 .6526
1 .6892
1 .6712

 

 

 

 

H-16 Descriptive Statistics for Impact Area Level Multipliers — VE2

Impact Level

1110!!!)

Mean
1 .8661
1 .9099
2.0121
2.0278

Median
1 .8253
1 .8901
2.0088
2.0303

StDev
0.2223
0.1 828
0.203

0.2089

SE Mean
0.0347
0.0215
0.0199
0.0206

Minimum
1.5506
1.4734
1 .5587
1.5144

Maximum
2.2757
2.2621
2.4034
2.4437

 

 

178

Appendix H (Cont.)

H-17. Descriptive Statistics for Impact Area Level Multipliers — VP1

 

Impact Level

1110!!!)

 

Mean
1 .3913
1 .4387
1 .4858
1 .4874

Median
1 .4042
1 .4301
1 .4814
1 .4733

StDev
0.0894
0.0974
0.1009
0.1094

SE Mean

0.014
0.01 15
0.0099
0.0108

Minimum

1 .1479
1 .2217
1.2079
1 .2422

Maximum

1 .5974
1.7591
1 .7735
1.9037

 

 

H418. Descriptive Statistics for Impact Area Level Multipliers 4 VP2

Impact Level

 

I110!!!)

Mean
1 .6327
1 .6812
1 .7881
1 .8056

Median
1 .622
1 .6856
1 .7877
1 .806

StDev
0.122
0.1299
0.1421
0.1387

SE Mean

0.0191
0.0153
0.0139
0.0137

Minimum

1 .3272
1 .3296
1 .3847
1 .4862

Maximum

1 .8577

2.0062
2.1842
2.2922

 

179

 

 

   

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